Astigmatism occurs when the obvious focal points of the two axes do not align. It restricts the laser beam's capacity to focus to a small spot size and makes focusing the output beam to a sharp, well-defined point more difficult.

The below article may help to resolve the problem.

Haiyin Sun, "Simplification of laser diode astigmatism measurement," Optical Engineering 50(10), 104202 (October 2011).

Thanks a lot Manish!!

I have opened this article ,but unfortunately it discusses only how to measure astigmatism experimentally . I wanted to know if there is a formula that can compute the astigmatism through the divergence of the slow and fast axis, and emitting region dimensions.

Astigmatism the beam parameters are not the same thing. While wavefront errors affect the divergence, so does diffraction which depends on the intensity profile. Also, astigmatism is not the only wavefront error that affects divergence. So, in short, they are not directly relatable.

Now, generally the wavefront at the output facet of a laser diode is pretty much flat. There are ways this doesn’t have to be true, but in practice it almost always is. It’s a plane wave. There is no astigmatism. There is no focal power. There aren‘t any of the other Seidel aberrations.

When that is the case, the divergence is determined by diffraction, and diffraction is determined by the transverse mode. Edge emitting diodes tend to be single mode in the thin dimension and multimode in the fat dimension. The divergence in the thin dimension is close to the best possible diffraction limited divergence, but because the nearly Gaussian beam is only on the order of 1 micron across, that still produces a large (20 -30 degree half width) divergence. In the fat dimension the beam might be 150 microns and the diffraction limit would allow divergence less than a degree. However because it is multimodal in that dimension it is usually more like 10 degrees. (M^2 >> 1)

The situation is similar in larger mode area lasers such as VCSELs. There may be a size above which thermal curvature of the facet results in significant low order wavefront terms, but you won’t be far off starting with the idea the wavefront is flat.

In Zemax use “Source Diode” to emulate the behavior of your diode. This let’s you describe the diffractive behavior and then defines the source rays accordingly so the proper behavior appears in the geometric ray tracing.