Maxwell’s equations can be solved analytically under certain ideal conditions, such as, Mie scattering due to infinite cylinders in 2D or spheres in 3D. Analytical solutions are important tools to check the validity of the results of numerical computations.
Reflectivity or transmissivity due to stack of thin films or 1D photonic crystals can also be computed analytically. This is a problem that has wide application in optics.
Key concepts covered include:
- Importance of analytical solutions
- Mie scattering formulations for infinite cylinders and spheres
- Approximate scattering solutions for ellipsoids
- Characteristic matrix for stack of thin films
- Using Characteristic matrix formulations to compute dispersive refractive indices of the material of a layer
- Coding in Python/Matlab and comparison of FDTD simulation results with analytical results