Optical ray paths in a quasi-periodic waveguide or a multipass cavity with smoothly varying properties

Ray paths in a quasi-periodic optical system (waveguide of cavity) with smoothly varying properties have been constructed along the ray path. The ray-transfer matrix is constructed for a large number of ray paths; it has been shown that the conventional stability condition (the modulus of the ray-transfer matrix trace for a ray path is smaller than two) does not ensure the boundedness of the beam path after a large number of paths.