Spatiotemporal solitons in birefringent media near the zero-dispersion point (original) (raw)
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Stabilization of spatiotemporal solitons in Kerr media by dispersive coupling
Optics letters, 2015
We introduce a mechanism to stabilize spatiotemporal solitons in Kerr nonlinear media, based on the dispersion of linear coupling between the field components forming the soliton states. Specifically, we consider solitons in a two-core guiding structure with inter-core coupling dispersion (CD). We show that CD profoundly affects properties of the solitons, causing the complete stabilization of the otherwise highly unstable spatiotemporal solitons in Kerr media with focusing nonlinearity. We also find that the presence of CD stimulates the formation of bound states, which, however, are unstable.
Asymmetric spatio-temporal optical solitons in media with quadratic nonlinearity
Optics Communications, 1998
We find exact one-parameter families of stationary two-dimensional light bullets in the form of solitons localized in space and time in diffractive and dispersive nonlinear media under conditions for second-harmonic generation. We study the shape and various features of the solitons, including their stability during propagation, with emphasis on the general case of unequal group-velocity dispersions for the fundamental and second-harmonic waves when the transverse spatio-temporal shape of the solitons is asymmetric. It is shown that, when propagating in two-dimensional geometries, most of the spatio-temporal solitons are dynamically stable. q 1998 Elsevier Science B.V. All rights reserved. 0030-4018r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved.
Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity
Physical Review E, 1997
We consider solutions to the second-harmonic generation equations in two-and three-dimensional dispersive media in the form of solitons localized in space and time. As is known, collapse does not take place in these models, which is why the solitons may be stable. The general solution is obtained in an approximate analytical form by means of a variational approach, which also allows the stability of the solutions to be predicted. Then, we directly simulate the two-dimensional case, taking the initial configuration as suggested by the variational approximation. We thus demonstrate that spatiotemporal solitons indeed exist and are stable. Furthermore, they are not, in the general case, equivalent to the previously known cylindrical spatial solitons. Direct simulations generate solitons with some internal oscillations. However, these oscillations neither grow nor do they exhibit any significant radiative damping. Numerical solutions of the stationary version of the equations produce the same solitons in their unperturbed form, i.e., without internal oscillations. Strictly stable solitons exist only if the system has anomalous dispersion at both the fundamental harmonic and second harmonic ͑SH͒, including the case of zero dispersion at SH. Quasistationary solitons, decaying extremely slowly into radiation, are found in the presence of weak normal dispersion at the second-harmonic frequency.
Communications in Nonlinear Science and Numerical Simulation, 2010
This paper studies optical solitons with non-Kerr law nonlinearity, in the presence of inter-modal dispersion. The coefficients of group velocity dispersion, nonlinearity and inter-modal dispersion terms have time-dependent coefficients. The types of nonlinearity that are considered are Kerr, power, parabolic and dual-power laws. The solitary wave ansatz is used to carry out the integration of the governing nonlinear Schrödinger's equation with time-dependent coefficients. Both, bright and dark optical solitons, are considered, in this paper. Finally, numerical simulations are also given in each of these cases. The only necessary condition for these solitons to exist is that these time-dependent coefficients of group velocity dispersion and inter-modal dispersion are Riemann integrable.
Spatiotemporal optical solitons
In the course of the past several years, a new level of understanding has been achieved about conditions for the existence, stability, and generation of spatiotemporal optical solitons, which are nondiffracting and nondispersing wavepackets propagating in nonlinear optical media. Experimentally, effectively two-dimensional (2D) spatiotemporal solitons that overcome diffraction in one transverse spatial dimension have been created in quadratic nonlinear media. With regard to the theory, fundamentally new features of light pulses that self-trap in one or two transverse spatial dimensions and do not spread out in time, when propagating in various optical media, were thoroughly investigated in models with various nonlinearities. Stable vorticity-carrying spatiotemporal solitons have been predicted too, in media with competing nonlinearities (quadratic–cubic or cubic–quintic). This article offers an up-to-date survey of experimental and theoretical results in this field. Both achievements and outstanding difficulties are reviewed, and open problems are highlighted. Also briefly described are recent predictions for stable 2D and 3D solitons in Bose–Einstein condensates supported by full or low-dimensional optical lattices.
Optical solitons in birefringent fibers with spatio-temporal dispersion
Optik, 2014
This paper studies the propagation of solitons through birefringent fibers in the presence of spatiotemporal dispersion. Both Kerr and parabolic laws of nonlinearity are addressed. The exact 1-soliton solutions are obtained. There are several constraint conditions that ensure soliton solutions are derived. Three types of solitons are obtained: bright, dark and singular solitons.
Multi-frequency spatial solitons in Kerr media
Optics Communications, 1994
We investigate an expanded class of self-guided beams (or spatial solitons), which consist of two or more different optical frequencies, in Kerr media. We show both analytically and numerically that when the nonlinearity is focussing, these sofitons are all very stable and may be excited by end-fire launching, while in defocussing media, they are all unstable and break into filaments on propagation. We also show that the variational method with simple trial functions, which is quite useful in describing single-frequency self-guided beams, does not give a satisfactory description of the interaction between two or more self-guided beams at different frequencies. J J J J J J J J x(~m) Fig. 2. Stable propagation of a perturbed three-frequency beam with ~/122 = 1.2 and 7/]23 = 1.45. Shown here is the second (mid-frequency) component, with initial W = 3.
Communications in Nonlinear Science and Numerical Simulation, 2018
The dynamics of two-component solitons is studied, analytically and numerically, in the framework of a system of coupled extended nonlinear Schrödinger equations, which incorporate the cross-phase modulation, pseudo-stimulated-Raman-scattering (pseudo-SRS), cross-pseudo-SRS, and spatially inhomogeneous second-order dispersion (SOD). The system models co-propagation of electromagnetic waves with orthogonal polarizations in plasmas. It is shown that the soliton's wavenumber downshift, caused by pseudo-SRS, may be compensated by an upshift, induced by the inhomogeneous SOD, to produce stable stationary two-component solitons. The corresponding approximate analytical solutions for stable solitons are found. Analytical results are well confirmed by their numerical counterparts. Further, the evolution of inputs composed of spatially even and odd components is investigated by means of systematic simulations, which reveal three different outcomes: formation of a breather which keeps opposite parities of the components; splitting into a pair of separating vector solitons; and spreading of the weak odd component into a small-amplitude pedestal with an embedded dark soliton. Highlights >Vector solitons in coupled extended nonlinear Schrödinger equations are studied. >We consider media with a pseudo-Raman-scattering and inhomogeneous dispersion. >Analytical and numerical methods are employed. >Soliton solutions are found and investigated. >Evolution of inputs with opposite parities of the two components is explored.
Chinese Journal of Physics, 2019
In this paper, we obtain optical soliton solutions for non-Kerr law nonlinear Schrödinger equation (NLSE) with third order (3OD) and fourth order dispersions (4OD). We will use two integration schemes, namely sincosine method and Bernoulli's equation approach with five laws of nonlinearities. Sine-cosine method is applicable to Kerr, power and anti-cubic laws, this method provides bright soliton solutions. The second method is applicable to parabolic and cubic quintic laws, this method generates dark soliton. The results may be used in discussing the propagation of optical solitons in highly dispersive media with Kerr, power, anti-cubic, parabolic and cubic quintic law nonlinearities.