Classes offered by faculty of Nano-Optics and Optoelectronics Research Laboratory

MIC631 Computational Electrodynamics

Instructor: Dr. Jaime Viegas, Dr. Anatoly Khilo
Next time offered:  n/a

Brief description:

This course covers principles and applications in electromagnetic device and material modeling and simulation. The most commonly used numerical methods for optical/microwave devices modeling are approached: finite-element, beam-propagation, finite-differences, finite-difference time-domain and boundary element methods. Also, application of finite-element and boundary element methods to quantum mechanics problems of technical interest is addressed.

Lecture schedule, by week:

Week 1: Introduction and overview; course description and structure; overview of Maxwell's equations, wave equations, Poynting vectors and boundary conditions for electromagnetic fields.
Week 2: Analytical methods for waveguide analysis: effective index method and Marcatili's method.
Week 3: Finite element methods (FEM): variational and Galerkin methods; area coordinates and triangular elements; derivation of eigenvalue matrix elements and boundary conditions.
Week 4: Finite-difference methods (FDM): approximations and finite-difference expression of wave equations; boundary conditions.
Week 5: Beam propagation methods (BPM): Fast Fourier Transform BPM, finite difference BPM, wide angle analysis using Pade approximant operators; three-dimensional semivectorial analysis; three-dimensional fully vectorial analysis.
Week 6: Finite-difference time domain method (FDTD): discretization of electromagnetic fields; stability condition; absorbing boundary conditions.
Week 7: Finite-difference time domain method in non-linear, dispersive media.
Week 8: Midterm exam.
Week 9: Schrödinger equation: time-dependent state, finite-difference analysis of time-independent state; finite-element analysis of time-independent state.
Week 10: Computational quantum mechanics applications: Quantum mechanical tunneling calculations with the FEM; quantum states in asymmetric wells.
Week 11: Wavefunction engineering: k·P theory of band structure. Designing mid-infrared lasers.
Week 12: Quantum wires and FEM; symmetry properties of the square wire; checkerboard superlattice (CBSL); optical nonlinearity in the CBSL.
Week 13: Quantum waveguides: quantization of resistance; the straight waveguide; quantum bound states in waveguides; the quantum interference transistor.
Week 14: The boundary element method (BEM): introduction; the boundary integral; numerical issues; multiregion BEM; application to 2D electron waveguides
Week 15: The BEM and surface plasmons: bulk and surface plasmons; surface-enhanced Raman scattering.
Week 16: Final Exam.


  • 20% Homework
  • 20% Midterm exams
  • 30% Computer Project
  • 30% Final exam