Periodical properties of the ray transfer matrix and generation of sideband modes in a stable laser resonator.

The paper describes a subclass of stable laser cavities, periodic stable laser cavities, in which perturbations consisting of deviations of the mode axis from the ideal direction are of a strictly periodic oscillatory nature. In such resonators, in addition to unperturbed longitudinal-transverse spatial modes with an ideal direction of the optical axis, additional modes can appear at sideband frequencies, associated with the resonant buildup of perturbation oscillations. These modes have approximately the same spatial structure as those of the unperturbed fundamental modes, and their frequency detuning from the frequencies of the fundamental modes is governed by the resonator geometry and the periodicity parameter, i.e., the number of passes in the resonator in one period of perturbation oscillations. For many repetitively pulsed laser systems emitting comb spectrum structures, such as free electron lasers, modern frequency standards using femtosecond lasers, and various comb spectrometers, it is desirable to avoid such periodic stable cavities in order to preserve the purity of the comb spectrum used in them. This may also be important for CW lasers with extreme radiation monochromaticity. In some repetitively pulsed lasers, on the contrary, it may be desirable to use such periodic stable laser cavities for a more complete frequency filling and higher quasi-continuity of their emission spectra.