OSE6125 - Computational Photonics

Computational methods for photonic guided wave structures, periodic structures, and integrated photonics structures and devices.

Credit Hours: 3 hours

Prerequisite: OSE-6111 or consent of instructor.

Learning outcomes:

Upon completion of this course, students will be familiar with the most widely used computational photonics techniques including: rigorous coupled-wave analysis (RCWA) frequency-domain eigen modes approach,, finite difference frequency-domain (FDFD), and finite difference time-domain (FDTD) methods:, students will be able to identify the computational method that is amenable to a specific class of photonic structures, and the method that should be avoided except in special circumstances and develop and use basic computational codes for a variety of realistic applications in integrated photonic structures.

Reference Materials:

1. Class notes and selected journal papers
2. “Optical Waveguide Analysis,” K Kawano and T. Kitoh, Wiley, 2001
3. “Computational Electrodynamics: Allen Taflove and Susan C. Hagness, Artech House, 2005, (Third Edition)
4. Any good “Mathematical Methods” textbook

Course Requirements and Grading Policy:

• Semester Projects 75%
• Final projects 25%

Course Outline:

Review of Electromagnetic Theory and Maxwell’s Equations

• Integral Maxwell’s equations
• Time–domain differential Maxwell’s Equations and the Wave equation
• Time harmonic Maxwell’s equation and Helmholtz Equations

Optical Waveguides

• Slab waveguides
• Multi-layer slab waveguides
• Numerical computations of the modes and field distribution
• Channel Waveguide and the effective index technique

Periodic Structures

• One and two-dimensional grating structures
• Modal Approach
• Rigorous Coupled-Wave Analysis (RCWA)
• Eigenmode formulation
• S-matrix approach in layered periodic structures
• Diffraction efficiency and field distribution within the structure
• Guide-mode resonant (GMR) devices

The RCWA in Integrated Optics

• The modal approach and effective medium theory
• Guide-mode resonant (GMR) devices
• Artificial periodic structures
• Perfect matching layers and absorbing boundaries
• Application to integrated waveguide output grating coupler

Finite Difference Analysis

• Finite difference approximations
• Taylor expansions for deriving math operators
• Absorbing boundary conditions, perfectly matched layers
• Eigenmode formulation
• Scattering matrices for discontinuities

Beam Propagation Methods

• FFT Beam Propagation Method (FFT-BPM)
• Finite Difference Beam Propagation Method (FD-BPM)
• TE and TM Formulations – equidistant discretization – mtability condition
• Transparent boundary condition

Finite-Difference Time-Domain Method:

• Discretization of the electromagnetic fields
• Yee grid
• Absorbing boundary condition
• Stability conditions, rate of conference, resolution, numerical artifacts