# Expressing plane wave as superposition

1. Oct 19, 2013

### Ishida52134

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
Er = Acos(kz-wt+phi1) + A sin(kz-wt+phi1)
El = Acos(kz-wt+phi2) - Asin(kz-wt+phi2)

3. 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?

Last edited: Oct 19, 2013
2. Oct 19, 2013

### Simon Bridge

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

3. Oct 20, 2013

### Ishida52134

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

4. Oct 20, 2013

### Simon Bridge

Good luck with that.