On 'A Quarter Waveplate (QWP) rotated between 2 Polarisers'

[warhammer]

While going through the book 'Problems & Solutions in Optics and Photonics' I was having difficulty in understanding a question & have some issues about my own conceptual know-how in this regard.

The Question is: A quarter-wave plate is rotated between two crossed polaroids. If an unpolarised beam is incident on the first polaroid, discuss the variation of intensity of the emergent beam as the quarter-wave plate is rotated. What will happen if we have a half-wave instead of a quarter-wave plate?

This is the solution that they have provided (attached below).

Now I am having trouble understanding:

i) If θ is the angle made with respect to the y-axis, why the E(x') component has a "cosθ" instead of a "sinθ" (or in other words how was Resolution carried out here)

ii) Assuming it should indeed be cosθ & after making necessary QWP adjustments of π/2 in the equations, why does only the E(y) propagate here? (Is it due to the fact that it is an E Wave that's not absorbed inside?)

iii) Why did we assume that the wave is x-polarised here, as in what was the purpose for the same and what would it entail if we assume it to be y-polarised instead (will that bring changes in the equation as well)
I would be extremely grateful if someone would guide me & help me plug my conceptual holes

 

[warhammer]

While going through the book 'Problems & Solutions in Optics and Photonics' I was having difficulty in understanding a question & have some issues about my own conceptual know-how in this regard.

The Question is: A quarter-wave plate is rotated between two crossed polaroids. If an unpolarised beam is incident on the first polaroid, discuss the variation of intensity of the emergent beam as the quarter-wave plate is rotated. What will happen if we have a half-wave instead of a quarter-wave plate?

This is the solution that they have provided (attached below).

Now I am having trouble understanding:

i) If θ is the angle made with respect to the y-axis, why the E(x') component has a "cosθ" instead of a "sinθ" (or in other words how was Resolution carried out here)

ii) Assuming it should indeed be cosθ & after making necessary QWP adjustments of π/2 in the equations, why does only the E(y) propagate here? (Is it due to the fact that it is an E Wave that's not absorbed inside?)

iii) Why did we assume that the wave is x-polarised here, as in what was the purpose for the same and what would it entail if we assume it to be y-polarised instead (will that bring changes in the equation as well)
I would be extremely grateful if someone would guide me & help me plug my conceptual holes

I realized that the image I uploaded seems very blurry. Please find below better quality images.

 

[Andy Resnick]

While going through the book 'Problems & Solutions in Optics and Photonics' I was having difficulty in understanding a question & have some issues about my own conceptual know-how in this regard.

The Question is: A quarter-wave plate is rotated between two crossed polaroids. If an unpolarised beam is incident on the first polaroid, discuss the variation of intensity of the emergent beam as the quarter-wave plate is rotated. What will happen if we have a half-wave instead of a quarter-wave plate?

This is the solution that they have provided (attached below).

Now I am having trouble understanding:

i) If θ is the angle made with respect to the y-axis, why the E(x') component has a "cosθ" instead of a "sinθ" (or in other words how was Resolution carried out here)

ii) Assuming it should indeed be cosθ & after making necessary QWP adjustments of π/2 in the equations, why does only the E(y) propagate here? (Is it due to the fact that it is an E Wave that's not absorbed inside?)

iii) Why did we assume that the wave is x-polarised here, as in what was the purpose for the same and what would it entail if we assume it to be y-polarised instead (will that bring changes in the equation as well)
I would be extremely grateful if someone would guide me & help me plug my conceptual holes

Are you familiar with Jones calculus and how vectors and matrices are used to represent polarization in an optical system?

https://en.wikipedia.org/wiki/Jones_calculus

 

[warhammer]

Are you familiar with Jones calculus and how vectors and matrices are used to represent polarization in an optical system?

https://en.wikipedia.org/wiki/Jones_calculus

I have heard of the same sir but not at all familiar with it. Moreover I am not sure if I would be 'permitted' to use this in my university for instance, as this is not in the curriculum

 

[Andy Resnick]

I have heard of the same sir but not at all familiar with it. Moreover I am not sure if I would be 'permitted' to use this in my university for instance, as this is not in the curriculum

I'm not sure what you mean by 'permitted'. It's not classified information...?

Anyhow, your questions are all answered by writing out the Jones matrix for the polarizer-QWP-polarizer system. It's not hard- the wiki link has the individual matrix elements, just multiply them together and you're done.

 

[warhammer]

Apologies for an extremely delayed response.

I'm not sure what you mean by 'permitted'. It's not classified information...?

If I wasn't clear before, what I meant was because it simplifies the question largely, in the university examinations the questions come accompanied with the tagline that one has to employ the traditional methods *other than* Jones Matrices.

Hence I seeked knowledge specifically on the derivation methods specified in the snippet for I had already seen how to apply Jones Matrices for solution of such problems.