We study different regimes of spatial-temporal pulses propagation in a waveguide under conditions of second harmonic generation. In comparison with a homogeneous medium the waveguide geometry allows us to increase the number of input parameter sets for which light bullets can be observed. We demonstrate that provided defocusing nonlinearity combined with a focusing waveguide the formation of spatial-temporal solitons is possible due to the waveguide geometry only. Stable propagation of two-component light bullets at normal dispersion is confirmed numerically.
We study a self-similar mode of femtosecond pulse propagation in a medium with non-resonant TPA of laser energy and with taking into account the TOD influence. Non-resonant TPA appears due to detuning between a carrier frequency of wave packet and doubled frequency corresponding to certain energy level transition of substance atoms. This pulse propagation mode appears for a pulse with nonlinear chirp of definite form. Moreover, the pulse shape is asymmetric, as a rule. Laser pulse propagation in nonlinear medium is described by nonlinear Schrödinger equation. Using the analytical approach we derive a soliton-like pulse shape and its chirp evolution in time. Analytical results are confirmed by computer simulation, based on nonlinear Schrödinger equation. We demonstrate that the analytical results are valid at a long propagation distance.
Three-dimensional light bullets in Kerr media are known to be unstable. Different schemes were proposed to overcome this obstacle. One of them is to use a nonlinear parametric interaction. Such a type of interaction can be achieved in anisotropic micro-dispersive media where space dispersion is of importance. These media allow us to reach a simultaneous approximate fulfillment of group and phase matching. To study the general (3+1)D case we apply both an approximate analytical approach and numerical simulations. We suggest that nonlinear refraction manifests itself earlier than diffraction and dispersion. Both the general (3+1)D case and axial-symmetry case are studied. With the help of averaged Lagrangian method analytical solutions are derived provided that the fixed relation between the negative coefficients of the group velocity dispersion on both harmonics holds. We demonstrate that a spatiotemporal light bullet propagates for at least 300 nonlinear lengths in anisotropic media at second harmonic generation.
We develop an analytical approach for finding of self-similar shape of an optical pulse at its propagation in a medium with non-instantaneous nonlinear absorption. The main feature of such pulse shape is asymmetric. Moreover, this mode of optical pulse propagation takes place only for a chirped pulse in contrast to well-known soliton solution of nonlinear Schrödinger equation (or set of such equations). Therefore, we discuss a new type of self-similar mode of laser pulse propagation: self-similar chirped pulse. An existence of this pulse takes place for certain distance of its propagation. We derive a relation between the problem parameters and shape of pulse and its chirp which are necessary for an occurrence of the self-similar mode for optical pulse propagation in a medium under consideration. The developed solution is confirmed by computer simulation results.