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: 
Finitedifference methods (FDM): approximations and finitedifference 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; threedimensional semivectorial analysis; threedimensional fully vectorial analysis.

Week 6: 
Finitedifference time domain method (FDTD): discretization of electromagnetic fields; stability condition; absorbing boundary conditions.

Week 7: 
Finitedifference time domain method in nonlinear, dispersive media.

Week 8: 
Midterm exam.

Week 9: 
Schrödinger equation: timedependent state, finitedifference analysis of timeindependent state; finiteelement analysis of timeindependent 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 midinfrared 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; surfaceenhanced Raman scattering.

Week 16: 
Final Exam.
