Transcript Slide 1
Slow light in photonic crystal waveguides Nikolay Primerov Outline • • • • • Why do we need slow light? What is slow light? Possibilities to make a slow light Slow light in photonic crystals waveguides Conclusions Doctoral program in photonics “Photonic crystals” by Romuald Houdré Nikolay Primerov Why do we need slow light? 1. Nonlinearities 2. Optical switching 3. Optical storage 4. Delay lines 5. Quantum optics T.F. Krauss, J. Phys. D: Appl. Phys. 40 (2007) 2666-2670 Z. Zhu et al., Science, 318 (2007) 748-750 F. Morichetti et al., Opt. Express, 16 (2008) 8395-8405 Doctoral program in photonics “Photonic crystals” by Romuald Houdré Nikolay Primerov What is a slow light? Doctoral program in photonics “Photonic crystals” by Romuald Houdré Nikolay Primerov What is a slow light? Pulse signal S( z, t) A e j k z t = + + + + Doctoral program in photonics “Photonic crystals” by Romuald Houdré Nikolay Primerov What is a slow light? Pulse signal S( z, t) A e j k z t d d n z t d d c dn n z t 0 c d z or t 0 Vg 1 The peak of the pulse propagates at the Group Velocity. Doctoral program in photonics “Photonic crystals” by Romuald Houdré Nikolay Primerov What is a slow light? Group velocity Group index dn ng n d dk Vg dw 1 c ng Thus, in a material and/or structure with large first order dispersion coefficient, Vg can be drastically increased Doctoral program in photonics “Photonic crystals” by Romuald Houdré Nikolay Primerov Possibilities to make a slow light Stimulated Brillouin Scattering (SBS) Stimulated Raman Scattering (SRS) Electromagneticaly induced transparency (EIT) Coherent population oscillation (CPO) Coupled ring resonators Photonic crystals and others Doctoral program in photonics “Photonic crystals” by Romuald Houdré Nikolay Primerov Slow light in photonic crystal waveguides Free space ω Periodically structured medium ω Band edge c= ω/k Medium with constant n Band gap Vg c/n= ω/k k Slow down factor S V Vg dw 0 dk π/a Maximum bandwidth d c c Vg dk ng 2 ng a w V k dw Vg dk Slow light: Science and application / editors, J.B. Khurgin and R. Tucker, 388 p. Doctoral program in photonics “Photonic crystals” by Romuald Houdré Nikolay Primerov k Slow light in photonic crystal waveguides 1)Backscattering Standing wave Slow mode optical mode is close to a resonance with the structure 2) Omnidirectional reflection No cut-off angle, mode at k≈0 slow modes of for k=0 standing wave The band edge is the most obvious place for the slow light T. F. Krauss, J. Phys. D: Appl. Phys. 40 (2007) 2666-2670 Doctoral program in photonics “Photonic crystals” by Romuald Houdré Nikolay Primerov Slow light in photonic crystal waveguides But there are some problems: 1) Dispersion curve near the gand edge is typically parabolic strong group velocity dispersion (GVD) 2) Band edge presents a cut off point propagation mode turns to evanescence mode 3) Fabrication tolerance It’s not the best region for the slow light to operate Dispersion engineering Doctoral program in photonics “Photonic crystals” by Romuald Houdré Nikolay Primerov Slow light in photonic crystal waveguides GVD handling Ng= 30, 50, 80 Section of constant group velocity over approximately 20% of Brillouin zone low GVD J.Li, T.P. White, et al. Opt. Express, 16(9) (2008), 6227-6232 Doctoral program in photonics “Photonic crystals” by Romuald Houdré Nikolay Primerov Slow light in photonic crystal waveguides Enhancement of the linear interaction Optical switching devices (for example, Mach-Zehnder configuration) Δφ=ΔkL=π Δk= Δnk0 We have to distinguish between nmat and neff Slow light regime Δk1 > fast light regime Δk2 kL k0 V Vg nmat L Slow light regime yields a large Δk for a given Δnmat Slow light coupler 5 um length with Δnmat = 4×10^-3. Conventinal coupler 200 um long T. F. Krauss, J. Phys. D: Appl. Phys. 40 (2007), 2666-2670 D. M Beggs, et al., Opt. Lett., 33 (2008), 147-149 Doctoral program in photonics “Photonic crystals” by Romuald Houdré Nikolay Primerov Conclusions Problems to overcome 1) 2) 3) 4) 5) Signal distortion by GVD Reflection losses due to modal mismatch between incident wave and guided wave Losses due to disordering in the structure Other loss sources Tunability Solutions: 1. Chirping the waveguide properties, changing the waveguide width, changing the hole size and position of the photonic lattice close to the waveguide. 2-4. Many different effects involved. Need of transition region to build up to reduce the mode-matching problem Slow light operation away from the band-edge 5. ?? Doctoral program in photonics “Photonic crystals” by Romuald Houdré Nikolay Primerov Conclusions Main Advantages: - Relatively large bandwidth from GHz up to few THz - Room temperature operation - Availability to tune the wavelength, slowdown factor and bandwidth with the structural design Main Disadvantages: - Tunability of the slowdown factor in given structure - Reflection and injection losses Doctoral program in photonics “Photonic crystals” by Romuald Houdré Nikolay Primerov Thank you for attention! Doctoral program in photonics “Photonic crystals” by Romuald Houdré Nikolay Primerov