Final Project Report

Transcription

1 DALHM IST Development and Analysis of Left-Handed Materials Final Project Report Project period Web-page: Project Co-ordinator: Costas M. Soukoulis (FORTH) Partners: 1) Foundation for Research and Technology, Hellas (FORTH) 2) Bilkent University (Bilkent) 3) Imperial College of Science Technology and Medicine Physics Department (ICSTM1) 4) Imperial College of Science Technology and Medicine Imaging Sciences Department (ICSTM2) Project funded by the European Community under the Information Society Technologies Programme ( )

2 DALHM Final report Page 2 Technical Point of Contact: E. N. Economou and C. M. Soukoulis IESL, FORTH Box 1527, Vassilika Vouton, Heraklion, Crete, Greece TEL: ; FAX: economou@admin.forth.gr soukouli@iesl.forth.gr kafesaki@iesl.forth.gr Administrative point of Contact: Evangelia Hatzidaki Contracts & Finance Division - Central Administration FORTH Vassilika Vouton, PO Box Heraklion, Crete, GREECE Tel: ; Fax: vxatzida@admin.forth.gr

3 DALHM Final report Page 3 Introduction Project objectives The main objective of the DALHM project, as its title also reveals, was the development of lefthanded materials (LHMs) and the understanding of their properties and of their underlying physics. - Left-handed materials (or metamaterials) are engineered composites whose response to an incident electromagnetic (EM) wave can be described by an effective negative dielectric permittivity, ε, and magnetic permeability, μ. Simultaneous negative ε and μ within a given frequency band of a left-handed composite gives rise to a negative index of refraction, n, thus, left-handed materials are also known as negative index materials (NIMs). The specific objectives of the DALHM project, as described in Annex 1 of its proposal, were the following: (a) Better understanding of the physics of left-handed (LH) materials. (b) Improvement of the existing modeling and simulation tools, with aim to study more complicated structures than the structures which can be studied today. (c) Fabrication of left-handed materials (ordered and disordered) using various approaches, materials and processes. (d) Identification of commercial telecommunication applications where such materials can make a big difference. (e) Testing of the electromagnetic behavior of these materials in the laboratory and in "relevant" environments. Towards the fulfillment of the above objectives we worked both theoretically and experimentally, aimed first to develop an infrastructure for the development and study of lefthanded materials and second to use and exploit this infrastructure to a detailed examination of those materials and their capabilities. During the course of the DALHM program, many left-handed and related metamaterial structures in the microwave, infrared and radio region were investigated. Those materials include split ring resonators (SRRs providing the negative μ), combinations of SRRs and wires (wires provide negative ε regimes), Swiss roll systems (providing negative μ) and also photonic crystals (the latter have negative refraction properties due to their complex band structure, and thus they can be considered also as negative refractive index materials). Moreover, many demonstrator systems, demonstrating the power of the negative refractive index and related metamaterials in the manipulation of EM waves, were developed. In what follows, we briefly describe the main steps towards the fulfillment of the project objectives and the main accomplishments within the 42 months of the project. For each issue mentioned, a citation of the related publications is given, where more details and a complete analysis of the related work can be found. WP1.1: Theory and Simulation efforts The first steps in our simulation efforts were the development of modeling tools. We developed and improved various modeling tools for the thorough theoretical investigation of left-handed materials. These tools include:

4 DALHM Final report Page 4 Transmission and reflection calculation tools, like the transfer matrix method [1,5] and the finite difference time domain method. Our existing transfer matrix method code was improved through the use of a more symmetric discretization scheme, which led to the elimination of spurious terms in the scattering parameters. Retrieval procedures which were deveoped for the extraction of effective parameters of a metamaterial from the transmission and reflection data. We developed two procedures: One considering a metamaterial as homogeneous effective medium [1,30,68] (homogenous effective medium approach), and a procedure considering a metamaterial as periodic effective medium ( periodic effective medium approach) [65]. We tested both approaches and we examined the validity regimes and the limitations of each one of them. Using the above tools we studied in detail various types of metamaterials, mainly metamaterials composed of split-ring resonators (SRRs providing a negative permeability (μ)) and/or continuous wires (providing a negative permittivity (ε)), and we tried to understand the electromagnetic response of those materials. Below we briefly mention the main findings of this study. Electromagnetic response of SRRs&wires systems Trying to understand the theoretical and experimental transmission spectra of materials composed of SRRs&wires and of their components, we realized some very crucial aspects of the electromagnetic behavior of those materials [32] see Fig.1. I.e., The electric response (effective ε) of a SRRs&wires material is not only the Drude-like response of the wires but it is a sum of a Drude-like and a Lorenz-like response, the second coming from the SRRs. Taking into account the SRRs electric response leads to a lower effective plasma frequency for the system, compared to that of only the wires, and makes more difficult the achievement of left-handed behavior. The closing of the SRR gaps destroys the magnetic SRR resonance, thus it can be used to identify the negative μ regime in SRRs transmission spectra. A system of closed SRRs carries all the electric response of a SRRs system, without its magnetic response; thus, combining closed-srrs with wires one can obtain the correct electric response of the corresponding SRRs&wires system and identify the true negative ε regimes. Based on the above, a simple criterion to identify the left-handed peaks in the transmission spectra of SRRs&wires systema was devised, extremely useful in experimental studies: A transmission peak is left-handed if it falls close to the magnetic SRRs resonance and disappears by closing the SRR gaps. This criterion was extensively used to identify the lefthanded regimes in our experimental systems.

5 DALHM Final report Page 5 (a) (b) (c) (d) (e) Fig. 1: The response to an electromagnetic field of various periodic metamaterials. This response is shown through the frequency dependence of transmission coefficient (left panels), dielectric function (middle panels) and magnetic permeability (right panels). Panels (a) show the response of a periodic system of wires, infinite in length. This response analogous to that of a bulk metal, i.e. there is a cut-off frequency ωp above which ε(ω) becomes positive from negative, and thus the system becomes transparent to the EM radiation. The system does not have any magnetic response. Panels (b) show the response of a system of cutwires (wires much sorter than the wavelength of the EM wave), or closed SRRs. The difference with the continuous wires is that here the negative ε regime has also a lower edge, ωo 0, due to the finite nature of the wires. The ε frequency dependence has the form shown in the middle graph. Again no magnetic response. Panels (c) show the response of a periodic system of SRRs. Their electric response is cut-wire like (like in panels (b)) and in their magnetic response there is a resonance (at frequency ωm), where the magnetic permeability (μ) jumps from positive to negative valuestransmission (left panel) becomes finite in the regions of positive με product and goes to zero for negative με. The relative order of the difference frequencies (ωm, ωp, ωo) depends of the parameters of each specific system. Panels (d) shows the response of a system of infinite wires plus closed SRRs (CCMM). This system contains in fact all the electric response of the CMM, without its magnetic response. The addition of the wires to the closed-srrs (cut-wires) system results to a new cut-off frequency, ωp, lower than ωp. Panels (e) show the full response of the CMM; its electric response is that of a system of wires plus cut-wires (see panels (d)) and its magnetic response is that of a periodic SRRs system (see panels (c)). Again the relative positions of the different characteristic frequencies depend on the specific system. Electric excitation of the magnetic SRR resonance For SRRs which are not symmetric in respect to the external electric field, we found that not only the external magnetic field can excite resonant circular currents around them but also the external electric field [33] see Fig. 2. This effect was called electric excitation of the magnetic SRR resonance (EEMR) and can be observed also for electromagnetic (EM) wave incidence normal to the SRR plane, where there is no magnetic flux going through the SRR. The effect of the resonant circular currents in the case of normal incidence is not a resonant μ but a resonant ε (due to non-zero average polarization induced by the resonant circular currents). This resonant ε, associated with strong positive ε values, is an unwanted feature if one aims the design of twodimensional (2D) and three-dimensional (3D) left-handed media, and makes necessary the use of symmetric SRRs. Thus, a major part of our subsequent research was turned to the design of symmetric SRRs. The EEMR effect is accompanied though by a great advantage for the study of small length scale structures: it offers the possibility to trace the magnetic resonance using normal incidence (for small scale structures one can not easily fabricate a thick stack of SRR layers and trace the magnetic resonance employing propagation parallel to the plane of SRRs). We exploited this possibility in the experimental study of μm scale SRRs

6 DALHM Final report Page 6 E Fig. 2: Explanation of the EEMR effect. Figure shows a single-ring SRR in two different orientations relative to external electric field (E). The shadow in the ring shows the current (black: negative, white: positive). The asymmetry in case (b) leads to different charge quantities at the ends of the SRR sides and thus to a potential difference which is compensated by a circular current flow. Symmetric SRR designs and 3D left-handed materials We studied in detail a variety of symmetric SRR structures, which do not suffer from the EEMR effect and therefore can be employed for the achievement of 3D left-handed materials. Moreover we studied 3D metamaterials made up of those symmetric SRRs combined with wires, we identified the design rules for the achievement of symmetric 3D metamaterials and we ended up with some optimum 3D left-handed material designs [67] see Fig. 3. (a) (b) (c) (d) Fig. 3: Symmetric 3D LH material designs and corresponding transmission data. (a): A structure based on 4-gap SRRs with gaps filled with a high index dielectric. The parameters of the structure are as to give LH behavior around 1 THz. (b): Transmission vs frequency (dimensionless) for TE and TM polarization of the incident EM field, for the structure of (a). The transmission remains unchanged if one changes the angle of incidence and of polarization. (c): Unit cell of a 3D symmetric structure made of opposed-ring SRRs. The structure parameters are: unit cell side= 2.5mm, ring side length = 2.2mm, wire width = 0.2mm, ring width = 0.2mm, opposed ring separation = 0.2mm. (d) Transmission amplitude vs frequency for the structure of (c), for TM and TE polarization of the incident EM field. Parametric study of SRRs&wires media To achieve left-handed behavior in a SRRs&wires medium is not a straightforward problem, as our studies have shown. One needs to design properly the various parameters of the system, knowing a priory the role of each one of the parameters. In the framework of DALHM we examined in detail how the various parameters of an SRRs&wires system affect its electromagnetic properties, and we identified optimum parameters [69,86] for achievement of left-handed behavior. Factors studied include: The SRR geometrical features, like metal width and thickness, SRR-gap-width, distance between the SRR rings (for double ring SRRs). The continuous wires features, like width and depth of the wires. Other features, like the SRR orientation, the properties of the board where SRRs and wires are printed, the unit cell dimensions and the relative position of wires and SRRs. Frequency limits of the negative magnetic SRR response Studying the possibility to extend the left-handed behavior in the optical regime, we examined in detail μm and nm scale SRRs and we tried to find out up to which frequency SRRs still maintain their capability to act as negative permeability materials. We found [81] that one can get negative μ using SRRs at frequencies up to ~500 THz (for the designs studied). Above this regime the losses in the metal weaken and finally kill the magnetic SRR resonance see Fig.

7 DALHM Final report Page 7 4(b). Moreover, while for mm scale SRRs the magnetic resonance frequency scales inversely proportional to the linear SRR size, for small scale SRRs this linear scaling breaks down and the resonance frequency saturates see Fig. 4(a); the saturation value depends on the SRR design. We found that this breaking of the linear scaling is due to the kinetic energy of the electrons in the SRR metal: The kinetic energy for small length scales becomes comparable to the magnetic energy and does not scale proportional to the structure size, as the magnetic energy. Fig. 4(a): Simulations of the magnetic resonance frequency as a function of the unit cell size for a SRR metamaterial composed of 1-, 2- and 4-cut SRRs (see right panel). Going to smaller length scales (higher frequencies), the magnetic resonance frequency stop to increases linearly with the decreasing of the SRR size but approaches a saturation value, different for each SRR-type Fig. 4(b): Simulation of the dependence of the shape and amplitude of the magnetic resonance in Re(μ) of the 4-cut SRR for unit cell size a=70, 56, 49 and 35 nm (left to right). Losses in a left-handed material Examining the origin of losses in left-handed materials, we found that the main source of loss in low frequency materials is the dielectric losses (losses in the dielectric boards); thus, extremely low-loss dielectric boards are required for the printing of high quality SRRs&wires systems. Losses in the metallic parts start to become dominant in the THz regime. Negative permeability and left-handed behavior in short-wires-pairs systems A system that provides a nice alternative to the SRR, with some important additional advantages, is a system made of a pair of short-wires. This system shows a resonant magnetic mode due to strong antiparallel currents in the two wires of the pair; therefore a collection of short-wire-pairs behaves as a negative μ system, such like a SRRs system. The additional advantage of such a system is that the negative magnetic response can be excited by an EM wave incident normally onto the system. Therefore, the short-wires-pair system provides a nice solution for the demonstration of negative permeability in μm scale and nm scale materials. Moreover, since the pair has also a resonant electric mode, associated by a negative permittivity, it can alone give left-handed behavior, by tuning properly its electric and magnetic resonance. Trying to design short-wire-pair-based left-handed materials, we examined in detail the design, we identified the conditions to achieve left-handed behavior using only short-wires-pairs, and we ended up with optimized designs for the achievement of negative μ and of left-handed behavior (in both GHz and THz regimes) employing short-wires-pairs only as well as combining short-wires-pairs with continuous wires see Fig. 5 [83,85,87].

8 DALHM Final report Page 8 E H k Fig. 5(a): A simple design consisting of a pair of short wires or strips can show a magnetic response. In combination with continuous wires (as shown in figure) it can give left-handed behavior Fig. 5(b): The retrieved real (black) and imaginary (red) parts of the effective impedance, z, the refractive index, n, the electric permittivity, ε, and the magnetic permeability, μ, for the cut and continuous wires pair design shown in Fig. 5(a). Analysis of the experimental data Apart of the systems that we proposed for experimental realization, we also examined in detail all the experimentally studied structures, we verified the left-handed behavior of those structures (if any) and we analyzed and explained all the data observed. Bessel beam generation using metamaterials Trying to explore the novel and unique capabilities not only of left-handed materials but also of the only negative ε or only negative μ materials, we examined the possibility to achieve Bessel beams using thin metallic films and exploiting coupling of the incident radiation with the surface plasmon modes of those films [77]. We found that electromagnetic wave transmission through thin metallic films (under certain conditions) can lead indeed lead to generation of Bessel beams, of evanescent nature. Moreover, using a system of distributed Bragg reflectors made of thin films, propagating Bessel beams can be generated, which can be maintained over a large propagation distance. Corner reflectors We demonstrated that among the unique capabilities of left-handed metamaterials is their capability to act as corner reflectors [76]: A slab made of a n=-1 material and having the shape of a corner can act as a perfect corner reflector as was revealed by our detailed analytical study. Complementary media A main concept in the negative material research is that of complementary media: It was known since the discovery of LHMs that a homogenous slab of n=-1 material can act as a perfect lens and can cancel the optical effect of an equal in width slab of air. Here we extended this concept in the case of inhomogeneous media (see Fig. 6): We found that a properly designed inhomogeneous material with ε and μ negative can cancel the optical effect of a positive (righthanded) material. This discovery extends the known capabilities of left-handed materials and

9 DALHM Final report Page 9 supports their characterization as optical antimatter. The concept of complementary media was not only proved analytically, but it was also demonstrated with realistic simulations. Part of those simulations were performed in the extremely near magnetic field regime, employing Swiss-roll systems and taking into account and exploiting only the magnetic properties of the systems see Fig. 7. Fig. 6: An alternative pair of complementary media, each canceling the effect of the other, is shown. The light does not necessarily follow a straight line path in each medium. but the overall effect is as if a section of space thickness were removed from the experiment. Y X Z Fig. 7(a): Schematic of a 2D isotropic Swiss Roll structure ( XZ Double Wall ), employed for the demonstration of the principle of complementary media. Fig. 7(b): Simulation of field distribution through the XZ Double Wall, showing the field propagating in a conical mode in the first medium, and being refocused by the complementary medium. Negative refraction properties of 2D photonic crystals Photonic crystals, due to their complex dispersion relation, can also act as negative refractive index materials. We studied in detail the negative refraction and the focusing properties of 2D photonic crystals of dielectric or metallic rods in air [7,21,22,26,34,80]. Many of the systems that were examined here were fabricated and tested experimentally (see experimental part for more details). Swiss roll systems Apart of the metamaterials operating in the GHz and THz range we also studied RF metamaterials, which are ideal for magnetic resonance imaging applications. Most of those materials were assemblies of Swiss-rolls [2,45], which behave as negative permeability materials operating in the very near magnetic field. Although the major part of the related research was experimental, we also performed theoretical analysis of the systems, both analytical and numerical. The main target of the numerical analysis was the demonstration of the validity of the effective medium approach for the description of uniaxial Swiss-roll systems [112,113]. WP2: Fabrication of left-handed materials

10 DALHM Final report Page 10 Most of the metamaterials studied within the project were materials operating in the few GHz regime. Those materials were fabricated using printed circuit board technology. We were designing those materials and we were assembling them in 1D and 2D arrangements (the fabrication was made by a company). Apart of the few GHz metamaterials we also studied materials operating at ~100 GHz and at few THz see Fig. 8. For the fabrication of those materials we developed and optimized procedures based on UV photolithography. Using UV photolithography and thermal metal deposition we fabricated structures made of SRRs and/or wires, operating at ~100 GHz, on glass substrate. Moreover, we fabricated μm scale SRR systems, operating at ~6 THz, on polyimide substrate. The main achievement in the THz SRRs fabrication was the fabrication not only of one layer but of a multistack of 5 layers of SRRs [66]. As was mentioned in the previous section, a large part of our effort within DALHM concerns MHz magnetic metamaterials. Those were metamaterials made of home-made Swiss-rolls: We fabricated a magnetic lens, consisting of 271 Swiss Rolls packed into a hexagonal prism [2,45,108,109], operating at 20 MHz, as well as a lens of Swiss-rolls packed into a tetragonal prism [112,113]. Finally, in the framework of our attempts in the MHz range, we fabricated devices based on resonant permeability elements, useful for efficient signal transferring in MRI systems [108], like a flux compressor [111], and a RF yoke [110,114] (see also demonstrators part and Appendix 2). Fig. 8(a): Left: Photo of a 10 GHz left-handed structure fabricated on textolite board. Right: Photomicrograph showing the sub-mm-wave SRRs&wires sample operating at ~100 GHz. The two patterns were aligned by aligning the edges of the glass substrates. Fig. 8(b): Left: View of the 6 THz SRR metamaterials fabricated. Right: The magnetic Swiss Rolls hexagonal lens WP1.2: LHMs characterization efforts In the framework of DALHM project we designed and characterized through free-space transmission and reflection measurements many materials composed of SRRs&wires (also of only SRRs and of only wires). We realized that the achievement of left-handed behavior in such materials is a non-trivial issue and a careful design of the structures is needed. To demonstrate left-handed behavior through transmission measurements we used a criterion derived by our theoretical studies (see theory and simulations section), which compares the transmission spectrum of an SRRs&wires system with the spectrum of the corresponding system of closed-srrs&wires.

11 DALHM Final report Page 11 Apart of the transmission/reflection measurements, alternative ways that we developed and employed for the demonstration of left-handed behavior were phase measurements and negative refraction experiments. Below we briefly describe our major efforts and achievements in the characterization domain: 1D SRR metamaterials operating in few GHz Using free space transmission measurements we demonstrated the electric response of the SRR, as predicted by our theoretical studies, as well as the upkeep of this electric response and the switch off of the magnetic response when the SRR gaps are closed [61,62] see Fig. 9. Fig. 9: Schematics: (a) split ring resonator (SRR) (b) a ring resonator with splits closed (CSRR). Panel (c) shows the transmission spectra of a periodic SRR medium (solid line) and a periodic closed SRR medium (dashed line) between 3-14 GHz. The negative permeability regime is at ~4 GHz, and disappears closing the SRRs, while the rest of the spectrum remains unchanged. Another important issue concerning SRRs that we demonstrated experimentally was the electric excitation of the magnetic SRR resonance (EEMR effect), predicted also by our theoretical studies [33] see Fig. 10. It is going for excitation of resonant circular currents by the external electric field, it is observed whenever SRR is asymmetric in respect to that field, and in transmission spectra is manifested as a gap/dip at the magnetic resonance. The EEMR effect occurs also for incidence normal to the SRR plane; thus it provides a way to trace the magnetic resonance of the SRR using normal incidence. (c) Fig. 10(a): Left-hand side: SRR geometry studied. Right-hand side: The four studied orientations of the SRR with respect to the triad k, E, H of the incident EM field. Fig. 10(b): Measured transmission spectra of a lattice of SRRs for the four different orientations shown in Fig. 10(a). Black line for orientation (a), red for (b), green for (c) and blue for (d). The T dip of the blue curve is due to the electric excitation of the magnetic resonance Other issues concerning GHz SRRs that we studied were: (a) The dependence of the magnetic resonance frequency of the SRR on the various SRR parameters. This study was done for many

12 DALHM Final report Page 12 SRR designs, using a single SRR unit cell and employing transmission measurements with monopole antennas as source and receiver [48]. (b) The influence of disorder on the transmission spectra of SRR materials. We studied various types of positional disorder, and we found that disorder in general acts against the strong negative magnetic SRR response, with more crucial the disorder at the plane of SRRs [57]. (The effect of disorder is more pronounced in combined SRRs and wires systems, where the disorder can kill the left-handed behavior.) Finally, we designed and characterized symmetric SRR structures, which avoid the electric excitation of the magnetic resonance (see theory part) keeping the magnetic resonance frequency at low values [102] see Fig. 11. Those SRR designs, due to their symmetry, are offered for achievement of 2D and 3D left-handed materials. Combining them with wires we indeed demonstrated the resulting left-handed behavior. Fig. 11: A symmetric SRR design known as labyrinth structure (left panel) and the transmission spectrum of a periodic system of such SRRs, as well as SRRs with closed gaps (right panel). 1D metamaterials of SRRs&wires operating in few GHz Concerning the study of mm scale metamaterials of SRRs and wires, among the first issues that we demonstrated experimentally (through free-space transmission measurements) was the role of the SRRs on the electric response of an SRRs&wires medium, as well as the validity of our theoretically devised criterion for the correct identification of left-handed peaks in such a medium see Fig. 12; this criterion, as has been already mentioned, is based on the comparison of the SRRs&wires transmission spectrum with the transmission spectrum of the corresponding closed-srrs&wires system. Using that criterion, we demonstrated left-handed behavior in many SRRs&wires systems, we examined the dependence of this behavior on the relative position of SRRs and wires [62], and, more importantly, we demonstrated the highest reported up to now left-handed transmission peak in metamaterials; the last was in a system of circular SRRs and wires, operating at ~4 GHz [61] see Fig.12.

13 DALHM Final report Page 13 Fig. 12(a): Measured transmission spectra of wires (dashed line) and of a combined metamaterial (solid line) composed of closed SRRs and wires arranged periodically. Figure demonstrates the influence of the electric response of the SRRs on the electric response of the SRRs&wires metamaterial. Fig. 12(b): Transmission spectrum of a metamaterial of SRRs and wires (solid line) showing a left-handed peak of very high intensity, at ~4 GHz. The transmission spectra of the only SRRs system (red dashed line) and the only wires (blue dotted line) are also shown. Apart of the demonstration of left-handed behavior through transmission measurements, we also established a phase measurement procedure [50] and we demonstrated the capability of this procedure to prove if a transmission peak in 1D metamaterials is left-handed or not. We used this procedure to further validate the left-handed behavior of many of SRRs&wires systems. 2D left-handed materials of SRRs and wires Using the experience from the study of 1D SRRs&wires meramaterials, we designed our first (and one of the first reported) two-dimensional left-handed material of SRRs&wires, showing left-handed behavior at around 4 GHz. To demonstrate the left-handed behavior in that material, apart of transmission measurements (see Fig. 13(b)) we also performed refraction experiments, using a wedge-type structure (see Fig. 13(a)). Through those experiments we demonstrated negative refraction at the left-handed transmission band of that material, proving unambiguously the negative refraction properties of the structure. Fig. 13(a): (a) Schematics of our 2D metamaterial structure (b) 2D Wedge structure used for negative refraction experiment. (c) Experimental setup used for refraction experiment. Fig. 13(a): Measured transmission spectra of a periodic SRR medium (solid line), periodic wire medium (dashed line) and the 2D composite medium of SRRs and wires (bold solid line) between 3-7 GHz. Lefthanded regime is at ~4 GHz.

14 DALHM Final report Page 14 Going one step further, we also demonstrated the focusing properties of a 2D SRRs&wires planar left-handed slab (at ~4 GHz). The resolution at the focusing was ~0.36 λ. 3D left-handed materials Since for best exploitation of the unique properties and capabilities of left-handed materials (e.g. superlensing) one needs isotropic left-handed material designs, we attempted to design and fabricate 3D left-handed structures. We achieved the first 3D left-handed structure, employing symmetric SRRs and wires, with LH behavior at around 6 GHz see Fig. 14. Using refraction experiments we demonstrated the negative refraction properties of the structure, as well as its focusing capabilities with resolution, λ/2.5. Fig.14: Left: Photo of our 3D left-handed sample, composed of SRRs and wires. Right: The transmission spectrum; the shadow regime is the left-handed regime. 1D metamaterials at ~100 GHz Attempting to achieve left-handed behavior in the higher than few GHz frequency regimes, we studied in detail SRRs&wires structures of sub-mm scale. We performed the first transmission measurements of SRRs and/or wires systems at around 100 GHz, and we demonstrated the first reported left-handed transmission peak at around 100 GHz in SRRs&wires materials [63] see Fig. 15. THz SRR systems Fig. 15: Left: Transmission spectra of a composite metamaterial of SRRs&wires (solid-line), showing a left-handed peak at ~100 GHz. Figure shows also the transmission for the system of Closed- SRRs&wires (dashed-line) and of only SRRs (dotted-line). Note the matching between left-handed transmission band of the SRRs&wires medium and negative permittivity gap of the SRRs. Top: A photo of the left-handed structure.

15 DALHM Final report Page 15 Continuing the attempts for the frequency extension of the negative magnetic response and LHbehavior towards the infrared, we fabricated and studied experimentally μm scale SRR structures. The characterization of those structures was done through transmission and reflection measurements. The first set of measurements was performed using normal incidence and exploiting the electric excitation of the magnetic resonance effect [66] see Fig. 16(a). Through those measurements we demonstrated the existence of a magnetic resonance at around 6 THz in those structures. The second set of measurements was performed using off-normal incidence, exciting the system through the external magnetic field; there, we demonstrated unambiguously the negative magnetic permeability at the ~6 THz resonance regime [91] see Fig. 16(b). (a) (b) Fig. 16(a): Measured transmission spectra for the SRRs, for orientations (a) (black) and (b) (red). The dip in the red curve at around 6 THz is due to the magnetic resonance of the structure. Fig. 16(b): Measured reflection off-normal incidence angle spectra for our μm scale SRRs system. The different curves denote different angles φ. The increase of the reflection at ~6 THz by decreasing the angle φ is due to the negative magnetic permeability of the SRRs. Moreover, using again normal incidence, we demonstrated magnetic response at frequencies up to 12 THz, in multigap SRRs, exploiting the asymmetry of those SRRs through the EEMR effect. Photonic crystals As was mentioned also in the simulations section, photonic crystals (PCs), due to their complex dispersion relation, can also act as negative refractive index materials. Thus, they constituted a category of systems that was extensively studied with DALHM. Fig. 17(a): Comparison between positive and negative refraction through the photonic crystal of alumina rods in air: a. Negative refraction. b. Positive refraction. c. Schematics of positive and negative refraction. Fig. 17(b): Measured power distribution (blue bullet) and calculated average intensity (solid line) at the image plane of the alumina in air PC. Calculated average intensity at this point without the photonic crystal is also shown (dashed line).

16 DALHM Final report Page 16 Employing refraction experiments we demonstrated for the first time negative refraction and focusing with subwavelength resolution in a 2D photonic crystal of mm scale, made of alumina rods in air see Fig. 17. The resolution obtained was around λ/3 [8,28,55,56,60]. Negative refraction and subwavelength resolution was also demonstrated in a metallodielectric PC [49,53] see Fig. 18. Fig. 18: Measured electric field intensities along the surface of a metallodielectric PC at the negative refraction band are shown, for incidence angles of 15, 25, 35, and 45. Incidence direction is shown by the arrow. The modified dispersion and density of states of a PC can lead also to modification of emission properties of sources placed into them or at their neighborhood. Here, placing monopole antennas into 2D and 3D PCs, we demonstrated the possibility to obtain enhanced emission and highly directive radiation [15,16,36,38,40,47] see Fig. 19 and Appendix 2. The 3D PC gave full angular confinement of the emitted radiation [47]. Fig. 19: Measured far field radiation patterns at the band edge frequency of a PC of alumina rods in air in the E-plane and H-plane. Another way to influence the radiation of sources using PCs is by exploiting the surface modes at the PC-environment interface. Here, utilizing the surface modes of a 2D PC we achieved highly directive, large bandwidth antenna systems [99,31] see also Appendix 2. MHz magnetic metamaterials made of Swiss-rolls In the MHz metamaterials domain, where the main targeted application was the MRI imaging, we characterized various Swiss-roll-based systems. Our main systems were a magnetic lens of hexagonal shape and one of tetragonal shape see Fig. 20. We examined the ability of those systems to preserve flux pattern in a MRI machine [2,45,108] and we demonstrated their ability

17 DALHM Final report Page 17 to generate images with subwavelength features, achieving a resolution of λ/64 at a frequency of 24.5 MHz [107]. 100 Frequency = MHz Y Distance /mm db -74 db -72 db -70 db -68 db -66 db -64 db -62 db -60 db -58 db -56 db -54 db -52 db -50 db Fig. 20(a): (left) An M-shaped antenna, constructed from two antiparallel wires held 1 mm apart. (right) The slab of Swiss Rolls placed on the antenna, and the scanning loop help above it X Distance /mm Fig. 20(b): The field pattern observed at 21.3 MHz in a plane approximately 2 mm above the surface of the Swiss Roll slab shown in Fig. 20(a). The Swiss Roll structure is overlaid. Tunable metamaterials One of the last issues studied with DALHM was the possibility to achieve tunable left-handed materials. As a first step to this direction we tried to create tunable SRRs. The approaches that we attempted was by incorporating in the SRRs (a) lumped capacitors and tuning by changing the voltage and (b) ferroelectric thin films and tuning by changing the temperature see Fig. 21. In both cases we demonstrated the tuning properties of our metamaterial structures. Using ferroelectrics we have achieved a 0.22 GHz tuning range, between 2.83 GHz and 3.05 GHz. Using capacitors we have achieved a 2.83 GHz tuning range, between 0.99 GHz and 3.82 GHz. Fig. 21: Measured transmission spectra of single SRRs covered with ferroelectric thin film. Temperature is varied between o C. Magnetic resonance frequency shifts downwards with an increase at the temperature. Short-wire-pair-based left-handed materials As was mentioned also in the theory part, pairs of short wires show negative magnetic response, and therefore they can provide a nice alternative to the SRR. Combining short-wires-pairs with continuous wires and adjusting properly the system parameters, one can achieve left-handed behavior, as was shown in Fig. 5. One of the surprising combinations of short-wires-pairs and continuous wires that we explored in the framework of DALHM is the so-called fishnet structure see Fig. 22. This structure was

18 DALHM Final report Page 18 studied extensively at the infrared frequency range, both theoretically and experimentally (the experiments were done outside DALHM consortium). It gave left-handed behavior at the telecommunication frequency of 1.5 μm; its most important quality though is the relatively low losses; it constitutes the most lossless up to date left-handed material at infrared frequencies. Fig. 22: Top panel: The fishnet combination of short-wire-pairs and continuous wires with LH behaviour at 1.5 μm. The lattice constant of the system is 600 nm; it is fabricated on quarz substrate using gold and MgF2 (n=1.38, thickness 30 nm) between the wires of the pair. Right panels show the extracted from the simulations effective system parameters, demonstrating the negative index material behaviour of the sample and the relatively low losses. WP3: LHMs-based demonstrators In the framework of the DALHM project we focused on various demonstrators. We demonstrated: Enhancement of radiation and high-directionality of sources placed inside photonic crystals. The efficiency of a Swiss-roll-based yoke in transferring the signal and improve signal detection in magnetic resonance imaging systems. The ability of SRR systems to act as compact, highly directional antennas. An efficient flux compressor composed of a sequence of resonant loops with progressively smaller diameter. The sub-wavelength imaging capability of an isotropic 2D system made of Swiss-rolls. The capabilities of a structure made of thin wires to act as an angular filter, for radiation in the regime where the effective index of refraction of the structure is less than one (0<n<1). The validity of the principle of optically complementary media (one cancels the optical effects of the other) in the extreme near field, using a system of Swiss-rolls. Enhanced transmission and high directionality of the wave coming out from PC waveguides when PC surface modes are involved. Enhanced directionality of sources placed into PCs when surface states at the surface of the crystal are present. Beam steering in the RF domain using properly shaped photonic crystals. Details on the above demonstrators are given in Appendix 2 of this report.

19 DALHM Final report Page 19 Appendix 1: Publications within DALHM project 1. P. Markos and C.M. Soukoulis, Transmission Properties and Effective Electromagnetic Parameters of Double Negative Metamaterials, Optics Express 11, 649 (2003). 2. M C K Wiltshire, J B Pendry, J V Hajnal, D J Edwards and C J Stevens, A metamaterial endoscope for magnetic field transfer: near field imaging with magnetic wires, Optics Express 11, (2003). 3. M C K Wiltshire, E Shamonina, I R Young, and L Solymar, Dispersion characteristics of magnetoinductive waves: comparison between theory and experiment, Electron. Lett. 39, (2003). 4. M. Bayindir, K. Aydin, E. Ozbay, P. Markos and C. M. Soukoulis, "Transmission properties of composite metamaterials in free space," Appl. Phys. Lett. 81, 120 (2002). 5. P. Markos, I. Rousochatzakis and C. M. Soukoulis, "Transmission losses in left-handed materials," Phys. Rev. E 66, (R) (2002). 6. S. Foteinopoulou, E. N. Economou and C. M. Soukoulis, "Refraction at Media with negative refractive index," Phys. Rev. Lett. 90, (2003). 7. S. Foteinopoulou and C. M. Soukoulis, "Negative refraction and left-handed behavior in 2d photonic crystals," Phys. Rev. B. 67, (2003). 8. E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou and C. M. Soukoulis, "Negative refraction by photonic crystals," Nature 423, 604 (2003). 9. P. Markos and C. M. Soukoulis, "Absorption losses in periodic arrays of thin metallic wires," Opt. Lett. 28, 846 (2003). 10. P. Markos and C. M. Soukoulis, "Left Handed Materials," in Wave Scattering in Complex Media: From Theory to Applications, ed. by Bart van Tiggelen and S. Skipetrov (Kluwer Publ. 2003) p P. Markos and C. M. Soukoulis, "Structures with negative index of refraction," Phys. Status Solidi A 197, 595 (2003). 12. E. N. Economou, "Controlling the flow of Electromagnetic waves", Europhysics News, March/ April 2003, p E. N. Economou, "Left turns", Scientific American, Greek edition, October 2003, p M. C. K. Wiltshire, E. Shamonina, I. R. Young, and L. Solymar, Dispersion characteristics of magneto-inductive waves: comparison between theory and experiment, Electron. Lett. 39, (2003). 15. Irfan Bulu, Humeyra Caglay, and Ekmel Ozbay, Radiation properties of sources inside photonic crystals, Physical Review B 67, (2003). 16. Irfan Bulu, Humeyra Caglay, and Ekmel Ozbay, Highly Directive Radiation From Sources Embedded Inside Photonic Crystals, Applied Physics Letters 83, 3263 (2003). 17. S. Anantha Ramakrishna, J. B. Pendry, M. C. K. Wiltshire and W. J. Stewart, Imaging the Near Field, J. Mod. Optics 50, (2003). 18. S. Anantha Ramakrishna and John B. Pendry, Removal of absorption and increase in resolution in a near-field lens via optical gain, Phys. Rev. B (2003). 19. J. B. Pendry and D. R. Smith, Comment on "Wave Refraction in Negative-Index Media: Always Positive and Very Inhomogeneous", Phys. Rev. Lett. 90, (2003). 20. J. B. Pendry, Comment on "Left-Handed Materials Do Not Make a Perfect Lens", Phys. Rev. Lett (2003). 21. M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Towards photonic Crystal Metamaterials: Creating Magnetic Emitters in Photonic Crystals, Appl. Phys. Lett. 82 (7), (2003).

20 DALHM Final report Page Chiyan Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Negative refraction without negative index in metallic photonic crystals, Opt. Express 11, (2003). 23. J. B. Pendry, Positively Negative, Nature 'News and Views' (2003). 24. J. B. Pendry, Perfect Cylindrical Lenses, Optics Express 11, (2003). 25. J. B. Pendry and S. A. Ramakrishna, Focussing Light Using Negative Refraction, J. Phys. [Condensed Matter] 15, 6345 (2003). 26. Chiyan Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Subwavelength imaging in photonic crystals, Phys. Rev. B 68, _1-15 (2003). 27. J. B. Pendry and S. A. Ramakrishna, Refining the Perfect Lens, Physica B (2003) (ETOPIM proceedings). 28. E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou and C. M. Soukoulis, Subwavelength Resolution in 2D Photonic-Crystal-Based Superlens, Phys. Rev. Lett. 91, (2003). 29. E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, Negative refraction by photonic crystals, Nature 423, 604 (2003). 30. T. Koschny, P. Markos, D. R. Smith and C. M. Soukoulis, Resonant and anti-resonant frequency dependence of the effective parameters of metamaterials, Phys. Rev. E 68, (R) (2003). 31. P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Muller, R. B. Wehrspohn, U. Gosele and V. Sandoghdar, Highly directional emission from photonic crystal waveguides of subwavelength width, Phys. Rev. Lett., 92, (2004). 32. T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Effective medium theory of lefthanded materials, Phys. Rev. Lett. 93, (2004). 33. N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou and C. M. Soukoulis, Electric coupling to the magnetic resonance of split ring resonators, Appl. Phys. Lett., 84, 2943 (2004). 34. R. Moussa, S. Foteinopoulou and C. M. Soukoulis, Delay-time investigation of electromagnetic waves through homogeneous medium and photonic crystal left-handed materials, Appl. Phys. Lett. 85, 1125 (2004). 35. E. Ozbay, K. Guven, K. Aydin, and M. Bayindir, Physics and applications of photonic nanocrystals, Int. J. Nanotechnology, 1, No.4, (2004), (invited paper, to be published). 36. E. Ozbay, I. Bulu, K. Aydin, H. Caglayan, K. Guven, and Boratay K. Alici, Highly directive radiation and negative refraction using photonic crystals, Int. J. Laser Phys., 15, (2005). 37. S. Akarca-Biyikli, I. Bulu, and E. Ozbay, Enhanced transmission of microwave radiation in onedimensional metallic gratings with sub-wavelength aperture, Appl. Phys. Lett. 85, 1098 (2004). 38. Bulu, H. Caglayan, and E. Ozbay, Highly directive radiation from sources embedded inside photonic crystals, Appl. Phys. Lett. 83, 3263 (2003). 39. E. Ozbay, K. Aydin, E. Cubukcu, and M. Bayindir, Transmission and reflection properties of composite double-negative metamaterials in free space, IEEE Trans. on Antennas and Propagation 51, 2592 (2003). 40. Irfan Bulu, Humeyra Caglay, and Ekmel Ozbay, Radiation properties of sources inside photonic crystals, Physical Review B 67, (2003). 41. J.B. Pendry and D.R. Smith, Reversing Light with Negative Refraction, Physics Today 57 [6] (June 2004). 42. J.B. Pendry, Negative Refraction, Contemporary Physics 45, 191 (2004). 43. S. O Brien, D. McPeake, S.A. Ramakrishna and J.B. Pendry, Near-Infrared Photonic Band Gaps and Nonlinear Effects in Negative Magnetic Materials, Phys. Rev. B 69, (2004). 44. J.B. Pendry, L. Martín-Moreno, and F.J. Garcia-Vidal, Mimicking Surface Plasmons with Structured Surfaces, Science 305, 847 (2004).

21 DALHM Final report Page D.R.Smith, J.B. Pendry, M.C.K. Wiltshire, Metamaterials and Negative Refractive Index, Science 305, 788 (2004). 46. M.C.K. Wiltshire, E.Shamonina, I.R.Young, and L.Solymar, Experimental and theoretical study of magneto-inductive waves supported by one-dimensional arrays of Swiss Rolls, J. Appl. Phys. 95, 4488 (2004). 47. Humeyra Caglayan, Irfan Bulu, and Ekmel Ozbay, Highly directional enhanced radiation from sources embedded inside three-dimensional photonic crystals, Optics Express 13, 7645 (2005). 48. Koray Aydin, Kaan Guven, Maria Kafesaki, Costas M. Soukoulis, and Ekmel Ozbay Investigation of magnetic resonances for different split-ring resonator parameters and designs, New Journal of Physics 7, 168 (2005). 49. Irfan Bulu, Humeyra Caglayan, and Ekmel Ozbay, Negative refraction and focusing of electromagnetic waves by metallodielectric photonic crystals, Physical Review B 72, (2005). 50. Koray Aydin, Kaan Guven, C. M. Soukoulis, and Ekmel Ozbay Observation of negative refraction and negative phase velocity in left-handed metamaterials, Applied Physics Letters 86, (2005). 51. Humeyra Caglayan, Irfan Bulu, and Ekmel Ozbay Extraordinary grating-coupled microwave transmission through a subwavelength annular aperture, Optics Express 13, 1666 (2005). 52. K. Guven, and E. Ozbay, Coupling and phase analysis of cavity structures in two-dimensional photonic crystals, Physical Review B 71, (2005). 53. Ekmel Ozbay, Irfan Bulu, Koray Aydin, Humeyra Caglayan, K. Bora Alici, and Kaan Guven, Highly Directive Radiation and Negative Refraction Using Photonic Crystals, Laser Physics Journal 15, 217 (2005). 54. S. Sena Akarca-Biyikli, Irfan Bulu, and Ekmel Ozbay, Resonant excitation of surface plasmons in one-dimensional metallic grating structures at microwave frequencies, J. Opt. A: Pure Appl. Opt. 7, 159 (2005). 55. R. Moussa, S. Foteinopoulou, Lei Zhang, G. Tuttle, K. Guven, E. Ozbay, and C. M. Soukoulis, Negative refraction and superlens behavior in a two-dimensional photonic crystal, Physical Review B. 71, (2005). 56. Ekmel Ozbay, Kaan Guven, Ertugrul Cubukcu, Koray Aydin and K. Bora Alici, Negative Refraction and Subwavelength Focusing using photonic crystals, Modern Physics Letters B 18, No. 25 (2004) Koray Aydin, Kaan Guven, Nikos Katsarakis, Costas M. Soukoulis, and Ekmel Ozbay Effect of disorder on magnetic resonance band gap of split-ring resonator structures, Optics Express 12, 5896 (2004). 58. Ekmel Ozbay, Irfan Bulu, Koray Aydin, Humeyra Caglayan, and Kaan Guven Physics and applications of photonic nanocrystals, International Journal of Nanotechnology 1, 379 (2004).2, 5896 (2004). 59. Ekmel Ozbay, Irfan Bulu, Koray Aydin, Humeyra Caglayan, and Kaan Guven Physics and applications of photonic crystals, Photonics and Nanostructures 2, 87 (2004). 60. K. Guven, K. Aydin, K. B. Alici, C. M. Soukoulis, and E. Ozbay, Spectral negative refraction and focusing analysis of a two-dimensional left-handed photonic crystal lens, Physical Review B 70, (2004). 61. K. Aydin, K. Guven, Lei Zhang, M. Kafesaki, C. M. Soukoulis, and E. Ozbay Experimental Observation of True Left-Handed Transmission Peak in Metamaterials, Optics Letters 29, 2623 (2004). 62. N. Katsarakis, T. Koschny, M. Kafesaki, E.N. Economou, E. Ozbay, C. M. Soukoulis, Left- and right-handed transmission peaks near the magnetic resonance frequency in composite metamaterials, Physical Review B. 70, (2004).

22 DALHM Final report Page M. Gokkavas, K. Guven, I. Bulu, K. Aydin, M. Kafesaki, R. S. Penciu, C. M. Soukoulis, and E. Ozbay, Experimental demonstration of a left-handed composite metamaterial operating at 100 GHz, Phys. Rev. B 73, (2006). 64. C. Enkrich, F. Perez-Willard, D. Gerthsen J. Zhou, T. Koschny, C. M. Soukoulis, M. Wegener and S. Linden, Focused-ion-beam nanofabrication of near-infrared magnetic metamaterials, Advanced Materials 17, 2547 (2005). 65. Th. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, Impact of the inherent periodic structure on the effective medium description of left-handed and related metamaterials, Phys. Rev. B 71, (2005). 66. N. Katsarakis, G. Konstantinidis, A. Kostopoulos, R. S. Penciu, T. F. Gundogdu, Th Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Magnetic response of split-ring resonators in the far infrared frequency regime, Optics Letters 30, 1348 (2005). 67. Th. Koschny, Lei Zhang, and C. M. Soukoulis, Isotropic three-dimensional left-handed metamaterials, Phys. Rev. B 71, (2005). 68. D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, Electromagnetic parameter retrieval from inhomogeneous metamaterials, Phys. Rev. E 71, (2005). 69. M. Kafesaki, Th. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou and C. M. Soukoulis, Left-handed metamaterials: detailed numerical studies of the transmission properties, J. Opt. A: Pure Appl. Opt. 7, S12 (2005). 70. S. Linden, C. Enkirch, M. Wegner, J. Zhou, T. Koschny and C. M. Soukoulis, Magnetic response in metamaterials at 100 THz, Science 306, 1351 (2004). 71. T. Koschny, P. Markos, D. R. Smith and C. M. Soukoulis, Reply to Comments on Resonant and antiresonant frequency dependence of the effective parameters of metamaterials, Phys. Rev. E 70, (2004). 72. JB Pendry, Manipulating the near field with metamaterials, Optics & Photonics News (2004). 73. SA Ramakrishna and JB Pendry, Spherical perfect lens: Solutions of Maxwell's equations for spherical geometry, Phys. Rev. B (2004). 74. FJ Garcia-Vidal, L Martin-Moreno, JB Pendry, Surfaces with holes in them: new plasmonic metamaterials, J. Opt. A Pure & Applied Optics 7 S97-S101 (2004). 75. JB Pendry, A Chiral Route to Negative Refraction, Science (2004). 76. Sébastien Guenneau, Boris Gralak, and J.B. Pendry, The perfect corner reflector, Optics Letters (2005). 77. WB Williams and JB Pendry, Generating Bessel beams by use of localized modes, J. Opt. Soc. Am., A (2005). 78. P. Kramper, M. Kafesaki, C. M. Soukoulis, A. Birner, F. Muller, R. B. Wehrspohn, U. Gosele and V. Sandoghdar, Near-field visualization of light confinement in a photonic crystal microresonator, Opt. Lett. 29, 174 (2004). 79. Lei Zhang, G. Tuttle and C. M. Soukoulis, GHz magnetic response of split ring resonators, Photonic and Nanostructures 2, 155 (2004). 80. S. Foteinopoulou and C. M. Soukoulis, Electromagnetic wave propagation in 2D photonic crystals: A study of anomalous refractive effects, Phys. Rev. B 72, (2005). 81. J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry and C. M. Soukoulis, Saturation of the magnetic response of split-ring resonators at optical frequencies, Phys. Rev. Lett. 95, (2005). 82. C. Enkrich, S. Linden, M. Wegener, S. Burger, L. Zswchiedrich, F. Schmidt, J. Zhou, T. Koschny and C. M. Soukoulis, Magnetic metamaterials at telecommunication and visible frequencies, Phys. Rev. Lett. 95, (2005).

23 DALHM Final report Page G. Dolling, C. Enkrich, M. Wegener, S. Linden J. Zhou, and C. M. Soukoulis, Cut-wire and plate capacitors as magnetic atoms for optical metamaterials, Opt. Lett. 30, 3198 (2005). 84. S. Burger, L. Zschiedrich, R. Klose, A. Schδdle, F. Schmidt, C. Enkrich, S. Linden, M. Wegener, C. M. Soukoulis, Numerical Investigation of Light Scattering off Split-Ring Resonators, Proc. SPIE 5955, 18 (2005) (cond-mat/ ). 85. J. Zhou, Lei Zhang, G. Tuttle, Th. Koschny and C. M. Soukoulis, Negative index materials using simple short wire pairs, Phys. Rev. B 73, (2006). 86. R. S. Penciu, M. Kafesaki, T. F. Gundogdu, E. N. Economou and C. M. Soukoulis, Theoretical study of left-handed behavior of composite metamaterials, Photonics and Nanostructures 4, 12 (2006). 87. J. Zhou, Lei Zhang, G. Tuttle, Th. Koschny and C. M. Soukoulis, Experimental demonstration of negative of index of refraction, Appl. Phys. Lett. 88, (2006). 88. Th. Koschny, R. Moussa and C. M. Soukoulis, Limits on the amplification of evanescent waves of left-handed materials, J. Opt. Soc. Am. B 23, 485 (2006). 89. M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis and S. Linden, Single-slit split-ring resonators at optical frequencies: Limits of size scaling, Opt. Lett. 31, 1259 (2006). 90. F. Koenderink, M. Kafesaki, C. M. Soukoulis, V. Sandoghdar, Spontaneous emission in the nearfield of two-dimensional photonic crystals, Opt. Lett. 30, 3210 (2005). 91. N. Katsarakis, I. Tsiapa, A. Kostopoulos, G. Konstantinidis, R. S. Penciu, T. F. Gundogdu, M. Kafesaki, E. N. Economou, Th. Koschny, and C. M. Soukoulis, Experimental demonstration of negative magnetic permeability in the far-infrared frequency regime, Appl. Phys. Lett. 89, (2006). 92. S. Linden, C. Enkrich, G. Dolling, M. W. Klein, J. Zhou, Th. Koschny, C. M. Soukoulis, S. Burger, F. Schmidt, and M. Wegener, Photonic metamaterials: Magnetism at optical frequencies, IEEE J. of Selected Topics in Quant. Electr. (accepted). 93. C. M. Soukoulis, M. Kafesaki and E. N. Economou Negative index materials: New frontiers in optics, Adv. Mater. 18, 1941 (2006). 94. H. Danithe, S. Foteinopoulou and C. M. Soukoulis, Omni-reflectance and enhanced resonant tunneling from multilayers containing left-handed materials, Photonics and Nanostructures, (accepted). 95. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis and S. Linden, Observation of simultaneous negative phase and group velocity of light, Science 312, 892 (2006). 96. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis and S. Linden, A low-loss negative index metamaterial at telecommunication wavelengths, Opt. Lett. 31, 1800 (2006). 97. E.N. Economou and C. Soukoulis, article in the six volume Encyclopedia of Condenced Matter Physics, ed. F. Bassani, G.L. Leidl, and P. Wyder, Elsevier (2005): Vol.1, p. 444 (2005). 98. E.N. Economou, Negative index materials: A new frontier in optics?, Ukr. J. Phys. 50, 8, 779 (2005). 99. Irfan Bulu, Humeyra Caglayan, and Ekmel Ozbay, Beaming of Light and Enhanced Transmission via Surface Modes of Photonic Crystals, Optics Letters 30, 3078 (2005) Irfan Bulu, Humeyra Caglayan, Koray Aydin and Ekmel Ozbay Compact size highly directive antennas based on the SRR metamaterial medium, New Journal of Physics 7, 223 (2005) Koray Aydin, Irfan Bulu and Ekmel Ozbay, "Focusing of electromagnetic waves by a lefthanded metamaterial flat lens", Optics Express 13, 8753 (2005) Irfan Bulu, Humeyra Caglayan, and Ekmel Ozbay Experimental demonstration of labyrinthbased left-handed metamaterials, Optics Express 13, (2005) Ekmel Ozbay, Plasmonics: Merging Photonics and Electronics at Nanoscale Dimensions, Review Article, Science, 311, 189 (2006).

24 DALHM Final report Page Koray Aydin and Ekmel Ozbay, Negative refraction through an impedance matched left-handed metamaterial slab, Journal of Optical Society of America B. 23, p. 415 (2006) Humeyra Caglayan, Irfan Bulu, and Ekmel Ozbay, Beaming of electromagnetic waves emitted through a subwavelength annular aperture, Journal of Optical Society of America B. 23, p. 419 (2006) K. Kempa, R. Ruppin, and J. B. Pendry, Electromagnetic response of a point-dipole crystal, Phys. Rev. B 72, (2005).

25 DALHM Final report Page 25 Appendix 2: Left-handed material based demonstrators In the present appendix we describe the demonstrators developed within DALHM. These demonstrators include: 1) RF lenses and mirrors 2) High gain antennas 3) Components for enhancing the performance of Magnetic resonance imaging devices. 4) Photonic crystals supporting surface modes for beaming of light and enhanced transmission. 5) Swiss-roll structures for subwavelength imaging 6) Swiss-roll structures as RF complementary media demonstrators. 1) RF lenses and mirror demonstrator - Beam steering Early on in the program, we identified a pathfinder application in which a negative index metamaterial can be utilized as a lens element. This pathfinder application serves as a testbed for many of properties of metamaterial lenses and was used to either validate or disprove some of the theoretically derived properties and characteristics of metamaterial composites. A negative index lens with index of n = -1 can be used to either collimate or focus radiation, and offers the advantages of decreased reflectance and compactness, compared to a positive index lens, as detailed simulations have shown. One other aspect of metamaterial lenses that became evident, after a systematic study was undertaken, was that negative index lenses appear to be far superior to normal positive index lenses with respect to aberrations. To this end, we performed a detailed evaluation of the aberrations of negative and positive index lenses. While these calculations are based on geometrical optics, they provide a strong indication that negative index lenses outperform positive index lenses for all imaging figures of merit. Of course, due to the frequency dispersion inherent in negative index materials, a negative index lens will exhibit more severe chromatic aberration than a positive index lens. However, for the proposed beam steering application, the typical bandwidth of the negative index materials is quite sufficient. If greater bandwidth is sought, it may be possible to produce compound lenses that increase bandwidth at the expense of increasing one or more of the other aberrations. The aberrations of both positive and negative index lenses were estimated using standard analytical methods of geometrical optics, and the results have been confirmed with ray tracing routines. It is of practical importance that an anisotropic medium can yield refraction results identical to those of an isotropic medium. Anisotropic samples are much easier to design and fabricate than are isotropic structures. Thus, a plano-concave focusing lens made from an anisotropic medium should have about the same focal properties as the equivalent lens made from isotropic media. The numerical results are shown in Figure 1. From the preceding analysis it becomes apparent how to design an anisotropic metamaterial lens that has focusing properties that are quite similar to those of an isotropic lens. It is also confirmed by the ray tracing diagram of Figure 2(b) for which either an isotropic or an anisotropic medium produce the same focus. Note also that in either case, isotropic or anisotropic, the plano-concave lens has a reduced spherical aberration, which is another advantage specific to negative refracting materials.

26 DALHM Final report Page 26 Fig. 1: (a) The field distribution at the focus of a left-handed (negative index) lens. In this case, the index has a value of n = -1 (ε = -1, μ = -1). In this simulation, the radius of curvature of the lens was R = 6 cm, with a wavelength chosen at λ = 3 cm. (b) The field distribution at the focus of a concave lens made of negative refracting indefinite media, for which ε z = -1 and μ x = - 1. All other material parameters are equal to unity. The axes are such that z is out of the plane, y is along the direction of propagation, and x is perpendicular to the direction of propagation. The field is polarized such that the electric field is along the z-axis. (c) The field pattern for the same type of lens as in (b), but with a step pattern introduced to mimic the finite unit cell size of a typical metamaterial. Fig. 2: (a) Ray tracing diagram for a positive index lens corrected for spherical aberration. (b) A n=-1 planoconcave lens, either isotropic or anisotropic, is inherently free from spherical aberration. Finally, we performed beam steering experiments using this cylindrical lens. The results are shown in Figure 3. The source was placed at 15.5 cm in front of the lens and area scans were made on the down stream side of the lens. The y position of the source was moved from 4.0 cm to 4.0 cm in 2.0 cm steps. As shown in the figure, the lens clearly steers the beam.

27 DALHM Final report Page 27 Fig. 3: Area contour plots of Ex on downstream side of lens when the illumination source is moved along y from 4.0 cm to 4.0 cm in 2.0 cm steps. This data clearly indicates that the cylindrical lens steers the illumination beam. Another way to get a beam steering is to use photonic crystals that posses a negative index of refraction. As can be seen in Figure 4, one can use a photonic crystal to focus a plane wave. Our DALHM collaboration has a lot of experience in using photonic crystals to get negative refraction. It is R well know that one can use the lens equation f = for both positive and negative index material. n 1 You can see that we get the same focal length f for n=3 and n=-1. However the negative n=-1 lens is much lighter that the positive n=3 lens and also has much less reflection. It is well known for a lefthanded material that we can have zero reflection if we fix its impedance to be equal to one. Our preliminary experiments agree very well with the experiments of the Northeastewrn group [1]. We have taken the liberty to present the results of the experiments of the Northeastern group in Figures 5 and 6. Our simulations agree pretty well with these results and our preliminary experiments give very similar results.

28 DALHM Final report Page 28 Fig. 4: A schematic diagram for a focusing experiment using photonic crystal of dielectric rods (taken from Ref. 1). Fig. 5: Focusing by a planoconcave PhC lens having radius of curvature 13.5 cm. The focus point observed at 9.31 GHz is 10.1 cm from the concave lens surface. On the left side, field map of the incoming plane wave is shown and on the right side, intensity of the focus point. Scale: On the left, the real part of S21 varies from to 0.025, on the right side intensity from 0 to Dimensions of the figure are 49 x 34 cm2. The photonic crystal lattice spacing is 1.8 cm and the packing density of the square lattice is determined from the ratio r /a= The dielectric roads are alumina roads with dielectric constant of 8.9. (Taken from Ref.1) Fig. 6: Field maps of the incident source and the emerging plane wave. Scale: On the left side intensity varies from to 0.055, on the right side the real part of S21 from to The dimensions are the same as in figure 5. (Taken from Ref. 1) 2) High gain antenna demonstrator a) Photonic crystal antenna We have experimentally and theoretically studied the angular distribution of power emitted from a radiation source embedded inside a photonic crystal. In our experiments and FDTD calculations we have

29 DALHM Final report Page 29 calculated and measured the angular distribution of power emitted from a monopole source embedded inside a 2D square array of cylindrical alumina rods whose radius is 1.55 mm and dielectric constant is The separation between the center of the rods along the lattice vectors is 1.1 cm. The monopole source used in the experiments is obtained by removing 0.5 cm of the cladding from a coaxial cable and leaving the metal part. An HP-8510C network analyzer is used to excite the monopole source and to measure the power emitted from the monopole source. We have measured the angular distribution of power at the upper band edge frequency for various crystal lengths. The measured and calculated far field radiation patterns are presented in Fig.7. Figure 7 shows that there is an optimum crystal length, which is found to be 24 layers in our case. The minimum half power beam width is obtained at 24 layers and it is found to be 6 degrees. We observe that as the number of layers is increased from the optimum layer number the change in the far field radiation pattern is not as strong as the change observed when the layer number is decreased from the optimum layer number. This can be explained by the fact that as we move away from the center radiator the amplitude of the radiators decrease very rapidly. Hence, as we increase the number of layers from the optimum layer number the effect of the increasing the number of radiators will be small compared to the effect of the decreasing the number of radiators. To our knowledge this is the minimum value obtained by using PCs. Fig. 7: Measured and calculated far field radiation patterns at the upper band edge frequency for various crystal lengths. a) layers b) layers c) layers d) layers In conclusion: We have experimentally and theoretically studied the angular distribution of power emitted from a radiation source embedded inside a photonic crystal. Our results show that it is possible to obtain highly directive radiation sources by using photonic crystals. Half power bandwidths as small as 6 degrees have been obtained. b) Split-ring resonators (SRRs) based antenna Two important properties of the SRR structure make it an interesting structure for antenna applications. First of all, at the resonance frequency, resonant in phase and solenoidal currents flow along the SRR structure. Figure 8 shows the induced surface current density along the SRR structure at the resonance frequency. Figure 8 indicates that the current flowing around the SRR structure at the resonance frequency is solenoidad. As a result, the SRR structure can be regarded as a resonant magnetic dipole at the resonance frequency. In addition, SRR structure localizes the incident electric field to its close vicinity at the resonance frequency. Figure 9 shows the electric field distribution within the unit cell of the SRR metamaterial medium. The incident field is highly localized near the SRR structure. The

30 DALHM Final report Page 30 amplitude of the electric field near the gaps of the SRR structure is 2 orders of magnitude larger than the incident field. In terms of intensity, this corresponds to a 4 orders of magnitude enhancement. These two properties of the SRR structure make it interesting for antenna applications. Due to these two properties, when SRRs are arranged in a regular pattern, the resulting SRR metamaterial may be regarded as an antenna array. One would expect to observe highly directive radiation from such a regular arrangement, since highly directive radiation is common to antenna arrays [2]. Fig. 8: The surface current flowing around the SRR structure. The incident magnetic field is perpendicular to the plane of SRR. Fig. 9: Electric field distribution within the unit cell of the SRR metamaterial medium. The incident field has unit amplitude. The resonant nature of the SRR structure is pronounced as a dip in the transmission spectrum. This dip can be easily observed by measuring the transmission spectrum of a single SRR structure by two monopole antennas, one transmitting and the other receiving. The monopole antennas that we used in our experiments are obtained by removing the dielectric cladding and the metal shield of a microwave coaxial cable. The left inner core has a length of 7 cm. The monopole length is optimized for operation around 4 GHz. The transmission coefficients of a single SRR structure placed between two monopole antennas is then measured by HP-8510C network analyzer. HP-8510C is a vector network analyzer capable of measuring both the S-parameters amplitude and phase. The SRR structure is manufactured by standard printed circuit board technology. The substrate is standard FR-4 material and the metal is copper with a thickness of 0.05 mm. The thickness of the board is 1.6 mm and the measured relative permittivity around 4 GHz is The measured transmission data and the results of the FDTD simulation are shown in Figure 10. For comparison, we have also measured the response of the closed SRR structure. In the closed SRR structure we have two complete rings. The transmission data for a single SRR structure shows a strong dip around 3.65 GHz. Note that this dip is not observed in the transmission spectrum of the closed SRR structure and is a signature of a magnetic resonance in this regime. The experimental setup that we used to study the transmission properties of the periodic SRR medium is depicted in Figure 11(a). The transmission setup consists of HP-8510C network analyzer and transmitting-receiving horn antennas. The measured metamaterial medium is obtained by arranging SRR structures in a rectangular array. The periodicity along z- and y-axes is equal to 8.8 mm. The periodicity along x-axes is 6.5 mm. There are 30 layers along y-axes. The distance between horn antennas and the structure is 15 cm, which is larger than the wavelength at 3 GHz. The measured transmission spectrum of the SRR metamaterial medium is shown in Figure 11(b). The orientation of the incident fields and the SRRs is such that the magnetic field is perpendicular to the plane of SRRs and electric field is oriented along z-axes. The transmission spectrum of metamaterial SRR medium exhibits a band-gap between 3.4 GHz and 4.3 GHz.

31 DALHM Final report Page 31 Fig. 10: Measured transmission spectrum of (A) single SRR, (B) single closed SRR structure. Simulated transmission spectrum of (C) single SRR, (D) single closed SRR structure. Fig. 11(a): The experimental setup that we used to study the transmission properties of the SRR metamaterial medium. Fig. 11(b): Transmission spectrum through the SRR metamaterial medium. Magnetic field is perpendicular into the plane of SRR structures.

32 DALHM Final report Page 32 For the far field radiation pattern measurements, we replaced the transmitting horn antenna with a monopole antenna and placed the monopole antenna inside the SRR metamaterial medium. The placement of the monopole antenna inside the SRR metamaterial medium was chosen such that the monopole antenna effectively excites the SRR particles at the surface of the medium. As a result, there are 3 layers of SRR planes in front of the monopole antenna. The orientation of the monopole antenna was along z-axes. Given the above dimensions the surface of the SRR metamaterial medium was 2 wavelengths long along y- and z- axes. The power spectrum of the radiation emitted by the monopole antenna was then measured at a distance of 1.5 meters away from the metamaterial SRR medium. The measurements were done by varying the angle in the x-y plane. Figure 12(a) shows the measured angular Fig. 12: (a) Far field radiation pattern from a monopole source embedded inside the SRR metamaterial medium near the resonance frequencies. (b) Far field radiation pattern from a monopole source embedded inside the SRR metamaterial medium at the pass band. distribution of power near the resonance frequency of a single SRR structure. The half power beam width was approximately 14 degrees for the frequencies near the resonance frequency. These results show that the emitted power is confined to a narrow angular region near the resonance frequency. The experimental far field radiation pattern near the pass-band frequencies is presented in Fig. 12(b). The half power beam width at 4.7 GHz is 36 degrees. In a previous work, we showed that photonic crystals may be used to obtain highly directive radiation from sources [3]. It is worth to compare these values with our previous results obtained by using photonic crystals. For the case of the photonic crystal, the radiation surface had an area equal to 44 l 2 where l is the operation frequency. On the other hand, the surface area in this work is only 3.8 l 2. This means that the surface area is approximately reduced by a factor of 11 times when compared to the photonic crystal. We believe that this improvement is important for compact size highly directional radiation sources. In conclusion, we showed that near the resonance frequency of the SRR structure the surface of the SRR metamaterial medium can be regarded as a collection of resonant magnetic dipoles. When excited with a monopole source the SRR metamaterial medium exhibited a highly directive radiation pattern. The obtained half power beamwidth is comparable with the results obtained by photonic crystals in the previous works. In addition, the surface area is appreciably reduced compared to the highly directive radiation source based on photonic crystals. 3) Magnetic Resonance Imaging applications Magnetic Resonance Imaging (MRI) offers an ideal proving ground for demonstrating the unique properties of left-handed metamaterials (LHM). In an MRI system, the main magnetic field (typically tesla) needs to be homogeneous to a few parts per million, thus ruling out the introduction of any conventional magnetic material. Nevertheless, it would be very useful to have access to magnetic materials with which to manipulate the radiofrequency (RF) signals (in the range MHz). Functions such as guiding, focusing and screening could substantially enhance the performance of MRI systems. Metamaterials can achieve this because they offer a means of obtaining magnetic properties at

33 DALHM Final report Page 33 RF (for example large positive or negative permeability) without affecting the other magnetic fields in the system. In the framework of the DALHM project we investigated potential metamaterial components for use at MRI systems. These components are: a) A RF lens (or, more accurately, a faceplate ) able to preserve flux ducting in a MRI machine. b) A RF yoke, which will assist in the delivery or detection of RF signals. c) A flux compressor that can expand or concentrate flux from a single roll yoke to multiple roll polepieces. a) A Swiss Roll based RF faceplate We have built a RF lens (or, more accurately, a faceplate ), composed of swiss-roll structures. This has been fully characterized, and its impact on the RF field distribution has been determined for the full range of permeability available from the material. We have used the lens to demonstrate a geometry preserving flux ducting in a 0.5 tesla MRI machine operating at 21.3 MHz. The Swiss Roll structure (see Figure 13) which is the building element of the faceplate is a particularly suitable metamaterial for use at RF frequencies up to ~100MHz, because of its inherently large-self inductance and self-capacitance. Fig. 13: Schematic of Swiss roll array and of an individual roll, and a photo of a typical roll used at 21.3 MHz. The magnetic permeability of an array of such rolls is given by F μω ( ) = 1 (1) 2 ω0 γ 1 + i 2 ω ω where F is the filling factor, ω 0 the resonant frequency, and γ represents the damping or loss. Using the material Espanex, which consists of a 12.5 μm polyimide sheet with 18μm of copper deposited on it, from which to manufacture the Swiss Rolls, we have made material with a Q ~ 60 at a resonant frequency of 21.3 MHz, to match the 0.5 tesla MRI machine.

34 DALHM Final report Page 34 The effective permeability can be determined by inserting a roll into a long solenoid, and measuring the changes in the complex impedance that result. A typical plot for the permeability is shown in Figure 14(a). On resonance the peak imaginary value of μ is about 35. Real Part Over 300 rolls, each 50 mm long were made, with their resonant frequencies centered on 21.3 (a) Imaginary Part (b) Frequency / MHz Fig. 14: (a) Real (red line and axis) and imaginary (blue line and axis) parts of the permeability of a Swiss Roll as a function of frequency, (b) the assembled hexagonal prism sample MHz. Although nominally identical, in practice there was a distribution of frequencies significantly greater than the width of any individual resonance, so it was necessary to tune each roll to the correct resonant frequency. Tuning was carried out by adding a capacitively coupled sleeve that extended 10 mm beyond the end of the roll. A hexagonal prism of uniform thickness 60 mm containing 271 rolls could thus be made. Figure 2(b) shows the assembled prism. Swiss-roll based faceplate: The hexagonal swiss-rolls prism shown in Fig. 14(b) was fully characterized and its ability to act as a faceplate able to preserve flux ducting in a MRI machine was demonstrated (in a 0.5 tesla MRI machine operating at 21.3 MHz). Measurements of flux ducting: The characterisation was carried out using 3 mm diameter loops as both source and receiver. The source was placed centrally on the outside of the base of the box, about 5 mm from the base of the Swiss Roll array. The receiver loop was scanned across the surface of the array, 68 mm above the source, and the signal was measured using a network analyzer. The intensities at 15 and 21.3 MHz are shown as the red lines in Fig. 15, as a function of distance from the centre of the slab measured along a diagonal. The material was then removed, and the scan repeated (at a height of 68 mm); the results are the black lines in Fig. 15. Finally, the receiver was set at a height of 8 mm, the equivalent height had the 60 mm long Swiss Rolls not been present, and the scan repeated. This is shown as the blue line in Fig. 15. At low frequency (15 MHz), the permeability is slightly elevated (μ = 1.4). The signal through the material slab lies between the two background scans, and the peak intensity is 20 db below the 8 mm reference level. At 21.3 MHz, however, the signal matches the reference level closely, across the whole extent of the scan, except at the nearest neighbour positions, where the reference signal passes through a minimum.

35 DALHM Final report Page Intensity /db Frequency 15.0 MHz Intensity /db Frequency 21.3 MHz Position / mm Position / mm Fig. 15: Surface scans at two frequencies, below resonance and on resonance. The source is a 3 mm diameter loop, 5 mm from the rear surface, on the centre line. Red lines: scanning across the surface of the material along a diagonal at a height of 68 mm. Black lines: scanning at a height of 68 mm with no material. Blue lines: scanning at a height of 8 mm with no material. The extent of the central roll is indicated by the dashed green lines. Scanning Measurements: To test the two-dimensional imaging performance of the material, we constructed an antenna from a pair of anti-parallel wires, bent into the shape of the letter M (Fig. 16(a)). This generated a line of magnetic flux, so providing a characteristic field pattern for imaging. It was placed horizontally, and the material was positioned on top of it (Fig. 16(b)). Fig. 16: (left) The M-shaped antenna, constructed from two antiparallel wires held 1 mm apart. (right) The slab of Swiss Rolls placed on the antenna, and the scanning loop help above it. The transmitted field was measured by scanning a 3 mm diameter loop probe in a horizontal plane, about 2 mm above the surface of the material (see Fig. 16b). Measurements were made on a grid, 2 mm square, using a network analyzer, in collaboration with Prof. David Edwards at Oxford. The pattern thus observed at 21.3 MHz is shown in Fig. 17, in which the Swiss Roll structure is overlaid on the field pattern. Figure 17 clearly shows that the material does indeed act as an image transfer device for the magnetic field. The shape of the antenna is faithfully reproduced in the output plane, both in the distribution of the peak intensity, and in the valleys that bound the M. These mimic the minima in the input field pattern either side of the central line of flux. The upper right arm of the M itself was twisted, so that the flux pattern was launched with a much reduced vertical component. This is reproduced in the weaker intensity observed in this region.

36 DALHM Final report Page Frequency = MHz Y Distance /mm db -74 db -72 db -70 db -68 db -66 db -64 db -62 db -60 db -58 db -56 db -54 db -52 db -50 db Fig. 17: The field pattern observed at 21.3 MHz in a plane approximately 2 mm above the surface of the material slab. The Swiss Roll structure is overlaid X Distance /mm MRI Experiments: We tested the face plate concept in the 0.5T Apollo MRI machine. A second M- shaped antenna was constructed and tuned to operate at 21.3 MHz. The plate was placed directly adjacent to the excitation antenna, and an NMR visible polymer sheet (Spenco) was placed against the opposite face of the plate (see Figure 18). Signal reception was either from an enveloping birdcage coil surrounding the whole assembly or the excitation coil was used in transmit-receive mode. Control experiments were performed with the Spenco sheet placed directly adjacent to the excitation coil. Following manual RF level setting, multi-slice spin echo imaging (TR400, TE10, 128x256matrix, 20cm FoV, 5mm slice thickness) was performed in planes parallel to the plate surface. Excited Spenco Excited Spenco M Antenna Swiss Roll Slab (60 mm) M Antenna Fig. 18: Schematic diagram of the MRI experiments. Left, the reference set-up, in which the Spenco sheet is placed directly on the antenna, and the spin pattern is excited as shown. Right, the Swiss Roll slab is introduced between the antenna and the Spenco, so that the excitation pulse and spin echo signal propagate though the material.

37 DALHM Final report Page 37 Reference Through Swiss Rolls Fig. 19: Localised flux patterns produced the letter M in transmit-receive mode. (Left) Direct coupling of the excitation coil to the image plane, (right) with the flux pattern transferred through the plate. The RF excitation level was set so that signals were received only from locations close to conductors, so that the conductor pattern was directly visualised in the image. When the metamaterial was placed between the excitation coil and Spenco sheet, the flux pattern was directly transferred with geometry preserved. No change of RF excitation amplitude was required to maximise signal. The letter M was clearly seen as a cluster of circular dots following the contour of the letter (Figure 19). Here, the material acts both to transmit the exciting field from the antenna into the Spenco, so that the M-shaped pattern is written in the spins, and then to detect the signal from this pattern. Clearly, the flux is being guided through the material, without lateral spreading, and the material is acting as a face plate. b) A swiss-roll based RF yoke for use in magnetic resonance imaging (MRI) We have investigated the concept of a yoke made of Swiss Roll metamaterial to provide a low reluctance pathway that could potentially assist in signal reception in magnetic resonance imaging and spectroscopy applications. For example, a yoke could enable a remote source to generate a field pattern between the pole-pieces of the yoke (see Fig. 20, using the magenta coil as the source loop), or conversely enable a remote detector (the magenta loop in Fig. 20) to receive signal from a source between the poles. Alternatively, we could achieve enhanced detection of a small source between the poles using a coplanar receiver coil (the blue loop in Fig. 20) outside the source object, because increased coupling between source and receiver would be achieved though the presence of the yoke. Fig. 20: Schematic diagram of an RF yoke, constructed from bundles of Swiss Rolls. The red star denotes either the source point or the required excitation volume within a sample, and the blue and magenta lines represent alternative position for exciting or receiver coils.

38 DALHM Final report Page 38 For this work, we used Swiss rolls which were constructed from Pryalux flexible circuit board material, wrapped on mandrels 8 mm in diameter. These rolls were designed to resonate at 21.5 MHz and they had a Q of ~ 30. Preliminary tests were made on single rolls, by injecting a signal through a coupling loop at one end, and recording the detected signal through a second loop that could be moved along the roll. The detected signal was independent of the position of the receiver, but did depend on the length of the roll, being smaller for longer rolls. Thus the rolls act as good magnetic flux conductors, and the signal is determined by the reluctance (i.e. the length) of the flux return path. We then considered joining individual rolls together. Each junction introduces extra loss, and 90 joints produce roughly double the loss of a straight joint between the same rolls. Because of these losses, a yoke constructed from butt-coupled single rolls would not be viable. To reduce the corner losses, we assembled bundles of seven rolls of different lengths, so that the corners were mitred at 45, as shown in Fig. 7. This arrangement was much less sensitive to alignment, and significantly reduced the corner losses, so that a full yoke became viable. The bundles were first assembled into or a linear array with a 15 mm gap between the pole pieces (Fig. 21). An 11 mm diameter untuned loop was used as a source and a co-planar 33 mm untuned loop was used for reception. A reference level (0 db) was taken from the source and receiver loops alone. These were then inserted between the pole pieces, and increasing amount of metamaterial components were Fig. 21: Schematic diagram of the linear array, and photo of the experimental set-up. The co-planar loops act as source and detector, and the array is built up in stages, monitoring the signal at each stage. added as the linear array was built up. Addition of the pole pieces introduced a parasitic tuned element and increased the output to +7.0 db. As more components were added the signal level fell, presumably because of increasing losses and the longer return path. In the full collinear arrangement the received signal had fallen to +5.6 db. When the elements were reconfigured to form the yoke, the signal rose to +6.1 db.

39 DALHM Final report Page 39 The performance of the yoke was also investigated by using a remote receiver loop to detect flux circulating through the metamaterial bundles from a source between the pole pieces. Once again, the Transmission Performance of LF7012 Yoke Signal through Yoke / Reference Frequency / MHz Fig. 22: The experimental yoke assembly, showing the source and co-planar detector in the pole-gap, and the remote detector loop at the far end of the yoke. The signal recorded by the remote detector demonstrates that the flux is being guided through the Swiss Roll bundles. reference level was defined from the two loops in a co-planar configuration without the metamaterial. We then measured the signal being guided around the yoke (Fig. 22). At first sight, this result shows perfect coupling, but it must be recalled that this is a resonant system, so we expect the signal on resonace to be much higher than the reference (we found +7 db for the pole pieces alone, see above). So although this result is encouraging, it also shows that the device must be much improved to be truly useful. Nevertheless, it does provide a proof of principle that metamaterial yokes could enhance signal reception by introducing a low reluctance flux return path. We have also examined our higher performance materials in which the permeability and Q are at least a factor of 2 higher than in the Pyralux material. In these, the signal down a 200 mm roll was increased from 4.2 db to 10.3 db, showing much improved flux ducting. However, the losses at joints, while reduced compared to those in the Pyralux system, are still unacceptable (see Table 1). We have therefore investigated the effect of an additional coupler in the form of two connected loops, that links the end of one roll with the next. This significantly improves the flux linkage, as shown in Table 1, but further work is necessary to optimise this approach. Table 1. Comparison of junction losses for straight and 90 joints in Pyralux, Espanex and coupled systems Signal (db) Pyralux Espanex Espanex + coupler Straight joint joint Another issue that affects the yoke performance is how uniform a field can be generated between the pole pieces or equivalently what resolution can be detected from a source in the gap. In our study of the resolution of the face-plate (see previous section), we found that the transmitted flux tends to be confined to the individual rolls. In that work, we showed that the faceplate resolution was accounted for by the

40 DALHM Final report Page 40 loss in the material. However, if we consider rather shorter pole-pieces, the resolution will be dominated by the size of the individual elements, producing a field distribution with uniform areas that are the same size as the rolls. This effect was also seen in our MRI experiments on the faceplate, and is clear in the data from the square prism sample. This suggests that the yoke needs to be constructed of rolls with the smallest possible diameter. However, in very recent experiments, we have found evidence, yet to be confirmed, to suggest that some details of the flux patterns may be transmitted through a single roll. Small, 3 mm diameter, loops were used as both source and detector, with the source being placed on axis at the entrance of a very large, 37 mm diameter, hollow roll, resonant near 6 MHz. The characteristic minima in the axial field of a small loop were also seen at the output of the roll, suggesting that some mapping of the input flux distribution to the output face does occur. More detailed scans of the output field distribution must be carried out to determine whether this is a real effect or an artefact. c) A flux compressor An important part of any future MRI device will be a flux compressor that can expand or concentrate flux from a single roll yoke to multiple roll pole-pieces. Here we examine the potential of an array of capacitively loaded loops with diameters progressively reduced in some predetermined manner to concentrate flux. Fig. 23: The prototype flux compressor consists of 13 segments, each of width 2.2 mm, whose diameter reduces by ~ 1 mm per segment from 20.5 mm to 7 mm. The number of turns, diameter and capacitance of each segment were selected to give resonance at ~21.3 MHz Loops pushed together d = 2.2 mm Loops separated by d = 5.2 mm Intensity [db] (a) Intensity [db] (b) H z,out / H z,in (c) H z,out / H z,in (d) Frequency [MHz] Frequency [MHz] Fig. 24: Performance of the multiple coil compressor. (a), (b) measured, (c), (d) theoretical results for different coil spacings Our compressor is built from a sequence of resonant loops, all tuned to the same frequency, and wound on different diameter formers. The coils were then assembled on a common insulating mandrel (Fig. 23).

41 DALHM Final report Page 41 The number of turns in each coil was allowed to vary to make it possible to tune each coil of the set to 21.3 MHz (for compatibility with a 0.5T MRI system) using readily available capacitors. In the simplest case the loops are equidistant from each other but this construction allowed the distance between the elements to be a free parameter so we could investigate the impact on concentration ratio of altering the element spacing. Numerical calculations were performed to investigate the performance of the device, in particular whether improved performance could be achieved by modifying the inter-element spacing. The calculations suggested that the concentration efficiency was unaffected, but the pass-band was reduced. The device was tested in two configurations: first with all the elements pushed close together, leading to a spacing of 2.2 mm, and second with the inter-element spacing increased to 5.2 mm. The comparisons between the measured and calculated spectra are shown in Fig. 24. Although the bandwidths of the devices and the details of the resonant peaks change, their overall transmission levels are little affected, so that the design of these devices can be seen to be quite robust. 4) Beaming of light and enhanced transmission via surface modes of photonic crystals Here we demonstrate enhanced transmission and beaming through photonic crystal (PC) waveguides of subwavelength width. The enhanced transmission and beaming is achieved using coupling of the guided mode with surface states at the surfaces of the PC. The PC used is composed of dielectric rods in free space and the surface states are created adding a proper corrugation at the surface of the PC. The modes of the PC have been analyzed by the plane-wave expansion method. We show the existence of surface propagating modes when the surface of the finite-size PC is properly corrugated. We demonstrate, both theoretically and experimentally, that the transmission through photonic crystal waveguides can be substantially increased by the existence of surface propagating modes at the input surface of the guide. In addition, the power emitted from the PC waveguide is confined to a narrow angular region when an appropriate surface corrugation is added to the output surface of the photonic crystal. A metallic surface and the surface of a corrugated PC have in common that both surfaces can support surface-propagating EM waves. The properties of surface-propagating modes on metallic surfaces have been extensively studied. Recently, extraordinary light transmission through a subwavelength aperture on a metallic surface surrounded by concentric grooves or a grating was demonstrated. This extraordinary transmission is attributed to the excitation of surface modes on the metallic surface. In addition to the extraordinary transmission, beaming of EM waves via surface modes on the metallic surfaces has been reported. Moreno et al. [4] theoretically demonstrated that similar effects such as enhanced transmission through a PC waveguide and beaming of EM waves can be observed by using PCs. Moreover, Kramper et al.[4] demonstrated a beaming effect in optical regions by using PC structures. Modes of an infinite PC can be calculated by using the plane-wave expansion method. The same method can be used to identify the modes of a finite size PC by employing a large enough supercell. We study TM-polarized (electric field parallel to the axis of the rods) EM waves throughout this work. The PC that we used in our study is a two-dimensional square array of circular alumina rods. The radius of the rods is 1.55 mm. The dielectric constant of alumina is 9.61, and the lattice constant is 11 mm. The supercell has a rectangular geometry, and it consists of 40 layers long along the y axis and 1 unit cell along the x axis; 15 unit cells along the y axis contain alumina rods, and the rest is free space. We fabricated a PC waveguide by removing one row of rods from a square array of circular alumina rods. The crystal is 15 layers long along the propagation direction. The measured and the calculated spectra transmitted through the PC waveguide are shown in Fig. 25. A waveguide band between 9.7 and 13.1 GHz is observed in the transmission spectrum of the PC waveguide. The overall

42 DALHM Final report Page 42 transmission efficiency is around 10% within the waveguide band compared with free-space transmission. We added an extra layer of rods with a radius of 0.76 mm to the input surface of the PC. As our calculations have shown, addition of this extra layer creates surface modes. In order to couple to the surface modes, we added the grating-like layer in front of the extra layer. Note that the grating-like layer results in efficient coupling to the surface-propagating modes around GHz (Fig. 25). The measured and calculated spectra transmitted through the PC waveguide with the input surface modulation are shown as curves C and D in Fig. 25. The transmission efficiency is increased by a factor of 5 around GHz when compared with the bare PC waveguide. These results indicate that efficient coupling to the PC waveguide modes can be achieved via surface propagating waves. Fig. 25: Curve A, measured and B, calculated transmission spectrum through the PC waveguide; curve C, measured and, D, calculated transmission spectrum through the PC waveguide when the surface corrugation and the grating like structure is added in front of the input surface of the PC waveguide. Fig. 26: (a) Measured far-field radiation pattern of the EM waves emitted from the PC waveguide at GHz. (b) Measured far-field radiation pattern of EM waves emitted from the PC waveguide with surface corrugation and a grating like layer. The PC waveguide that we used in this study has a width smaller than the operation wavelength. The operation wavelength is around 2.5 cm, whereas the waveguide width is 1.9 cm. Hence the EM waves emitted through the PC waveguide would diffract in all directions from the PC waveguide aperture. The far-field radiation pattern of the waves emitted through the PC waveguide is shown in Fig. 26(a). Figure 26(a) shows that the emitted power spreads into a wide angular region. The surface modes can be excited by the PC waveguide. The excited surface modes can be coupled to the radiating modes of free space when a grating like layer is added in front of the corrugation. The measured far-field radiation patterns of the EM waves emitted from the PC waveguide with surface corrugation and the grating-like layer are shown in Fig. 26(b). Figure 26(b) shows that with the surface corrugation and the grating-like layer the

43 DALHM Final report Page 43 emitted power is confined to a very narrow angular region with a half-power beam width of 10. In addition, the measured electric field intensity at GHz over a 35cm 50cm area on the exit side of the PC waveguide in the presence of corrugation and the grating-like layer is shown in Fig. 27. Figure 27 shows that the electric field intensity is confined to a narrow spatial region and propagates without diffracting into a wide angular region. Fig. 27: Measured intensity distribution at the exit side of the PC waveguide when the corrugation and grating like layer are added to the exit surface of the PC waveguide. The Y axis is parallel to the PC surface. In conclusion, we have demonstrated beaming and enhanced transmission of EM waves through PC waveguides of subwavelength width by using surface modes of corrugated PC structures. The measured transmission of a PC waveguide structure without surface corrugation was about 10%. The transmission increased to 55% when a surface corrugation with a grating-like layer was added to the input surface of the PC waveguide. In addition, we demonstrated that the electric field emitted through the PC waveguide in the presence of the surface corrugation and the grating-like layer was confined to a narrow angular region. Similar results are expected if we have a narrow waveguide surrounded by a left-handed material. So the surface waves can increase the directionality and the transmission of subwavelength beaming. 5) Swiss-roll structures for subwavelength imaging Here we demonstrate a swiss-roll made isotropic metamaterial which can offer sub-wavelength imaging with a resolution of ~λ/70. Fig. 28: Schematic of the 2D isotropic Swiss Roll structure. It is now well known that a metamaterial with a refractive index n = -1, achieved by arranging ε = -1 and μ = -1 simultaneously, can act as a perfect lens, producing an image with a resolution that is not determined by the rules of conventional optics, but by the loss in the medium. In particular, such material can manipulate not only the propagating radiation, but also the evanescent field, thus potentially recovering all the spatial information in an object and achieving sub-wavelength resolution. In the very near field, where all relevant length scales are much smaller than a wavelength, the electric and magnetic components of radiation are decoupled, and we can use the quasistatic approximation. So we can manipulate the field from a magnetic source by arranging a metamaterial to have just the required permeability, without having to control the permittivity. Such a metamaterial can be achieved by using Swiss roll structures (see Section 3). When we consider the prescription for the perfect lens in this approximation, it is clear that to image magnetic sources, we only need to achieve μ = Y X Z

44 DALHM Final report Page However, this permeability must be isotropic, at least in two dimensions; the highly anisotropic permeability of the Swiss Roll prism described in Section 3 does not produce imaging. Such a two dimensional isotropy can readily be achieved by stacking the rolls as a log pile as shown in Figure 28, so that μ x = μ z = μ(ω) and μ y = 1. We have re-assembled the prism into a wall, 384 mm wide, 60 mm thick and 90 mm high. The performance that can be achieved with this material can be estimated analytically. It has been shown that the resolution, Δ, is given by Δ 2π d ln( μ 2) where d is the thickness and μ is the imaginary part of the permeability. Using d = 60 mm and μ = 0.14 as appropriate for this material, we find Δ 140 mm, so two sources 140 mm apart should be distinguishable in the image plane. In the experimental measurements, a pair of 2D magnetic sources, each consisting of two antiparallel wires that generate a line of magnetic flux, were placed 25 mm behind the wall in such a way that their separation could be changed between 80 mm and 140 mm. A long narrow rectangular loop was used to measure the longitudinal component of the magnetic field, H z, and was scanned in the output space using our custom-built x-y table. This table has a range of 300 mm, and this, combined with the finite length of the wall, imposed a restriction on the source separation to about 150 mm, so smaller (albeit less well-resolved) separations were investigated. Measurements of the emerging H z were made using an Agilent 8753ES network analyser, at 400 frequency points between 15 and 35 MHz. We note that the wavelength of electromagnetic radiation at 25 MHz is ~12 m, more than 100 times all the length scales in the experiment. When the material is assembled in this way, it is not known exactly what the effective value of the packing fraction is, and so the frequency at which μ = -1 is uncertain. Accordingly, we have used the MicroWaveStudio software to model the system, and predict the field pattern in the image plane as a function of frequency, as shown in Figure 29. Then knowing when μ = -1 in the simulation (marked with a dashed line), we can establish the correct frequency to investigate in the experiment, by plotting the data in the same way and matching characteristic features. By this means, we see that μ = -1 at MHz for this sample. 25 A 25 B Frequency / MHz Frequency / MHz X distance / mm X distance / mm Fig. 29: Maps of the field magnitude through the metamaterial as a function of frequency and position in the image plane, obtained from two sources spaced 100 mm apart. (A) The simulated distribution: the dashed line shows the frequency for which μ = -1 (B) The measured distribution which shows a similar structure at a slightly higher frequency: the dashed line is at MHz, identifying where μ = -1

45 DALHM Final report Page A B Z distance / mm Z distance / mm X distance / mm X distance / mm Fig. 30: Measured distributions of H z field intensity (db) at MHz. (A) from two sources spaced 100 mm apart in free space, (B) as (A) but with the metamaterial slab in place. In these frames, the position of the metamaterial is indicated by the dashed magenta line, and the image plane by the dashed black line.. The experimental data were then re-plotted to show the spatial distribution in the image space at MHz. This is shown in Figure 30. Here, Figure 30A shows the distribution of H z arising just from the two sources, spaced 100 mm apart. We note that there is no discernible structure beyond ~80 mm from the source plane. When the slab of metamaterial is introduced with a position indicated in Fig 30 (A and B), the fields in the image plane are enhanced by a factor of ~15, and significant structure is obtained. Near the surface of the metamaterial, there are strong fields with rapid spatial variation, and no longitudinal focusing is observed. In the image plane, however, distinct modulation can be seen, indicating that some focusing is occurring. Plotting the field magnitude as a function of position in the image plane shows two peaks (Figure 31, green line). Moreover, when the source separation is increased, the separation of the peaks in the image plane and their definition increases, showing that the structure in the image plane does indeed arise from imaging the sources, and we can clearly resolve two sources 140 mm apart, a resolution of λ/80.

46 DALHM Final report Page Field Amplitude H z X distance / mm Fig. 31: Measured variation of the field amplitude in the image plane z = 120 mm without the metamaterial (black line, X 10), and with the metamaterial when the sources are spaced 80 (blue line), 100 (green line), 120 (red line) and 140 mm (cyan line) apart. The formal measure of the performance of an imaging element is its transfer function, the transmission of the device as a function of the spatial frequency k of the incoming signal. The transfer function for a slab of negative index material is given by Smith et al. (Applied Physics Letters 82, 1506 (Mar, 2003)), and in that paper they showed results for a slab with d/λ = 0.1, that gave resolutions of k/k 0 ~ 10. In the present case, we have d/λ = 0.005, so our system should be more tolerant to loss, and still achieve higher resolution. We have used their formula to calculate the transfer function for our sample thickness, with values of μ = 0.1, 0.2 and 0.3 in addition to the predicted value of These are shown as the continuous curves in Figure 20. To measure the transfer function, we replaced the two sources by a single source, and carried out a line scan in the image plane. These data were then Fourier transformed to generate the transmission as a function of transverse wavevector, and the resulting points are also plotted in Figure 32. From these plots, it appears that the effective value of μ is about Nevertheless, it is clear that our sample does indeed give sub-wavelength imaging, with a resolution limit of k/k 0 ~ 70. In conclusion, by using a suitable magnetic metamaterial (made of swiss rolls) that has quite low loss when μ = -1, we have demonstrated that sub-wavelength imaging with a resolution of λ/70 can be achieved.

47 DALHM Final report Page Transmission Function τ Measured mu" = 0.1 mu" = 0.14 mu" = 0.2 mu" = Transverse Wavevector (k/k 0 ) Fig. 32: Measured (points) and calculated (lines) transmission function for a 60 mm slab of metamaterial with μ = -1 at MHz. 6) Demonstration of complementary media using RF metamaterials The way that a medium with n = -1 compensates for vacuum with n = +1 can be generalized, so that a medium with any arbitrary distribution of μ and ε can be exactly compensated by a second medium with the negative of that distribution (see DALHM reports). Moreover, in the extreme near field, we need only to consider the variation of μ or ε, as appropriate. In particular, a slab of material with μ x = +1, μ z = - 1 should exactly compensate a slab with μ x = -1 and μ z = +1. These can both be constructed from the Wall that we described in the previous section, by separating the longitudinal and transverse rolls, and reassembling them as separate slabs to form an XZ Double Wall, as shown in Figure 33. X - Wall Z - Wall Y X O Z Fig. 33: Schematic diagram of the two anisotropic slabs that comprise the double wall. In the X Wall, the elements are aligned parallel to the x axis, whereas for the Z Wall they are parallel to the z axis; the source generates a field H z.

48 DALHM Final report Page 48 These two slabs, the X Wall and the Z Wall have been assembled, maintaining the element packing that was used in the 2-D isotropic wall used for the RF imaging work, and their performance has been measured. Preliminary modelling showed that the field pattern on the input face is indeed reconstructed on the output face when the permeabilities are μ = ±1. As before, however, we do not know the exact frequency when this condition is met, so we have used the simulation to guide us. We have calculated the field distribution on the exit face arising from a line source placed 5 mm from the input face, both for the individual walls and their combination, as a function of frequency. We can then compare these with the measurements and hence determine the correct frequency of operation. The simulation results (using MicroWave Studio) are shown as the top row in Figure 34. As has been shown in the past (see DALHM reports), the modes inside the medium are conical: the cone angle depends on the size of the permeability and its sign on the sign of the anisotropy. Accordingly, we expect the Z-wall result (Figure 34B) to have a strong central peak at the resonant frequency, and at higher frequency we expect the pattern to consist of two peaks whose spacing increases as the frequency increases. When the permeability passes through zero, no intensity is transmitted because there is an infinite impedance mismatch between the medium and vacuum. The X-wall result should be the complement of this pattern, with the two peaks well-separated at low frequency, and coming together as the frequency is increased. When the active μ = -1, at 24.3 MHz (dashed line in Figure 34 A and B), the materials should match, and the peaks should be at the same distance in the two cases.

49 DALHM Final report Page 49 A B C D Fig. 34: Plots of H z field distribution along the exit face of anisotropic walls as a function of frequency, arising from a line source on axis. Simulated results for (A) the X-wall and (B) the Z-Wall (the dashed line shows the frequency when μ = -1). Measured result for (C) the X-wall and (D) the Z-wall. The experimental result for the Z-Wall is quite similar to the simulation, except for the region at high frequency where no intensity is predicted in the model. In the negative μ regime, two peaks are observed, whose frequency dependence matches the prediction. However, the data for the X-Wall is more problematic. In the 2D isotropic wall, the transverse rolls were held slightly apart to balance their permeability with that of the longitudinal rolls, and this structure was initially maintained in the present experiment. This led to the X-wall data being dominated by signal from the ends of the rolls. The wall was re-configured so that the rolls were nearly continuous in the transverse direction. The data still showed flux leaking from the joints between the rolls, but to a lesser extent than before. This was overcome by considering the spectrum at each x-point, and normalising to its maximum intensity; this normalised distribution is shown in Figure 34C, and shows a promising similarity to the simulated result. However, re-packing the material to remove the gaps between the rolls has increased the filling factor and altered the frequency at which μ x = -1 (note the larger frequency range in Figure 34C), so that it no longer matches that of the Z-Wall. Further work is required to re-balance the materials. References: 1) P. Vodo, P. V. Parimi, W. T. Lu and S. Sridhar. Appl. Phys. Lett. 86, (2005) 2) C. A. Balanis Antenna Theory: Analysis and Design (Wiley, New York, 1997). 3) I. Bulu, H. Caglayan, and E. Ozbay Appl. Phys. Lett. 83, 20 (2003). 4) Irfan Bulu, Humeyra Caglayan, and Ekmel Ozbay, Opt. Lett. 30, 3078 (2005) and references there in.