The existence and robustness of dark vortices in bi-dispersive and/or normally dispersive self-defocusing nonlinear
media is demonstrated. The underlying equation is the bi-dispersive three-dimensional nonlinear Schrödinger
equation. These solutions can be considered as extensions of two-dimensional dark vortex solitons which, along
the third dimension, remain localized due to the interplay between diffraction and nonlinearity. Such vortex
solitons can be observed in optical media with normal dispersion, normal diffraction, and defocusing nonlinearity.
In this work we investigate the dynamics of a spatial soliton pulse under the presence of a linear Periodic Wave
(PW), which dynamically induces a photonic lattice. We consider that propagation phenomena are governed by
the well-known non-linear Schrodinger equation (NLSE), while Kerr-type non-linearity is in effect. Interaction
phenomena are analyzed by forming a non-linear coupled differential equation system of the evolution of the
soliton-beam parameters. Direct numerical simulations of the NLS equation are shown to be in good agreement
with the solution of the dynamical system, for a wide range of the parameters.
Optical spatio-temporal X-wave-like pattern formation is investigated in a voltage-controlled array of channel
waveguides in nematic liquid crystals and in generic optically dispersive nonlocal nonlinear media as well. The nonlinear
response of the system is governed by the spatio-temporal diffusion equation for the medium's response to the optical
field, while the respective equation for the evolving light pulse may incorporate normal temporal dispersion. The
associated discrete nonlinear Schr&diaero;dinger equation which governs the evolution of the temporal profiles of a discrete set
of modes is derived and is studied numerically. The results are obtained via full numerical investigation of the array with
beam propagation techniques.
Optical pattern formation in space and time in slab nematic liquid crystal cells is investigated. The nonlinear response of
the system is governed by the spatiotemporal diffusion equation for the molecular reorientation while the respective
coupled equation for the evolving light pulse may incorporate normal or anomalous temporal dispersion, for the sake of
generality in potential applications. Continuous-wave background enhancement of pattern formation is demonstrated.
Evolution of the optical field is studied numerically via the beam propagation technique.
The dynamics of dark spatial soliton beams and their interactions under the presence of a continuous wave (CW),
which dynamically induces a photonic lattice, are investigated. It is shown that appropriate selections of the
characteristic parameters of the CW result in different soliton propagation and interaction scenarios, suggesting
a reconfigurable soliton control mechanism. Our analytical approach, based on the variational perturbation
method, provides a dynamical system for the dark soliton evolution parameters. Analytical results are shown in
good agreement with direct numerical simulations.
We study the dynamics of beams propagating in a planar waveguide with Kerr-type nonlinearity where a Bragg
grating is written and diffraction is taken under consideration. The interaction of the forward field with the
backscattered one due to the presence of the grating is considered both in the case of planar waves, and in the
case of pulse propagation. Our results are demonstrated via numerical simulation of the governing propagation
equations.
The existence and robustness of dark vortices in bi-dispersive and/or normally dispersive self-defocusing nonlinear
media is demonstrated. The underlying equation is the bi-dispersive three-dimensional nonlinear Schrdinger
equation. The dark vortices are investigated numerically as well as variationally. These vortices can be considered
as extensions of two-dimensional dark vortex solitons which, along the third dimension, remain localized due
to the interplay between diffraction and nonlinearity. Linear stability analysis predicts that for fairly long
propagation distances these objects are subject to a very weak transverse instability (in the temporal domain).
On this basis the maximum growth rate of the instability is estimated. However, numerical simulations depict
that 3D vortices are robust objects. Instability is observed only in the case where the vortex is subjected to
relatively strong transverse perturbation. Furthermore, in our simulation is observed that a dark vortex does not
break into vortices of a lower vorticity. The variational approach predicts that the synenergy content (the finite
ambient energy that remains when the infinite energy of the dark object is excluded) of a vortex of high vorticity
is lower than the sum of the synenergies of unitary vortices with the same pedestal. Such vortex solitary objects
can be observed in optical media with normal dispersion, normal diffraction, and defocusing nonlinearity such
as specific AlGaAs alloys.
We investigate the possibility of signal waveguiding, through the formation of spatial solitons in slab cells containing a nematic liquid crystal, biased externally by a quasi-static electric field. The model equations assume a non-local response on the coupling between the optical beam and the elastic properties of the molecules. A semi-analytical approach is achieved via the variational method. Comparison with numerical results from the full model equations is shown and the selection of suitable initial profiles, as far as stability is concerned, is investigated.
In this work we investigate the dynamics of a spatial soliton pulse under the presence of a linear Periodic Wave (PW), which dynamically induces a photonic lattice. We consider that propagation phenomena are governed by the well-known non-linear Schrodinger equation (NLSE), while Kerr-type non-linearity is in effect. Interaction
phenomena are analyzed by forming a non-linear coupled differential equation system of the evolution of the soliton-beam parameters, which are the pulse amplitude, the transverse velocity, the mean position and the phase. The dynamical system governing the evolution of soliton parameters is derived by utilizing a quasi-particle
approach based on the perturbed inverse scattering method. Direct numerical simulations of the NLS equation are shown to be in good agreement with the solution of the dynamical system, for a wide range of the parameters. The results show that efficient photon management, in terms of soliton control and beam steering, can occur for appropriate choices of the characteristics of the periodic lattice, which are the amplitude, the period, the pulse duration, the relative position with respect to the soliton beam in the transverse dimension
and the initial transverse velocity.
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