Hermite hyperbolic/sinusoidal Gaussian beams in ABCD systems

For a Hermite hyperbolic/sinusoidal Gaussian beam with focusing properties, passing through an arbitrarily shaped rectangular aperture on the source plane and an on-axis x–y asymmetric ABCD system, the receiver plane expression is derived using the Collins integral. The specific example of a single thin lens placed on the propagation path is examined at selected source, propagation and optical element parameters. Viewing the progress of the beam in propagation, we find that subjecting the source beam to an aperture will give rise to excessive spreading during propagation. The lens setup will act to concentrate the energy of the beam around its focal point as expected, while in some circumstances it will also execute beam profile changes. By adjusting the aperture opening in the shape of a narrow slit, the beam will become aligned in the opposite direction after propagating after having traveled sufficiently. The results are presented as intensity graphs in the form of contour plots and 3D illustrations.