Electromagnetically Induced Transparency with Hybrid Silicon-Plasmonic Travelling-Wave Resonators

Transcription

1 XXI International Workshop on Optical Wave & Waveguide Theory and Numerical Modelling April 2013 Enschede, The Netherlands Session: Nanophotonics Electromagnetically Induced Transparency with Hybrid Silicon-Plasmonic Travelling-Wave Resonators D. Ketzaki, O. Tsilipakos, T. V. Yioultsis, E. E. Kriezis Aristotle University of Thessaloniki Department of Electrical & Computer Engineering

2 Presentation Outline Introduction Plasmonic waveguides Conductor-Gap-Silicon (CGS) waveguide CGS-based passive components CGS-based travelling-wave resonator filters Microring resonator filters Comparison with coupled mode theory Microdisk resonator filters Electromagnetically Induced Transparency Two-microring-resonator structure Comparison with coupled mode theory Two-microdisk-resonator structure Tunability / Switching Capabilities Conclusion Friday, 19 April

3 Introduction Plasmonic Waveguides Surface Plasmon Polaritons (SPP): Transverse magnetic (TM)-polarized optical surface waves 2D Plasmonic Waveguides: SPP mode is confined in the plane transverse to the direction of propagation Trade-off between mode confinement and propagation losses Trade-off overview Berini & De Leon, Nat. Phot., 2012 Stripe Channel / Gap Dielectric Loaded Hybrid W>λ Η < λ/10 W Η ~ (λ/3) 2 gap < λ/10 Long-Range SPP (L prop >1mm) but very poor confinement Excellent confinement, but dramatic losses. Fabrication issues Fair compromise between stripe & channel, but still not good enough Low-index gap material interplay High confinement, limited losses, Friday, 19 April

4 Introduction Hybrid Plasmonic Waveguides Key idea: low-index dielectric gap sandwiched between a high-index medium and a conductor. Electric field highly confined in the low-index sub-wavelength layer High-index (~3.5) Merging with silicon platform Oulton et al., 2008, Nature Photonics. Wu et al., 2010, Optics Express CGS: Conductor-Gap-Silicon Concept: Dielectric cylindrical nano-wire separated by a metallic half-space with a dielectric gap - Planar version - Efficient coupling with underlying SOI-waveguide Friday, 19 April

5 Dept. of Electrical & Computer Engineering Aristotle University of Thessaloniki Introduction CGS waveguide - Modal characteristics Ex nsio2 = 1.45 Ey Ez Modal characteristics of the quasi-tm fundamental mode: nsi = 3.48 Ey dominant component nag = i Confinement in the SiO2 gap Small effective mode area: Aeff = μm2 Effective refractive index: 1550nm : i Low propagation losses (Lprop 60 μm) Axial component in Si region Strong optical field confinement and limited propagation losses Friday, 19 April

6 Introduction CGS-based components Passive CGS-based components: Wu et al., Opt. Express 18, 2010 Taper Couplers Waveguide Bends Splitters Song et al., J. Opt., 2011 Chu et al., J. Opt. Soc. Am. B, 2011 Wavelength-selective components Ring/Disk resonators Add-drop filters Friday, 19 April

7 Outline Introduction Plasmonic waveguides Conductor-Gap-Silicon (CGS) waveguide CGS-based passive components CGS-based travelling-wave resonator filters Microring resonator filters Comparison with coupled mode theory Microdisk resonator filters Electromagnetically Induced Transparency Two-microring-resonator structure Comparison with coupled mode theory Two-microdisk-resonator structure Tunability / Switching Capabilities Conclusion Friday, 19 April

8 Dept. of Electrical & Computer Engineering Aristotle University of Thessaloniki Microring Resonator Eigenvalue Analysis Sub-micron resonator footprint Eigenvalue analysis results λ (nm) Azimuthal mode number (m) Q Outer ring radius: 930 nm Re(Ey) on a mid - plane of SiO2 gap m=8 Relatively high intrinsic Q At 1556 nm Q=355 z m=7 m=6 x Modes tightly confined Candidate for filtering applications Friday, 19 April

9 Dept. of Electrical & Computer Engineering Aristotle University of Thessaloniki Microring Resonator Lightwave filtering (1/2) Radius=0.93 μm 2 gap=120 nm Critical coupling achieved 1 3 Re(Ey) on the mid-plane of the SiO2 gap High loaded quality factors: Q>120 Free Spectral Range: ΔλFSR 140nm Minimal insertion loss (IL < 0.2 db) Efficient lightwave filtering Friday, 19 April 2013 z x 9

10 Microring Resonator Lightwave filtering (2/2) Comparison between propagation and eigenvalue analysis Eigenvalue Analysis (unloaded) Azimuthal mode number m = 7 Eigenvalue Analysis (loaded) Propagation Analysis Eigenvalue Analysis (unloaded) Azimuthal mode number m = 8 Eigenvalue Analysis (loaded) Propagation Analysis λ res (nm) Quality Factor In the presence of the bus waveguide the resonance wavelength is slightly reduced (Coupling-Induced resonance Frequency Shift-CIFS) whereas the quality factor decreases due to coupling. Resonance wavelengths and quality factors for the loaded eigenvalue problem and the propagation analysis are in very good agreement. Excellent agreement between eigenvalue and propagation results Friday, 19 April

11 Dept. of Electrical & Computer Engineering Aristotle University of Thessaloniki Filter Response Comparison with Coupled Mode Theory (1/2) Coupled Mode Theory in time si a1 (t ) κ1 st Comparison between FEM and CMT CMT fed with intrinsic and loaded quality factors 1 da (t ) = jωl a (t ) a (t ) j κ si dt τ si, st a (t ) Waveguide mode amplitudes 2 Energy stored in the cavity κ Coupling Coefficient ωl Loaded cavity resonant frequency 1/τ Decay rate for the loaded resonator Friday, 19 April 2013 Good agreement between CMT and FEM response CMT: Useful prediction tool 11

12 Filter Response Comparison with Coupled Mode Theory (2/2) CMT needs only two FEM eigenvalue analyses for each resonance Eigenvalue analysis of uncoupled ring resonator Q intrinsic Q waveguide κ Eigenvalue analysis of ring coupled to waveguide Q loaded 1/τ ω L CMT fed with eigenvalue FEM simulation results Clear indication of the transmission spectrum before the time consuming FEM simulation Beneficial for more complex structures Friday, 19 April

13 Dept. of Electrical & Computer Engineering Aristotle University of Thessaloniki Microdisk Resonator Eigenvalue Analysis (1/2) An alternative to the ring resonator Lower radiation losses (absence of inner boundary) Busy spectrum due to possible excitation of higher radial order modes Eigenvalue analysis results λ (nm) Azimuthal 8 mode number (m) Radial 1 mode number (n) Q Re(Ey) on xz-planes Submicron footprint Disk radius: 850 nm m=8 n=1 m=5 n= High quality factor At 1550 nm Q 1000 Higher radial order modes Friday, 19 April 2013 m=7 n=1 m=7 n=1 m=6 n=1 m=4 n=2 13

14 Microdisk Resonator Eigenvalue Analysis (2/2) E 2 on a vertical xy-plane y x nm nm nm nm nm nm First-radial order modes: 1, 4 Second-radial order modes: 2, 6 Photonic modes located in Si layer: 3, 5 The transmission spectrum of a filtering structure using disk resonators is expected to be more complex Friday, 19 April

15 Dept. of Electrical & Computer Engineering Aristotle University of Thessaloniki Microdisk Resonator Lightwave filtering Radius=0.85μm Footprint < 1µm2 gap=120nm High quality factors: Q>160 Minimal insertion loss (IL < 0.5 db) 1 & 4 : First-radial-order SiO2 gap modes 2 & 6 : Second-radial-order SiO2 gap modes 3 & 5 : First-radial-order Si modes Can second-radial-order modes located in the SiO2 gap be eliminated using a donut shape? Friday, 19 April

16 Dept. of Electrical & Computer Engineering Aristotle University of Thessaloniki Donut Resonator Lightwave filtering Radius=0.85μm Submicron footprint gap=120nm High quality factors: Q>160 Minimal insertion loss (IL < 0.5 db) 1 & 4 : First-radial-order SiO2 gap modes 2 & 6 : Second-radial-order SiO2 gap modes 3 & 5 : First-radial-order Si modes Second-radial-order modes located in the SiO2 gap be eliminated using a donut resonator Friday, 19 April

17 Outline Introduction Plasmonic waveguides Conductor-Gap-Silicon (CGS) waveguide CGS-based passive components CGS-based travelling-wave resonator filters Microring resonator filters Comparison with coupled mode theory Microdisk resonator filters Electromagnetically Induced Transparency Two-microring-resonator structure Comparison with coupled mode theory Two-microdisk-resonator structure Tunability / Switching Capabilities Conclusion Friday, 19 April

18 Electromagnetically Induced Transparency - EIT Photonic analogs of Electromagnetically Induced Transparency Standing-wave resonator structures Kekapture et al., Phys. R. Lett., 2010 Lu et al., Optics Letters, 2011 Lu et al., Phys. Rev. A, 2012 Travelling-wave resonators Silicon photonics Control the EIT resonance based on the adjustment of the spacing between detuned rings Xu et al, Phys. Rev. Lett., 2006 EIT-Response with hybrid silicon plasmonic travelling-wave resonators Friday, 19 April

19 Dept. of Electrical & Computer Engineering Aristotle University of Thessaloniki EIT-like Response Ring Resonators Slightly detuned resonators (R0= 1.3 μm) FEM analysis for three detuning scenarios δr = 5nm / δλres = 9nm ER Phase accumulating between the detuned resonators ϕ = ω neff s / c s m= λg mλ0 / neff For distances= Symmetric EIT-like response Friday, 19 April 2013 δλres (nm) Qpeak Extinction Ratio (db)

20 EIT-like Response Parametric Analysis Varying gap size Higher Q peak values for longer gaps but lower extinction Transmission minima change (critical coupling) Mismatched interelement spacing EIT peak moves to different directions for ±50nm mismatch. Sharper peaks suffer more from mismatched distances. Friday, 19 April

21 EIT-like Response Comparison with Coupled Mode Theory Coupled Mode Theory in time Comparison between FEM and CMT s1i κ 1 s 2r κ 1 κ 2 a () t a () t 1 2 s 2i κ 2 st δr=5nm da1 () t 1 = jωa () t a () t j κ s j κ s dt i 1 2r τ1 da2() t 1 = jω a () t a () t j κ s dt i τ 2 CMT fed with intrinsic and loaded quality factors 4(+1) eigenvalue problems solved Unloaded and loaded eigenvalue analysis for each resonator + Waveguide eigenvalue problem Good agreement between CMT and FEM response Friday, 19 April

22 Dept. of Electrical & Computer Engineering Aristotle University of Thessaloniki EIT-like Response Disk Resonators Detuned disk resonators (Ro = 0.85 μm) FEM analysis for three detuning scenarios δr=5nm / δλres=15.5nm EIT-like response Higher values of Qpeak than ring resonator configuration Observable transparency peak for even ±3nm radius detuning Friday, 19 April 2013 δλres (nm) Qpeak Extinction Ratio (db)

23 Tunability / Switching Capabilities Thermo-optic effect Si: Thermo-optic coefficient (TOC) ~ Δλ res ~ 4 nm shift for ΔΤ = 60 Κ 1560nm: Extinction ratio ~ 8dB EIT peak is replaced by a minimum transmission region 4nm Heating: Current passing through Si region E axial component located in the Si layer Heating stages Ag layer can be used 8dB Friday, 19 April

24 Conclusions Advantageous characteristics of disk resonators for filtering applications Donut structure for a cleaner transmission spectrum EIT-like spectrum responses using hybrid plasmonic travelling-wave resonators Disk resonators offer higher Q peak values Simulation responses predicted using a CMT-based analysis fed by FEM eigenvalue simulation results Tunability through thermo-optic effect - Switching capabilities This research has been co-financed by the European Union (European Social Fund ESF) and Greek national funds through the Operational Program "Education and Lifelong Learning" of the National Strategic Reference Framework (NSRF) - Research Funding Program: THALES. Investing in knowledge society through the European Social Fund. Friday, 19 April