Polarization Of Plane Waves

The polarization of an uniform and plane wave describes the time changing behaviour of the electric field in a given point of the space. As we saw in our Maxwell’s equations post, we can obtain the magnetic field from the electric one.

TYPES OF POLARIZATION

Linear Polarization

The electric field vector of the plane wave keeps fixed in a given direction.

Elliptical Polarization

It’s the superposition of two waves linearly polarized, with orthogonal directions and a phase shift of 180º. The vector of the electric field is the sum of the two linearly polarized waves in spatial and temporal quadrature and which have different amplitudes.

In this type of polarization there are two types of movements:

In the right polarization, the waves move clockwise.

In the left polarization, the waves move counter clockwise, as in the following image:

Circular Polarization

This is a particular case of the elliptical polarization, with a phase shift of 90º. In addition, the waves’ amplitudes are the same. The following image shows an example of right circular polarization:

 

POLARIZATION PRACTICE EXERCISE

A plane wave as the following electric vector component:

What is the type of polarization? Determine if it’s right or left polarization.

SOLUTION

The first step when determining the type of polarization is to obtain the phase shift between both orthogonal components that form the field vector. In the case the field is not written as a sum of two orthogonal components, it could be because there is only one component and it’s a linear polarization.

However, it could be the case where the two components are not clearly separated. In these cases, we need to write an orthogonal base b1 and b2 (both orthogonal with respect each other)  and write the field vector as a function of that base:

 

Therefore, we can separate the two components in order to calculate b1 and b2:

 

As we can observe, none of the components is zero and their absolute values or module are different.

In this case, we have a elliptical polarization.

Now, in order to determine if it’s right or left polarization, we make kz=0:

By plotting the direction of movement of the base components, we can observe that we have a right elliptical polarization:

We hope this post helped you to understand a bit more about the polarization phenome! Our next post in this section will be highly related to this study: it’s the reflexion and Snell’s Law.

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