Trapping of two-component light bullets in a gradient waveguide with normal group dispersion.

In this paper we consider the process of the second harmonic generation in a gradient waveguide, taking into account diffraction and relatively weak temporal dispersion. Using the slowly varying envelope approximation and neglecting the dispersion of the nonlinear part of the response of the medium we obtain the system of parabolic equations for the envelopes of both harmonics. We also derive integrals of motion of this system. To solve it numerically we construct a nonlinear finite-difference scheme based on the Crank-Nicolson method preserving the integrals. Primarily, we focus our investigations on the processes of a two-component light bullets generation. We demonstrate that the generation of a coupled pair is possible in a planar waveguide even at normal group velocity dispersion.

Conservative finite-difference scheme for the problem of THz pulse interaction with multilevel layer covered by disordered structure based on the density matrix formalism and 1D Maxwell's equation.

On the basis of the Crank-Nicolson method, we develop a conservative finite-difference scheme for investigation of the THz pulse interaction with a multilevel medium, covered by a disordered layered structure, in the framework of the Maxwell-Bloch equations, describing the substance evolution and the electromagnetic field evolution. For this set of the partial differential equations, the conservation laws are derived and proved. We generalize the Bloch invariant with respect to the multilevel medium. The approximation order of the developed finite-difference scheme is investigated and its conservatism property is also proved. To solve the difference equations, which are nonlinear with respect to the electric field strength, we propose an iteration method and its convergence is proved. To increase the computer simulation efficiency, we use the well-known solution of Maxwell's equations in 1D case as artificial boundary condition. It is approximated using Cabaret scheme with the second order of an accuracy. On the basis of developed finite-difference scheme, we investigate the broadband THz pulse interaction with a medium covered by a disordered structure. This problem is of interest for the substance detection and identification. We show that the disordered structure dramatically induces an appearance of the substance false absorption frequencies. We demonstrate also that the spectrum for the transmitted and reflected pulses becomes broader due to the cascade mechanism of the high energy levels excitation of molecules. It leads to the substance emission at the frequencies, which are far from the frequency range for the incident pulse spectrum. Time-dependent spectral intensities at these frequencies are weakly disturbed by the disordered cover and, hence, they can be used for the substance identification.

New Possibilities of Substance Identification Based on THz Time Domain Spectroscopy Using a Cascade Mechanism of High Energy Level Excitation.

Using an experiment with thin paper layers and computer simulation, we demonstrate the principal limitations of standard Time Domain Spectroscopy (TDS) based on using a broadband THz pulse for the detection and identification of a substance placed inside a disordered structure. We demonstrate the spectrum broadening of both transmitted and reflected pulses due to the cascade mechanism of the high energy level excitation considering, for example, a three-energy level medium. The pulse spectrum in the range of high frequencies remains undisturbed in the presence of a disordered structure. To avoid false absorption frequencies detection, we apply the spectral dynamics analysis method (SDA-method) together with certain integral correlation criteria (ICC).

Planar light bullets under conditions of second-harmonic generation.

We study solutions to second-harmonic-generation equations in two-dimensional media with anomalous dispersion. The analytical solution is obtained in an approximate form of the planar spatiotemporal two-component soliton by means of the averaged Lagrangian method. It is shown that a decrease in the amplitudes of both soliton components and an increase in the value of the transverse coordinate are accompanied by an increase in their temporal duration. Within this variational approach, we have managed to find a stability criterion for the light bullet and a period of oscillations of soliton parameters. Then, we use the obtained form as an initial configuration to carry out the direct numerical simulation of soliton dynamics. We demonstrate stable propagation of spatiotemporal solitons undergoing small oscillations predicted analytically for a long distance. The formation of a two-component light bullet is shown when we launch a pulse only at the fundamental frequency. In addition, we investigate the phase and group-velocity mismatch effects on the propagation of pulses.