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.