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OSE5421

OSE6421 - Integrated Optics

Almost all real-life problems of interest involving Maxwell’s Equations have no closed-form analytical solution. Yet, on the solution of these problems hinges the successful design of many critical photonic components of our technology-driven society. The course will provide an Introduction to fundamentals of computational methods for photonic waveguide optics and integrated photonic devices. In particular, the propagation and loss characteristics in dielectric optical waveguides, fundamental concepts of both integrated and fiber optic devices, and numerical modeling of complex integrated optical components will be discussed.

Credit Hours:

  • 3 hours

Prerequisites:

  • Graduate standing or consent of instructor
  • Completion of OSE-6111, OSE6432 is strongly recommended

Reference Materials:

  1. Class notes and selected journal papers
  2. "Computational Electrodynamics: The Finite-Difference Time-Domain Method," Allen Taflove and Susan C. Hagness, Artech House, 2005, (Third Edition)
  3. "Optical Waveguide Analysis," K Kawano and T. Kitoh, Wiley, 2001
  4. Any good "Mathematical Method" textbook

List of topics

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
The RCWA in Integrated Optics
  • 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 – Stability 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
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