Optical rectification is a prominent method to generate a broadband terahertz pulse. It is known that generation is possible at the resonance condition of Zakharov-Benney. To increase generation efficiency, in particular, optical component shortening is applied. Thus, while studying this process analytically and modeling it numerically one should consider non-zero third order dispersion. The case is especially interesting when the carrier frequency of the initial optical radiation is situated near zero value of the second-order dispersion. In this work, using numerical simulation, we study the influence of third-order dispersion on terahertz generation efficiency.
We study with the help of numerical simulation the generation of second optical harmonic neglecting group velocity dispersion but taking into account third order dispersion effect at either fundamental or doubled frequency. At that, a component at another frequency usually undergoes second order dispersion in experiments. Varying values and signs of the third order dispersion at quasi-zero values of the second-order dispersion we reveal the conditions of bullet formation and stable propagation.
We study two-color soliton-like propagation of laser radiation in a quadratic nonlinear medium under both second- and thirdorder dispersion (TOD) actions. The main feature of this soliton-like propagation is an asymmetric pulse shape and the presence of nonlinear chirp. We propose approximate formulas for the pulses shapes and their chirps. We clarify the limits of applicability of these formulas on basis of numerical simulation and show that the propagation dynamics matches analytical formulas at a rather long propagation distance. It is remarkable that the pulse amplitude evolution demonstrates an explicit dependence on the TOD coefficient.
In general, optical spatiotemporal solitons with phase singularities, known as optical vortex bullets, are unstable. In particular, it is very difficult to preserve a vortex structure of a propagating localized wave. In this paper we propose to introduce absorption to the model used for the process description. By means of numerical simulation we study the formation and propagation of an optical vortex bullet at different regimes. Our goal is to find the conditions of bullet stabilization.
Nowadays the generation of terahertz pulses using the mechanism of optical rectification is intensively studied both theoretically and experimentally. If the group velocity of an optical pulse is equal to the phase velocity in the terahertz range of a medium with quadratic nonlinearity, then a two-component optical-terahertz temporal soliton can be formed. In the present work, we study the possibility of forming an optical-terahertz spatiotemporal soliton (optical-terahertz bullet) in a gradient focusing waveguide. If the duration of the input optical pulse lies in the femtosecond region, then when generating a terahertz signal, the nonlinearity dispersion is important. This also leads to the influence of the phase modulation of the optical pulse on the generation process. We take this circumstance into account when considering the formation of optical-terahertz bullets. The system of related equations for the complex envelope of the optical pulse and the electric field of the THz pulse is solved numerically. The original conservative nonlinear finite-difference scheme is realized with the help of a pseudo-spectral method. We find the conditions under which it is possible to trap an optical terahertz pulse into a focusing waveguide with the formation of optical-terahertz bullets.
In this work we present results of our study of light bullets in inhomogeneous media with quadratic nonlinearity. We consider the second harmonics generation by few-cycle pulses having about 3 – 5 oscillations under the envelope. We give reasons to apply “slowly varying envelope approximation” in this case. The self-consistent system of nonlinear equations for the envelopes of both harmonics is substantially modified in comparison with the case of quasimonochromatic signals. This system is supplemented by a third order group dispersion and by a dispersion of nonlinearity. The diffraction terms are also modified. The appropriate system of parabolic equations for the envelopes of both harmonics is obtained. To solve an arising 2D+1 system numerically we construct an original nonlinear finitedifference scheme based on the Crank-Nicolson and pseudo-spectral methods preserving the integrals of motion. We discuss different regimes of pulse propagation depending on the competition among nonlinearity, diffraction, temporal dispersion and waveguide geometry.
By means of numerical simulation we investigate vortex solitons comprised of coupled pulses with phase singularity under conditions of second harmonic generation. They are usually known for their low stability. We carefully examine homogeneous or inhomogeneous media. Our principal interest is to obtain a stable two-component bullet at normal dispersion. We demonstrate that such bullet can form if spreading tendencies compete with the proper focusing waveguide geometry.
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.