Modeling and Simulation of Photonic Devices and Circuits I (Passive Devices and Circuits) A course on: Optical wave and wave propagation Material optical property Optical waveguide Numerical solution techniques Photonic device and circuit design and analysis examples

Course Outline Introduction Maxwell’s equations Material optical property Numerical solution technique I - FDTD Wave equation and wave propagation Reflection and refraction Optical waveguide and resonator Numerical solution technique II - Mode solver and mode matching Optical diffraction Numerical solution technique III - Ray tracing and BPM Photonic device and circuit design and modeling examples Beam splitter (Y and MMI) Wavelength demultiplexer (AWG) Optical filters (MZ, ring, and grating) Polarization rotator

Introduction - Motivation Increased complexity in component design to meet the enhanced performance on demand Monolithic integration for cost effectiveness - similarity to the development of electronic integrated circuits Maturity of fabrication technologies Better understanding on device physics Maturity of numerical techniques Unlimited computing resources – from parallel/grid to cloud computing which leads to the recent rapid progress on the computer-aided design, modeling and simulation of photonic devices

Introduction - Motivation Conventional Approach New idea New idea Computer-aided design and modeling “Back of envelop” design Simulation Experiment (costly) Works? No (very likely) Yes Works? No (very likely) Experiment (costly) Yes End Works? No (less likely) Effective Approach Yes End

Introduction - Physics Processes in Photonic Device Potential and carrier distribution (Poisson and continuity equations) Bias I(t) or V(t) Material optical property Temperature distribution (Thermal diffusion equation) Ambient temperature T(t) Optical field distribution (Maxwell’s equations) Optical input Optical output

Comparison - Physics Processes in Optoelectronic Device Bias I(t) or V(t) Ambient temperature T(t) Potential and carrier distribution (The Poisson and continuity equations) Temperature distribution (The thermal diffusion equation) Material gain and refractive index change (The Heisenberg equation) Band structure (The SchrÖdinger equation) Optical field distribution (The Maxwell’s equations) Output Recombinations Saturation and detuning

Introduction – from Devices to Circuits Device level: Optical field distribution (Maxwell’s equations) Optical input Optical output Parameterization: S-matrix extraction Layout: topology analysis Circuit analysis: from S-matrix to T-matrix Device 1 Device 2 Device 3 Circuit Device 4 Device N

Introduction - Description of Physics Processes From external bias to carrier and potential distribution – carrier transport model (Maxwell’s equations in its quasi-static electric field form) From ambient temperature to device temperature distribution – thermal diffusion model Material model (usually empirical or phenomenological) From material optical property and 3D waveguide geometrical structure to wave propagation and device function – Maxwell’s equations in its full dynamic form

Introduction - Course Organization Lectures: Maxwell’s equations: 6 hours Material optical property: 1.5 hours Numerical solution technique I - FDTD: 1.5 hours Wave equation and wave propagation: 1.5 hours Reflection and refraction: 1.5 hours Optical waveguide and resonator: 3 hours Numerical solution technique II – Mode solver and mode matching: 1.5 hours Optical diffraction: 1.5 hours Numerical solution technique III – Ray tracing and BPM: 3 hours Photonic device and circuit design examples: 9 hours Total: 30 hours Reference books: Jackson’s Classical Electrodynamics Marcuse’s Theory of Dielectric Optical Waveguides Born and Wolf’s Principles of Optics Huang’s PIER 10 and 11 – Methods for Modeling and Simulation of Guided-Wave Optoelectronic Devices Assessment: 4 assignments: 20% FDTD minor project: 40% Choose one of the following 4 minor projects: 40% (1) Mode solver (2) Mode matching (3) BPM (4) Ray tracing