Rotating the intensity distribution of Gaussian beams propagating through paraxial ABCD systems with parallelogram apertures

By using the method of expanding the aperture function into a finite sum of complex Gaussian functions, approximate closed-form propagation equations of Gaussian beams through a paraxial ABCD optical system with parallelogram apertures are derived and illustrated with numerical examples. It is found that the intensity distribution pattern rotates round the propagation axis during the propagation.