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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