Transformation of Hermitian–Gaussian beams in a squarelaw medium exhibiting simple astigmatism

It is shown that the matrix methods can be used to determine the parameters of the transformation of Hermitian–Gaussian beams in a square-law medium with simple astigmatism. Formulas are obtained for the transformation of the general form of such beams. The proposed method is used to calculate the spatial structure of the radiation in a plane-mirror resonator which is filled completely by an inhomogeneous medium.