Interaction of self-modulation and relaxation oscillations, and its role in nonlinear dynamics of a solid-state ring laser

Theoretical and experimental investigations were made of the frequency of relaxation oscillations and of the operational dynamics of a solid-state ring laser when the frequency of self-modulation oscillations was varied within a wide range by altering one of the feedback coefficients of counterpropagating waves. The generally accepted formula for the relaxation frequency $\omega_r = \sqrt{(\omega/Q)\eta/T_1}$ is valid only in the limited range of self-modulation oscillation frequencies; here, ($\omega/Q$) is the cavity bandwidth, $\eta$ is the excess above the pumping threshold, and $T_1$ is the relaxation time of the population inversion. A strong interdependence of the frequencies of self-modulation and relaxation oscillations, as well as mutual locking of these frequencies in the region of a parametric resonance were observed. Period doubling of self-modulation oscillations and dynamic chaos were investigated in the region of a parametric resonance between self-modulation and relaxation oscillations.