A novel method is presented for the analytical construction of solitary wave solutions of the nonlinear Kronig-Penney
model in a photonic structure. In order to overcome the restrictions of the coupled-mode theory and the tight-binding
approximation and study the solitary wave formation in a unified model, we consider the original NLSE, with
periodically varying coefficients, modeling a waveguide array structure. The analytically obtained solutions correspond
to gap solitons and form a class of self-localized solutions existing under quite generic conditions. A remarkable
robustness of the solutions under propagation is shown, thus providing potentiality for various applications.
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 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.
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.
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.
In the current work we study beam interaction in media with normal dispersion and self focusing nonlinearity, ruled by
the two dimensional NLSE. The circular or elliptical Gaussian beams propagate over a continuous wave background
(CW) which raises the X-like gain profile of Modulational Instability. That, along with self-focusing nonlinearity, can
lead the beams to collision along the spatial dimension, then to fusion and finally to splitting and creation of two major
filaments that move along the temporal dimension. Thus, the energy and momentum of the beams are effectively
"reallocated" from one dimension to the other. By conducting primarily a numerical study, we reveal the relation of the
resulting filaments to the interacting beams and the characteristics of the CW. Analytical description of this relation is
also attempted and a new mechanism of beam-control is proposed. Explanation of the physical phenomena involved is
also offered.
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.
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.
A novel phase-space method is employed for the construction of analytical stationary solitary waves located at the
interface between a periodic nonlinear lattice of the Kronig-Penney type and a linear (or nonlinear) homogeneous
medium. The method provides physical insight and understanding of the shape of the solitary wave profile and
results to generic classes of localized solutions having a zero background or nonzero semi-infinite background. For
all cases, the method provides conditions for the values of the propagation constant of the stationary solutions and
the linear refractive index in each part in order to assure existence of solutions with specific profile characteristics.
The evolution of the analytical solutions under propagation is investigated for cases of realistic configurations
and interesting features are presented while their remarkable robustness is shown to facilitate their experimental
observation.
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.
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.
The propagation of self-frequency shift of femtosecond soliton pulses is inevitably faced by self-frequency shift, which arises from the Raman effect. The non-linear phenomenon of cross phase modulation (XPM), arising from the collisions between pulses of different frequency, has been proposed as a way to counterbalance the shift in frequency and the subsequent time displacement. However, the co-existence of different frequency channels gives rise to new phenomena, like cross frequency shift and energy exchange between the channels, again due to the Raman effect. The current work is an analytical approach to the phenomena that arise during the co-propagation of sub-picosecond soliton pulses of different frequency. The analysis is based on the direct perturbation method, used on two couple NLS equations and provides insight to the spectral and temporal evolution of the pulses, and to their amplitudes' evolution as well. We look into the effects of incomplete and complete pulse collisions, while the pulses used in the examination are not only of equal widths.
In this work we analyze the optical propagation in a composite dielectric ridged waveguide calculating several parameters that characterize the linear and the nonlinear phenomena. This novel composite waveguide consists of a circular central core and many circular sectoral waveguides at the periphery, while the whole device can be considered as an nonlinear optical coupler. Firstly, we analyze the linear optical propagation in a sectoral dielectric birefringent waveguide calculating the propagation constant, the effective refractive index and the normalized propagation constant in the weak-guidance regime. Several simulations are performed varying some of the parameters of the geometry and the optical frequency in order to produce dispersion diagrams. Following, the electric and magnetic field distributions for the fundamental linear guided modes are derived. Finally, we calculate the linear coupling coefficient between two identical sectoral waveguides, the linear coupling coefficient between a sectoral waveguide and the circular-core waveguide, and the sectoral waveguide mode effective area for the evaluation of Kerr nonlinear coefficient.
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