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.
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.
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
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
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.
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.