1 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 examples

2 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

3 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

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

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

6 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 Schr Ö dinger equation) Optical field distribution (The Maxwell’s equations) Output Recombinations Saturation and detuning

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

8 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

9 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