Poincaré maps for studying relaxation oscillations in periodically pumped solid-state lasers

We present an asymptotic analysis of relaxation oscillations in periodically pumped single- and multimode class-B lasers. Discrete maps which allow one to describe the hierarchy of coexisting periodic attractors are obtained and their bifurcations leading to period-doubling regimes and quasi-periodic and chaotic oscillations are studied analytically. For systems of coupled longitudinal modes, the maps determine conditions for antiphase dynamics.