Matrix Representation Of Multimode Beam Transformation

The transformation of laser beams passing through optical systems is analized using a TEM modal decomposition. The laser beam is decomposed like a serie expansion and the optical system is described by a matrix that relates the modal composition of the input and output beams. The hard aperture and the parabolic and Gaussian soft apertures are given like typical examples. The matrices that characterize these apertures allow to analize the losses of laser resonators including finite and/or variable reflectivity mirrors. The modal decomposition is used for defining modified ABCD matrices that include any kind of apertures