Spectrum of the transverse modes of a laser with static distributed feedback by a phase grating

A solution is obtained of the problem of the spatial structure of the output radiation field of a distributed-feedback laser with a static phase grating pumped longitudinally by a beam with a parabolic intensity profile. The spectrum of the normal transverse modes is found for a distributed-feedback laser. The spectrum is described by a superposition of Hermite — Gauss polynomials. An analogy is established between the problem in hand and the spatial structure of a light beam in a medium with quadratic variation of the complex permittivity.