Mode structure of a resonator with non-Gaussian components. I. Axial mode structures

A study is made of the mode structure of a resonator containing a component with non-Gaussian optical inhomogeneities. Use is made of geometric optics to show that, in addition to the traditional axial structure, fundamentally new non-Gaussian mode systems can appear in a non-Gaussian resonator. In particular, new systems include multipass off-axial structures, regions with stochastic behaviour of rays, and ray fluxes with a complex structure. An analytic investigation is reported of the structure of the axial region. It is shown that for certain resonator parameters a radical modification of the axial mode structure may be induced by even small aberrations. Complex ray fluxes and paraxial multipass systems are formed. The analytic results are illustrated by a large number of examples of numerical modelling of the behaviour of rays in a non-Gaussian resonator.