# Polarization and Azimuthal Angle

## Homework Statement

Determine the state of polarization of the following wave and its azimuthal angle:

##E= \sqrt{3} E_0 \cos(kz-\omega t) \hat{x} + E_0 \cos(kz- \omega t + \pi) \hat{y}##

## The Attempt at a Solution

How do I calculate the azimuthal angle? My textbook only says: "the azimuthal angle is defined as the angle between the plane of vibration and the plane of incidence". Since no diagrams are provided I'm not sure if I understand it correctly... Is this the angle it makes with the x-axis if it is linearly polarized (or if elliptically polarized, the angle of the major axis with respect to the x-axis)?

I think the state of polarization is linearly polarized since Ey lags Ex by π, right? Also the Ex has a greater amplitude than Ey by a factor of √3.

Any help is greatly appreciated.

It doesn't give the definition of the "azimuthal angle". I believe it's the angle θ I've marked in the attached diagram. How can it be calculated?

#### Attachments

• 2013-09-23 01.58.18.jpg
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How do I calculate azimuthal angle for this wave? I know it's not 45° because ##E_x \neq E_y##. Is it valid to use trig like this:

##\tan \theta = \frac{E_y}{E_x} = \frac{E_0}{\sqrt{3} E_0} \implies \theta = 30°##

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