We demonstrate a new type of soliton formation arising from the interaction of multiple two-dimensional Airy beams in a nonlinear medium. While in linear regime, interference effects of two or four spatially displaced Airy beams lead to accelerated intensity structures that can be used for optical induction of novel light guiding refractive index structures, the nonlinear cross-interaction between the Airy beams decelerates their bending and enables the formation of straight propagating solitary states. Our experimental results represent an intriguing combination of two fundamental effects, accelerated optical beams and nonlinearity, together enable novel mechanisms of soliton formation that will find applications in all-optical light localization and switching architectures. Our experimental results are supported by corresponding numerical simulations.
Dynamical and steady-state behavior of beams propagating in nematic liquid crystals (NLCs) is analyzed. A well-known model for the beam propagation and the director reorientation angle in a NLC cell is treated numerically in space and time. The formation of steady-state soliton breathers in a threshold region of beam intensities is displayed. Below the region the beams diffract, above the region spatiotemporal instabilities develop, as the input intensity and the material parameters are varied. Curiously, the only kind of solitons we could demonstrate in our numerical studies was the breathers. Despite repeated efforts, we could not find the solitons with a steady profile propagating in the NLC model at hand.
In order to meet experimental conditions, the generation, evolution, and self-stabilization of optical dissipative light bullets from non-spherically-symmetric input pulses is studied. Steady-state solutions of the ͑3+1͒-dimensional complex cubic-quintic Ginzburg-Landau equation are computed using the variational approach with a trial function asymmetric with respect to three transverse coordinates. The analytical stability criterion is extended to systems without spherical symmetry, allowing determination of the domain of dissipative parameters for stable solitonic solutions. The analytical predictions are confirmed by numerical evolution of the asymmetric input pulses toward stable dissipative light bullets. Once established, the dissipative light bullet remains surprisingly robust.Complex nonlinear dissipative systems are now a subject of very broad interest ͓1͔. A wide class of such systems, ranging from nonlinear optics, plasma physics, and fluid dynamics to superfluidity, superconductivity, and Bose-Einstein condensates, can be modeled by complex Ginzburg-Landau equations ͓2͔. Stable exact analytical solutions of multidimensional complex cubic-quintic Ginzburg-Landau equations ͑CQGLEs͒ do not exist ͓3͔. Such nonintegrable systems can be solved only numerically. The domains of parameters where the solutions are stable, giving fully localized spatiotemporal dissipative solitons, have been obtained only by numerical simulations ͓4,5͔. However, an analytical approach, even though approximate, is needed in order to guide simulations and to avoid the tedious numerical computations necessary to determine the stability domain point by point ͓6͔. In a recent publication ͓7͔ we used the variational method extended to dissipative systems, to establish this stability domain of parameters for a spherically symmetric CQGLE. Indeed, an analytical stability criterion for dissipative one-, two-, and three-dimensional solitons was established and confirmed by exhaustive numerical simulations. Such a criterion provides analytically a broad domain of input parameters for generation of stable ͑3+1͒-dimensional solitons called dissipative light bullets.The objective of the present work is to extend the synergy of our analytical and numerical approach in order to study a much broader class of Ginzburg-Landau systems involving no spherical symmetry. In spherically symmetric CQGLEs, second-order derivatives are made with respect to the light bullet radius r = ͱ x 2 + y 2 + t 2 , imposing constraints on the independent transverse space ͑x and y͒ and time ͑t͒ variables ͑see Eq. ͑1͒ in Refs. ͓6,7͔͒. Such a constraint on input pulses seriously limits the class of considered systems and their experimental realization ͓8,9͔. Therefore, here we study the ͑3+1͒-dimensional complex cubic-quintic Ginzburg-Landau equations for the normalized field envelope E, describing separately the diffractions along the x and y coordinates and the anomalous group velocity dispersion in time t without such a constraint,In order to prevent wave collapse a s...
We investigate numerically the propagation of self-trapped optical beams in nematic liquid crystals. Our analysis includes both spatial and temporal behavior. We display the formation of stable solitons in a narrow threshold region of beam intensities for fixed birefringence, and depict their spatiotemporal instabilities as the input intensity and the birefringence are increased. We demonstrate the breathing and filamentation of solitons above the threshold with increasing input intensity, and discover a convective instability with increasing birefringence. We consider the propagation of complex beam structures in nematic liquid crystals, such as dipoles, beam arrays, and vortices.
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