Comparison of two numerical simulation methods for hard-edged diffracted beams

By using the methods of matrix representation and complex Gaussian function expansion, the recurrence propagation formulae of a flattened Gaussian beam through multi-apertured optical ABCD systems are derived. Numerical examples are given to compare the two numerical simulation methods. It is shown that the form of matrix formulae is simple, and the matrix formulation is applicable to the Fraunhofer and Fresnel regions. However, this method is suited only to circularly symmetric optical beams and systems. On the other hand, the form of formulae derived by the method of complex Gaussian function expansion is complex, and its calculation errors become noticeable in the near Fresnel region closer to the aperture. But this method is suited to both circularly symmetric and circularly un-symmetr