Dynamical model of two-dimensional self-induced-transparency-solitons and pattern formation in nonlinear optical waveguides and semiconductor microcavities

We propose a novel multidimensional dynamical model for description of the coherent interactions of ultrashort high-intensity optical pulses with the resonant nonlinearities in planar optical waveguides and semiconductor microresonators. The model is based on the self-consistent solution of the full-wave vectorial Maxwell's equations coupled via polarization source terms to the evolution equations of a discrete multilevel quantum system. The latter are derived employing a group-theoretical approach exploiting symmetric properties of the system Hamiltonian. In particular, the resonant nonlinearity is modelled by a degenerate three-level system of saturable absorbers in order to account for the two-dimensional medium polarization. The resulting Maxwell-pseudospin equations are solved in the time domain using the finite-difference time-domain (FDTD) method. The model is applied for studying conditions of onset of self-induced transparency (SIT) lossless regime of propagation. Numerical evidence of multidimensional solitons localized both in space and in time is given for the planar optical waveguides. Pattern formation and cavity SIT-soliton formation are demonstrated for the special case of a passive semiconductor microcavity filled with saturable absorbers.