Visualization of Maxwell’s wave equation in 3-D

Introduction
Maxwell equation unifies and explains all electromagnetic phenomena. In fact, his equations are credited as being the greatest contribution towards our modern society. These equations influenced the creation of TVs, phones, transformers, electric motors, wireless and fiber optic communications. Also, Albert Einstein used Maxwell’s equation to derive and prove his theory of Relativity. In a quote taken from Feynman Lecture of Physics stated that “From a long view of the history of mankind-seen from, say, ten thousand years from now-there can be little doubt that the most significant event of the 19th century will be judged as Maxwell’s discovery of the laws of electrodynamics. The American Civil War will pale into provincial insignificance in comparison with the important scientific even to the same decade.”

Maxwell equations Historically, Maxwell used his equation to calculate the speed of light to be 3x10^6 m/s, which was experimentally validated to be correct, and had stated that his equations will allow for wireless communication, that too was validated by Hertz with the discovery of the radio wave.

Maxwell equation for time harmonics fields Maxwell equations for time-harmonics fields For this project, the time was considered as being the z axis, and thus kz in the equation above was the phase shift.

For communication purposes, the magnetic and magnetic fields become polarized. The main objective of this project is to visualize the electromagnetic wave propagating and to view how polarization changes the electric and magnetic field.

Design
The purpose of this project is to visualize Maxwell electromagnetic waves in three dimensions. Since there are an infinite amount of situations of electromagnetic waves propagation, the main focus of this design is to visualize the electromagnetic wave propagation of linear, circular, and elliptical polarization.

Objective
- Write a small Matlab program that simulates the propagation of electromagnetic fields for linear polarization, circular polarization and elliptical polarization
- Create a quick time movie to visualize electromagnetic wave propagation by using Capvte and adobe Premiere
- Create a web page to publish the results

Movie

circular

elliptical