Circularly polarized waves as an orthonormal state

[Hammed]

Homework Statement

Show that any plane wave can be written as the sum of a left-circularly polarized wave and a right-circularly polarized wave of suitable amplitudes and phase

Homework Equations

The Attempt at a Solution

If I assume the plane wave polarizes in the z direction. It is possible to split amplitudes of waves into the x-component and y-component, after which, I do not know how to proceed with the question any longer.

 

[kuruman]

Can you write expressions for the E-vectors for right and left circularly polarized waves? If so, add them and see what you get. At some point you may have to look up trig identities.

 

[Hammed]

Can you write expressions for the E-vectors for right and left circularly polarized waves? If so, add them and see what you get. At some point you may have to look up trig identities.

Thanks, I will be able to do that.