2D FDTD of a region having two different permittivities

Youtube links:
http://www.youtube.com/watch?v=UypOjW4flSw
http://www.youtube.com/watch?v=9iJ2jSU8Y00

Written for Course :-
Computational Electromagnetics, Fall 2011
Department of Electrical Engineering
Indian Institute of Technology Madras (IITM)
Chennai - 600036, India

Authors :-
Sathya Swaroop Ganta, B.Tech., M.Tech. Electrical Engg.
Kayatri, M.S. Engineering Design
Pankaj, M.S. Electrical Engg.
Sumantra Chaudhuri, M.S. Electrical Engg.
Projesh Basu, M.S. Electrical Engg.
Nikhil Kumar CS, M.S. Electrical Engg.

Instructor :-
Dr. Ananth Krishnan
Assistant Professor
Department of Electrical Engineering
Indian Institute of Technology Madras
http://www.ee.iitm.ac.in/~ananthk

Description :-

A 2D TM wave containing the xy-plane polarized magnetic field having components Hy and Hx and z-polarized electric field Ez. The fields are updated at every timestep, in a unitless space, where all physical parameters of free space are normalized to 1. The update is done using standard update equations obtained from the difference form of Maxwell's curl equations. The field points are defined in a grid described by Yee's algorithm. The H fields are defined at every half coordinate of spacesteps. More precisely, the Hx part is defined at every half y-coordinate and full x-coordinate and the Hy part is defined at every half x-coordinate and full y-coordinate and E fields i.e the Ez part is defined at every full x and full y-coordinate points. Also, the time update is done using Leapfrog time-stepping. Here, H-fields i.e Hx and Hy are updated every half time-step and E fields i.e Ez are updated every full time-step. This is shown by three alternating for-loop updates in groups of two (for H) and one (for E) spanning entire spatial grid inside a main for-loop for time update spanning the entire time-grid. A source of electric field is defined at the center (vertical line) of the spatial domain, which is hard , in that it does not change its value due to interference from external fields i.e in other words, the source is a perfect electric conductor. The form of the source can be varied using the variables sine, gaussian and impulse. The source is available in four standard forms- Gaussian and Sinusoidal forms. The permittivity on the two sides of the vertical line source is different to show difference in traveling velocity and wavelength in the two materials.