Polarization of light using Mueller matrix

[Nur Ziadah]

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.

 

[Andy Resnick]

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)?

 

[Nur Ziadah]

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.

 

[Andy Resnick]

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.

 

[Nur Ziadah]

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.