Rounded tip axicon modelling

  • 6 August 2021
  • 7 replies


Hi all,

I hope you are well!

I have been doing some axial intensity modelling of various Thorlabs axicons via the Physical Optics Propagation feature. In particular, I am interested in using the AX2520-B axicon. I have imported this using the Lens Catalog, but I am now interested in trying to model the effect of the rounded tip which is a common manufacturing error (as opposed to the perfectly sharp tip which is assumed in the “ideal” case). This radius of tip curvature is typically within the range of 10s of microns, but I am unsure how to go about implementing this within the Lens Data window for carrying out further Physical Optics Propagation analysis?

Thank you for your time and consideration.


Best answer by Mark.Nicholson 6 August 2021, 19:54

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7 replies

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Hi Donald,

Thanks for posting here in the forum!

Very good question, unfortunately you wont be able to simply insert a non-sequential component (E.g. the STEP file of the lens) because that will turn the POP into Ray Tracing in the NSC part. So to stay in the SEQ mode, I would recommend to apply a Freeform optic

Here you got a overview for Freeform optics

More specifically, you could apply one of the following:

Please feel free to reach out if you need more help or you have a follow-up question.


Userlevel 5
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Look at the Help file entry for the Standard surface. You’ll see a discussion of using the Standard surface to model an axicon with a rounded surface. That should do what you need.

Also, if using POP with an axicon, use the Plane phase reference rather than the pilot beam reference. An axicon destroys the chief-ray-referenced nature of the wavefront, unless a second axicon restores it. You’ll need huge sampling, but with so much phase error rays will probably be completely accurate in any case.






Hi both,

Thank you for the helpful pointers. 

I have sourced the Help file entry for the Standard surface which covers the modelling of an imperfect axicon tip.

However, in the attached zip file (which has the imported lens file from Thorlabs), the conical surface (Surface 3) type is “Odd Asphere” as opposed to “Standard” and upon changing the “Radius” property (to try and input a radius of curvature of between 10 and 30 microns) the surface loses its conical shape/structure.

Do I need to input the calculated k value within the “Conic” field entry for surface 3, with a placeholder value used for the radius of curvature (with the Help file entry stating that the exactness of this is insignificant as it is roughly three or more orders of magnitude smaller than the radial aperture of the axicon in this instance)?

Thanks again for your time and consideration,


Userlevel 5
Badge +3

Us the R and k method, OR use the Odd Asphere coefficients, but don’t use both. Best to just switch to the Standard surface so the temptation doesn’t arise :nerd:


BTW, your zip file contained the .SES but not the .ZMX file



Regarding the R and k method, I assume R goes under the “Radius” field within the Lens Data window? Additionally, I was wondering how the Odd Asphere coefficients can be manipulated to account for this curvature, as upon changing R it loses its conical form? Based on your response however I imagine this is somewhat less trivial.

My apologies - please see the .ZMX file attached here. 

Thanks again.

Userlevel 2

Hi Donald,

I’ve just looked over your system and I think I can clear some issues up, assuming you have not already resolved it. You are correct that the R goes in the Radius field. It is the radius of curvature, and according the help page, as long as it is about three orders of magnitude smaller than the radius of the lens surface (i.e. the semi-diameter or other aperture) then the approximation is very good. With your SD of 12.7 mm, a 10 to 30 micron radius for the smoothed tip is just fine. There will be a very slight change in the overall shape, but it is tiny. For an R value going from -.0127 to -.0381 (a three-fold increase), the overall thickness of the axicon changes by only about 3 microns.

Regarding the Odd Asphere coefficients, right now you have only the linear term. This will always produce a point vertex. You should be able to smooth this off by giving any non-zero value to any of the higher order terms because then the local derivative will be defined (and will be zero) at the vertex. You would have to consider the math to relate this curvature to that of the actual tip, but I’ll let you decide if that’s worth it or not. For your system, though, alpha is 20 degrees so k should be -8.54863217. If you try it you should find that the system is only imperceptibly different from the original.


Hi Kevin,

Thanks for taking the time to make the insightful response.

I played around with some of the higher order terms in combination with the conic term as per your suggestion, but the model still produces very subtle intensity fluctuations as you (and the help function) say it is still fairly similar to the ideal case. I am happy with this now though, as experimentally I have measured a more significant (but not drastically so) fluctuation range.

My current predicament involves trying to model the axial intensity profile of a reimaged Bessel-Gauss beam - forum thread linked here. Unfortunately the phase sampling issue seems a difficult one to get around for the range over which I am simulating it.

Thanks again,