In this work, we numerically investigate and analyze the properties of an optical structure composed of successive thin film layers that can possess high values of nonlinear susceptibility, affecting the refractive index and/or the absorption coefficient. By applying the transmission line method properly modified to resolve the inclusion of third-order nonlinearity, the spectral reflectivity and transmission of such a device are presented. Specifically, the method is applied to a conceptual design of a distributed Bragg reflector. Optical bistability can be observed, which translates not only to a change in the value of reflectivity as the input power increases, but also to a shift of the Bragg wavelength.
In this work we numerically investigate and analyse the properties of an optical structure comprised of successive thin film layers that can possess high values of nonlinear susceptibility, affecting the refractive index and/or the absorption coefficient. By applying the Transmission Line Method (TLM), properly modified to resolve the inclusion of third order nonlinearity, the spectral reflectivity and transmission of such a device are presented. Specifically, the method is applied for the case of conceptual design of a Distributed Bragg Reflector (DBR). Optical bistability can be observed, which translates not only to a change in the value of reflectivity, as the input power increases, but also to a shift of the Bragg wavelength.
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.
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.
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.
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 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.
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.
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