On nonlinear propagation of extremely short pulses in optically uniaxial media

Nonlinear wave equations describing the propagation of optical pulses of duration up to a period of electromagnetic oscillations in transparent media with uniaxial optical anisotropy are derived on the basis of a quantum-mechanical model of material response. The electron and electron-vibrational nonlinearities, electron and ion dispersion, and diffraction are taken into account. It is shown that the inclusion of the electron response alone leads to a system of two constitutive equations for the ordinary and extraordinary polarization components. When a pulse propagates across the optical axis, this system is reduced to an inhomogeneous model of the Henon-Heiles type and, hence, generalizes the Lorentz classical electron model. In order to take into account stimulated Raman scattering (SRS) processes, an anisotropic analog of the Bloembergen-Shen quantum-mechanical model taking into account the population dynamics of SRS sublevels is obtained. The generation of an extraordinary wave video pulse with the help of the high-frequency ordinary component in the Zakharov-Benney resonance mode is investigated. Some analytic soliton-like solutions in the form of propagating bound states of ordinary and extraordinary video pulses corresponding to different birefringence modes are considered and their stability to self-focusing is analyzed.