# Polarization of light using Mueller matrix

In summary, the paper states that light can be polarized using a half wave plate, however, when the angle of polarization is changed, the polarization changes as well.
Hi everyone
First of all, I am a computer science student and I have a question regarding the polarization of light as stated in an article entitled "Multi-stage quantum secure communication using polarization hopping" by Rifai et al.,2015.
Given the Mueller matrix:

The input of light state is:

And lastly, the operation to produce the output of light after it go through a half wave plate:

After I do the calculation, the S_out for the θx=0° is [1 1 0 0] meaning that the light is horizontally polarized. However, when the θx=45°, I didn't get the vertical light polarization [1 -1 0 0] as stated in wikipedia:

This is the result of my calculation using Python programming language:

It seems that my vertical polarization of light is wrong. I hope that anyone may help me to clarify this problem.
Thank you so much & regards.

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Hi everyone
First of all, I am a computer science student and I have a question regarding the polarization of light as stated in an article entitled "Multi-stage quantum secure communication using polarization hopping" by Rifai et al.,2015.

I did a quick read of the paper, and I'm a little confused by the parameter 'θx'. How does θx relate to θA and/or θB (referring to Figure 3)?

Andy Resnick said:
I did a quick read of the paper, and I'm a little confused by the parameter 'θx'. How does θx relate to θA and/or θB (referring to Figure 3)?
θA is the rotational of half wave plate at Alice side while θB is rotational at Bob and they are unitary transformation.

θA is the rotational of half wave plate at Alice side while θB is rotational at Bob and they are unitary transformation.

Ok, I read through the paper more carefully and was able to reproduce most of their equations. I did indeed get vertical polarization for θx=45°. I'm not sure why your Python script returned a different result. Try it by hand, leaving θx as a free parameter, then after you calculate Sout, put in different values for θx.

Andy Resnick said:
Ok, I read through the paper more carefully and was able to reproduce most of their equations. I did indeed get vertical polarization for θx=45°. I'm not sure why your Python script returned a different result. Try it by hand, leaving θx as a free parameter, then after you calculate Sout, put in different values for θx.

Finally I got the true result. Something mistakes happened in my Python codes. Anyway, thank you for your explanation.

## 1. What is polarization of light?

Polarization of light refers to the orientation of the electric field of a light wave. It can be described as either linear, circular, or elliptical, depending on the direction and shape of the electric field.

## 2. What is the Mueller matrix?

The Mueller matrix is a mathematical representation of the polarization properties of a material or system. It is a 4x4 matrix that describes how the polarization state of incident light is transformed after passing through the material or system.

## 3. How is the Mueller matrix used to characterize polarization of light?

The Mueller matrix is used to analyze the polarization of light by measuring how it changes as it passes through a material. By analyzing the elements of the matrix, we can determine the polarization properties of the material, such as its degree of polarization, retardance, and diattenuation.

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

Linear polarization refers to light waves whose electric field oscillates in a single plane, while circular polarization refers to light waves whose electric field rotates in a circular motion. Linearly polarized light can be further categorized as either horizontal or vertical, depending on the orientation of the electric field.

## 5. What are some applications of polarization of light using Mueller matrix?

Some applications of polarization of light using Mueller matrix include remote sensing, biomedical imaging, and optical communication. It can also be used in materials analysis, such as determining the quality of plastics or detecting defects in crystals.

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