Influence of periodic loss modulation on the dynamics of self-modulation oscillations in a solid-state ring laser

A theoretical investigation is made of the influence of periodic modulation of intracavity losses on the dynamics of a solid-state ring laser operating in a type I self-modulation regime. Analytic solutions are obtained for describing dynamic locking of the frequency ω_m of self-modulation oscillations to the frequency ω_p of periodic loss modulation and a quasi-periodic regime characterised by low-frequency modulation of self-modulation oscillations at the difference frequency ω_m – ω_p. Analytic expressions are obtained for the width of the region in which locking of the frequency of self-modulation oscillations takes place. Numerical simulation of the dynamics of a solid-state ring laser is used to study the transition of this laser to dynamic chaos when the loss modulation depth h is increased. It is shown that the operational regimes of the laser and the conditions for its transition to dynamic chaos are significantly different in the frequency ranges ω_m > ω_p and ω_m < ω_p. The boundaries separating regimes with chaotic, periodic, and quasiperiodic dynamics are found in the (ω_p, h) plane.