Slow Light Waveguide Optimization

Transcription

1 Slow Light Waveguide Optimization Sebastian Dütsch, Corrado Fraschina, Patric Strasser, Roman Kappeler, Peter Kaspar, Heinz Jäckel Communication Photonics Group, Electronics Laboratory Patric Strasser, CPG, IfE, ETHZ 21. August 2008

2 Photonic Crystals (PhC) Periodic modulation of the refractive index Vertically guided by slab waveguide structure (InP n=3.17 / InGaAsP n=3.35 / InP n=3.17) Deeply etched holes in a triangular array (diameter ~250nm, depth >3μm) Devices Introducing defects into the lattice Omitting holes, shifting holes, changing hole size Waveguides, splitters, Future: Active devices (SOA) Area-size is the driver for success Requires slow-light 21 August 2008 Patric Strasser, CPG, IfE, ETHZ 2

3 Slow-Light Modes Dispersion W1 waveguide Along waveguide direction 21 August 2008 Patric Strasser, CPG, IfE, ETHZ 3

4 Slow-Light Modes (even) slowlight regimes Dispersion W1 waveguide slow-light Slow-Light Modes Stronger light-matter interaction Slow light smaller devices High propagation losses Difficult to couple in Along waveguide direction Slow down factors up to 300 measured [1] Simulations show: ν g 0 21 August 2008 Patric Strasser, CPG, IfE, ETHZ 4

5 Overview Part 1: Incoupling into slow light Optimization by the use of a genetic algorithm Reduction of the calculation time Part 2: Loss reduction of slow-light waveguides Wide waveguides Extension of the gap map concept to detect slow-light modes 21 August 2008 Patric Strasser, CPG, IfE, ETHZ 5

6 Incoupling into Slow-Light Modes Difficult due to Mode mismatch Group velocity (refractive index) mismatch Published solutions: Intuitive approaches (Tapers, butt-coupling) but PhC s are not very intuitive Can we do it better? genetic algorithm 21 August 2008 Patric Strasser, CPG, IfE, ETHZ 6

7 Simulation Ridge WG Interface W1 PML COMSOL (FEM) 2D No time evolution Scripting interface Simulation setup Automatic generation by scripts (No user interaction required) PML adaptation (Suppress reflections) Interface reflections (Area integration method) power flow (x-direc., time avg.) magnetic field (z-comp) 21 August 2008 Patric Strasser, CPG, IfE, ETHZ 7

8 Genetic Algorithm (GA) Fitness-function: Evaluates the quality of the solution Averaged transmission for 3 frequencies Breeder Algorithm init. population with random solutions (e.g., 50) start iteration: random selection of two recombination by crossing mutation evaluation by a fitness function Better than worst in population? next iteration 21 August 2008 Patric Strasser, CPG, IfE, ETHZ 8

9 Challenges Fitness-function Only 3 frequencies investigated (broadband/accuracy vs. calculation speed) Reflections at the interface require area integration method GA parameters Adaptive mutation rate constant mutationrate: best in population worst in population adaptive mutationrate: 21 August 2008 Patric Strasser, CPG, IfE, ETHZ 9

10 Result Examples GA Holes with variable diameters References (Literature) Linear taper: Butt coupling: Shift holes along the y-direction Lattice constant tapering [Krauss] 21 August 2008 Patric Strasser, CPG, IfE, ETHZ 10

11 Transmission Spectra Simulation results: good transmission achieved by using a GA quite narrow band (requires more probed frequencies) Probed frequencies 10nm 21 August 2008 Patric Strasser, CPG, IfE, ETHZ 11

12 Overview Part 1: Incoupling into slow light Optimization by the use of a genetic algorithm Reduction of the calculation time Part 2: Loss reduction of slow-light waveguides Wide waveguides Extension of the gap map concept to detect slow-light modes 21 August 2008 Patric Strasser, CPG, IfE, ETHZ 12

13 How to Design a Slow-Light Waveguide? Slow-light waveguides suffer from tremendously high losses Reducing losses is deciding for their usability Reduce losses by wider waveguides Assumption: Wider waveguides have lower losses (observed also by comparison of a W1 to a W3) Relaxed condition for electrical contacts on top of the waveguide Losses cannot be included into the optimization (theoretically not well understood) Boundary conditions Slow light Single mode waveguide (Producibility) 21 August 2008 Patric Strasser, CPG, IfE, ETHZ 13

14 Extension of the Gap Maps for Waveguides Simulation of all possible waveguide types (e.g. waveguide width) creates huge amount of data (dispersion diagrams) Aggregation of the data into one single viewgraph Plot density of states against frequency Slow-light modes have a high density of states easy to identify classical gap map for undisturbed PhC 21 August 2008 Patric Strasser, CPG, IfE, ETHZ

15 Gap Maps Contain Condensed Informations slow light region of a guided mode slow light region of a guided mode 21 August 2008 Patric Strasser, CPG, IfE, ETHZ 15

16 Gap Maps and Design Parameters SM disappears SM disappears 21 August 2008 Patric Strasser, CPG, IfE, ETHZ 16

17 Optimized Waveguide Designs Use knowledge about the individual parameters to restrict the search area for a rigorous parameter sweep single-mode W1.3 Lattice constant: 332nm Channel width: 489nm - Increased by 113nm Single-mode band: 55nm W1.4 W August 2008 Patric Strasser, CPG, IfE, ETHZ 17

18 Summary and Conclusions The slow-light modes are a key feature of photonic crystals Loss problem must be solved Incoupling optimization by a GA Find the proper GA parameters Reduce calculation time per generation Wider waveguides beneficial An extension of the gap map concept will help to find useable slow-light modes 21 August 2008 Patric Strasser, CPG, IfE, ETHZ 18

19 Questions? References: [1] Y. A. Vlasov, et al., Active control of slow light on a chip with photonic crystal waveguides, Nature [Krauss] J. P. Hugonin, T. F. Krauss, et al., Coupling into slow-mode photonic crystal waveguides, Opt. Lett. 21 August 2008 Patric Strasser, CPG, IfE, ETHZ 19