Solved

Laguerre Gaussian beam setup on POP

  • 3 August 2020
  • 6 replies
  • 527 views
K

Does anybody know the way to model Laguerre-Gaussian beam for 01* mode which is doughnut shaped? 


 


I would like to simulate 'VCSEL' beam with its shape similar to doughnut and M2 value 2.1.


The Laguerre-Gaunnian beam of mode 01* (not 01) would give similar result, but I could not find the way to model it in Zemax. 


 


For another trial, I have used the 'mixed mode' to simulate M2 value. The beam file was as below.


COHERENT

!DLL 0.2 Laguerre 0.0 0.0 0.00259 0.0

DLL 0.5 'Laguerre beam'     0.0     0.0     0.00275     90.0

DLL 0.4 'Laguerre beam'     1.0     0.0     0.00275        90.0

DLL 0.4 'Laguerre beam'     0.0     1.0     0.00275        90.0


 


Will the mixed beam give the same result with the normal Laguerre beam POP simulation? Should I use coherent beam or incoherent beam?

icon

Best answer by Nicholas Herringer 4 August 2020, 01:13

View original

6 replies

Nicholas Herringer
Rank
Userlevel 2
Badge +1

Hi Kiho, 


You should be able to do this by taking the incoherent sum of a TEM01 and TEM10 beam via the Multimode Beam Type in the Physical Optics Propagation Beam Definition.


 



 


There's a sample donut beam file in file '\Documents\Zemax\POP\BEAMFILES,' and it's defined below. I've also attached a quick sample file using this file. 


 


! command    weight    param1    param2    param3    param4    param5    param6    param7    param8

! Sample for defining donut mode by incoherent sum of TEM 01 and TEM 10

INCOHERENT

GW            1.0        1.0        1.0        0.0        0.0        0.0        0.0        0.0        1.0

GW            1.0        1.0        1.0        0.0        0.0        0.0        0.0        1.0        0.0


 


Take a look in the OpticStudio Help Files under 'The Analyze Tab (sequential ui mode) > Laser and Fibers Group > About Physical Optics Propagation > Defining the Initial Beam > Multimode' for a description of what the above parameters mean. 


With respect to your question about modeling this type of beam using Mixed Mode, I would not expect this to yeild the same results as Physical Optics Propagation (POP). The primary reason for this is because in Mixed Mode, in order for light to interact with Non-Sequential Components, it must be converted to non-sequential rays. This conversion will often lead to the loss of important phase information required by POP. That said, I would not recommend using POP with Mixed Mode systems. 


Let me know if you have any other questions, and I'll be happy to help!


Cheers,


Nick

1 Attachment
K

Dear Nick,


 


Thank you very much for your kind and prompt help!


As you have worried about, mixing of coherent beams in incoherent mode will lose the phase value of the beam and will give us different result than the coherent beam.


I tried to check by putting one GW beam of below.


INCOHERENT

!GW            1.0      0.0015       0.0015        0        0      0.0      0.0        0.0        1.0

GW            1.0      0.0015       0.0015         0        0     0.0      0.0        1.0        0.0


 


This is the same beam as below.



But, as you see, it gives different result.



 


Will there be any way to do POP calculation for the doughnut beam in coherent mode?


Is there any definition in 'Laguerre-Gaussian' beam for the doughnut beam which is 01* mode?


 


Kiho

Haosheng.Hu
Rank
Userlevel 2
Badge +1

Hi Kiho,


I noticed there is a support request email you sent to support@zemax.com with same question as well, please allow me to answer your question at here instead.


As Nick descibed, dount beam profile should be modeled with ZMM file above with incoherent way. In my knowledge, that is the most direct way we can define donut beam in POP with its intensity profile, which means donut beam can be only modeled by sum TEM01 and TEM10 incoherently. If you sum TEM10 and TEM01 coherently, result beam is something other than dount:



As you may know, Gaussian Waist beam in OpticStudio is defined with Hermite- Gaussian, there is no direct way to model beam with Laguerre-Gaussian except using DLL to program the beam profile. For more information about DLL beam in POP, you can refer to help manual section below:


The Analyze Tab (sequential ui mode) > Laser and Fibers Group > About Physical Optics Propagation > Defining the Initial Beam > DLL


Also, we have a sample C code for Laguerre-Gaussian, which can be found at:


C:\Users\XXXXXXX\Documents\Zemax\DLL\PhysicalOptics\Laguerre beam.c


I am not very familar with Laguerre-Gaussian mode and I did some online search. If my understanding is correct, the donut beam in Laguerre-Gaussian should be 1,3 based on figure below:



 


For your other question, the reasone why you observed beams are not corresponded with Multimode and Gaussian Waist is surfaces you used to observe the beam are not same (surface #5 and #40). I tested if surface are exactly same, beam profiles are same as well. Princlples of beam modeling behind GW in ZMM and Gaussian Waist are exactly same.


 


Hope the answer can help you, please feel free to let us know if you have further questions.


 


Best regards,


Haosheng

K

Hi Haosheng:


 


Thank you very much!


Yes, I should have seen at the same surface.


The latter surfaces up to 40 is the direct imaging lens to make the conjugate.


When, I re-do the calculation at the same surface, the results are different.


Please see below.


 




 


I was using the 'Laguerre-Gaussian' DLL for the beam simulation but still having problem finding beam shape doughnut and M2 value around 2.


 


Sincerely,


 


Kiho

Angel Morales
Rank
Userlevel 5
Badge +1

Hi Kiho,


Thanks for your follow-up here!


I've set up similar starting points using a modified 'donut.zmm' file (I believe you commented out the first GW command) and a Gaussian Waist beam definition that is equivalent. As we can see, the starting irradiance profile of the two beams are identical:




But, if we take a look at the phase data, we can see they aren't identical, and therefore we can't expect identical propagation between the two, I think:



So, it seems like the difference in propagation is due to the difference in initial phase definition due to the INCOHERENT command for the .ZMM file.


As for using the Laguerre Gaussian DLL to get the donut beam you'd like, I also wasn't able to produce the 01* mode as you're looking for after trying a few different COHERENT sum definitions using the 'Laguerre beam' DLL. I suspect the best route forward to make the most comprehensive representation of this beam definition is likely to write a DLL which would generate the necessary irradiance profile and phase definition for proper propagation.


Please let us know how these thoughts work out for you!


~ Angel

1 Attachment
Angel Morales | Senior Application Engineer | Zemax
Nick

I know I’m late to the party here but I ran into this same problem a while back. As people mentioned above Zemax defines the beams in a Hermite space, but both Hermite and LG form complete basis so you can describe one (eg LG 10) with the proper combination of HG beams. For the LG 10 mode you need an HG 10 and HG 01 but with a phase shift added in as well. This picture shows what I’m trying to describe

From this paper (https://www.tandfonline.com/doi/abs/10.1080/001075100750012777)

So in Zemax terms to model the LG 10 mode you need to include the 90 phase rotation in the .zmm so it looks like

 

COHERENT

GW            1.00000000000        1.0        1.0        0.0        0.0        0.0        0.0        1.0        0.0
PHASE 90
GW            1.00000000000        1.0        1.0        0.0        0.0        0.0        0.0        0.0        1.0

 

Here’s the POP of the collimated LG 10 beam

Here’s the phase

And then here’s the focus from a cylindrical lens which forms a split line focus (sorry about the aspect ratio I just threw this together)

Here’s what the POP looks like without that Phase 90 term in the .zmm

and the phase

Hope this helps!!

Reply


Community Posting GuidelinesCookie settings


Zemax Community

Need more help?

To Chinese users:

Do not provide any information or data that is restricted by applicable law, including by the People’s Republic of China’s Cybersecurity and Data Security Laws ( e.g., Important Data, National Core Data, etc.).


不要提供任何受适用法律，包括中华人民共和国的网络安全和数据安全法限制的信息或数据（如重要数据、国家核心数据等）。



Privacy policy   License Agreements    Terms of service    Cookie Policy   Zemax Account Licensing Policies