Studies focusing on formation and stable propagation of two-color solitons in active periodic structures are essential and in great demand. Previously, the formation of four-wave soliton in active periodic structure under SHG was investigated analytically and numerically for group synchronism of interacting waves in the framework of the coupled waves approach. In the present work, we focus on the peculiarities of the four-wave soliton formation under strong group mismatch of the interaction waves. Our investigation is based on the four coupled Schrödinger-type equations for forward and backward waves on the fundamental and doubled frequencies. The influence of the difference in the waves velocities on the transmitting and reflective properties of the active periodic structure was also studied.
In this study we investigate the formation and propagation of pulse pairs in a quadratically nonlinear crystal containing two waveguides. The analysis focuses on how changes in parameters such as the relative positions of the waveguides, waveguide widths, and angle of entry influence the system. We observe that the pulse propagation mode varies with changes in the characteristics of the waveguides and the angle at which the pulses enter the medium.
We study the process of THz soliton-like mode generation when an optical pulse with tilted wave front is launched into a crystal. Crucial role of the wave front tilt for the trapping of optical-terahertz solitons of a new type was proved theoretically and in experiments as well. These modes were developed as solutions of coupled Zakharov–Boussinesqtype equations. At that, diffraction was a contributing factor for soliton formation. Scenarios for soliton generation of terahertz radiation are quite possible to be observed in crystals with a characteristic size of a few millimeters. In the present work, using numerical simulation, we tackle the question of such soliton stability which still remains open.
We study a possibility spatiotemporal optical vortices propagating in a structure consisting of two connected waveguides with quadratic nonlinearity. The system under study is a planar nonlinear crystal whose refractive index in cross-section has two maxima corresponding to two waveguides. In this case, the electromagnetic field can penetrate between the waveguides, and due to that a communication between waveguides is realized. We focus on the study of the propagation dynamics of spatiotemporal optical vortices in such a system varying the distance between waveguides, the initial time shift between beams, and the initial phase shift between them.
Light propagation in media with absorption and amplification of optical radiation is in the focus of numerous studies. In such active periodic structures with quadratic nonlinearity, under certain conditions, the formation of two-color solitons is possible. Recently, based on four coupled nonlinear Schrödinger equations, we numerically investigated the impact of the incident beam width on reflection/propagation properties of active periodic structures under strong Bragg coupling at the fundamental frequency and the weak one at the doubled frequency. We demonstrated the solitons trapping only for wide beams. In the present report, we focus on Bragg coupling at doubled frequency. We study the reflection properties of active PT-symmetry periodic structures with quadratic nonlinearity and the formation of trapped soliton in such structures, taking into account the strong Bragg coupling at both the fundamental and the second harmonics.
We expect an increase in the efficiency of terahertz radiation generation both due to the short period of the optical pulse containing 2–3 oscillations, and due to the fact that the process is modeled in a gradient waveguide. The generation process can be accompanied by the formation of spatiotemporal optical-terahertz solitons (optical-terahertz bullets). In the case of an intense and short optical signal, for the optical component, it is necessary to take into account the group dispersion of the third order, the dispersion of the quadratic optical-terahertz nonlinearity. For the terahertz component, one should take into account its dispersion, intrinsic quadratic nonlinearity, and quadratic nonlinearity, which carries information about the phase of the optical pulse.
Our studies are focused on high intensity spatiotemporal parametric processes in a microdispersive non-centrosymmetric medium. We solve numerically the system of coupled parabolic equations for second harmonic generation that are supplemented with terms responsible for self- and cross- modulations. Joint influence of quadratic and cubic nonlinearities is studied for the case of anomalous dispersion at both frequencies. Recently it was demonstrated that provided small phase mismatches a stable two-color light bullet may be generated and then it propagates in a medium with pure quadratic nonlinearity. At the same time, pure Kerr nonlinearity is responsible for bullet instability. In our investigations we reveal a threshold condition of the two-color bullet stability in the medium with combined quadraticcubic nonlinearity.
Recently a possibility of the formation of “dancing” light bullets was analytically shown in graded-index waveguides with both Kerr and quadratic nonlinearities. At that, a two-color “dancing” light bullet in a quadratic nonlinear waveguide may form at both anomalous and normal group velocity dispersion at the fundamental frequency. Here and in what follows we refer as “dancing” light (optical) bullets spatiotemporal solitons whose trajectories can be spatial Lissajous figures with anisotropic spatial distribution of the refractive index in the cross section of the waveguide. Stability of a two-color “dancing” light bullet was theoretically demonstrated without additional conditions for its temporal duration, aperture, and power. These results were established with the help of the averaged Lagrangian method in the framework of the quasi-optical approach under the conditions of phase and group matching. The mentioned conditions are known to be hardly achievable in experiment. In the present work we study two- color “dancing” light bullet generation by means of numerical simulation including the cases when only one of the conditions of synchronism is fulfilled. We demonstrate that a pulse at the doubled frequency is generated in the waveguide at second harmonic generation (SHG), followed by the formation of the bound state of both harmonics representing a two-color “dancing” light bullet
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.
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.
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 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.
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.
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.
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