Sinusoidal Plane-wave Solutions of The Electromagnetic Wave Equation - Plane Waves

Plane Waves

The plane sinusoidal solution for an electromagnetic wave traveling in the z direction is (cgs units and SI units)

for the electric field and

for the magnetic field, where k is the wavenumber,

is the angular frequency of the wave, and is the speed of light. The hats on the vectors indicate unit vectors in the x, y, and z directions.

The plane wave is parameterized by the amplitudes

and phases

where

.

and

.