Kyriakos Hizanidis

Power dependent soliton location and stability in complex photonic structures

The presence of spatial inhomogeneity in a nonlinear medium results in the breaking of the translational invariance of the underlying propagation equation. As a result traveling wave soliton solutions do not exist in general for such systems, while stationary solitons are located in fixed positions with respect to the inhomogeneous spatial structure. In simple photonic structures with monochromatic modulation of the linear refractive index, soliton position and stability do not depend on the characteristics of the soliton such as power, width and propagation constant. In this work, we show that for more complex photonic structures where either one of the refractive indices (linear or nonlinear) is modulated by more than one wavenumbers, or both of them are modulated, soliton position and stability depends strongly on its characteristics. The latter results in additional functionality related to soliton discrimination in such structures. The respective power (or width/propagation constant) dependent bifurcations are studied in terms of a Melnikov-type theory. The latter is used for the determination of the specific positions, with respect to the spatial structure, where solitons can be located. A wide variety of cases are studied, including solitons in periodic and quasiperiodic lattices where both the linear and the nonlinear refractive index are spatially modulated. The investigation of a wide variety of inhomogeneities provides physical insight for the design of a spatial structure and the control of the position and stability of a localized wave.

Lattice solitons in self-defocusing optical media: analytical solutions of the nonlinear Kronig-Penney model

A novel method for obtaining analytical solitary wave solutions of the nonlinear Kronig-Penney model in periodic photonic structures with self-defocusing nonlinearity is applied for providing generic families of solutions corresponding to the gaps of the linear band structure. Characteristic cases are shown to be quite robust under propagation.

Surface solitons in waveguide arrays: Analytical solutions

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 as well as at the interface between two dissimilar nonlinear lattices. The method provides physical insight and understanding of the shape of the solitary wave profile and results to generic classes of localized solutions having either zero or nonzero semi-infinite backgrounds. For all cases, the method provides conditions involving the values of the propagation constant of the stationary solutions, the linear refractive index and the dimensions of 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 such as their remarkable robustness which could facilitate their experimental observation.

X - waves in nonlinear normally dispersive waveguide arrays

We theoretically demonstrate that optical discrete X-waves are possible in normally dispersive nonlinear waveguide arrays. We show that such X-waves can be effectively excited for a wide range of initial conditions and in certain occasions can be generated in cascade. The possibility of observing this family of waves in AlGaAs array systems is investigated in terms of pertinent examples.

Fokker–Planck description of the scattering of radio frequency waves at the plasma edge

In magnetic fusion devices, radio frequency (rf) waves in the electron cyclotron (EC) and lower hybrid (LH) range of frequencies are being commonly used to modify the plasma current profile. In ITER, EC waves are expected to stabilize the neoclassical tearing mode (NTM) by providing current in the island region [R. Aymar et al., Nucl. Fusion 41, 1301 (2001)]. The appearance of NTMs severely limits the plasma pressure and leads to the degradation of plasma confinement. LH waves could be used in ITER to modify the current profile closer to the edge of the plasma. These rf waves propagate from the excitation structures to the core of the plasma through an edge region, which is characterized by turbulence—in particular, density fluctuations. These fluctuations, in the form of blobs, can modify the propagation properties of the waves by refraction. In this paper, the effect on rf due to randomly distributed blobs in the edge region is studied. The waves are represented as geometric optics rays and the refracti...

Universal Probability Distribution Function for Bursty Transport in Plasma Turbulence

Bursty transport phenomena associated with convective motion present universal statistical characteristics among different physical systems. In this Letter, a stochastic univariate model and the associated probability distribution function for the description of bursty transport in plasma turbulence is presented. The proposed stochastic process recovers the universal distribution of density fluctuations observed in plasma edge of several magnetic confinement devices and the remarkable scaling between their skewness S and kurtosis K. Similar statistical characteristics of variabilities have been also observed in other physical systems that are characterized by convection such as the x-ray fluctuations emitted by the Cygnus X-1 accretion disc plasmas and the sea surface temperature fluctuations.

Stabilizing soliton transmission by third-order dispersion in dispersion-compensated fibre links

By means of systematic numerical simulations of pulse (soliton) transmission through a very long nearly dispersion-compensated nonlinear fibre link, including third-order dispersion (TOD), we demonstrate that, for a fixed pulse width, there is a broad interval of values of the pulses peak power in which TOD stabilizes the transmission. In particular, TOD prevents decay of the pulse in the case when the mean second dispersion is (weakly) normal, , and in the case where , TOD suppresses strong internal vibrations of the non-fundamental soliton, making it close to the fundamental one.

STABLE ANTI-DARK LIGHT BULLETS SUPPORTED BY THE THIRD-ORDER DISPERSION

Abstract We consider transverse dynamics of quasi-one-dimensional (Q1D) spatio-temporal solitons governed by the nonlinear Schrodinger equation with the higher-order dispersion. We obtain stable Q1D dark solitons, unstable Q1D anti-dark solitons and stable anti-dark lump solitons in the form of light bullets.

Exact travelling wave solutions for a generalized nonlinear Schrödinger equation

A wide class of exact travelling wave solutions of a generalized nonlinear Schrodinger equation (GNLS) is obtained and analysed in detail. This class of solutions incorporates bright and dark solitary waves, periodic waves, unbounded waves and other solitary waves as asymptotic limits of the periodic or unbounded modes. The method of analysis adopted is based on reducing the GNLS to an ordinary differential equation and studying the phase plane of the resulting dynamical system. Application of the obtained results to the problem of propagation of femtosecond duration pulses in nonlinear optical fibres is also discussed.

An analytical treatment of the effect of axial inhomogeneity on femtosecond solitary waves near the zero dispersion point

A perturbed nonlinear Schrodinger equation, valid for femtosecond pulse propagation in axially inhomogeneous optical fibers near the zero dispersion point, is considered. It is found that for a weak axial nonuniformity, and under certain conditions, this equation can be treated analytically. Exact bright and dark solitary wave solutions are derived and their behavior in the presence of the inhomogeneity is analyzed. The nonuniformity induced time shift of the solitary waves is also obtained. The potential use of this parameter as a diagnostic tool for estimating characteristic parameters of the axial variations is discussed and its range of values is investigated.