Theoretical modeling of relaxation oscillations in Er-doped waveguide lasers

An analysis of relaxation oscillations (λ_s~1.5 μm) in locally Er-doped optically pumped (λ_p~1.48 μm) waveguide lasers is reported. The theoretical model is based on time dependent rate equations for a quasi-two-level-system and on the equation of continuity for a gain medium. For the first time a numerically reliable simulation of the elementary properties of the laser oscillations was possible: the build-up time and decay of the relaxation oscillations, the time-dependent repetition period, the steady state signal output power and the evolution of the pump power versus time. Mathematically the problem can be characterized as a large boundary value problem, which can approximately be replaced by a stiff initial value problem of ordinary differential equations. In this report, pump- and signal evolution versus time are presented for planar Er-diffused Ti:LiNbO₃ waveguide lasers. The numerically obtained results show a good quantitatively agreement with experimental investigations