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Coordinate system for skew gaussian beam propagation

Dirk.Broemme
Ultraviolet

Hello,

I have a question regarding skew gaussian beam propagation mode:

A simple astigmatic gaussian beam can be described by two separate caustic hyperbolas.
These two hyperbolas belong to two perpendicular planes (e.g. xz-plane and yz-plane, z:propagation direction).
The x and y-axis are parallel to the principal axes of the elliptical intensity profile of this beam.

Now let’s assume that we have a spherical convex mirror. The simple astigmatic beam hits this mirror in an arbitrary point on the spherical curved surface. Now let’s assume that the coordinate system of the beam (defined by the principal axis of its elliptical intensity profile) is not parallel to the sagittal and the tangential plane of this reflection scenario.

Which physical model does Zemax use to simulate such a scenario?
How can I get the information about the orientation of the new principal axis coordinate system of the intensity profile after reflection? I did not find any formulas in the help manual…

Does the physical model Zemax uses allow to calculate the beam parameters for the scenario I described?  From my understanding in the example I described  the simple astigmatism changes into a so called general astigmatism. For such a beam the principal axis coordinate system continously rotates when propagating in z-direction.

Can you help to bring some light into the darkness?

Thanks in advance and kind regards
Dirk

 

Best answer by PhGeek

Hi, Dirk.

Over the last couple of years I have seen (and participated in several Community discussions regarding generally-astigmatic Gaussian beams.  I’ll collect them into this post for yours (and others’) convenience.

Sequential mode:

Your question appears to be how to treat generally astigmatic beams in Sequential mode.  Paul Colbourne is definitely the Zemax expert there.  And I, too, was confused (as you can see in this thread

also discussing Non-sequential) by the “Skew Gaussian Beam” Sequential analysis feature, which as David correctly says, only treats SIMPLY astigmatic beams.  Paul’s Skew Ray technique is completely different, and his latest ZPL macros handle generally astigmatic beams.

For reference, Colbourne gave the latest version of his webinar on April 14, 2022; he had given it a year before, and I think added some of the ZPL macros in between.

https://support.zemax.com/hc/en-us/articles/1500005489661-Using-skew-rays-to-model-Gaussian-beams-webinar

Note for future reference that this is also listed as Knowledgebase Article KA-01772.

The macros and other demonstration files for the Webinar can be downloaded from the Q&A thread for the 2022 webinar:

 and also the webinar slides themselves lower down in that thread!

Non-Sequential mode:

My original question was requesting a Source DLL for Non-sequential mode to generate astigmatic (simply at least) elliptical Gaussian beams having both different widths in X and Y and also different M^2 in X and Y.

There is a confusing number of Source DLLs with Gaussian in the name--built-in, or user-contributed--having some of the desired features, but not all (GaussianSource, Source Gaussian, Source Diode...).  Paul Colbourne himself has also written some Nonsequential DLLs that are useful.

But you know about that, since YOUR and Steffen Erhard’s Source DLL “AstigmaticGaussian.dll” is currently my favorite Nonsequential DLL (thanks again to you two!).  It appears to model a generally astigmatic source beam.

The availability of this, since it is not a built-in OpticStudio Nonsequential Source, but has to be discovered in the Code Exchange, is not well known. Zemax Support.  Therefore similar questions arise periodically, e.g.:

David Nguyen has written and posted his own versions, but I still like Steffen’s and yours the best.

====

Built-in features for handling generally astigmatic Gaussian beams (both Sequential and Non-sequential) deserve to be implemented into OpticStudio, and are promised, but are not yet available; see Sandrine Auriol’s comments in the last thread quoted above.

I hope this collection of threads proves useful to you and others.

-- Greg Magel

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12 replies

Dirk.Broemme
Ultraviolet
  • Dirk.Broemme
  • Author
  • Ultraviolet
  • 42 replies
  • December 16, 2022

Dear Zemax-Team,

can someone help me please?

Kind regards

Dirk

 

David.Nguyen
Luminary
Forum|alt.badge.img+2
  • David.Nguyen
  • Luminary
  • 1085 replies
  • December 16, 2022

Hi Dirk,

 

You’re right, the problem you describe is in the realm of general astigmatism and to the best of my knowledge, only POP (Physical Optics Propagation) can account for it in OpticStudio. Although, POP has its own limitations as well, so it is difficult to say if it’ll work for you without seeing a more concrete example first. Bottom line, you shouldn’t use the Skew Gaussian Beam, which only treats simply astigmatic beams.

Paul Colbourne gave a webinar about Using skew rays to model Gaussian beams. I strongly suggest to have a look at it if you haven’t already.

I hope this helps a bit and take care,

 

David

P
Ultraviolet
Forum|alt.badge.img
  • PhGeek
  • Ultraviolet
  • 67 replies
  • Answer
  • December 18, 2022

Hi, Dirk.

Over the last couple of years I have seen (and participated in several Community discussions regarding generally-astigmatic Gaussian beams.  I’ll collect them into this post for yours (and others’) convenience.

Sequential mode:

Your question appears to be how to treat generally astigmatic beams in Sequential mode.  Paul Colbourne is definitely the Zemax expert there.  And I, too, was confused (as you can see in this thread

also discussing Non-sequential) by the “Skew Gaussian Beam” Sequential analysis feature, which as David correctly says, only treats SIMPLY astigmatic beams.  Paul’s Skew Ray technique is completely different, and his latest ZPL macros handle generally astigmatic beams.

For reference, Colbourne gave the latest version of his webinar on April 14, 2022; he had given it a year before, and I think added some of the ZPL macros in between.

https://support.zemax.com/hc/en-us/articles/1500005489661-Using-skew-rays-to-model-Gaussian-beams-webinar

Note for future reference that this is also listed as Knowledgebase Article KA-01772.

The macros and other demonstration files for the Webinar can be downloaded from the Q&A thread for the 2022 webinar:

 and also the webinar slides themselves lower down in that thread!

Non-Sequential mode:

My original question was requesting a Source DLL for Non-sequential mode to generate astigmatic (simply at least) elliptical Gaussian beams having both different widths in X and Y and also different M^2 in X and Y.

There is a confusing number of Source DLLs with Gaussian in the name--built-in, or user-contributed--having some of the desired features, but not all (GaussianSource, Source Gaussian, Source Diode...).  Paul Colbourne himself has also written some Nonsequential DLLs that are useful.

But you know about that, since YOUR and Steffen Erhard’s Source DLL “AstigmaticGaussian.dll” is currently my favorite Nonsequential DLL (thanks again to you two!).  It appears to model a generally astigmatic source beam.

The availability of this, since it is not a built-in OpticStudio Nonsequential Source, but has to be discovered in the Code Exchange, is not well known. Zemax Support.  Therefore similar questions arise periodically, e.g.:

David Nguyen has written and posted his own versions, but I still like Steffen’s and yours the best.

====

Built-in features for handling generally astigmatic Gaussian beams (both Sequential and Non-sequential) deserve to be implemented into OpticStudio, and are promised, but are not yet available; see Sandrine Auriol’s comments in the last thread quoted above.

I hope this collection of threads proves useful to you and others.

-- Greg Magel

David
1 person likes this
  • David
    David
Dirk.Broemme
Ultraviolet
  • Dirk.Broemme
  • Author
  • Ultraviolet
  • 42 replies
  • April 17, 2023

Hello David and Greg,

thanks a lot your answers and sorry for my very late reply.

From my understanding the skew gaussian beam waist modelling mode in Optic Studio (OS) is based on ABCD matrix transformation. Does someone know if this is right?
If yes, can someone tell me, which ABCD matrices are used, if the optical elements are tilted or decentered?

The problem is, that if you use the skew gaussian beam mode in OS and you run a tolerance analysis with tilts and decenters, in general you will get a general astigmatic beam. And in this case the wellknown matrix transformation (aka q-parameter transformation) has to be modified. And I am sure, that OS does not do this. So skew gaussian beam mode in OS does not work properly if the optical system consists of tilted / decentered optical elements.
I hint in the OS manual would be helpful.

Best regards
Dirk




 

Dirk.Broemme
Ultraviolet
  • Dirk.Broemme
  • Author
  • Ultraviolet
  • 42 replies
  • May 16, 2023

@Sandrine Auriol 
Is there someone who can answer to my question?
This would be great..

Thanks 
Dirk

Mark.Nicholson
Luminary
Forum|alt.badge.img+3

Hey Dirk, do you still have a question that wasn’t answered by PhGeek’s post?

MichaelH
Ansys Staff
Forum|alt.badge.img+2
  • MichaelH
  • Ansys Staff
  • 342 replies
  • May 16, 2023

Hi Dirk,

I don’t know the answer to your first question of “which ABCD matrix is used”, but as for your second concern about tilted/decentered systems, I believe the Skew Gaussian Beam Data accounts for this.

OpticStudio’s workhorse function is the ray trace and I’m not aware of a single analysis that does not use the ray trace function.  Unless the ray trace type is paraxial (and this would be mentioned in the Help Files) and the System Explorer > Advanced > Paraxial Rays is set to “Ignore Coordinate Breaks”, all ray trace calls inherently recognize Coordinate Breaks (and thus tilts/decenters).  

For the Skew Gaussian Beam Data, it mentions that the analysis uses real rays and the system doesn’t have to be symmetric, so this analysis considers tilts/decenters:

 

~Michael
Dirk.Broemme
Ultraviolet
  • Dirk.Broemme
  • Author
  • Ultraviolet
  • 42 replies
  • May 17, 2023
Mark.Nicholson wrote:

Hey Dirk, do you still have a question that wasn’t answered by PhGeek’s post?

Hi Mark,

thanks for your answer. Just for clearification, can you please tell me if skew gaussian beam propagation in OS is based on ABCD matrices? If yes it does not account for aberrations. 
And is there a reference for the used ABCD matrices for the tilted optical surfaces?
And are coordinate breaks considered when using skew gaussian beam propagation?

Thanks and kind regards
Dirk

Dirk.Broemme
Ultraviolet
  • Dirk.Broemme
  • Author
  • Ultraviolet
  • 42 replies
  • June 2, 2023

@Mark.Nicholson 
Can you tell me if skew gaussian beam propagation in OS is based on ABCD matrices? 

Thanks and kind regards
Dirk

Mark.Nicholson
Luminary
Forum|alt.badge.img+3

Hi Dirk,

Zemax support should be able to give the definitive reply, but as far as I know it is just based on the paraxial Gaussian beam data, scaled by the top & bottom, and left & right marginal rays for the given field point.

  • Mark
Mark.Nicholson
Luminary
Forum|alt.badge.img+3

I should also add that this feature was developed to support POP...it is used to provide the reference (or pilot) beam data. Paul Colborne’s skew Gaussian stuff is much more robust, and an update to the code to make this a built-in feature and a reference for POP is long overdue IMHO.

  • Mark
Dirk.Broemme
Ultraviolet
  • Dirk.Broemme
  • Author
  • Ultraviolet
  • 42 replies
  • June 21, 2023

@Mark.Nicholson 
Thanks for your answer.
I have sent Zemax support an email, but unfortunately I did not get an answer

Dirk

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