Spatiotemporal evolution of continuous-wave field and dark soliton formation in a microcavity with normal dispersion

Stable dark soliton and dark pulse formation in normally dispersive and red-detuned microcavities are investigated by numerically solving the normalized Lugiato-Lefever equation. The soliton essence is proved by fitting the calculated field intensity profile with the analytical formula of a dark soliton. Meanwhile, we find that a dark soliton can be generated either from the nonlinear evolution of an optical shock wave or narrowing of a locally broad dark pulse with smoother fronts. Explicit analytical expression is obtained to describe the oscillatory fronts of the optical shock wave. Furthermore, from the calculation results, we show that for smaller frequency detunings, e.g., $\alpha <3$, in addition to the dark soliton formation, a single dark pulse with an oscillatory dip can also arise and propagate stably in the microcavity under proper pump detuning and pump strength combination. The existence region together with various field intensity profiles and the corresponding spectra of single dark pulse are demonstrated. (paper)