Editing Gaussian beam (section)

===Elliptical and astigmatic beams===
Many laser beams have an elliptical cross-section.  Also common are beams with waist positions which are different for the two transverse dimensions, called astigmatic beams.  These beams can be dealt with using the above two evolution equations, but with distinct values of each parameter for {{mvar|x}} and {{mvar|y}} and distinct definitions of the {{math|1=''z'' = 0}} point. The Gouy phase is a single value calculated correctly by summing the contribution from each dimension, with a Gouy phase within the range {{math|±''π''/4}} contributed by each dimension.

An elliptical beam will invert its ellipticity ratio as it propagates from the far field to the waist. The dimension which was the larger far from the waist, will be the smaller near the waist.