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written by Dr. Enrique Galvez
This is a Matlab program to generate a forked diffraction pattern that produces Laguerre-Gauss (LG) beams. Its primary use is for loading it onto a spatial light modulator (Cambridge correlators). The program can produce a phase blaze as well as a binary grating. The phase blaze is for improving the diffraction efficiency. A binary-grating pattern could be printed and the negative of a black & white photograph of it could become a passive diffraction grating.  

Other parameters that can be varied are:
-the line density of the pattern, which controls the diffraction angle,
-the topological charge "l" of the fork, which ends up generating an LG beam with topological charge on first-order diffraction. In LG beams the phase varies with angle, so "l" is the number of times that the phase changes by 2-pi per turn around the center of the beam. The center of the beam has an optical vortex. For more information see: E.J. Galvez, Am. J. Phys. 74, 355-361 (2006).
-an option for amplitude modulation, which generates a purer spatial mode
-an option to correct when the SLM does not vary from 0 to 2-pi in phase encoding.

This program will be referred to in an upcoming article in the Am. J. Phys. on a new undergraduate lab on Poincare beams, which first generate LG beams.
2 supplemental documents are available
Subjects Levels Resource Types
- Diffraction
- Modern Optics
- Graduate/Professional
- Upper Undergraduate
- Lower Undergraduate
- Instructional Material
= Laboratory
- Tool
= Software
Intended Users Formats Ratings
- Educators
- Learners
- Researchers
- application/matlab
- application/pdf
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Free access
This material is released into the Public Domain. No restrictions for non-commercial purposes.
Rights Holder:
Enrique Galvez
Matlab program
Diffraction grating, Laguerre-Gauss beams
Record Creator:
Metadata instance created March 2, 2016 by Enrique Galvez
Record Updated:
March 16, 2016 by Bruce Mason
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AIP Format
E. Galvez, Computer Program FORKED DIFFRACTION PATTERN, Version 1.0 (2016), WWW Document, (
E. Galvez, Computer Program FORKED DIFFRACTION PATTERN, Version 1.0 (2016), <>.
APA Format
Galvez, E. (2016). Forked diffraction pattern (Version 1.0) [Computer software]. Retrieved July 24, 2024, from
Chicago Format
Galvez, Enrique. "Forked diffraction pattern." Version 1.0. (accessed 24 July 2024).
MLA Format
Galvez, Enrique. Forked diffraction pattern. Vers. 1.0. Computer software. 2016. Matlab program. 24 July 2024 <>.
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@misc{ Author = "Enrique Galvez", Title = {Forked diffraction pattern}, Year = {2016} }
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%A Enrique Galvez %T Forked diffraction pattern %D 2016 %U %O 1.0 %O Matlab program %O application/matlab %O Matlab program

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%0 Computer Program %A Galvez, Enrique %D 2016 %T Forked diffraction pattern %7 1.0 %9 Matlab program %U

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