ABSTRACT
The self-structuring of laser light in an artificial optical medium composed of a colloidal suspension of nanoparticles is demonstrated using variational and numerical methods extended to dissipative systems. In such engineered materials, competing nonlinear susceptibilities are enhanced by the light induced migration of nanoparticles. The compensation of diffraction by competing focusing and defocusing nonlinearities, together with a balance between loss and gain, allow for self-organization of light and the formation of stable dissipative breathing vortex solitons. Due to their robustness, the breathers may be used for selective dynamic photonic tweezing of nanoparticles in colloidal nanosuspensions.
ABSTRACT
Using a combination of the variation approximation and direct simulations, we consider the model of the light transmission in nonlinearly amplified bulk media, taking into account the localization of the gain, i.e., the linear loss shaped as a parabolic function of the transverse radius, with a minimum at the center. The balance of the transverse diffraction, self-focusing, gain, and the inhomogeneous loss provides for the hitherto elusive stabilization of vortex solitons, in a large zone of the parameter space. Adjacent to it, stability domains are found for several novel kinds of localized vortices, including spinning elliptically shaped ones, eccentric elliptic vortices which feature double rotation, spinning crescents, and breathing vortices.
ABSTRACT
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.
ABSTRACT
The generation and nonlinear dynamics of multidimensional optical dissipative solitonic pulses are examined. The variational method is extended to complex dissipative systems, in order to obtain steady state solutions of the (D + 1)-dimensional complex cubic-quintic Ginzburg-Landau equation (D = 1, 2, 3). A stability criterion is established fixing a domain of dissipative parameters for stable steady state solutions. Following numerical simulations, evolution of any input pulse from this domain leads to stable dissipative solitons.
ABSTRACT
The behavior of counterpropagating self-trapped optical beam structures in nematic liquid crystals is investigated. A time-dependent model for the beam propagation and the director reorientation in a nematic liquid crystal is numerically treated in three spatial dimensions and time. We find that the stable vector solitons can only exist in a narrow threshold region of control parameters. Below this region the beams diffract, above they self-focus into a series of focal spots. Spatiotemporal instabilities are observed as the input intensity, the propagation distance, and the birefringence are increased. We demonstrate undulation, filamentation, and convective dynamical instabilities of counterpropagating beams. Qualitatively similar behavior as of the copropagating beams is observed, except that it happens at lower values of control parameters.
ABSTRACT
The nonlinear dynamics of laser beams carrying phase singularity in media with cubic-quintic nonlinearity changing from self-focusing to self-defocusing is examined. A novel kind of stable nonlocalized optical vortices appears in such media as well as localized vortex solitons. Linear stability analysis and numerical simulations show the stability of localized vortices only in the defocusing region.
