Unconditional instability of the degenerate backward optical parametric oscillator

Abstract

Generation of ultra-short optical pulses in CW-pumped cavities are mostly associated with mode locking in active media, such as doped fibers or solid-state lasers. The cavity contains not only a gain element (atoms or ions) but also a nonlinear element permitting self-phase modulation (SPM) or intensity dependent absorption. Spontaneous generation of a pulse in CW-pumped optical cavities without population inversion may also take place through the nonlinear three-wave counter-streaming interaction. It has been shown that the same mechanism, responsible for symbiotic solitary wave morphogenesis in the Brillouin-fiber-ring laser [1], may act for picosecond pulse generation in a quadratic optical parametric oscillator [2]. The resonant condition is automatically satisfied in stimulated Brillouin backscattering. However, in order to achieve quasi-phase matching (QPM) between the three optical counter-streaming waves in the x(2) medium, so that both signal and idler waves propagate backward with respect to the pump wave, a polarization inverted grating of sub-μm period is required. QPM second-harmonic (SH) generation for copropagating waves, in which the wave mismatch between the fundamental and SH waves is compensated with the assistance of spatial gratings of nonlinear or linear material constants, has been extensively studied [3], If a grating with a sufficient short period is available, both waves traveling in opposite directions can be phase matched and the SH wave is generated in reflections [4]-[8]. Recent experiments of backward SH generation in periodically-poled LiNbO3 [8] [9] and KTP [10] avoid the technical difficulty of a sub-μm QPM by using higher-order gratings. Studies of QPM SH generation by backward propagating interaction have been done and the stability analysis of the counter-propagating interaction in the cavity has been performed, showing complex temporal pattern formation and self-pulsing [11].