Photonic Integrated Circuits using Crystal Optics IST Progress report, covering the period March 2000-February 2001

Transcription

1 Photonic Integrated Circuits using Crystal Optics IST Progress report, covering the period March 2000-February 2001 March 2001 Editor: Thomas F. Krauss - 1 -

2 Table of contents Chapter 1 - Executive summary 3 1. Executive summary; 2. Contribution from partners; 3. Publications; 4. Interactions between partners Chapter 2 - Milestones and Deliverables 8 1. WP1 Deliverable 1; 2. WP1 Milestone 2; 3.WP3 Milestone 13; 4. WP4 Deliverable 8; 5. WP4 Milestone 20; 6. WP5 Deliverable 10; Chapter 3 - Workpart Introduction / State-of-the-art; 2. Design considerations; 3. Experimental results; 4. Conclusion; 5. References Chapter 4 - Workpart Introduction / State-of-the-art; 2. Design of monolithic wavelength converter; 3. Epitaxial growth; 4. Fabrication; 5. Optical characterisation; 6. Redesign; 7. References Chapter 5 - Workpart Introduction / State-of-the-art; 2. Comparison between tools (FDTD/EME); 3. CAMFR mode expansion; 4. Development of mode epansion by Photon Design; 5. Shooting technique; 6. Multiple scattering technique; 7. Designing finite height photonic crystals; 8. Efficient FDTD for 3-D problems; 9.References Chapter 6 - Workpart Introduction / State-of-the-art; 2. Facilities and materials; 3. Experimental; 4. Conclusion Appendices Deliverable 8 (Modelling) with Appendix A-J Appendix A Notations and definitions related to polarisation Appendix B Overview of available modelling tools Appendix C Overview of the benchmark structures Appendix D What tools can handle whioch benchmark? Appendix E Report on numerical techniques for study of propagation in quadratically nonlinear dispersive media Appendix F Report on the multiple scattering numerical technique Appendix G Comparison of FDTD and Eigenmode Expansion Appendix H Comparison of numerical methods for propagation in non-linear media Appendix J Photonic crystal modelling at Photon Design - 2 -

3 Chapter 1 Executive summary Chapter 1 Executive summary 1. Executive summary 1.1 Scientific aspects We achieved the first quantitative assessment of waveguide losses (2dB/100µm) early on in the project, which gave us the first indication that integrated optics based on photonic crystals is a viable concept. It also gave us a benchmark against which to measure progress and pointed towards several important issues, namely the origin of losses, the waveguide geometry (high/low index contrast cladding) and the importance of the waveguide boundary. Regarding the latter point, we learned that the boundary has a profound impact on the transmission behaviour, leading, for example, to mini-stopbands within the transmission band. These issues have lead to a flurry of modelling activity, which we formalised by drawing up a number of benchmark structures. Modelling of the benchmark structures has the dual purpose of guiding the experimental work as well as understanding the advantages and limitations of each modelling tool. The extensive comparison between tools summarised in Deliverable 8 will be invaluable for the modelling activity during the remainder of the project. One very important outcome of the modelling activity was the assessment of the out-of-plane scattering losses, an issue addressed by both COM and IMEC. The key result is the insight into the restriuction of the hole size on the cladding index in order to avoid radiation losses, and the understanding of the origin of losses in high and low contrast waveguides; high contrast waveguides tend to suffer large interfacial losses but allow modes to propagate virtually loss-free, whereas low contrast waveguides are characterised by low interface losses yet have unavoidable propagation losses. Either type therefore offers itself to different types of devices. On the fabrication front, COM developed a process for fabricating silicon on insulator (SOI) structures, so we now have a capability for both high (Si/SiO 2 ) and low (GaAs/AlGaAs) contrast waveguide structures available within the project. The parametric wavelength converter targeted in Workpart 3 turned out to be more difficult to realise than initially envisaged, which led to a re-design and a redefinition of targets. The problem of interfacing photonic crystal circuits to the outside world is being addressed by an out-of-plane fibre coupler, for which we calculated an efficiency of up to 74%. This remarkable number needs yet to be confirmed experimentally, but it indicates the possibilities available. Progress has also been made in the area of deep UV lithography, where we already demonstrated structures of the right periodicity and fill-factor for 1.55µm operation. Issues such as optical - 3 -

4 Chapter 1 Executive summary proximity effects, which deteriorate poerformance, have been recognised and are currently being addressed. 1.2 Commercial aspects Photon Design has made substantial advances in being able to offer full photonic crystal modelling capability in its commercial tools. Pirelli is establishing expertise in fabricating photonic crystal components on a commercial scale

5 Chapter 1 Executive summary 2. Contribution from partners to workparts 2.1 Workpart 1 Glasgow/St.Andrews: Fabrication of GaAs/AlGaAs waveguide structures used in loss measurements and integration with cavities (section 3.2). Initial development of coupled cavity waveguides (CCW) (section 3.3). Establishment of 1.3 µm transmission setup (section 3.4). Supply of samples to Aalborg (section 3.5) COM: Drawing up of design rules for photonic crystal waveguides (section 2.2). Development of SOI fabrication process (section 3.1). IMEC: Assessment of out-of plane scattering losses (section 2.1). Design of out-of plane fibre coupler (section 2.4). Bookham: Processiung of SOI samples in conjunction with COM. Design of waveguide coupler (section 2.5). Udine: Development of impedance matching concept for photonic crystyasl waveguides of finite length (section 2.3). Aalborg: Establishment of Scanning near-field scanning microscop (section 3.5) and initial testing of samples made at Glasgow. 2.2 Workpart 2 Due to start in year Workpart 3 Glasgow/ St. Andrews: Contribution to design work. Development of fabrication process for parametric wavelength converter. Supply of test samples to COM. COM: Characterisation of waveguides made at Glasgow and Pirelli. IMEC: Epitaxial growth of material. Pirelli: Key driving force in the development of the parametric wavelength converter. Design, Fabrication and Characterisation of structures. Udine: Modelling of nonlinear effects. 2.4 Workpart 4 COM: Comparison of tools against benchmarks. Assessment of scattering-matrix method

6 Chapter 1 Executive summary IMEC: Comparison of finite difference time domain (FDTD) and eigenmode expansion (EME) methods (section 2). Photon Design: Development of mode expansion technique (FIMMPROP-3D) and testing of newe code on various waveguide components. Udine: Development of shooting technique for the simulation of nonlinear waveguides. 2.5 Workpart 5 IMEC: Testing of DUV lithography on relevant structures, identification of optical proximity effect and design of test mask to compensate for this effect

7 Chapter 1 Executive summary 3. Publications directly arising from within PICCO 3.1 Glasgow/St.Andrews 1. C.J. M. Smith, R. M. De La Rue, T. F. Krauss, H. Benisty, S. Olivier, M. Rattier, C. Weisbuch, R. Houdré and U. Oesterle, Quantitative analysis of photonic crystal waveguides, Appl. Phys. Lett., 77 (18), pp , C.J.M. Smith, T.F. Krauss, H. Benisty, M. Rattier, C. Weisbuch, U. Oesterle and R. Houdre, "Directionally dependent confinement in photonic-crystal microcavities", Journ. Opt. Soc. Am. B, 17 (12), pp , S. Olivier, M. Rattier, H. Benisty, C. J. M. Smith, R. M. De La Rue, T. F. Krauss, U. Oesterle, R. Houdré and C. Weisbuch, Mini stopbands of a one dimensional system: the channel waveguide in a two-dimensional photonic crystal, submitted to Phys. Rev. B, H. Benisty, Ph. Lalanne, S. Olivier, M. Rattier, C. Weisbuch, C.J.M. Smith, T.F. Krauss, C. Jouanin and D. Cassagne, "Finite-depth and intrinsic losses in vertically etched twodimensional photonic crystals", submitted to Opt. Quant. Electronics, S. Olivier, H. Benisty, C.J.M. Smith, M. Rattier, C. Weisbuch and T. F. Krauss, "Transmission properties of two-dimensional photonic crystal channel waveguides", submitted to Opt. Quant. Elec, T.F.Krauss; Invited presentations on the topic of "Photonic Crystal Integrated Optics" at NATO Summer School in Crete, Greece (June 2000); EOS Summer School in Erice, Italy (July 2000); Summer School on Semiconductor Microcavity Photonics in Monte Verita, Switzerland, (October 2000); Workshop "Let there be light" within IST Conference, Nice, France, (November 2000); ECIO Conference, Paderborn, Germany (April 2001). 3.2 COM 1. T. Søndergaard, A. Bjarklev, M. Kristensen, J. Erland and J. Broeng, "Designing Finite-height Two-Dimensional Photonic Crystal Waveguides", Appl. Phys. Lett. 77 (6), (2000) 2. T. Søndergaard, A. Bjarklev, J. Arentoft, M. Kristensen, J. Erland, J. Broeng and S.E. Barkou Libori, "Finite height photonic crystal waveguides; confinement of light and dispersion relations", Submitted to Optics Communications (2001) 3. J. Arentoft, M. Kristensen, A. Boltasseva and T. Søndergaard, "Silica/silicon/silica crystal waveguides with 90 degree bends", Submitted to "Workshop on Photonic and Electromagnetic Crystal Structures", June 9-14, 2001 in St. Andrews, Scotland 3.3 IMEC - 7 -

8 Chapter 1 Executive summary 1. W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, D. De Zutter, Out-of-plane scattering in photonic crystral slabs., Accepted for publication in Phot. Technol. Lett.(2001) 2. W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, D. De Zutter, Out-of-plane scattering in 1D photonic crystral slabs., Accepted for publication in Optics and Quant. Electron.(2000) 3. W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, Out-of-plane scattering in photonic crystal slabs, Conference Proceedings of LEOS'2000, The 13th Annual Meeting, Puerto Rico, Costa Rica, p.pd W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, Out-pf-plane scattering losses in 1D photonic crystal slabs, Proceedings Symposium IEEE/LEOS Benelux Chapter,2000, Delft, The Netherlands, p W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, Out-of-plane scattering in 1D photonic cruystal slabs, Summer School and European Optical Society Topical Meeting in Semiconductor Microcavity Photonics, Centro Stefano Franscini, Switzerland 3.4 Udine/Pirelli 1. M. Midrio, L. Socci, M. Romagnoli, Frequency conversion in one-dimensional stratified media with quadratic non-linearity, submit to Josa B. 2. M. Midrio, L. Socci, M. Romagnoli, Efficient Phase-Matched Down-Conversion in Highly Dispersive 1D-PBG, accepted for CLEO Interactions within PICCO A separate meeting between the consortium members involved in modelling (COM, IMEC, Photon Design, Udine) in Brussels in May 2000 to allocate workloads and discuss modelling strategy. A visit by Dr A. Harpin of Bookham Technology to COM in January 2001 to discuss SOI processing and details of the collaboration between the two partners. A 1 week visit by Dr A.Lavrinenko of COM to IMEC (Jan/Feb 2001) to get acquainted with IMEC's modelling tools and to discuss modelling strategy. A 1 week vist by Pirelli scientists to COM in February 2001 to perform measurements on structures made at Pirelli. Several visits between scientists from Pirelli and Udine to discuss progress on the wavelength converter (WP3). Frequent visits between scientists from Glasgow and St.Andrews throughout the year

9 Chapter 2 Milestones and Deliverables 1. WP1 Deliverable 1 Chapter 2 Milestones and Deliverables Report on design of basic ultra-compact building blocks. Decision on particular waveguide structure (photonic crystal waveguide vs. photonic wire). [month 12]. We have established the following design rules: 1.1. High vs. low contrast waveguide. The losses arising in high contrast waveguides (e.g. membrane, SOI) occur mainly at interfaces and defects, whereas the losses arising in low contrast waveguides (e.g. GaAs/AlGaAs) increase monotonically. High-contrast waveguides are therefore more suited for propagation through the lattice (e.g. for the superprism that will be studied in WP2), and low-contrast waveguides will be better for structures that incorporate many discontinuities, e.g. defects and intersections. For more detail, please refer to chapter 3-section Leakage-free guidance We investigated the parameter space for leakage-free guiding, depending on the refractive indices of the top and bottom cladding of the waveguide. The key result is that the hole diameter should decrease with an increase in cladding index, a result that was known qualitatively and has now been quantified. For more detail, please refer to chapter 3-section Impedance matching and finite length The absolute length of the structure matters, due to interface reflectivities, and we demonstrated that impedance matching reminiscent of a "double-stub" in the microwave regime can eliminate the reflected wave thereby increasing transmission. For more detail, please refer to chapter 3 - section Boundaries and mini-stopbands Transmission measurements on channel waveguides consisting of 3 rows of missing holes revealed the occurance of a mini-stopband due to anticrossing between the fundamental and higher order modes. The waveguide boundary must therefore be taken into account, and cannot simply be treated a perfectly reflecting mirror. For more detail, please refer to chapter 3-section Coupling between cavities and waveguides A cavity and waveguide, when separated by only two rows of holes, can interact very strongly. This observation can leadf to many useful applications, e.g. for WDM filtering. For more detail, please refer to chapter 3-section Photonic crystals vs. photonic wires - 9 -

10 Chapter 2 Milestones and Deliverables In the proposal, we decided that the photonic wire approach would be evaluated as a possible alternative to photonic crystal defect-type channel waveguides. We hereby propose to delay this aspect of deliverable D1 for 12 months to give a realistic possibility of it being fulfilled. The main reason for this delay is the personnel situation at Glasgow, the partner responsible for this action, who had a gap in personnel between Nov 2000 (Chris Smith leaving) and March 2001 (Harold Chong joining). Photonic wire waveguides require high aspect-ratio parallel-sided 'fins' projecting out of a supporting substrate. Vertical confinement can be obtained by including a higher index core region, well above the substrate. The transverse confinement of the photonic wire is large because it is determined, e.g., by the index contrast: air-semiconductor-air. The resulting requirement for singlemode propagation is that the transverse ('horizontal') dimension should be small, no more than a half-wavelength in the high index medium. For example, at λ 0 ~ 1.5 µm the fin width is approximately 0.25 µm, taking the refractive index value to n~3. Glasgow have now initiated attempts at fabricating photonic wire-type structures in which the highindex core will be at the top of the fin, maximising isolation from the substrate for a given total etch depth. If this approach begins to look promising, we shall explore both junction and 'bend' structures based on photonic wire waveguides, incorporating very small, accurately shaped resonator features at the waveguide intersection points. The impact of fabrication limitations on waveguide quality will also be assessed, together with modifications to the vertical configuration where the waveguide core is located below the top of the fin - so that the modal distribution is approximately symmetrical in the vertical direction. Given sufficient progress, a further extension of photonic wire-based work will be attempted, the evaluation of WDM functionality using coupled resonator structures. The aim initially will be to achieve relatively low frequency selectivity with strongly coupled and dimensionally less critical structures. 2. WP1 Milestone 2 Technology development of multilayer SOI process [month 12]. A procedure for full processing of silicon-on-insulator (SOI) based photonic crystal waveguides has been developed. The fabricated structures consist of silica/silicon/silica trilayers with air holes arranged in a triangular lattice and extending through all three layers. Details of structures and their characterisation can be found in chapter 3, section

11 Chapter 2 Milestones and Deliverables 3. WP3 Milestone 13 Design of phase-matched parametric waveguide [month 12] For the technical details of this milestone, please refer to chapter 4, section 2. A photonic crystal parametric wavelength converter has been designed. The periodic structure consists of N unit cells of four alternate layers of material and air. Using four (instead of typically 2) alternating layers greatly increases the design freedom, which is necessary to achieve phase matching at the pump (775 nm) and the signal/idler wavelengths ( 1550 nm). We have designed two types of devices, Fully tunable: both pump and signal tunable (to be used in optical networks) Limited tunable: pump fixed, signal tunable (to be used in optical transmission systems) The performance, the tolerances, losses, and bandwidth of these devices have also been investigated. The basic features of the parametric waveguide are essentially: 1. Single mode at both pump and signal wavelenghts 2. Good overlap between pump and signal fields 3. Good fraction of both pump and signal fields must be in the etched zone (( 1 ( 2 _m) 4. Effective indexes at pump and signal in a range suitable for designing the PBG Our design meets all of these criteria. During the first year, it became evident that progress was slower than expected, which is related to the sensitive interplay between dispersion and losses and the relatively narrow range of wavelength for which high conversion edfficiency can be expected. We therefore developed a new design that may be more robust and have less stringent requirements on fabrication tolerances (chapter 4, section 6) a) Figure 1 Comparison of two different designs for parametric wavelength converter. a) Initial design, using a periodic structure perpendicular to the direction of propagation to achieve phasematching. b) New design, with a periodic structure parallel to the direction of propagation. Due to the problems encountered and the higher than expected difficulty in achieving our aim, we now propose to spend more time on developing an efficient wavelength converter rather than moving on to the monlithically integrated laser-waveguide system as proposed initially. The

12 Chapter 2 Milestones and Deliverables process of shifting the electronic bandgap, which is necessary to combine passive and active elements on the same substrate, would add a further parameter and increase the uncertainty of knowing the dispersive properties of the material, thereby significantly reducing the chances of success. As a consequence, we propose to replace the list of milestones and deliverables. WORKPART 3 - List of milestones and deliverables as in proposal Deliverables D6: Optical test on wavelength converter waveguide with periodic structure for phase matching using external Ti:Sapphire pump laser. [month 18]. D7: Full system test of packaged, monolithic device. Assessment of penalty due to wavelength converter. Assessment of industrial feasibility [month 36]. Milestones and expected result M13 Design of phase-matched parametric waveguide [month 12]. M14 Laser with photonic microstructured mirrors to operate at 775nm [month 18]. M15 Fabrication and initial test of phase-matched parametric waveguide [month 12]. M16 Pump laser with low-loss waveguides via quantum well intermixing [month 24]. M17 Monolithic device featuring microlaser + phase-matched parametric waveguide [month 30]. M18 Pigtailed and packaged device for system test [month 32]. WORKPART 3 - Proposed new list of milestones and deliverables Deliverables D6: Optical test on wavelength converter waveguide with periodic structure for phase matching using external Ti:Sapphire pump laser. [month 18]. D7: Full system test of packaged device. Assessment of penalty due to wavelength converter. Assessment of industrial feasibility [month 36]. Milestones and expected result M13 Design of phase-matched parametric waveguide [month 12]. M14 Optimisation of new design [month 18]. M15 Fabrication and initial test of phase-matched parametric waveguide [month 18]. M16 Investigation of the phase matching conditions in 2-D structures [month 24]. M17 Implementation of coupling stategy developed in WP1 [month 30]. M18 Pigtailed and packaged device for system test [month 32]

13 Chapter 2 Milestones and Deliverables 4. WP4 Deliverable 8 Comparison of strengths/weaknesses of existing numerical tools and outlining of modelling strategy [month 12] This deliberable is rather extensive and therefore added separately with a number of appendices. A short synopsis is given below. In the frame of the PICCO project we have now a few running software packages: CAMFR (IMEC), finite difference time domain technique (IMEC), FIMMPROP (Photon Design), ONYX-2 (COM), plane wave expansion method (COM), and a number of methods for nonlinear dispersive media (UNIUD). All of the codes have been successfully tested in 2D. CAMFR and FIMMPROP are based on eigenmode expansion technique (EME). They might be the fastest routines for different problems of waveguide propagation in 2D for structures with a preferential propagation direction and a piecewise constant refractive index. However, handling of curved objects (holes) is not a straightforward matter in the frames of EME. These methods can model reflection-transmission characteristics, field patterns and dispersion curves. FIMMPROP has a very user-friendly interface with both text and graphical input-output abilities. Its restrictions are connected with the real-value solver, which forbids so far the implementation of ABC (PML for example). Such boundary conditions (PML) are, however, included in CAMFR to squeeze spurious backward reflections. It is used inside the Phyton scripting language shell, which requires some initial skills, but can be rather tractable after studying the basic material. Both tools have potential for 3D generalization in the future for structures with explicit periodicity included. The finite difference time domain (FDTD) technique from Ghent was tested on 2D and 3D problems. For 2D it gave results being several orders of magnitude slower than that of EME. A test on a 3D system was dragging on for weeks without any distinct results. The ONYX-2 code has inherited the principal advantages of the FDTD techniques such as versatility and robustness. It can be used as a universal platform for different types of 2D and 3D modelling of PBG structures such as reflection-transmission calculations, field components imaging, determination of band diagrams and computation of the optical density of states for both types of polarization. The order N (N, for example, number of space points) scaling property of ONYX-2 code magnifies its attraction for 3D calculations. The usefulness of 2D and 3D FDTD methods in analysis of PCW bends and splitters has been confirmed by several groups [14,21,26,29]. And in principle the ONYX-2 code is not an exception of this rule. Nevertheless, some disadvantages of ONYX-2 code are noticeable. It is rather sensitive to the interplay of PML characteristics and initial field distributions. Its universality feeds back with additional spending of time and memory resources. For example, a band diagram is simpler to calculate with the PWEM, and 2-D waveguide reflection-transmission computation is faster with the EME method. PWE is suited for the following 2D problems:

14 Chapter 2 Milestones and Deliverables 1) Calculation of vectorial electromagnetic Bloch states in infinite periodic dielectric structures. The periodicity of the structure is taken advantage of through the fact that the solutions to Maxwell's equations for the electromagnetic fields can be written as Bloch states. 2) Calculation of e.g. field distributions, Poynting vectors, dispersion relations, energy velocities for waveguides obtained by creating a line-defect in a photonic crystal. 3) Calculation of the electromagnetic modes of photonic crystal microcavities and coupled cavities. The structure of interest in this case is not periodic, and it is therefore necessary to approximate the cavity by a periodic structure using a supercell. The numerical method is not suited for the following problems: 1) Dielectric structures with amplifying or absorbing media. 2) Quantitative evaluation of scattering losses out of waveguides and cavities. 3) Transmission and reflection of light incident on a finite size photonic crystal material, and transmission/reflection of light through a bend or a junction such as Y- and T-junctions. Finite size crystals and junctions do not have periodicities, and the PWE is developed for modelling of periodic structures. In principle, some electromagnetic properties of such structures may be calculated by approximating the structure of interest with a periodic structure using a large supercell. However, the method has some good perspectives incurring from its 3D generalization (see, for example [23]). At UNIUD there is a software tool available for nonlinear optics; it includes their shooting technique (ST). UNIUD also has a multiple scattering method (MSM), a PWE in frequency domain and a FDTD code in time domain. Each technique has its own advantages, some of them have already been mentioned (PWE and FDTD). Therefore we emphasize only the advantages/disadvantages of ST and MSM. ST is an extremely fast method, three to four orders of magnitude faster than any of the above methods. But it is limited to 1D problems; also its frequency domain basis cannot simulate propagation of pulsed fields. MSM is apt for 2D structures with circular holes and finite length, but so far it works only with linear dielectrics. It is faster than the FDTD technique. As for the FDTD methods, material dispersion and nonlinearities can be handled only in the 1D case. Expansion of the whole set of PICCO software tools is anticipated during the second year

15 Chapter 2 Milestones and Deliverables 5. WP4 Milestone 20 Establishment of modelling strategy for realistic, high-contrast structures [month12] The general recommendation for a modelling strategy using the tools described above is as follows: 1. Develop efficient 3D software tools for analysis and design of the experimental structures to be produced within the PICCO project WP1 and WP3. 2. Test the different tools available in the consortium on well-defined benchmark structures (especially from the series 3 and 4). 3. There are some special areas, where there is a strong need for efficient 3D modelling tools such as for calculating scattering losses from PCW structures and coupling of light into and out of the structures. The partners are encouraged to find methods, which can deal effectively with these issues. The specific recommendation for selected problems is as follows: 1. The 3D generalization of eigen mode expansion technique (the CAMFR and FIMMPROP3D tools) will provide suitable and fast instrument for straight PCW analysis. 2. The 3D plane wave expansion (PWE) is useful for the determination of band gaps and dispersion curves. 3. The effective yet time-intensive FDTD method (in COM and IMEC) will be applied for transmission-reflection calculations of waveguide components from WP1. 4. Appropriate updating of the shooting technique and the FDTD method (in UNIUD) on 2D will allow supporting the nonlinear calculations arising in the problems of WP

16 Chapter 2 Milestones and Deliverables 6. WP5 Deliverable 10 Process validation test phase mask [month 12] Following the success of being able to reproduce photonic lattices with square holes of the required dimensions (360 nm holes on a 500 nm pitch), and having recognised the problem of optical proximity correction, we have now designed a mask that will be used to test all parameters relevant for photonic crystals made by DUV lithography. For technical detail, please refer to chapter

17 Chapter 3 Workpart 1 Chapter 3 Workpart 1 1. Introduction 1.1 Objectives The overall objective of WP1 is to develop a range of generic optical building blocks in high index contrast waveguides and to interface these to fibres and standard waveguides. In order to reach these objectives, we need to determine the optimum material and method of processing, establish the optimum design for the building blocks and establish advanced methods of optical characterisation. 1.2 World-wide state-of-the-art Waveguide losses There is surprisingly little data available on waveguide losses. Most groups report the observation of scattered light as viewed with a camera from above. The Caltech/Corning collaboration [7] has reported waveguide propagation losses as low as 8dB/cm by measuring the scattered light and making "suitable" assumptions about the detector sensitivity, without having measured the light throughput at the output facet. Their value is therefore difficult to justify, but it suggests that low propagation losses may indeed be achievable. The first reliable measurements were reported from within the PICCO/PCIC consortia (section 3.2) and reported waveguide propagation losses of 200dB/cm, two orders of magnitude higher. Somewhat better values are being reported now (110dB/cm) from within the PCIC, and most remarkably, with InP waveguides [18]. Overall, PICCO can clearly still be considered to be at the forefront, a position we will build on for our work in year 2. Waveguide geometry There is a remarkable convergence of photonic lattice and waveguide geometries; whereas, a year or two ago, the MIT/Sandia collaboration was still proclaiming the advantages of air waveguides with pillar lattices or lattices with large holes, their recent work is on dielectric waveguides with small holes. Equally, Noda s group in Japan, who were working on 3-D geometries, are now mainly publishing results obtained with semiconductor slabs [1]. This vindicates the approach put forward in the PICCO proposal (restriction to 2-D, dielectric waveguides with small holes), but also means that the competition has recognised the error of their ways and is homing in on our approach. As far as the question of high vs. low index contrast for the vertical waveguide is concerned, which lead to the dual approach (GaAs/AlGaAs and SOI) pursued in PICCO, there is no obvious favourite emerging as yet. A likely outcome is along the lines proposed by Bogaerts et al. (of PICCO-partner IMEC, section 2.1), whereby we suggest to use high-contrast waveguides for

18 Chapter 3 Workpart 1 functions that require continuous lattices, such as the superprism, and low-contrast waveguides appear more suitable for structures with discontinuities and defects, such as waveguides with intersections and cavities. We anticipate that during year 2, we will have much more experimental data available to assess the merit of each approach. Waveguide bends The ubiquitous 90 waveguide bend first proposed by Joannopoulos et al. can not readily be transferred into other geometries. Their model system consisting of infinitely extended dielectric rods in air can not easily be repeated with dielectric waveguides in air-hole photonic lattices. Several groups have demonstrated strong scattering at such bends with transmission data either unavailable or very poor. There is also a surprising lack of modelling data which suggests that the air-hole system is much more difficult than appears at first sight. The only finite difference time domain (FDTD) calculations [6] that indicate good transmission use a single line of missing holes and a 60 bend. Recent experimental results from Sandia Nat l labs [6] indicate that high transmission may be achievable only over a very limited wavelength range, as the group reports % transmission only for a narrow wavelength range. This data suggests that the notion of a photonic crystal as a "perfect mirror" within the bandgap range needs to be revised, and that the properties of the boundaries need to be taken into account, a fact already highlighted within PICCO (section 3.2). 2. Design considerations 2.1 Out-of-plane scattering y d a n clad x z Fig. 1 1D periodic structure with etched air slots. d core P n core n clad N slots d core = 0.225µm P = 0.55 µm d a = 0.28 µm Photonic crystal slabs combine a slab waveguide with an in-plane photonic crystal. Light is then confined in plane by the photonic crystal and out-of-plane by the slab waveguide. The etched structure of the photonic crystal holes will cause light to scatter out of the waveguide plane. We studied the out-of-plane scattering losses using a 2D approximation of this 3D structure, with etched slots instead of holes (Fig. 1). Our simulation techniques include mode expansion with PML absorbing boundary conditions and FDTD as verification. These simulations show that different scattering regimes exist depending on the choice of layer structure among other factors. Details of this study are given in Milestone report M1 and deliverable D1. Fig. 2 shows the out-ofplane scattering losses plotted against the refractive index contrast of the vertical layer structure. The index contrast is expressed as, with and the refractive index of the slab waveguide's core and cladding respectively. For low refractive index contrasts, losses increase with increasing refractive index contrasts. For high contrasts losses are very high unless one can excite a Bloch mode of the periodic structure below the light line. This is shown in Fig. 2, when the losses drop suddenly and transmission peaks. These two regimes are favourable to reduce undesired out-of-plane scattering,

19 Chapter 3 Workpart 1 depending on the application. In a compact structure with many close-packed defects (cavities, bends,...) a low refractive index contrast is preferable, as in this regime defects scatter only a modest amount of light, as does each crystal period. For large structures with little or no defects, a lossless Bloch mode, only possible with high refractive index contrasts, is the obvious option. 40% Loss a. De =2.0 (weak guide) 20% b. De =10.92 (strong guide) Number of periods Fig. 2 Comparison of propagation loss for a) weak and b) strong guides as a function of the distance from a discontinuity. The weak guides suffer less loss for short propagation distances, because of the lower impedance mismatch at the interface, whereas the high contrast structures experience almost no loss once the light has been coupled in. 2.2 Design rules for SOI-based photonic crystal waveguides At present numerical methods for rigorous modelling of a large design parameter space for threedimensional photonic crystal structures are not practical. However, it is possible to obtain guidelines for the design of finite height photonic crystal structures by comparing two-dimensional calculations for infinite height crystals with dispersion relations for the media above and below the finite height crystal. From such dispersion relations one finds the existence of fundamental upper frequency limits for leakage free guidance of light related to the properties of the media above and below the finite height waveguide. By inserting these limits in existing diagrams of bandgaps versus design parameters (2D calculations) we can now as a design rule choose those design parameters that provide large bandgaps below these frequency limits. An example of the approach is illustrated in Fig.3 showing bandgaps for TE and TM polarised light as a function of the hole diameter D in a photonic crystal. The photonic crystal consists of air-holes arranged on a triangular lattice in silicon. Here Λ is the lattice constant of the crystal, and λ is the free space wavelength of light. The fundamental upper frequency limits for the media air and silica are shown as the air-limit and the silica-limit, respectively. These are the appropriate limits when designing a waveguide by introducing a line defect in a photonic crystal. If a finite height photonic crystal waveguide is placed on top of silica then leakage free guidance of light is not possible for frequencies above the silica limit. Clearly, if the air-holes are chosen too large the bandgaps move above the silica limit, and bandgap guidance of light using these bandgaps

20 Chapter 3 Workpart 1 is no longer possible. If the air-hole diameter is chosen too small, there are no bandgaps. A reasonable choice of air-hole diameter in this case is D=0.7Λ, since in this case a reasonably large bandgap exists below the silica-limit. An operating frequency near the centre of the bandgap is in this case Λ/λ =0.27, and for the optical wavelength λ =1550nm this results in the lattice constant Λ=419nm and the hole diameter D=293nm. The basic idea behind obtaining these guidelines for photonic crystal design parameters is general and can be applied to many other diagrams existing already in the literature. If the waveguide is not placed on top of silica but is instead suspended in air we have to be concerned with the air-limit. In this case we can choose a larger air-hole diameter D=0.9 Λ and take advantage of guiding light using both polarisations TE and TM (bandgaps for both polarisations exist below the air-limit). Λ/λ D/Λ Fig.3: In-plane photonic bandgaps for TE and TM polarised light as a function of the air-hole diameter D for a photonic crystal with air-holes arranged on a triangular lattice in silicon. The airlimit and the silica-limit represent fundamental upper frequency limits for leakage free guidance of light for finite height photonic crystal waveguides. 2.3 Impedance Matching in 2-D Photonic Crystal Waveguides Electromagnetic properties of photonic crystal waveguides with finite length have been investigated and it has been proven that, by borrowing some elementary concepts of wave propagation from transmission lines, a simple but general characterisation of the finite- length waveguide can be done if the parameters of the infinitely long guide are known. The key point is to define the wave impedance, both for the infinite and for the finite length guide. Indeed, it allows to simply show in a closed form that, if a guide is terminated on a generic load impedance, and no particular care is taken, reflected waves appear in the guide. Those may be analytically computed with the same tools that are customarily used in the study of microwaves or of propagation in transmission lines, for instance the reflection coefficient and the standing wave ratio

21 Chapter 3 Workpart 1 a) L i ght i n b ) Y S 2 Y S 1 Y L Fig. 4 a) Photonic crystal guide with the defects that realise the double-stub. b) Equivalent circuit. Given the strong analogy between photonic crystal guides and conventional transmission lines, a further interesting fact has been demonstrated. The reflected waves can be cancelled by means of an equivalent impedance matching network, based on the well-known double-stub impedance matching technique. The layout of the double-stub network is sketched in Fig. 4, and its principle of operation is the following. Two localised defects are inserted in a photonic crystal guide that is formed by a linear defect embedded in a suitable crystal arrangement. In the vicinity of the localised defects, higher order modes are excited. If those modes are not allowed to propagate in the guide, as it in a single mode guide, they present a purely reactive wave impedance, i.e. they behave as localised inductive or capacitive lumped elements. In the figure, these elements are represented as capacitors with admittances YS1 and YS2, respectively. Whereas, YL is the admittance of the load at the end of the crystal guide. Once it has been proved that these localised defect indeed work as lumped reactive components, the impedance matching network can be designed in the same way as it is customarily done in microwave circuits [16]. 2.4 Out-of-plane fibre coupler Single mode fiber core Fig. 5 Out-of-plane fibre coupler: principle. The fibre coupler uses the strong diffractive properties of a specifically designed photonic crystal to couple light from a planar waveguide into a butt-coupled fibre perpendicular to the surface. The first designs use 1-dimensional lattices. We have optimised the lattice-parameters, using the CAMFR-simulation tool, which is based on eigenmode expansion and propagation with PML boundary conditions. We used 2D simulations with the E-field parallel to the grating grooves. For the structures we discuss here, the 2D approach is a good approximation for the 3D problem. With the 2D simulations, we solve the problem of 'bending' the light in a 90 turn from the slab waveguide to the fibre or from the fibre to the slab waveguide. We have now designed these structures for both GaAs and SOI. Fabrication of test devices in GaAs has started and fabrication of devices in SOI will start in the coming months

22 Chapter 3 Workpart 1 In the GaAs case, the designs are optimised for the following layer structures: -240nm GaAs/600nm AlOx -240nm GaAs/290 nm AlOx /115nm GaAs/240nm AlOx /115nm GaAs/240 nm AlOx These wafers have been grown at IMEC. The oxide layer (AlOx) is obtained by wet oxidation of a 94% AlGaAs layer at the end of the processing. efficiency into fibe fiber coupler : bandwidth GaAs fiber coupler wavelength ( m m ) structure 1 structure2 structure 2R coupling efficiency to fiber SOI fiber coupler SOI fiber coupler wavelength (nm) structure 1 structure2 Fig. 6 Coupling efficiency of designed structures (simulation results). The designs for GaAs/AlOx are summarised in Table 1 and efficiency as function of wavelength is shown in Fig. 6. Structure 1 is a 2nd order grating. Structure 2 is a combination of a 2nd order and a 1st order grating. Structure 2R has the same grating as structure 2, but with a 2-pair DBR under the waveguide core. The coupling efficiency is calculated as the fraction of the power in the waveguide mode that couples to a single mode fibre. To verify these results, test structures will be made and the coupling efficiency from fibre to ridge waveguide measured. The first GaAs coupler has been fabricated and is ready for characterisation. The grating was made by e-beam lithography and RIE at Glasgow University. The ridge waveguides were etched and oxidised at IMEC. To define the ridge waveguides and oxidation trenches an optical lithography mask was designed and made. For the SOI fibre coupler, gratings have been designed and optimised for the following layer structures: - 205nm Si / 400nm SiO2 (Soitec standard wafer) - 100nm SiO2 / 240nm Si / 1000nm SiO2 (multilayer SOI used by COM in other WP1 work) The results obtained for SOI are similar to those of GaAs/AlOx because the refractive indices of both materials are similar. The results for SOI are shown in Table 1and efficiency as function of wavelength is plotted in Fig. 6. For the multilayer SOI with an oxide top layer, a 2nd order grating has been designed (see Table 1). As it is difficult to model the additional oxidation step accurately in the simulations, the first SOI test devices will be made in 'normal' SOI. We have designed 1D-grating structures for the fibre coupler in GaAs and SOI. Simulation results show that > 25% coupling efficiency is possible with some of these structures. Test devices are being fabricated. After characterisation of these test structures, the designs will be further optimised

23 Chapter 3 Workpart 1 Grating period Etch depth Coupling efficiency GaAs Structure 1 580nm 65nm 14% Structure 2 566nm / 280nm 38nm 27% Structure 2R 566nm / 280nm 38nm 74% SOI Structure 1 578nm 40nm 22% Structure 2 572nm / 286nm 30nm 44% Multilayer SOI Structure 1 560nm 60nm 18% Table 1. Summary of optimised grating parameters. 2.5 Tapered waveguide coupler The small height of the PBG guiding layer (approx nm) will give fibre coupling losses in excess of 10dB when using standard telecomm fibre. For the devices produced to be viable, this coupling loss must be reduced to fractions of a db. We propose to achieve this with adiabatic tapering in the horizontal, as shown schematically below. Initially a separate chip is planned, followed by full integration The numbers show the depth of silicon; the precise dimensions will be agreed after further design work. The length of this structure is approximately 1.1mm. 3. Experimental results 3.1 SOI waveguide fabrication A procedure for full processing of silicon-on-insulator (SOI) based photonic crystal waveguides has been developed. The fabricated structures consist of silica/silicon/silica trilayers with air holes (arranged in a triangular lattice) extending through all three layers, see Fig. 7. The developed procedure allows us to fabricate structures corresponding to the designs developed in section

24 Chapter 3 Workpart 1 Sample surface Thermally grown silica Silicon Silica Silicon substrate Fig. 7. Cross sectional view of a SOI multilayer photonic crystal sample (SEM micrograph). E-beam lithography is used to generate photonic crystal waveguide patterns. Holes are then etched through silicon and silica using reactive ion etching (RIE). Finally, silicon is thermally oxidised to grow a top cladding layer and a glass layer on the walls of the air holes. The glass on the hole walls creates a gradual index transition between silicon and air and this might reduce scattering losses taking place here. In addition, the structure is significantly more environmentally stable than an aircladding version. Due to instabilities in our E-beam writing system the size of our patterns is presently limited to 40 µm by 40 µm or smaller. In order to be able to make transmission studies of waveguides defined within these small areas, we have designed a 90 bend. The 90 bend, which is shown in Fig. 8, enables us to access the waveguides from two perpendicular facets (perpendicular facets are most easily obtained when cleaving silicon). The design of the bend is purely intuitive and is obtained by gradual rotation of the crystal lattice. Fig bend (SEM micrograph). We have optically characterised fabricated photonic crystal (PC) waveguides in various ways. As described in more detail below, promising results have been obtained from transmission measurements and by looking at samples from above with an infrared camera. Reflection studies have also been carried out, but these did not yield clear information. Samples for optical characterisation have been either cleaved or polished in order to access the areas of interest. Transmission measurements were performed on a sample with 90 bent PC waveguides. On the sample we had also defined 250 µm long tapered ridge waveguides leading light to the photonic crystal area. Unfortunately, the alignment between PC waveguides and ridge waveguides was very

25 Chapter 3 Workpart 1 poor on this sample. The transmission measurements showed a total loss (from input fibre to output fibre) of ~40 db. This figure is not high considering the poor fibre-to-sample coupling (expected to account for up to 20 db coupling loss) and the poor alignment mentioned above. We also studied guiding of light in the same sample with an infrared camera. Due to scattering at the points of poor alignment, we were able to follow clearly the path of guided light. One of the pictures is shown in Fig. 9. From the IR pictures we were able to conclude that the PC waveguides efficiently transmit light from the input ridge waveguide to the output ridge waveguide. We therefore estimate that the propagation loss in the bent PC waveguides is quite small. In the near future, we expect to be able to determine values for the exact propagation and bending losses. Photonic crystal area (40 mm by 40 mm) Ligh t input Li ght output Sampl e corner Fig. 9. IR top view of SOI-based photonic crystal waveguide sample. 3.2 Experimental results in GaAs at 1 µm wavelength Work described in this section involve the group at Ecole Polytechnique Palaiseau, who are formally not in PICCO but in another IST project, PCIC. The collaboration with EPP predates PICCO, and based on the very good results obtained, the collaboration carried over into PICCO for some time. Using a modified "cutback method" [3] we obtained a loss figure of 50 cm-1 or 200dB/cm, (2dB/100µm) for a waveguide consisting of a line of 3 missing holes. Despite the loss being rather high compared to silica and other materials commonly used in integrated optics, this figure points in the right direction for miniaturised circuits and is a first clear indication that photonic crystal integrated circuits are viable. Furthermore, it is a benchmark against which we can compare different designs and improve losses at a time when most groups world-wide are only able to report qualitative results or observations of scattered intensities

26 Chapter 3 Workpart 1 Fig. 10. Photonic crystal channel waveguide of the type used to establish the loss figure of 2dB/100µm. The transmission measurements led to a very important discovery, which we believe is caused by the corrugated boundary of the channel waveguides: The boundary being periodic leads to a ministopband within the waveguide transmission spectrum. Fig. 11. Transmission dip near the centre of the passband for a photonic crystal channel waveguide. On closer examination, dispersion calculations (conducted at Palaiseau) revealed an anti-crossingtype behaviour between the first and third waveguide mode, with a corresponding mini-stopband width (ω/ω 0 ) of approx. 1%. This width corresponds to the width of the stopband measured experimentally (Fig. 11)

27 Chapter 3 Workpart 1 Fig. 12 Explanation of the transmission dip observed in Fig. 11. We explain this dip with an anticrossing between the first and third order waveguide mode caused by the periodic boundary of the channel waveguide. a) Dispersion relationship for a waveguide consisting of 3 missing holes as in Fig. 10. The number of modes is relatively high because of the width of the waveguide (3 rows of missing holes) and the fact that the waveguide is in the high-index region of the photonic crystal. b) Enlarged section of the ω-k diagram to highlight the anticrossing behaviour. c) and d) Contour plots of the intensity of the waveguide branches indicated in b), highlighting the fact that the intensity distribution changes at the crossover point, as expected from a typical anticrossing. Following the interesting results obtained with the simple waveguide system, we proceeded to investigate the coupling between a cavity and a waveguide. This is the first step towards an integrated photonic crystal circuit and highlights some of the problems as well as the opportunities inherent in such a system. Fig. 13 shows the experimental set-up

28 Chapter 3 Workpart 1 Fig. 13 Localised photoluminescence set-up showing the different excitation points either near the guide entrance (E1) or in the microcavity (E2). Collection from both the cleaved edge (S1) and through the excitation objective (S2 & S3) is used. SEM micrograph image is for 260 nm period photonic crystal. The anticrossing behaviour already observed with the waveguides is again instrumental in understanding the operation of this coupled system: (A) PC-WG (B) K=2š/a ω anticrossing 3 1 PC-MC -π/a π/a k// Fig. 14 a) Schematic of coupling mechanism: Energy radiates across the intermediate boundary consisting of 2 rows of holes, where it can couple to the higher order modes of the waveguide (white arrows), that can then couple to the fundamental mode (black arrows) by means of the waveguide anti-crossing mechanism. The nature of the modes that are intrinsic to the photonic crystal channel gives rise to an unusual type of waveguide coupling that proves particularly effective in coupling the microcavity to the waveguide. Moreover, the interaction satisfies an important requirement for photonic integrated circuits, namely the capacity to couple elements such as cavities and lasers with minimal losses. The cavity modes radiate preferentially through the wall with a large transverse momentum (transverse with respect to the waveguide propagation axis), in other words they couple to the higher order transverse mode of the waveguide. More detailed conclusions can be drawn from the spectra shown in Fig. 15:

29 Chapter 3 Workpart 1 (a) S1 N = 5 rows (b) N = 4 rows S1 (c) N = 2 rows S1 Intensity (a.u.) (d) N = 2 rows S3 (e) N = 2 rows S2 (f) N = 5 rows S Wavelength (nm) Fig. 15 Spectra for the uncoupled (a,f) and the coupled (b-e) elements. (a) Signal S1 for excitation near the waveguide entrance (E1) and N=5 rows. The fast oscillations are the Fabry-Pérot fringes between the cleaved edge and the PC. Signal S1 for excitation in the PC-MC (E2) and (b) N=4 rows and (c) N=2 rows. (d) Signal S3 and (e) S2 for excitation in the PC-MC and a strongly coupled case (N=2 rows). (f) Signal S3 for N=5 rows, the reference "uncoupled" PC-MC. All clusters have similar intensities. The terms "Ex" and "Sx" refer to the position of the excitation and sampling points shown in the insets on the right and defined in Fig. 13. Some key observations include: a) Different coupling regimes. The spectra shown in Fig. 15a and Fig. 15f underline the fact that the intrinsic characteristics of the waveguide and cavity are well defined even when in relatively close proximity (5 rows = 1.12 µm separation). If we now excite inside the cavity but bring the waveguide to within 4 rows of the microcavity, light is coupled from the microcavity into the waveguide as shown by the extra peaks in the spectrum (Fig. 15b). If the distance is decreased to 2 rows, the peaks are larger and more numerous, i. e. coupling is stronger (Fig. 15c). b) High quality modes. Previously, we have investigated isolated microcavities of the same type [17] in the E2-S3 configuration (without any guide) and observed that the confinement provided by these cavities is good. Peaks with resolution-limited linewidths (Q 1000) gave direct evidence of high quality, discrete cavity modes. Similar spectral features are observed here for these cavities when the waveguide is 5 rows from the microcavity (Fig. 15f). We attribute the observed modes to

30 Chapter 3 Workpart 1 "quasi-radial" or "Fabry-Perot" resonances of the cavity, with wavefronts parallel to the cavity boundary, giving rise to sufficient scattered far-field signal to allow detection from above. Overall, the results demonstrate low-loss coupling between a cavity and a waveguide when the separation is only 2 rows of holes. This interaction can be reduced to zero when the distance is increased to 5 rows of holes without influencing the quality factor of the respective modes, which suggests that the modes must be understood as the modes of the system rather than of the isolated elements. 3.3 Coupled cavity waveguides A novel type of waveguide, the coupled cavity waveguide (CCW) or coupled-resonator optical waveguide CROW [11], is being studied theoretically at INTEC and experimentally at St. Andrews. Instead of guiding the light by means of total internal reflection as in a conventional waveguide, or via photonic crystal mirrors, the light in a CROW propagates by hopping from one resonator to another. Once a resonance is established in the first cavity, light can then propagate along the line of cavities as long as there is sufficient overlap between adjacent cavities. In practice these resonators can consist of missing air holes in a 2D Photonic Crystal or of semiconductor cylinders on top of a substrate. The working principle of CCWs has been extensively proved in the microwave domain [12][13][14]. First results at INTEC show that next to FDTD [15], also eigenmode-expansion can be very useful in the 2D-simulation of a CROW. In the future, both these methods shall be used to model practical waveguides and to examine the use of CROW as a compact taper, that could serve as a connection between a fibre coupler an a conventional PhC-waveguide. a) b) Fig. 16 a) Operating principle of coupled cavity waveguides. b) Spectral control achievable with CCWs as a function of cavity spacing. The legend refers to the separation between cavities, i.e. a) would be a "1 in 3". Courtesy of A. Reynolds, University of Glasgow. The interest in CCWs is twofold, i.e. spatial (Fig. 16a) and spectral (Fig. 16b) control of light propagation through a photonic crystal. The spatial control has already been demonstrated in the microwave regime, in a 3D photonic crystal [12] where it was shown that light couples to adjacent cavities in any direction, and both straight waveguides, bends and "zig-zag" paths can be realised with similar transmission. The spectral control relies on the fact that closely coupled cavities form a "miniband" within the stopband, which narrows as the separation between cavities is increased (Fig. 16b)

31 Chapter 3 Workpart 1 Waveguides with coupled cavity sections have been made and characterised, but so far, no spectral features have been identified. Since no band-edges were found on samples without cavities, we believe that a more fundamental fault is responsible, most likely insufficient etch depth. This fault is currently being addressed. Fig. 17 SEM micrograph of a "1 in 2" coupled cavity waveguide. Neither Glasgow nor St. Andrews had a transmission measurement set-up available in the "long" (>1µm) wavelength regime. Although the role of these two partners is mainly on the fabrication side, it is useful to perform initial tests by the fabricator before sending samples to other partners for more detailed investigation. 1E-04 1E-05 Signal (Current on photodetector) 1E-06 1E-07 1E-08 1E-09 1E Wavelength (microns) Fig. 18 Characterisation of measurement set-up. Fibre Slab waveguide Ridge waveguide Photonic crystal The various curves taken on the newly installed set-up highlight several important issues: a) Coupling from the fibre to the slab waveguide incurs a substantial loss, on the order of 20dB. This highlights the need for alternative coupling geometries, such as a fibre coupler (chapter 3, section 2.4) and the adiabatic coupler proposed by Bookham

32 Chapter 3 Workpart 1 b) The ridge waveguide incorporated an enlarged middle section (as in Fig. 18) for placement of the photonic crystal. This enlarged section leads to Fabry-Perot resonances and should therefore be avoided. c) All photonic crystal sections only showed very weak transmission and no spectral features, the most likely cause of which is insufficient etch depth of the particular sample. This problem is being addressed via material redesign and repeated processing. 3.5 Scanning Near-field Optical Microscopy (SNOM) Fig. 19 Schematic of the experimental set-up for near- and far-field microscopy of light propagation in the PBG waveguiding structures. The main activity at the Institute of Physics, Aalborg University (participants: PhD-student V. S. Volkov, Associate Professor S. I. Bozhevolnyi) is concerned with characterisation of light propagation and scattering in the PBG structures by making use of high spatial resolution microscopies, e.g., scanning near-field optical microscopy (SNOM). Current work is concentrated one the construction and testing of a microscopic arrangement that allows one to combine the farand near-field techniques (Fig. 19). Furthermore, we are incorporating two tuneable lasers as radiation sources in order to be able to characterise the PBG structures not only at the telecommunication wavelength of 1.55 µm, but also in the near-infrared region ( µm), which is exploited in the GaAs-based PBG components. Preliminary experiments showed that the efficient coupling from a fibre to a channel waveguide leading to the PBG structure is of crucial importance for the SNOM imaging. The problem is that the evanescent wave of a guided mode penetrates into air with only a tiny fraction of its field. Therefore, the radiation picked up by a fibre tip of the SNOM is weak and can be easily obscured by noise, e.g., by stray light coming out of the place of fibre-to-waveguide coupling. The conventional technique for the optimisation of the fibreto-waveguide coupling relies on maximisation of the light throughput in a waveguide structure, and this might be difficult when the radiation should first pass the PBG structure. The technique adopted here is based on the observation of the fibre alignment with respect to the channel waveguide (insert in Fig. 19) via the microscope objective and a properly adjusted CCD camera. Using this far-field technique, it will probably also be possible to track the light propagation through the PBG structure by monitoring the radiation scattered out the PBG structure. Actually,

33 Chapter 3 Workpart 1 this technique has been increasingly used in the recent experiments on PBG waveguiding. At present most of the components needed to implement the microscopic arrangement described above have arrived and the rest has been ordered. The mechanical construction including the supports of the SNOM head and the IR-sensitive CCD camera is still at the design stage because its design is very sensitive to the configuration of the commercial translation stages that are expected to arrive within a few weeks. 4 Conclusion The key result of WP1 is the establishment of a loss figure for photonic crystal waveguides. Reducing this loss by at least an order of magnitude is necessary to keep the industrial interest in this area alive. We believe that the losses in both GaAs/AlGaAs waveguides (2dB/100µm = 200dB/cm) and in SOI-based waveguides can be reduced sufficiently in the near future to meet this requirement. Theoretical work by Lalanne and Benisty [19] indicates that deeper etching will reduce losses in GaAs/AlGaAs waveguides, by an order of magnitude or possibly more. St. Andrews has obtained funds from elsewhere to install a Chemically Assisted Ion Beam Etching machine, which, in principle, can achieve aspect ratios of 20:1 (as demonstrated by the Caltechgroup) [20], e.g. 100 nm holes etched 2 µm deep. The tool is now on order and will be installed and run up in early summer For the SOI waveguides significant improvements are expected when the initial alignment errors are eliminated and when tapered coupling structures fabricated by Bookham can be used. During year 2 we will also design and fabricate many new types of waveguide components (including splitters, couplers and ring cavities), so that we can take advantage of some of the immense new possibilities offered by crystal waveguides compared to classical waveguides. Finally, we will fabricate the vertical fibre coupler. 5. References 1. Chutinan and S. Noda, Phys. Rev. B Vol. 62, pp (2000). 2. T. Søndergaard, A. Bjarklev, M. Kristensen, J. Erland Østergaard, and J. Broeng, Appl. Phys. Lett., vol. 77, 785 (2000). 3. S. Johnson, S. Fan, P.R. Villeneuve, J.D. Joannopoulos and L.A. Kolodziejski, Phys.Rev.B,60 (8), 5752 (1999). 4. W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets and D. De Zutter, "Out-of-plane scattering in photonic crystal slabs", accepted for publ. In Phot. Technol. Lett. (2001). 5. J. M. Smith, H. Benisty, S. Olivier, M. Rattier, C. Weisbuch, T. F. Krauss, R. M. De La Rue, R. Houdré and U. Oesterle, "Low-loss channel waveguides with two-dimensional photonic crystal boundaries", Appl. Phys. Lett. 77 (18), pp , (2000). 6. E. Chow, S.Y. Lin. J.R. Wendt, S.G. Johnson and J.D. Joannopoulos,"Quantitative analysis of bending efficiency in photonic-crystal waveguide bends at λ=1.55 µm wavelengths", Optics Lett., Vol. 26 (5), pp (2001). 7. Marko Loncar, Dusan Nedeljkovic, Theodor Doll, Jelena Vuckovic, Axel Scherer, and Thomas P. Pearsall, "Waveguiding in planar photonic crystals", Appl. Phys. Lett., Vol. 77 (13), pp (200). 8. D. Nedeljkovic, M. Loncar, S. Kuchinsky, M. Mikhailov, A. Scherer and T.P. Pearsall, 'Waveguiding at 1550nm using Photonic Crystal Structures in Silicon on Insulator Wafers',

34 Chapter 3 Workpart 1 OFC'01 paper TuC6, Technical Digest Series Tuesday (2), p. C6-1 - C6-3, Anaheim CA, USA, March (2001). 9. M. Tokushima, H. Kosaka, A. Tomita and H. Yamada, Appl. Phys. Lett., 76 (8), (2000). 10. S.W. Leonard, H.M. van driel, A. Birner, U. Gösele and P.R. Villeneuve, Optics Lett., Vol. 25 (20), pp (2000). 11. Yariv A., Xu Y., Lee R.K. and Scherer A., "Coupled-resonator optical waveguide: a proposal and analysis", Optics Lett., Vol. 24, No. 11, pp (1999). 12. Bayindir M., Temelkuran B., Ozbay E., "Propagation of photons by hopping: A waveguiding mechanism through localized coupled cavities in three-dimensional photonic crystals, Phys. Rev. B, Vol. 61, No. 18, pp (2000). 13. Bayindir M., Ozbay E., "Heavy photons at coupled-cavity waveguide band edges in a threedimensional photonic crysta"l, Phys. Rev. B, Vol. 62, No. 4, pp (2000). 14. Bayindir M., Temelkuran B., Ozbay E., "Photonic-crystal-base beam splitters", Appl. Phys. Lett., Vol. 77, No. 24, pp (2000). 15. Xu Y., Lee R.K., Scherer A., Yariv A., "Propagation and second-harmonic generation of electromagnetic waves in a coupled-resonator optical waveguide", J. Opt. Soc. Am. B, Vol. 17, No. 3, pp (2000). 16. S. Boscolo, C. Conti, M. Midrio, G. G. Someda, "Electromagnetic Analysis and Impedance Matching in 2-D Photonic Crystal Waveguides with Finite Length", submitted to IEEE - JLT. 17. C. J. M. Smith, H. Benisty, D. Labilloy, U. Oesterle, R. Houdre, T. F. Krauss, R. M. De La Rue, and C. Weisbuch, Electr. Lett. 35, (1999). 18. A. Talneau, L. Le Gouezigou, N. Bouadma, "1.55 µm low loss planar photonic crystal waveguides on InP substrate", Paper WeA2.4, ECIO, Paderborn, Germany, April P. Lalanne P and H. Benisty H, "Out-of-plane losses of two-dimensional photonic crystals waveguides: Electromagnetic analysis", Journ. of Appl. Phys., 89, pp (2001). 20. J. O'Brien, O. Painter, R. Lee, C. C. Cheng, A. Yariv and A. Scherer, "Laser incorporating 2D photonic bandgap mirrors", Electronics Letters 32 (24), , (1996)

35 Chapter 4 Workpart 3 Chapter 4 Workpart 3 1. Introduction 1.1 Objectives and expected achievements for the first year The objective of workpackage WP3 is the realisation of a photonic crystal based wavelength converter monolithically integrated with the pump. The device is to be used in the framework of the project for laboratory characterization and system test. In the first year the work to be done was: design, fabrication and initial test of the phase matched parametric waveguide. Partners 4 (Pir) and 7 (Uniud) carried out the design in collaboration with partner 1 (GU). Growth of the slab waveguide has been done by partner 3 (Imec). Fabrication has been performed by partner 1 (GU) and by partner 4 (Pir). Finally experimental characterization has been performed by partner 2 (COM). All the step required have been completed even if the experimental test has not been completely successful due to unexpected difficulties and new problems as discussed below. On the base of the experience acquired, new solutions have been proposed that should permit to overcome the unexpected difficulties. The developing of the new ideas constitutes the basis for the future work to be carried out in the second year. 1.2 Worldwide state of the art To the best of our knowledge few research groups are currently working on non linear processes in photonic crystals. The research direction can be basically grouped in the following categories: 1. SH harmonic generation in a multilayered 1D medium with low index contrast. 2. SH generation using form birefringence. 3. All optical switching with non linear photonic bandgap structure 4. Accessing the optical non linearity of metals with metal-dielectric PBG structures. SH generation in a multilayered 1D medium with low index contrast The research in this field is basically carried on by the group of M. Scalora, M. Bloemer, J. Dowling et. Al.[1] and by the group of Balakin et. Al [2]. They numerically study the enhancement of second harmonic generation (SHG) in 1D low index contrast PBG. The enhancement is shown to arise because the pump and generated fields are both tuned at the band edge. Up to the present moment only theoretical investigations have been carried out. Those researches constituted the starting point of the work done in Picco. We investigated on the properties of layered media in the framework of frequency downconversion (FDC). The major difference between SHG and FDC is related to bandwidth requirements due to the need of tunability of the FDC's. The extension from SHG generation to FDC is infact not obvious in a photonic crystal since different phase matching conditions must be found

36 Chapter 4 Workpart 3 SH generation using form birefringence The research in this field is basically carried out by the group of V. Berger from Thomson [3]. This group has investigated the possibility of phase matching non linear interactions using optical eterostructures. A waveguide composed of a stack of AlGaAs and AlAs has been used in order to exploit the form birefringence. The experimental realization of this proposal has been achieved recently. As discussed below in Picco we will also exploit the form birefringence for phase matching non linear processes. The birefringence will be obtained by etching the waveguide instead of using stack of different material. Following this approach an enhancement of the form birefringence should be obtained due to the high index contrast. All optical switching with non linear photonic bandgap structure The research in this field is basically carried out by the group of P. Tran from Naval air warfare centre weapons division [4]. He investigated a pump-probe optical switching mechanism that exploits a Kerr nonlinear chiral PBG. The switching is achieved by shifting the band-gap of the structure. Experimental observation of such switching has never been tried since the power levels required are too high. Accessing the optical non linearity of metals with metal-dielectric PBG structures. The research in this field is basically carried out by the group of R. Boyd from University of Rochester, New York [5]. Metals typically have very large optical non linearity but because they are nearly opaque their non linear properties are inaccessible. However a multilayer metaldielectric stack can have a significant transmission making accessible the huge non linearities of metal. Up to the present moment this research are only theoretical. 2. Design of the photonic crystal based wavelength converter 2.1 Modeling We analyzed an AlGaAs based waveguide with superimposed longitudinal PBG structure obtained by periodic deep etching as showed in Fig.1. Fig. 1 Structure of the photonic crystal based wavelength converter To evaluate phase-matching we considered an equivalent 1D structure consisting of a stack of N elementary cells. Each elementary cell contains four alternate layers of material and air. The refractive index of the material layer corresponds to the effective index of the AlGaAs waveguide designed to be single mode at both pump and signal frequency. Using a transfer matrix approach we calculated the linear properties of our device: both the complex transmission function and the

37 Chapter 4 Workpart 3 density of modes (DOM) of the electromagnetic field inside the structure. The knowledge of the complex transmission function allows us to compute the phase matching rules in terms of the parameters of the device. To simulate the nonlinear propagation along the periodic structure we have directly solved Maxwell equation without any approximation. The algorithm is based on an one dimensional Finite Difference Time Domain numerical routine (FDTD) accounting for both material nonlinearity and dispersion. The impact of the scattering losses on conversion efficiency has also been investigated. 2.2 Design of the waveguide for parametric conversion The basic features that a waveguide must possess in order to be used in a photonic crystal based wavelength converter are essentially: 1. Single mode at both pump and signal wavelengths 2. Good overlap between pump and signal fields 1. Good fraction of both pump and signal fields must be in the etched zone (1-2 µm) 4. Effective indexes at pump and signal in a range suitable for designing the PBG A waveguide meeting all of those features is sketched in Fig µ m 3 µm Ridg e 4 0 n m (A l % = 0.2 5) Etching Depth 1.0 µ m Top C ladding C ore B ottom Cladd in g I B ottom Cladd in g II 140 nm (Al % = 0.25 ) 140 nm (Al % = 0.20 ) 14 0 nm (Al % = 0.30 ) (Al % = 0.5 0) 2 µ m Fig. 2 Designed waveguide profile. With the parameters showed we 775 nm singlemode, 99 % of the field is in the etched zone, neff = 1550 nm singlemode, 99 % of the field is in the etched zone, neff = % modal overlap The proposed waveguide is therefore suitable for designing the photonic crystal. 2.3 Design of the PBG : phase matching condition We had to satisfy phase matching condition keeping into account the bandwidth requirements for pump and signal. We will describe the general design rules to obtain phase-matching in a periodically layered material for the following process:

38 Chapter 4 Workpart 3 ω ω ( sig nal) ω + ω ( id ler ) 2 ω ( p u m p ) in je cted g en er at ed M id d le of th e p ass b a nd B an d ed g e o r M id d le o f th e pa ss b an d Fig. 3 Proposed wavelength conversion scheme for frequency down conversion with the signal at 1550 nm and the pump at 775 nm both injected into the waveguide Our method is based on the use of a multi-layer unit cell and applies even for highly dispersive materials. For the purpose of wavelength conversion, a large bandwidth of the signal is required. Tunability of the pump is instead necessary only for some particular applications (i.e. network applications). For this reasons two different devices have been designed: a "limited tunable" device (signal tunable, pump fixed, high efficient short device) a "fully tunable" device (signal tunable, pump tunable, moderately efficient long device) To design the "only signal tunable" FDC with signal/idler frequency at ω s,i = ω 0 +/- ω and pump at ω p =2ω 0 the steps to follow are: a) design a stack with one transmission peak tuned to ω s,i located in the band between gaps J and J+1. The signal output phase will be Φ(ω s,i ) = NJ + N 2 π Φ(ω s,i ) = NJ + N ±1 2 π odd N even N b) tune the pump frequency ω p at the edge of the K-th band gap. The output phase of the pump will be: Φ(ω p ) = NK ±1 [ ]π where the signs +/- apply respectively to higher/lower frequency band edge

39 Chapter 4 Workpart 3 c) impose the phase-matching condition Φ(ω p ) = 2 Φ(ω 0 ) that implies i) K = 2J + 1, i.e. if ω s,i is tuned in between the band gaps J and J+1 the pump frequency must be on the edge of the (2J + 1)-th pass-band. ii) the stack has to be constist of an odd number N of unit cells. Fig. 4a shows the structure of the 4 layers unit cell we have designed for the "limited tunable" wavelength converter. The transmission of this structure is depicted in Fig. 4B) (1) dnl (1) dnl (1) ( 2) dair d nl (1) dnl 4-layers unit cell ( 2) dair T ra n s m is si o n λ p = 780nm λ 0 = 1560 nm Wavelength(µm) Fig. 4 a) Unit cell. The layer thicknesses are d 1,nl =407 nm, d 1,air =155 nm, d 2,nl =570, nm, d 2,air =100 nm. b) Transmission for the stack with N = 13 elementary cells. To design the "fully tunable" wavelength converter it is possible to follow a similar approach as for the limited tunable one. In this case the relevant condition on the number of unit cells is: (N-1) / 4 = Integer number Fig. 5a shows the structure of the 4 layer unit cell that we have designed for the "fully tunable" wavelength converter. The transmission of such structure is depicted in Fig. 5b. It is evident that both pump and signal lie in the middle of a pass band. (1) d nl (1) d air (2 ) d nl (2) d air 4-layers unit cell Fig. 5 a) Unit cell. The layer thicknesses are d 1,nl =315 nm, d 1,air =100 nm, d 2,nl =120 nm, d 2,air =100 nm. b) transmission for the stack with N = 13 elementary cells

40 Chapter 4 Workpart Predicted Performance The performances are evaluated considering basically two parameters: conversion efficiency and converted signal power. For the use in a high bit rate transmission system is a certain level of converted power must be achieved otherwise amplification of the converted signal could be necessary with the consequent decrease of the SNR. In particular, for a bit rate of 40 Gbit/s, a converted power greater than 50 µw (-13dbm) is required. We focus on the only signal tunable device that was the one actually fabricated. In Fig. 6) are reported respectively the conversion efficiency and the pump power as a function of the length of the device for a loss less device. A length of the device of only 150 µm is needed for achieving the threshold of -13 dbm required for 40 Gbit/s transmission. This is a remarkable result very promising for miniaturization. A saturation of the conversion efficiency is evident from Fig. 6a. Such behaviour is basically due to two narrowing of the transmission peak at pump wavelength. For the simulated device the bandwidth of the pump is about 0.1 nm. The bandwidth of the signal is anyway very large: about 80 nm. As discussed below apodized structure could be used to decrease the sharpness of the transmission function. We now focus on the scattering losses due to the etching of the waveguide. The material absorption has been neglected since the material is transparent for the Aluminium concentrations we used. In Fig. 7, we reported respectively the conversion efficiency and the pump transmission as a function of the diffraction from the single air layer. A reduction of the performances is expected due to scattering losses and the responsible is the reduction of the pump transmission. The design of our structure assures that the diffraction loss for single air layer is much less than 0.1 db. A reduction of a maximum of 5 db in conversion efficiency is therefore expected for the proposed devices with respect to the loss less case examinated before. in ) / p (P 0 o (d -0.5 (Pp ) ut C b) Only signal tunable (d o B -1.5 P n ) -2 ve u -2.5 rs m io p -3 n tr -3.5 ef an -4 fi s ci -4.5 m en cy is Number ofunitcells N si Number of unit cells N o 310 µm 310 µm n Fig. 6 Performances versus length. P Pump = 25 mw, P Signal = 3 mw, χ (2) = 100 p/v. d ) b ( te m d si g na l C p o n w ve r er

41 Chapter 4 Workpart 3 Conversion Efficiency (db) Diff raction loss per air layer (db) Fig. 7 Conversion efficiency versus scattering losses. P Pump = 25 mw, P Signal = 3 mw, 11 cells (20 µm) 3. Epitaxial growth The growth of the wafers to be etched has been carried out at the optoelectronics department of IMEC in Gent. The technique used was: MOVPE (Metal Organic Vapour Phase Epitaxy). Two 2" wafers were grown following the design described above. 4. Fabrication The photonic crystal based wavelength converter represents a great challenge for fabricators. The necessity of phase matching implies the realisation of structures in the nanometer scale with high aspect ratio. The complexity of the structure and the nature of the four layer unit cell requires therefore considerable refinement of the fabrication process. Fabrication is generally performed in two separate steps: lithography and etching. Regarding the lithography, the most important refinement was the introduction of proximity correction software for e-beam exposure. Proximity effect consists of an unavoidable scattering of electrons from the substrate into the areas surrounding the pattern which causes an undesired overexposure condition. The proximity correction algorithm permitted to make more uniform structures that did not taper off towards the sides. Note the considerable improvement between Figs. 8 and 9 brought about by general refinement and the introduction of proximity correction software. 0 ower 780 nm(db)

42 Chapter 4 Workpart 3 Fig. 8 First fabrication tests showing signs of the proximity effect (overexposure towards the middle of the structure) and mechanical instability due to underetching. Fig. 9 Improved fabrication due to proximity correction software and more vertical etching. The structures depicted in Figs. 8 and 9 have been processed with e-beam lithography system in Glasgow. Fig.10 shows a detail of the edge of a structure fabricated at Pirelli after e-beam lithographic definition with proximity effect correction. Fig. 10 SEM photo of the edge of the structure after lithographic definition. The partners have used different techniques and machines for the dry etching. In Glasgow, a standard Reactive Ion Etching (RIE) was used, while Pirelli used an Inductive Coupled Plasma etching system (ICP). For the RIE process, the etching process must be refined for each material, as the aluminium concentration in the AlGaAs alloy requires different conditions to achieve verticality

43 Chapter 4 Workpart 3 Fig. 11 Poor (left) and improved (right) etching. The "bulging" of the slots on the right hand side of picture 11 can be further minimised, but indicates one of the major limitations of the RIE process that we use currently. The observed increase in lateral etch rate is related to the relatively high pressure in an RIE reactor, because the bombarding reactiv ions collide with the reaction products and gain transverse momentum. This high pressure limitation is one of the reasons for the installation of a chemically assisted ion beam etching (CAIBE) system at St. Andrews, because the pressure in the reactor can be kept an order of magnitude lower than in an RIE system. With ICP technique it was possible to etch with high density plasma, high physical component, and very low pressure; as a consequence, the etching rate for each layer was almost constant. In Fig. 12, we show a detail of a structure after etching with ICP technique. In conclusion, we can confirm that the target of µm etch depth with vertical sidewalls and good centre-edge uniformity has been achieved. It is important to note that all the fabrications previously described have not been performed on the ridge waveguide originally designed and showed in Fig. 2. Fig. 12 SEM tilted micrograph after etching. Etching a ridge waveguide requires infact a double etching process that represents a further complicance of an already difficult process. Since the ridge was not strictly necessary at this stage, it was decided to use a simpler slab waveguide. This required further design of the unit cell in order to use the slab waveguide. In Figs.13) and 14) are sketched respectively the waveguides actually etched in Glasgow and in Pirelli. Top view Front view 700 µm (not in scale) Input waveguide 700µm Output waveguide 3 µ m Etching Depth 1.0 µ m To p Cladding Core Bottom Cladding I Bottom Cladding II (not in scale) 3 µm 140 nm (Al % = 0.25) 140 nm (Al % = 0.20) 140 nm (Al % = 0.30) 2 µm (Al % = 0.50) Grating (5,10 or 20 unitary cells)

44 Chapter 4 Workpart 3 Fig. 13 Waveguide actually etched in Glasgow Top view (not in scale) 200 µm 1000 µm Input waveguide Output waveguide 600 µ m Etching Depth 1.5 µ m Front view (not in scale) 600 µm To p Cladding 140 nm (Al % = 0.25) Core 140 nm (Al % = 0.20) Bottom C ladding I 140 nm (Al % = 0.30) Bottom Cladding II (Al % = 0.50) 2 µm Grating (99 o r 13 unitary cells) 1 Unitary cell is 1.23 µm Fig. 14) Waveguide actually etched in Pirelli The first fabrication run in Pirelli did not involve the realization of the input/output waveguides, Such waveguides are currently being processed, including the fine-tuning of all relevant process parameters. Samples will be sent to COM for testing once finished. 5 Optical Characterization of the photonic crystal waveguides The experimental characterization of the photonic crystal waveguide has been carried out at COM. Both samples fabricated in Pirelli and in Glasgow have been measured. The characterization consisted of measuring the linear transmission function at both pump (780 nm) and signal (1550 nm) wavelengths. Measurements have been done on both etched and unetched samples in order to have a reference and to understand the behaviour of the slab waveguide. Different coupling techniques have been used for the two different wavelengths. In Fig.15) are sketched the experimental setup used for the characterization at pump and signal wavelengths. For the transmission measurements around 1.55 µm two tapered fibers were used to couple light at the input/output of the sample. Red light source has been used to align the fibers to the input/output waveguides by means of the optical microscope. 775 nm 1550 nm CCD camera nm Ti:Sapphire Photodetector LED + Er-fiber OSA N.A N.A. 0.3 Fig. 15 Experimental setup for pump and signal wavelength

45 Chapter 4 Workpart 3 For transmission measurements around 775 nm CW Ti:Sapphire laser was scanned from 740 nm to 840 nm with 1 nm step. Laser beam of about 1 µw power was focused on the input waveguide by microobjective with N.A Height alignment and focusing adjustments were made by means of optical microscope. Microobjective with N.A. 0.3 was used to couple light at the output surface of the waveguide. For imaging the output of the waveguide and final focusing adjustments CCD camera was used. Transmission spectra were recorded using a photodetector; a pinhole has been used to block the part of the light beam that had not pass through the waveguide. Fig.16 shows the experimental transmission in the pump region around 780 nm. It wasn't a success to register expected transmission peaks around µm because the signal was below detection limit for <785 nm. The output signal was too noisy to speak about predicted modulation in this spectral range. Our estimations show that the losses for the empty waveguides in this spectral region were about 20 db while for PC waveguides with periodic arrays losses were about 30 db. A possible explanation of the observed results is that Al content in the waveguides may be too low resulting in the reduced transmission because of absorption. This hypothesis will be checked in further measurements. 0,7 0,6 0,5 etched 0,4 0,3 0,2 below detection limit 0,1 0, λ, nm Fig. 16 Transmission versus 780 nm Figs.17 and 18 we show the transmission spectra for different samples using LED around 1.55 µm. For all the investigated sample a 20 db extra loss has been observed in the etched waveguide with respect to the unetched ones. A weak modulation of the transmission function with the period of about 7 nm is evident for the unetched waveguides. Such modulation appears in all the investigated cells. This effect is probably due to the coupling between the waveguide and the tapered fiber used for coupling. Concerning the etched waveguides, a modulation period of about 3-4 nm results for the 10 periods structures and 7-8 nm for 20 periods ones. Those modulations are not due to the presence of the photonic crystal. According to the theoretical calculations infact a modulation period around nm is expected in the spectral range from 1.5 µm to 1.6 µm

46 10 perio dsof 345 n m, 10 nm, 130 nm, 10 nm Chapter 4 Workpart 3-25 cell 6-25 cell empty WGs em pty WGs periods periods of 345 nm, of 345, 110 nm, , nm, 130, nm WGs with arrays λ -45 WGs with a rra ys per periods i of 345 of nm 3, 45, 110 nm 110,130, 130, nm, nm λ Fig. 17 Transmission versus 1550 nm for the structure with 10 unit cells (left) and 20 unit cells (right) The presence of those modulations in the transmission function of the etched waveguides remains somehow obscure, we suggest that they could be originated by some other cavity in the sample. In conclusion the first optical characterization was not completely successful. It must underline anyway that the samples under test belong to a first set of fabricated structures in which the proximity correction had not been done. An investigation with an optical microscope showed infact that the depth of the etching was not uniform along the grating. This may explain the difficulties in observing expected transmission modulation. Further experiments will be performed soon on a new set of etched samples with the proximity effect correction; moreover such structures will also have an improved coupling section so that we are confident that better results will be achieved. 6. Redesign: new solutions and future work From the previous discussions and on the basis of experiments performed with the first fabricated structures, results that the PC WC is theoretically a very efficient device but at the same time it's a very critical device. The reasons of such criticality relies on the many simultaneous requirements that must be satisfied in designing such a device in order to ensure phase matching and single mode operation at the same time. Since the phase evolutions depends on all the multiple reflections at all the interfaces of the PC, the device results to be very sensible to a variation in the "optical path" i.e. a variation in the index of refraction and/or in the thicknesses of the etched zones. Particularly sensible are the long and high index contrast structures. Scattering losses also play an important role in decreasing the performances even if they can be minimized by keeping small the size of the etched zones. Another important constraint is that the waveguide must single mode at both pump and signal wavelength, this is because the pump has to be directly injected into the waveguide. As a consequence the modal area is very small (order of 1 µm 2 ) leading to a reduced coupling efficiency. The last is more an experimental complicance than a real criticality but in union with the other aspects has made impossible to obtain the desired results i.e. the observing the wavelength conversion

47 Chapter 4 Workpart 3 For all those reasons new approaches to the problem of wavelength conversion in PC must be examinated in the second year of the project. We will basically follow two distinct approaches: a) Make an endeavour to make the existing device more tolerant. b) Pursue a new approach intrinsically tolerant in designing the WC. Regarding point a) two different approach will be basically pursued. The first one consists in controlling the temperature of the sample in order to compensate the variation of the effective index of the waveguide. The second approach consists in an apodization of the PC structure in order to smooth the transmission function of the device. Such result could be particularly useful for high index contrast structures that exhibit sharp peaks in the transmission function. This second way is not completely obvious since the compatibility of apodization with phase matching conditions is not evident "a priori". From preliminary studies anyway results an indication that such compatibility may exist. Of course temperature control and apodization can also be used together in order to increase the tolerances of the device. The idea of the new approach anticipated in point b) arises from the observation that all the criticality of the WC derives from the fact that phase matching is achieved trough a PC transversal with respect to light propagation. As a consequence light must cross all the air cuts giving rise to enhanced scattering losses and an enhanced sensitivity to parameter variation. If phase matching could be achieved with a PC exploiting longitudinal lateral trenches (i.e. in the direction of light propagation), many of the critical features previously described could be eliminated; in particular the presence of very sharp peaks in the transmission function of the device. A substantial reduction of the scattering losses could also be achieved. What we propose is therefore a waveguide with almost the same vertical structure than the one described previously but with the cuts arranged longitudinally to form a photonic crystal around a central defect in which the light is guided, as shown in Fig. 18. TM Pump ( λ = 780 nm) Signal (λ = 1560 nm) Upper cladding Waveguide Core Lower cladding TE Fig. 18 New proposed design and wavelenght conversion scheme In the latter case the role of the PBG is twofold: first it could be used to enhance the form birefringence of the waveguide, second it could also assure the lateral confinement. Vertical confiment is instead assured by a conventional index contrast waveguide. On the base of the previous considerations we are going to propose the following scheme for the wavelength conversion: Pump and signal must be injected into the waveguide with orthogonal polarization in order to exploit the form birefringence provided by the PBG for phase matching

48 Chapter 4 Workpart 3 purpose. At the same time the design of the PBG must assure that waveguide remains single mode at both pump and signal wavelength. The degrees of freedom that can conveniently be exploited are number and the thicknesses of the lateral trenches and of the central defect along with the vertical waveguide design. From preliminary studies on the new structure, we have the evidence that phase matching can be achieved with the proposed scheme of Fig. 18. Details of the designed structure are showed in Fig. 19. In Fig. 20 is instead reported the effective index of the waveguide versus wavelength for both the polarizations. It's clear that pump and signal orthogonal polarized are phase matched. 160 nm 100 nm 120 nm Etching Depth 1.5 µ m Top Cladding 140 nm (Al % = 0.25) Core 140 nm (Al % = 0.20) Bottom Cladding I 140 nm (Al % = 0.30) Bottom Cladding II 2 µ m (Al % = 0.50) Fig. 19 Design of the new waveguide The waveguide depicted in Fig. 19 is not still single mode at pump frequency, but the higher order modes are very near to cut-off so that we believe it possible to make the waveguide single mode by narrowing the central defect. Future work towards this direction will consists in make the waveguide single mode at pump frequency along with trying to make the modal area as large as possible in order to increase coupling efficiency and reducing experimental difficulties. 3.5 Effective index TE TM λ (µm)

49 Chapter 4 Workpart 3 Fig. 20 Effective index vs. wavelenght for both polarizations 2D structures will also be investigated i.e. various arrangement of etched holes around a defect. Preliminary results about 2D photonic crystal show infact that such structures are good candidates for phase matching purpose using photonic crystal induced form birefringence. An example of the structure we want to use is sketched in Fig. 21). Lateral confinement is assured by the PBG while vertical confinement is given by a traditional index contrast waveguide. Unit cell Line defect Fig. 21 Example of 2D structure A triangular lattice of etched holes has been studied since such structure exhibits a lateral band gap at both pump and signal wavelength. Moreover for properly chosen values of the holes diameter and distance the structure is single mode at both pump and signal frequency. As for 1D structure the form birefringence will be exploited to ensure phase matching so that orthogonal polarized fields will be injected into the waveguide. For all these reasons, we believe that 2D structures are very promising candidates for wavelength conversion purpose. The work that will be carried out in the second year on such structures will be fundamentally of understanding the phase behaviour of the block field in order to obtain phase matching. To this purpose hybrid structures will also be investigated. By hybrid structure we mean a structure which possess a modulation of the PC also along the propagation direction. Studies on chirped photonic crystal will be also carried out. The work within the workpackage will be divided as in the previous year. The design will be carried out basically in Pirelli and at the University of Udine with the help of the team at St. Andrews. The designed devices will be fabricated at the University of S. Andrews and in Pirelli while the slab waveguides will be provided by IMEC. Experimental test will be performed at COM and Pirelli. Summarizing the future work will consist of the following points: 1D structures: 1. Optimisation of the existing transversal device to increase the robustness with respect to parameter variation: temperature control, apodization. 2. Study of longitudinal structures

50 Chapter 4 Workpart 3 2D structures: 1. Investigation of the phase matching conditions in simple triangular lattice. 2. Investigation of the phase matching conditions in hybrid and chirped lattices. Fabrication and characterization: 1. Characterization of the new transversal structures already fabricated with proximity correction and improved coupling waveguides. 2. Fabrication and characterization of the new 1D and 2D structures as soon as the design will be completed. 7. References 1. M. Scalora et Al., Physical Review A, Vol. 56 No 4, Oct. 15, A. V. Balakin et Al., Optics Letters, Vol. 24 No 12, June. 15, A.Fiore et Al., Nature, Vol. 391, 29 January P. Tran, JOSA B, Vol. 16 No 1, January 1, Bennick et Al., Optics Letters, Vol. 24 No 20, Oct. 15,

51 Chapter 5 Workpart

52 Chapter 5 Workpart 4 Chapter 5 Workpart 4 1. Introduction 1.1 Objective The initial purpose of the work is to provide an overview of existing theoretical methods suitable for modelling of high-index-contrast wavelength-scale structures, like 2D and 3D photonic crystal waveguides (PCWs). A special 4-series set of benchmarks structures has been elaborated to point out the methods most suitable to model the structures that are to be investigated in the project. We are comparing the computational efficiency of the software tools on the benchmarks examples. The results obtained using different methods are evaluated giving us the necessary facts for deciding our modelling strategy for the next year Worldwide state-of the-art We consider now the state-of-the-art in computer modelling activity throughout the world. We restrict ourselves to papers in the referenced international journals issued within the years , and which contain results on numerical methods or calculations for PBG structures. As a guidance line we will consider the state of the art concerning modelling of the PICCO benchmark structures (Appendix C). Series 1. 1-D periodic photonic crystal slabs, i.e. slab waveguides with etched air slots The benchmarks of this series have been thoroughly investigated at IMEC (see this report), so we mention briefly that rigorous coupled wave analysis (RCWA) together with the scattering matrix method (SMM) was used in [1], and the eigenmode expansion technique (EME) was used in [2] for transmission calculations. Series 2. Basic 2D photonic crystal components, i.e. 2D photonic crystals consisting of air holes in high index material. The air holes can be lossy material to simulate out-of-plane scattering loss. Due to a rather "long history" of calculations for this series the modelling activity for these examples is now slowing down. The transfer matrix method (TMM) and RCWA with SMM are rather popular for reflectiontransmission calculations for Benchmarks 2A and 2B [3-5]. The plane wave expansion method (PWE) is commonly used for obtaining band diagrams for the different polarizations of the radiation in Benchmarks 2C (straight waveguide) and 2E (microcavity) [6-8]. Propagation through some waveguide bends, Y- and T-branches and directional couplers (Benchmarks 2C, 2F, 2H) were analysed in [9] by the modified beam propagation method (BPM). The FDTD methods have shown their versatile character by being used for band diagrams, reflection-transmission and fields calculations [7, 10-14] for Benchmarks 2A, 2C and 2H. Series 3. Complex 2D photonic crystal components, mainly combinations of simple photonic crystal components, like a waveguide or a cavity

53 Chapter 5 Workpart 4 There are only few recent papers on modelling of the benchmarks of the third series. We only mention paper [15], where the FDTD code was used for simulating transmission of Benchmark 3G. This might be explained by the rather complicated character of coupling problems and by the intensive investigations in previous years. Series 4. 2D photonic crystal slabs, i.e. 3D structures with a 2D periodic photonic crystal in one direction and a slab waveguide in the other. This series embraces the most complicated structures for simulations, and for modelling of these structures full 3D tools are needed. Accordingly benchmark scheme 4A is a layered waveguide with a perfect 2D photonic crystal pattern. It may, for example, be a simple perforated slab in air. Their dispersion diagrams were thoroughly investigated by PWE in [16,17] and by FDTD in [18]. Transmission spectra were presented in [18] (FDTD), [19] (SMM) and [20] (however, the TMM analysis is 2D). Benchmark 4B is a straight photonic crystal waveguide (PCW) in a three layered system. It was investigated in a number of papers. Dispersion diagrams were presented in [21-29], where PWE was used in [22-24] and FDTD in [21,27-29]. Unfortunately, the authors of papers [25,26] did not pay attention to the description of the software used. Fields and transmitted intensities were found in [24-26,30], but again only the authors of papers [24,26] specified the FDTD code as their tool for computation, while the authors of [25,30] did not specify their method. We can only guess that they used the FDTD code, because only this numerical tool can deal with such complicated tasks at present. Finally, transmittance and reflectance from Benchmark 4C (PCW bend) were studied in papers [26-29]. The FDTD numerical tools were successfully applied, corroborating once more their universal and effective character. A new interesting approach to the waveguiding problems, different from the standard methods, has been developed recently. The approach concerns reflection and transmission of light impinging onto the upper plane of a PCW or a thin photonic crystal layer. Applying SMM or TMM methods permits one to obtain photon dispersion relations [31-33], to design single-mode leakage-free PCW [34], to get high-q vertical surfaces emitting devices [35], and to establish a new optical property as for example trirefringence [36]. 1.3 Conclusion and open questions in modelling activity Dispersion diagrams for 3D structures have been thoroughly investigated in several papers. A typical structure under study is a high-dielectric index slab with 2D PBG pattern and a line defect, producing a PCW. Light is confined to the waveguide by two mechanisms. In the plane light is confined to the waveguide due to the photonic band gap of the surrounding crystal slab, and confinement in the vertical direction is achieved by total internal reflection as in a usual planar waveguide. These mechanisms have been proved to be rather efficient, giving possibilities of single or double mode operation of such waveguides. It is confirmed by reflection-transmission calculations, which show good possibilities for straight waveguiding and even sharp bending or splitting of the light into two branches. Recently a series of papers have shown results on relative transmission efficiency for straight waveguides as well as for waveguides with bends [25,26]. By selecting the spatial structure of the devices this efficiency has been optimised up to 100%. Unfortunately no numbers for the computed transmission through the PCWs have been published. There is still a lack of numerical analysis of the following items:

54 Chapter 5 Workpart 4 1. Full 3D treatment of mode losses in PCWs. It is very important to be able to calculate outof-plane scattering in order to determine the major transmission losses, especially at bending or splitting points. 2. 3D evaluations of coupling schemes for optical signals into and out of a PCW. 3. Estimation of the decay of electromagnetic fields in transverse photonic crystal structures. Accurate estimation will provide important information about the number of rows sufficient for light confinement in PCWs, which may be used to reduce the computation grid in the FDTD methods. 2. Comparison between tools (Comparison of FDTD and eigenmode expansion (EME)) IMEC-Gent has performed a comparison of the performance of its Finite-Difference-Time- Domain tool (FDTD) and CAMFR Eigenmode expansion tool (EME) for Benchmarks 1A, 1B and 1C. These benchmark structures consist of a three-layer slab waveguide with etched air slots. Benchmark 1 (Figure 1a) has a single air slot; Benchmark 1B (figure 1b) has a finite 1D periodic lattice of air slots, while Benchmark 1C is an infinite periodic lattice of slots. They are designed to determine the out of plane scattering by calculating the transmission and reflection of the guided mode(s). In the comparison both methods are used to calculate these parameters versus the index difference between core and cladding in the structures. As both tools implement the PML absorbing boundary conditions, open structures can be simulated. For these benchmarks, the simulation results of FDTD and EME match within a few percent. These mismatches are mostly due to the discretisation of the FDTD mesh and the finite number of eigenmodes taken in the mode expansion. Increasing both these values improves accuracy but increases the computation time dramatically. More details of this study can be found in the Milestone report M19 and deliverable D8. We conclude that both EME and FDTD can be used to simulate structures with large refractive index contrasts. While FDTD has the advantage of versatility, EME is far more powerful for structures with a preferential propagation direction and a piecewise constant refractive index. Moreover, EME can make explicit use of periodicity. For the benchmark structures 1A and 1B, EME performed several orders of magnitude faster that FDTD, while the latter was not even pushed to the required accuracy. n clad d air n air infinite top cladding d air n air n co re d core N slots (a) n clad infinite bottom cladding (b) P x y z Figure 1 (a) Benchmark 1A, a single air slot etched into a 3-layer slab waveguide and (b) Benchmark 1B: a periodic arrangement of air slots etched into a slab waveguide

55 Chapter 5 Workpart 4 100% a b c d 80% 60% Losses 40% Reflection 20% Transmission Figure 2 Reflection, Transmission and Losses of periodic arrangements of air slots with both Mode Expansion (Continuous lines) and FDTD (R: Triangles, T: Circles, L: Squares) ε 3. CAMFR mode expansion tool for Photonic Crystals The CAMFR tool was originally designed for the modelling of layered cavity structures (hence the name Cavity Modelling Framework). The modelling of these structures in CAMFR is based on vectorial eigenmode expansion and perfectly matched layer (PML) boundary conditions. The structure is divided into sections with a constant refractive index profile along the propagation axis, and the field in each of these sections is expanded onto the eigenmodes of that particular section. In order to get a discrete set of radiation modes; the structure is placed between two perfectly conducting metal walls. These walls can be coated with PML, so as to eliminate the parasitic reflections from them, thereby effectively simulating an open structure. At the interfaces between different waveguide sections, mode matching is used to decompose the field into the eigenmodes of the new section, which ultimately gives rise to a scattering matrix describing the entire structure. This technique allows us to calculate reflection and transmission of finite structures, but is also suited for the calculation of band structures for infinite periodic structures, by imposing Bloch boundary conditions in the propagation direction. Originally, CAMFR was designed for structures with cylindrical symmetry (like VCSELs). The last year its functionality has been extended to include more general structures in a 2D cartesian coordinate system. This allowed for the simulation of photonic crystal like structures, both in top-down view (as a 2D array of holes with an optional defect) or in cross-section (as a 1D arrangement of air slots). Moreover, Bloch boundary conditions have been added to the boundaries in the propagation direction, such that the band structures of 1D periodic structures can be calculated. By mirroring the simulated unit cell, the band structure of 2D periodic lattices can also be calculated. The PML absorbing boundary conditions also allows for the simulation of open structures. We used this possibility to simulate the out-of-plane scattering loss in a 1D photonic crystal consisting of a three-layer slab waveguide with etched air slots. A more detailed description of this study is included in Milestone report M1 of Workpackage 1. Other photonic crystal simulations with CAMFR include the simulation of 2D photonic crystal waveguides with bends and splitters. 4. Development of mode expansion technique by Photon Design

56 Chapter 5 Workpart FIMMPROP-3D - application to photonic crystal simulations FIMMPROP-3D is a bi-directional propagation tool based on modal expansion. The algorithm represents a solution of Maxwell's Equations in terms of a superposition of the forward and backward travelling local modes of the cross-section. Where the cross-section changes continuously such as with the circular holes of a photonic crystal, the algorithm must use a staircase approximation. FIMMPROP-3D's implementation of the method is in principle fully 3 dimensional, though currently it is only practical to do 2D photonic crystal simulations due to memory and computation time limitations. The CAMFR tool developed by IMEC uses a similar technique, though it differs in many implementation details. 4.2 Progress Work on FIMMPROP-3D under the PICCO project has concentrated on the following areas 1. Optimising the tool for photonic crystal simulation in the following areas: Increasing the speed of the algorithms - the engines now run 5 or 10 times faster. FIMMPROP-3D is now probably the fastest tool available today for simulating a wide variety of photonic crystal devices. Increasing the stability of the algorithms - the photonic crystal simulations pose some special problems for modal expansion techniques. In particular, parts of the device become optically decoupled from their surroundings and this situation must be treated with care. Validating the tool for both E and H polarisations. The algorithms are now able to model also the much harder H-polarisation. 2. Creation of interface tools and utilities to facilitate the specification and computation of 2D photonic crystal devices, including structures with line defects, Y-branches, couplers, resonators, and also allowing special modifications of the lattice such as single "atom" displacement from lattice point. 4.3 H-Polarisation Simulations This section will outline some of the simulations that have been recently demonstrated for the computationally more difficult (and more useful) H-Polarisation. FIMMPROP-3D cannot currently compute band diagrams directly but its S-matrix architecture can simultaneously calculate the transmission through a lattice for all incidence angles of the optical excitation - each angle is represented by one eigenmode of the basis set of the left-most section. Figure 4 shows the simulation plane used - the circles represent air holes, the lattice having a refractive index of 2.5. This simulation is equivalent to PICCO simulation Benchmark 2A. Notice that each hole is approximated by a set of rectangular regions. A close up of one hole is shown below. This discretisation is fundamental to the modal expansion technique

57 Chapter 5 Workpart 4 Figure 3 showing detail of a discretised hole. The discretisation is necessary for the modematching algorithm. Figure 4 Simulation plane to compute transmission and reflection from a uniform hexagonal lattice of holes. Figure 5 transmission curves for hex-lattice of round holes. Minimum transmission is Figure 5 shows a set of transmission curves for the structure of Figure 4 - the right hand figure being on an expanded vertical scale. Each curve in the plots represents the fraction of power transmitted for a plane wave incident at a given angle on the left. The curves cover all allowed angles (discretised by the boundary conditions). This structure clearly shows a strong bandgap from 1.4um to 1.55um. To determine the effect of the hole discretisation, the simulation was repeated with square holes, of equal area

58 Chapter 5 Workpart 4 Figure 6 -Hex lattice with square holes Figure 6 is the equivalent lattice with square holes and the transmission curves for this structure are shown in Figure 7. Figure 7 Transmission curves for structure of Fig. 6. Right figure is the same as left figure with an expanded y-axis. Minimum transmission is Figure 8 Intensity plot showing response of hex lattice (round holes) similar to Figure 4, to plane wave excitation. (lambda = 1.6_m) The tool FIMMPROP-3D can provide plots of fields and intensities too - this is a separate calculation that must be made after the S-matrix of the component has been obtained. Figure 8 shows the intensity distribution of the Figure 4 device, illuminated by a plane wave from the left

59 Chapter 5 Workpart Design of Y Branch Simulations suggest that the obvious Y-branch structure of Figure 9 is not efficient. Figure 9 (left) an "obvious" Y-branch structure, such as given in Benchmark 2H. All holes are at lattice points. (right) an intensity plot of the structure excited from the left hand side. The right hand figure clearly indicates that most light is being reflected. Clearly the simple design for such a branch is not useful. The simulation was repeated by adding a hole one lattice point to the right of the vertex. The resulting lattice and intensity plots are shown in figure 10. Figure 10 (Left) a modified Y-branch structure with an additional hole to left of vertex. (Right) an intensity plot of the structure excited from the left hand side

60 Chapter 5 Workpart Simulation Speed Much progress has been made in optimising tools for photonic crystal simulations, with significant speed improvements. The following table outlines some of the computational times required for the simulations in this document. Simulation S-matrix Field Plot Benchmark 2B -hex lattice (Figure 8) 39s 5m 45s Benchmark 2B -hex lattice, square holes 15s 5m 45s (Figure 8) Benchmark 2C Straight waveguide, 8 periods. 48s 11m 30s Benchmark 2H Y- Branch (Figure 9) 3m 3s 11m 40s These simulations were run with 100 1D modes on an 800MHz Pentium III. Computation time is cubic with the number of 1D modes and linear with the number of discrete sections in the z- direction. I.e. the computation time is proportional to Nx3*Nz, where Nx and Nz are the number of lattice cells in the x and z directions. However, the simulations can take advantage of any periodicity or repetition in the structure - evaluation time of the S-matrix of a periodic structure (such as the straight waveguide of Benchmark 2C), is logarithmic with the number of periods D Crystal Device Layout Generator Utilities have now been written that will automatically generate the complex file structures needed for FIMMPROP-3D to compute 2D photonic crystal structures. The utilities allow the user to write Python scripts, with the following functionality: 1. Generate a device filled with uniform hexagonal lattice of holes (or rods) 2. Remove a single hole from lattice 3. Remove a line of holes from lattice 4. Displace an atom from lattice point The utilities also take care of the discretisation of the holes - so that an optimal discretisation is chosen. The devices shown in Figures 4, 9, 10 have been generated automatically by the Layout Generator. 4.7 Conclusion Photon Design has now demonstrated a tool ready to be used for real design work, which will work with both polarisations and is highly efficient for general 2D photonic crystal devices. Utilities are now available to assist the designer in defining the devices. Simulations suggest that the obvious arrangement of 60 deg bends and Y-branches is not efficient and will cause significant back reflection. 5. Shooting technique for computation of nonlinear effects in 1D layered photonic crystals The shooting technique is a spectral code that computes reflection and transmission through arbitrarily shaped 1D dielectric media, both linear and non-linear

61 Chapter 5 Workpart 4 The problem may be stated as follows. We suppose to launch an assigned monochromatic field into an inhomogeneous and possibly non-linear one-dimensional structure from one of its faces (assume this is the face at the coordinate z=0). What we look for are the fields that are reflected and transmitted by the structure. It is important to stress that, since the assigned input field impinges on the structure on one face only, at the opposite face, the "output'' face z = Lz, the field must be constituted by forward travelling waves only. This is the core point of the numerical approach we used. As a matter of fact, it implies that the electric and magnetic field on the output face z = Lz must obey the Sommerfeld radiation conditions, irrespectively of how the dielectric within the device is made, and this fact may be used to construct the numerical solution by means of a shooting iterative procedure. The scheme is the following. We mentioned that we know the input field, and ignore both the reflected and the transmitted fields. Suppose we make a guess on the reflected field. Through continuity conditions, the sum of incident and reflected waves give the initial conditions for the propagation inside the dielectric structure we want to investigate. We numerically propagate this field through the structure, until it reaches the output face. When this is done, all what we are left to understand is whether the final field satisfies the Sommerfeld radiation conditions, or if it does not. If not, we must conclude we made a wrong guess: we choose a field that can exist on the input face if, at the output face, there is a suitable combination of waves that travel from the structure towards +8 and waves that come back from +8 to the structure, but this is not the solution of the problem we wanted to study. The shooting routine works out this basic idea: make a guess on the reflected field, and iteratively update it until the field at the output face becomes compatible with the presence of forward waves only. In this way transmission and reflection from any arbitrarily shaped 1D dielectric medium, both linear and non-linear may be computed, because the criterium we use to stop the iterative routine holds irrespectively of how the medium is made. Note further that the numerical routine needed to propagate the field from the input to the output face of the dielectric medium is a purely forward propagation routine that does not need to trace the back reflections inside the dielectric structure. These are accounted for by the shooting procedure. In the framework of the first year activity, the shooting routine was used at the University of Udine to efficiently compute second harmonic generation and frequency conversion efficiency in a layered photonic crystal discussed in chapter 4 (WP3). 6. Multiple scattering technique for characterization of 2D photonic crystals with finite length The scattering-matrix method is used to characterize systems composed of a finite set of parallel dielectric cylinders in homogeneous medium. The arrangement of the cylinders can be arbitrary (even random), cylinders can be of arbitrary shapes and differ one from another. The method works for both in-plane propagation and for out-of-plane propagation of radiation and arbitrarily directed incident plane waves. The method relies on the fact that both the excited and scattered fields using Fourier-Bessel expansion. Assigning to a j-th cylinder, a local polarcoordinate system (), the vector of the field components around this cylinder (in the point Q) can be written in the following form r r ( F j ( Q) = F 1) J j,n n [ χr ( j Q ) ]+ F r ( 2) H ( 2 ) { [ χ r ( j,n n j Q ) ]}exp[ in ϕ j ( Q) ] n= where Jn, Hn are the Bessel and Hankel functions, and χ denotes the radial wave number. The first term of this equation describes the incident field as well as the field diffracted by other

62 Chapter 5 Workpart 4 cylinders. The second term describes the local diffracted field. Properties of Hankel functions ( 1 allow us to obtain a linear relation between the coefficients F ) ( 2 j,n and F ) j,n, and, finally, to find the total field far away from the system as a sum of the incident and scattered fields. In the framework of the first year activity, the method was used at the University of Udine to characterize the electromagnetic behaviour of 2D photonic crystals with finite length, and to illustrate how they may be modelled by resorting to an analogy with common transmission lines. The analogy was also used to design a photonic crystal layout, which may act as an equivalent double-stub impedance matching network. The design is described in more detail in chaper 3, section Designing finite height photonic crystal waveguides One of the aims concerning modelling of photonic crystals within the PICCO project is to find methods that will ease the numerical requirements for investigation of finite height photonic crystals. A rigorous numerical investigation of finite height photonic crystal waveguides requires full-vectorial three-dimensional calculations of the electromagnetic fields, which is a formidable numerical task. Such rigorous methods would be very cumbersome for obtaining an analysis of a large design parameter space. At COM we have developed ideas [23] that will allow us to obtain straightforward guidelines for design of a large range of finite height photonic crystal waveguides. These ideas are based on comparing two-dimensional calculations for infinite height photonic crystal waveguides with dispersion relations for the media above and below the corresponding finite height waveguide. Using two-dimensional calculations instead of three-dimensional calculations to obtain a broad picture of what are the relevant designs gives a tremendous reduction in numerical requirements. An example of the approach is given in Fig. 11 for a photonic crystal waveguide, where a line defect (or a waveguide) is introduced in a photonic crystal material with air-holes arranged on a triangular lattice in silicon. The figure shows the allowed frequencies Λ/λ as a function of the component of the Bloch wave vector k in the direction of the waveguide (Λ is the photonic crystal lattice constant, and λ is the free space wavelength). The continuum represents modes allowed in the photonic crystal material surrounding the waveguide, whereas the discrete bands represent the modes guided by the waveguide. The figure also shows the air-line being the dispersion relation for free space. For a finite height waveguide suspended in air leakage free guidance of light requires that the waveguide is operated below the air-line. If the finite height waveguide is placed on top of a silica substrate we instead have to operate the waveguide below the corresponding silica line

63 Chapter 5 Workpart 4 Figure 11 Dispersion relations for a photonic crystal waveguide, where a line defect (or a waveguide) has been introduced in a photonic bandgap material with air-holes arranged on a triangular lattice in silicon. The shaded regions represent the continuum of modes allowed in the bandgap material, whereas the discrete bands represent the modes guided by the waveguide. Also shown is the dispersion relation for free space At the edge of the Brillouin zone the air-line and silica-line reach a fundamental upper frequency limit for leakage free guidance of light. By inserting these limits in existing diagrams of bandgaps versus design parameters (2D calculations) we can now as a design rule choose those design parameters that provide large bandgaps below these frequency limits. 8. Efficient FDTD for 3D problems. Modelling activity at COM. The FDTD methods are widely known due to their versatility and robustness. They can be applied to many electromagnetic problems, including problems of propagation in complex structures with drastic changes of electric and magnetic characteristics on a subwavelength scale. One of their main shortcomings is a large consumption of memory and CPU resources. This relates especially to calculations in 3D space. Recently A.Ward and J.Pendry have matured a so-called Order-N [37] version of FDTD code, which has scaling properties that are proportional to the number of space points and to the number of time steps as well. The second version of this code called ONYX-2 [38] is supposed to handle reflection-transmission from the complex structures, band diagram determination and optical density of states (Green functions) calculations. It can be applied to an arbitrary system of coordinates, which can be useful for nonrectangular schemes of photonic crystal design. At COM we have only tested the code provided by the library for transmission and reflection from 2D photonic band gap structures without defects. Its implementation for the 3D cases either for straight waveguiding propagation or guiding through bends and splitting is now one of the focus areas of WP4. The core of the calculations is usually a set of equations in finite differences, which approximate space and time derivatives in Maxwell's equations. Assuming an initial distribution of field in a structure we start a progressive marching in time for a certain number of time steps. Storing of some field components during all time steps in mesh points at the first and last planes of the sample allows us then to move to the frequency domain through fast Fourier transformation. A complete system of eigenmodes in every mesh point where the fields were stored is used to project field vectors onto them for any particular frequency. After

64 Chapter 5 Workpart 4 normalization with respect to the input energy current, the output currents give transmission and reflection coefficients of the waveguide. If we store the fields at points distributed inside the computational space instead of storing the fields at the boundaries, we can from postprocessing of the fields extract the harmonics with the strongest intensities. Thus we obtain band diagrams. The two most serious questions connected with FDTD implementation are 1) the initial field source and 2) boundary conditions. The initial source might be an impulse (rather short to cover the interesting frequency range and not to intersect with outgoing radiation), a bundle of plane waves or Gauss-shaped field distribution. The initial field has to be divergence-free, otherwise it includes some constantly operating sources, which violate energy conservation in reflectiontransmission calculations. The boundary conditions traditionally imposed on the grid structure are periodic - Bloch conditions or perfect conductive ones. In order to avoid spurious reflected waves, returning energy into the system after interaction with the external boundaries of the integration space, some absorbing boundary conditions are included in the computer scheme also. Perfect match layer (PML) and Mur's absorbing boundary conditions are the most popular among them. As a sample for testing we have taken Benchmark 4B. A layered photonic crystal waveguide represents a perfect 3D system for the analysis. The photonic crystal has a triangular pattern of circular holes with lattice constant 500 nm, made in a SiO2-Si-SiO2 stack. The central layer is 200 nm thick, whilst holes radius is 175 nm. We assign 20 mesh points for every lattice constant. Thus the whole system is 100x23x170 points. Holes are arranged in (-K position ((-J according to some authors [21]) relative to the z axis. We impose Bloch boundary conditions in the x and z directions, while the y direction is capped by mirror condition at the center of the waveguide channel and PML above the system. Two additional PML are placed in the z direction. Up until now the results of calculations have suffered from spurious violations of energy conservation, expressed in lifting the sum of transmission and reflection coefficients beyond unity at certain frequencies. It is sometimes observed, when transmission-reflection coefficients are determined near the PCW cutoff frequency as mentioned in [27,39]. Such results can be associated with non-zero divergence of the sources. This must be taken into account when preparing an initial field distribution. However, there may be other reasons for violation of conservation of the total energy. For example, energy hops above unity can be seen in [28,39], where the authors associated them with existence of modes with practically zero group velocity near the cutoff frequency (quasi localized modes). So some further steps are suggested. First of all a really divergence free field has to be used as initial conditions for the FDTD method, for example, pulsed Huygens source [11]. Secondly, one has to include discrepancy in the systems of eigenmodes in different homogeneous layers. 9. References 1. Lalanne P. and Silberstein E., "Fourier-modal methods applied to waveguide computational problems", OPT LETT 25 (2000) Ctyroky J., "Photonic bandgap structures in planar waveguides", J OPT SOC AM A 18 (2001) Centeno E. and Felbacq D., "Rigorous vector diffraction of electromagnetic waves by bidimensional photonic crystals", J OPT SOC AM A 17 (2000) Reynolds A.L. et al, "Transmission response for in-plane and out of plane propagation for a 2D photonic crystal with a planar cavity", SYNTHETIC MET 116 (2001) Foteinopoulou S, et al, "In- and out-of-plane propagation of electromagnetic waves in low index contrast two dimensional photonic crystals", J APPL PHYS, 89 (2001)

65 Chapter 5 Workpart 4 6. Smith C. et al, "Directionally dependent confinement in photonic-crystal microcavities" J OPT SOC AM B, 17 (2000) Sondergaard T and Dridi K.H., "Energy flow in photonic crystal waveguides", PHYS REV B 61 (2000) Sondergaard T. et al, "Designing finite-height two-dimensional photonic crystal waveguides", APPL PHYS LETT 77 (2000) Koshiba M. et al, "Time-domain beam propagation method and its application to photonic crystal circuits", J LIGHTWAVE TECHNOL 18 (2000) Adibi A et al, "Design of photonic crystal optical waveguides with singlemode propagation in the photonic bandgap" ELECTRON LETT 36 (2000) Adibi A. et al, "Properties of the slab modes in photonic crystal optical waveguides", J LIGHTWAVE TECHNOL 18 (2000) Xu Y. et al, "Adiabatic coupling between conventional dielectric waveguides and waveguides with discrete translational symmetry", OPT LETT, 25 (2000) Lee R.K. et al, "Modified spontaneous emission from a two-dimensional photonic bandgap crystal slab", J OPT SOC AM B 17 (2000) Fan S. et al, "Waveguide branches in photonic crystals", J OPT SOC AM B, 18 (2001) Agio M. et al, "Impurity modes in a two-dimensional photonic crystal: coupling efficiency and Q factor", J OPT SOC AM B, 17 (2000) Netti M.C. et al, "Visible photonic band gap engineering in silicon nitride waveguides", APPL PHYS LETT 76 (2000) Ryu H.Y. et al, "Conditions of single guided mode in two-dimensional triangular photonic crystal slab waveguides", J APPL PHYS 88 (2000) Chow E. et al, "Three-dimensional control of light in a two-dimensional photonic crystal slab", NATURE, 407 (2000) Lalanne P. and Benisty H., "Out-of-plane losses of two-dimensional photonic crystals waveguides: Electromagnetic analysis", J APPL PHYS 89 (2001) Benisty H. et al, "Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate", APPL PHYS LETT, 76 (2000) Loncar M. et al, "Design and fabrication of silicon photonic crystal optical waveguides", J LIGHTWAVE TECHNOL 18 (2000) Kuchinsky S. et al, "3D localization in a channel waveguide in a photonic crystal with 2D periodicity", OPT COMMUNIC 175 (2000) Johnson S.G. et al, "Linear waveguides in photonic-crystal slabs", PHYS REV B, 62 (2000) Charlton M.D.B. et al, "Experimental investigation of photonic crystal waveguide devices and line-defect waveguide bends", MAT SCI ENGIN, B74 (2000) Lin S.Y. et al, " Demonstration of highly efficient waveguiding in a photonic crystal slab at the 1.5-(m wavelength", OPT LETT, 25 (2000) 1297; 26. Chow E. et al, "Quantitative analysis of bending efficiency in photonic-crystal waveguide bends at (=1.55 (m wavelengths" OPT LETT, 26 (2001) Chutinan A. and Noda S., "Analysis of waveguides and waveguide bends in photonic crystal slab", JPN J APPL PHYS 39 (2000) Chutinan A. and Noda S., "Design for waveguides in three-dimensional photonic crystals", JPN J APPL PHYS 39 (2000) L Chutinan A. and Noda S., "Waveguides and waveguide bends in two-dimensional photonic crystal slabs", PHYS REV B, 62 (2000) Leonard S.W. et al, "Single-mode transmission in two-dimensional macroporous silicon photonic crystal waveguides", OPT LETT 25 (2000)

66 Chapter 5 Workpart Astratov V.N. et al, "Reflectivity studies of photonic band structure effects in twodimensional air/semiconductor lattices", PHYS STAT SOL A178 (2000) Astratov V.N. et al, "Heavy photon dispersions in photonic crystal waveguides", APPL PHYS LETT, 77 (2000) Culshaw I.S. et al, "Determination of the band structure of photonic crystal waveguides", PHYSICA E, 7 (2000) Silvestre E. et al, "Design of thin-film photonic crystal waveguides", APPL PHYS LETT 77 (2000) Pottage J.M. et al, "Vertical-cavity surface-emitting resonances in photonic crystal films", J OPT SOC AM A 18 (2001) Netti M.C. et al, "Optical trifringence in photonic crystal waveguides", PHYS REV LETT 86 (2001) Chen C.T., Yu Q.L. and Ho K.M. "Order-N spectral method for electromagnetic waves", PHYS REV B, 51, (1995) 16635; 38. Ward A.J. and Pendry J.B., "A program for calculating photonic band structures, Green's functions and transmission/reflection coefficients using a non-orthogonal FDTD method", COMPUT PHYS COMMUN 128 (2000) 590; 39. Mekis A. et al, "High transmission through sharp bends in photonic crystal waveguides", PHYS REV LETT 77 (1996)

67 Chapter 6 Workpart 5 Chapter 6 Workpart 5 1. Introduction 1.1. Objective If ultra-compact photonic integrated circuits (PIC) should become an economically viable solution for widespread optical fibre-based telecom networks, a reliable mass-fabrication technology for these components is required. In these components photonic crystals will most probably be used for many functions, so any fabrication technology for ultra-compact PICs should be able to reproduce the fine features of photonic crystals. State-of-the-art photonic crystal structures today are defined using e-beam lithography. This method has the required accuracy, but is far too time-consuming to employ for mass-fabrication. Optical lithography, the most common technique for the fabrication of conventional PICs, can handle the throughput for mass-fabrication, but lacks the resolution to define photonic crystal structures for telecom wavelengths. Deep UV lithography is an optical lithography technology that operates at wavelengths of 248nm and shorter. At this illumination wavelengths photonic crystal structures with pitches of down to 400nm are a possibility. As 248nm-based deep UV lithography is now introduced into the state-of-the-art CMOS fabs, its viability for mass-fabrication is obvious. For the PICCO project, we explore this route using the deep UV facilities at IMEC. In this first year, early lithography and etching experiments prove that this technique can be further developed for the manufacturing of photonic crystal-based PICs Worldwide state-of the-art The only published work on photonic crystals made by optical lithography is the work by Tokushima at NEC, where an i-line (λ=365 nm) stepper was used to generate an 800µm pitch lattice for operation at 1.55µm. [M. Tokushima, H. Kosaka, A. Tomita and H. Yamada, Appl. Phys. Lett., 76 (8), (2000)]. 2. Facilities and materials The facilities at IMEC consist of an ASML PAS 5500/300 DUV stepper attached to an automated wafer processing track. Etching equipment provide a variety of etch chemistries. As these facilities can only handle 8" silicon-based wafers, we chose Silicon-on-Insulator (SOI) as our basic material. This material is transparent at the wavelength of 1.55(m and has a high refractive index contrast between the top Si-layer and the buried oxide layer. The top layer acts as an optical waveguide with a Silicon core and an SiO2 cladding. SOI wafers were purchased from Soitec, with a oxide thickness of 400nm and a top Si-layer of 205nm. Lithography experiments First lithography experiments were conducted on plain silicon wafers using an existing mask. The Concleave2000 mask is designed for the process development of small contact holes for

68 Chapter 6 Workpart 5 CMOS applications. The mask consists of various large lattices of holes with different pitches and hole sizes. Each lattice has a slightly skewed square geometry to allow evaluation in crosssection when cleaving through the lattice. The fill factor of the lattices range from isolated (Mark:Space of 1:7) to dense (Mark:Space of 1:1) holes. As many photonic crystal structures have superdense lattices (Mark:Space of 1:0.x), these structures can not be simulated directly with this mask. However, two techniques were used to increase the hole size beyond the 1:1 ratio. Overexposure in the lithography process causes an increase of the hole size. Another factor that can be used to increase the hole diameter is the bias between the etched hole and the hole printed by lithography. Using both overexposure and litho-etch-bias, we tried to fabricate lattices of superdensely packed holes. Hereby we looked for 5 different targets, ranging from 300nm dense holes to 200nm dense holes. The list of targets are given in Table 1. For lithography tests, four 8" wafers were coated with 2 different resist thicknesses of UV3 resist and illuminated under 2 different illumination conditions. Each wafer was filled with a matrix with varying focus and illumination doses (a focus-exposure matrix). The wafer was then inspected to look for the optimal conditions for the photonic crystal-like lattices at the different targets. For each target, the depth of focus and latitude in exposure dose were examined to print the target within 10% of its nominal value. For each of the targets, these values were satisfying. Figure 1 shows a resist pattern with a lattice of superdense holes with a pitch of 500nm and a hole size targeted at 350nm using extreme overexposure. 3. Experimental 3.1 Etching experiments Once the required lithography parameters for the different targets was determined, etch tests were undertaken. To reduce the costs connected with 8" SOI wafers, ordinary silicon wafers were coated 400nm of Oxide and then with 205nm of amorphous silicon. While optically different from crystalline silicon, amorphous silicon has similar etch properties. A first batch of wafers using two different etch parameters show good results for targets A through D. Figure 2 shows a cross section view and a top-down view for 250nm holes (target A). The holes are etched down through the top layer and the buried oxide and show straight sidewalls and little sidewall roughness. 3.2 Optical Proximity Corrections One of the major drawbacks of optical lithography with densely packed structures (like Photonic Crystals) is the occurrence of optical proximity effects. When these structures are illuminated, the pattern of each hole interferes slightly with that of neighbouring holes, thereby modifying the hole size and shape. This is illustrated in figure 3, where holes at the borders and corners of the lattice are misshapen and smaller than the holes in the bulk. As the size of Photonic Crystal holes shows a dependency to the density of the lattice, defect structures in photonic crystals (e.g. channel waveguides or cavities), where holes lacks neighbours in certain directions, might print differently than holes fully surrounded in the lattice. A solution is to include optical proximity corrections (OPC) on the mask to compensate for this effect. 3.3 Test Mask for Photonic Crystal Structures First lithography tests were performed using square lattices of densely packed holes. To simulate photonic crystal structures we used overexposure to print superdense holes on the

69 Chapter 6 Workpart 5 wafer. With these tests we proved that superdense lattices can be printed with deep UV lithography. To further develop the fabrication process for Photonic Crystals, a mask has been designed with photonic crystal structures. Because we want to perform both geometric and optical measurements on different kinds of photonic crystal structures, 4 independent layers have been included on the mask: 3. Layer 1: Cleavable photonic crystals. This layer contains large triangular lattices of photonic crystals that are slightly rotated to make easy cleaving possible. These lattices have superdensely packed holes, to avoid the need of overexposure. These lattices will be characterised using an SEM in both top-down view as cross section. 4. Layer 2: Photonic Crystal lattices for OPC. This layer consists of a 'typical' photonic crystal component illustrated in Figure 4. This component consists of a lattice with several types of defects, like waveguides, cavities, bends and splitters. The holes neighbouring these defects are modified to compensate for optical proximity effects. This component is repeated several thousand times over the mask varying the lattice parameters and optical proximity corrections. This layer will be characterised using an SEM in top-down view. 5. Layer 3: Fiber coupler structures. This layer contains the first fiber coupler designs of Workpackage 1 optimised for the given SOI layer structure. The fiber couplers are interfaced with different rigde waveguides for easy coupling and measurements. This layer will first be characterised geometrically using an SEM, and then subjected to optical measurements. 6. Layer 4: Optical measurable Photonic Crystal components. This layer contains first designs of SOI photonic crystal components with simple optical functions like waveguides, cavities and bends. This layer will be measured optically to measure waveguide properties. 4. Conclusion First tests on lithography and etching prove that deep UV lithography is a viable technique for the manufacturing of photonic crystal-based photonic integrated circuits. Lithography tests show that superdense lattices can be printed with this technique, and first etch tests resulted in holes with straight sidewalls and very little roughness. A test mask has been designed to continue testing on real photonic crystal structures hole size pitch A 250nm 500nm B 300nm 600nm C nm* 560nm D nm* 520nm E 200nm 400nm * using overexposure Table 1: Different targets for early photonic crystal lithography tests

70 Chapter 6 Workpart 5 diameter = 358nm 0.1µm 1µm (a) (b) Figure 1 Resist pattern of lattice with 360nm holes and 500nm pitch printed using overexposure. 0.5µm 0.5µm (a) (b) Figure 2 Etched holes in cross section and top-down view. The etch is 600nm deep (through the top Si-layer and buried oxide). Lattice constant is 500nm, hole size is targeted at 250nm. Bulk of lattice Corner Border 500nm 500nm Figure 3 illustration of optical proximity effects. Through interference between the holes the hole patterns holes at the edges and borders have different shape and size than holes in the bulk of the lattice