Spatiotemporal optical solitons

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.

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.

Pramana, 2001

Recent developments in the study of optical spatiotemporal solitons are reviewed.

2006

We demonstrate the existence of stable three-dimensional spatiotemporal solitons (STSs) in media with a nonlocal cubic nonlinearity. Fundamental (nonspinning) STSs forming one-parameter families are stable if their propagation constant exceeds a certain critical value, that is inversely proportional to the range of nonlocality of nonlinear response. All spinning three-dimensional STSs are found to be unstable.

Optics Communications, 2000

We investigate the possibility of forming spatiotemporal solitons optical bullets in inhomogeneous, dispersive nonlinear media using a graded-index Kerr medium as an example. We use a variational approach to solve the multidimensional, inhomogeneous, nonlinear Schrodinger equation and show that spatiotemporal solitons can be stabilized under certain conditions. We verify their existence by means of a full numerical analysis and show that such solitons should be observable experimentally.

Physical Review A, 2009

By using a powerful reductive perturbation technique, or a multiscale analysis, a generic Kadomtsev-Petviashvili evolution equation governing the propagation of femtosecond spatiotemporal optical solitons in quadratic nonlinear media beyond the slowly-varying envelope approximation is put forward. Direct numerical simulations show the formation, from adequately chosen few-cycle input pulses, of both stable line solitons (in the case of a quadratic medium with normal dispersion) and of stable lumps (for a quadratic medium with anomalous dispersion). Besides, a typical example of the decay of the perturbed unstable line soliton into stable lumps for a quadratic nonlinear medium with anomalous dispersion is also given.

Nature Photonics, 2008

Incoherent optical spatial solitons are self-trapped beams with a multimodal structure that varies randomly in time. They form when their diffraction-broadening, which is governed by their spatial correlations, is balanced by nonlinear interaction between the waves and the medium, resulting in the stationary propagation of the time-averaged intensity structure of the beam. The experimental observation of incoherent solitons has opened up exciting new avenues in soliton science. However, all incoherent spatial solitons observed to date have been supported by nonlinearities with a slow response time, t, that is much longer than the characteristic fluctuation time of the beam, t c ( t. Here, we demonstrate incoherent solitons in effectively instantaneous nonlocal nonlinear media where t ( t c . These solitons exhibit fundamentally new features (for example, propagation at random trajectories), and can be created in various optically nonlinear media, as well as in other fields where the nonlinearity is nonlocal and very fast.

Physical Review E, 2004

We investigate the existence and stability of three-dimensional spatiotemporal solitons in self-focusing cubic Kerr-type optical media with an imprinted two-dimensional harmonic transverse modulation of the refractive index. We demonstrate that two-dimensional photonic Kerr-type nonlinear lattices can support stable oneparameter families of three-dimensional spatiotemporal solitons provided that their energy is within a certain interval and the strength of the lattice potential, which is proportional to the refractive index modulation depth, is above a certain threshold value.

Physical Review E, 2011

We report that defocusing cubic media with spatially inhomogeneous nonlinearity, whose strength increases rapidly enough toward the periphery, can support stable bright localized modes. Such nonlinearity landscapes give rise to a variety of stable solitons in all three dimensions, including 1D fundamental and multihump states, 2D vortex solitons with arbitrarily high topological charges, and fundamental solitons in 3D. Solitons maintain their coherence in the state of motion, oscillating in the nonlinear potential as robust quasi-particles and colliding elastically. In addition to numerically found soliton families, particular solutions are found in an exact analytical form, and accurate approximations are developed for the entire families, including moving solitons.

Physical Review E, 2006

We show that the quadratic ͑ ͑2͒ ͒ interaction of fundamental and second harmonics in a bulk dispersive medium, combined with self-focusing cubic ͑ ͑3͒ ͒ nonlinearity, give rise to stable three-dimensional spatiotemporal solitons ͑STSs͒, despite the possibility of the supercritical collapse, induced by the ͑3͒ nonlinearity. At exact phase matching ͑␤ =0͒, the STSs are stable for energies from zero up to a certain maximum value, while for ␤ 0 the solitons are stable in energy intervals between finite limits.