Space-time coupled stability of optical solitons in a nonlinear resonator consisting of periodic layered Kerr media.

The dynamics and stabilization of solitons are essential for a large variety of fundamental processes in nonlinear optics, condensed matter physics and biology. Taking the solitary propagation of femtosecond pulses in periodic layered Kerr media as an example, we investigate the space-time coupling of optical solitons in a nonlinear resonator. A universal relationship between the beam size and the critical nonlinear phase of the solitary modes is revealed, defining different regions of the resonator stability. Space-time coupling is shown to strongly influence the spectral, spatial and temporal profiles of femtosecond pulses. The sustainable propagation of femtosecond pulses with a GW peak power is demonstrated on resonance, which can be regarded as temporally confined spatial solitons. Taking advantage of the unique characters of these solitary modes, we demonstrate single-stage supercontinuum generation and compression of femtosecond pulses from initially 170 fs down to 22 fs with an efficiency >90%. We also provide evidence of efficient mode self-cleaning which suggests rich spatial-temporal self-organization processes of laser beams in a nonlinear resonator.