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Quarter wave plate with added phase error (Jone matrix)

  • September 11, 2024
  • 5 replies
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Isbjoern

Hello

I want to simulate the effect of a quarter wave plate that creates an additional shift in the polarization of lets say 10° in a plarimeters. The polarimeter is comprised of a lens, collimating the polarized beam, a quarter wave plate, and an analyser plate. To determine the polarization state, the quarter wave plate is rotated azimutally by 180°. With the data I calculate the stokes parameter. It all works fine for the ideal case, but not for an added phase shift between both polarization states.
I am using the Jones matrix for the exact quarter wave plate in the form of:

A_real=1
A_img=0
D_real=0
D_img=1

the result for this quarter wave plate is as expected. The result is the same when I use, for testing purpose, the non-factored version Jones matrix of the quarter wave plate:

A_real=0.707
A_img=0.707
D_real=0.707
D_img=-0.707

Now I add to the lambda/4 phase shift an additional shift of 10° in the Jone matrix, which results in the Jones matrix in Zemax notation:

A_real=0.573576
A_img=0.819152
D_real=0.573576
D_img=-0.819152

With this Jones matrix I get a lower system transmission (stokes parameter S0) than before and a polarization degree beyond 1 (stokes parameter S1).

 

Can anyone help with getting the correct Jones matrix for an “arbitrary” phase shift (e.g. retarder plate)?

 

Best answer by Isbjoern

@David.Nguyen 

Dear David,

indeed I used the same formula. The approach to separate both retardances in Zemax is doing the trick.

Interestingly, when I matrix multiply the Jone matricies of lambda/4 and 10° mathematically and put the result into Zemax I get a wrong result. The stokes parameter “polarization degree” (S2) is bigger than one.
When I put both retardances seperately into Zemax it works. I guess Zemax does some normalization in the background that it finally results in a polarization degree (S2) below 1. This is unexpected it should, from mathematical point of view, work both ways.
Anyhow, thank you for pointing out the solution!

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5 replies

David.Nguyen
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  • September 13, 2024

@Isbjoern

 

I’ve been doing some Jones calculations with OS lately, but I’m not an expert at all. What’s your matrix definition for the retarder (10° shift)?

I’m using this formula, from this article:

To avoid calculation errors, I recommend letting OS compute the matrix product, i.e. define one Jones Matrix surface per matrix you have (1 quarter-wave plate, 1 retarder, 1 polarizer or analyzer). Also, I prefer to just have a dummy surface where I can change the parameter of interest, such as φ in Eq. 19 above, and let OS calculate the matrix using ZPL and pickup solves. Here is how I would setup the retrarder:

And I have the following ZPL solves on the A real/imag columns:

CONS_PI = 2 * ACOS(0)

phi_deg = THIC( SURC("PHASE SHIFT IN DEG ON THICKNESS") )
phi_rad = phi_deg / 180 * CONS_PI

SOLVERETURN COSI( phi_rad / 2 )
CONS_PI = 2 * ACOS(0)

phi_deg = THIC( SURC("PHASE SHIFT IN DEG ON THICKNESS") )
phi_rad = phi_deg / 180 * CONS_PI

SOLVERETURN SINE( phi_rad / 2 )

It is not the most optimal in terms of computation (you could do the deg to rad conversion once elsewhere), but I hope you get the point.

It seems to work for me. When the Thickness of Surface 1 is 0 (or 0°):

When the Thickness of Surface 1 is 10 (or 10°):

The retardance measured with CODA in the Merit Function also gives 10°:

And the Jones Matrix looks like so:

Last confirmation was a retardance of 90° since we expect circular polarization:

I hope this helps.

Take care,

 

David


Isbjoern
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  • Single Emitter
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  • Answer
  • September 13, 2024

@David.Nguyen 

Dear David,

indeed I used the same formula. The approach to separate both retardances in Zemax is doing the trick.

Interestingly, when I matrix multiply the Jone matricies of lambda/4 and 10° mathematically and put the result into Zemax I get a wrong result. The stokes parameter “polarization degree” (S2) is bigger than one.
When I put both retardances seperately into Zemax it works. I guess Zemax does some normalization in the background that it finally results in a polarization degree (S2) below 1. This is unexpected it should, from mathematical point of view, work both ways.
Anyhow, thank you for pointing out the solution!


David.Nguyen
Luminary
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  • Luminary
  • 1099 replies
  • September 13, 2024

@Isbjoern

 

No worries, its good to know that the product doesn’t work when done outside OS though. I’ve made a sort of polarimeter recently, although not with a quarter-wave plate and in the context of polarization-resolved SHG. DM me if you’re interested to share about your experience making such a device.

Take care,


David


Isbjoern
  • Author
  • Single Emitter
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  • September 13, 2024

Sorry, I marked my post as answer. It should have been your post. Do you know how to change it? You should get the credit for it.

 


David.Nguyen
Luminary
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  • Luminary
  • 1099 replies
  • September 13, 2024

@Isbjoern 

 

Don’t worry about it. As far as I know, only Ansys personnel can do it. Your answer also has meaningful information in it 😊

Have a great weekend,

 

David


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