Semi major and minor axis of polarization ellipse

[henil]

how can he we derive equations for semi major and minor axes of the polarization ellipse?

 

[DrDu]

From what?

 

[samcarano]

Use these equations

to derive this equations

I just thought of one delta as dy-dx so only one of the first 2 equations actually has a delta in it
Rearranged one of the first equations, the one that no longer has a delta in it, for Ex/Ax=cos(wt-kz)

I then used a few trig identities on the second equation

squared the result then substituted the rearranged equation 1 into the cos(wt-kz) spot and the cos2(wt-kz) spot to get equation 3

Now to derive these equations from the result which are the semi major axis and semi minor axis

just use a rotation martix

where x'=a, y'=b, x=Ax, y=Ay and square each component

This is where I am stuck as I do not have the cos(delta) in the final answer so anyone that knows better can help you (and me) with the correct answer