Question

Consider a right circularly polarized light and a left circularly polarized light having common angular frequency and wave number both propagating in the z - direction. a). Write out the appropriate expressions representing right circularly polarized light and a left circularly polarized light respectively. b) Combine the two waves and state the conditions under which the combination to yeild a plane wave.

Answer 1

Here is the solution to the problem:

A) To create circularly polarized light, we must be able to control the relative phase of the x- and y- components.

We can do so by selecting the proper material such that linearly polarized light will travel at different velocities

along two transverse axes. We begin with the following expression:

Considering a shift of 90° the wave can now be represented as

The equivalent forms for right and left circulary polarized waves are respectively:

B) Combining the equations we get

In this case there is no phase shift (0°) resulting in a plane wave.