# Polarization and Azimuthal Angle

• roam
In summary, the conversation discusses determining the state of polarization and azimuthal angle of a given wave. The definition of the azimuthal angle is provided as the angle between the plane of vibration and plane of incidence. The individual then asks for clarification on how to calculate the azimuthal angle and suggests using trigonometry to find it. They also mention that the state of polarization is linear, with the electric field in the y-direction lagging behind the x-direction by π and the amplitude of the x-direction being greater than the y-direction by √3.

## 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.

UltrafastPED said:

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?

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• 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°##

Last edited:

I would suggest using the Jones calculus method to determine the state of polarization and azimuthal angle of the given wave. This method involves using a matrix representation of the electric field components to calculate the polarization state and angle.

To calculate the azimuthal angle, you can use the following formula:

θ = tan^-1(Ey/Ex)

Where Ey and Ex are the amplitudes of the electric field components along the y and x axes, respectively.

In this case, the state of polarization is indeed linear, as Ey lags behind Ex by π, indicating a phase difference of 180 degrees. The azimuthal angle can be calculated as:

θ = tan^-1(1/√3) = 30 degrees

This means that the wave is linearly polarized at an angle of 30 degrees with respect to the x-axis.

It is important to note that the azimuthal angle can also be calculated using the complex representation of the wave, known as the Stokes parameters. However, the Jones calculus method is simpler and more straightforward in this case.

I hope this helps in understanding the concept of polarization and azimuthal angle.

## 1. What is polarization?

Polarization is the orientation of electromagnetic waves in a specific direction. It describes the direction of the electric field vector in relation to the direction of wave propagation.

## 2. How is polarization measured?

Polarization is measured using a polarimeter, which is an instrument that can detect the orientation of the electric field vector of the incoming wave. This measurement is usually represented by a value between 0 and 180 degrees.

## 3. What is the difference between linear and circular polarization?

Linear polarization refers to waves that have their electric field vector oscillating in a single plane, while circular polarization refers to waves that have their electric field vector rotating in a circular motion. Linear polarization can be either horizontal or vertical, while circular polarization can be either clockwise or counterclockwise.

## 4. How does polarization affect the propagation of electromagnetic waves?

Polarization affects the propagation of electromagnetic waves by determining the orientation of the wave as it travels through space. Different polarizations have different effects on how the wave interacts with other objects and media, such as reflections, refractions, and diffraction.

## 5. What is the azimuthal angle in relation to polarization?

The azimuthal angle is the angle between the direction of propagation of the wave and a reference direction, usually the x-axis. In polarization, the azimuthal angle is used to describe the direction of the electric field vector in relation to the direction of wave propagation.