Expressing plane wave as superposition

[Ishida52134]

Homework Statement

So, given a unpolarized monochromatic plane wave E = summation ai cos(kz - wt + bi), i from 1 to N where b is a phase constant. how would you describe this as the superposition of a right handed and left handed polarized beam?

Homework Equations

Er = Acos(kz-wt+phi1) + A sin(kz-wt+phi1)
El = Acos(kz-wt+phi2) - Asin(kz-wt+phi2)

The Attempt at a Solution

I know if I add both up I would get a linearly polarized wave.
I'm not sure how to write the sum as such a summation. Would you use the fact that any finite linear combinations of cosine terms can add up to the sum which would show that the summation can be written in terms of one cosine function?

 

[Simon Bridge]

Have you tried expanding each term in the sum as a linear sum of specific Er and El.

 

[Ishida52134]

I think it'd be the superposition of one right and one left circular polarized beam that describes the whole summation.

 

[Simon Bridge]

Good luck with that.