Yannis Kominis

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.

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...

Scattering of radio frequency waves by blobs in tokamak plasmasa)

The density fluctuations and blobs present in the edge region of magnetic fusion devices can scatter radio frequency (RF) waves through refraction, reflection, diffraction, and coupling to other plasma waves. This, in turn, affects the spectrum of the RF waves and the electromagnetic power that reaches the core of the plasma. The usual geometric optics analysis of RF scattering by density blobs accounts for only refractive effects. It is valid when the amplitude of the fluctuations is small, of the order of 10%, compared to the background density. In experiments, density fluctuations with much larger amplitudes are routinely observed, so that a more general treatment of the scattering process is needed. In this paper, a full-wave model for the scattering of RF waves by a blob is developed. The full-wave approach extends the range of validity well beyond that of geometric optics; however, it is theoretically and computationally much more challenging. The theoretical procedure, although similar to that foll...

Interlaced linear-nonlinear optical waveguide arrays

The system of coupled discrete equations describing a two-component superlattice with interlaced linear and nonlinear constituents is studied as a basis for investigating binary waveguide arrays, such as ribbed AlGaAs structures, among others. Compared to the single nonlinear lattice, the interlaced system exhibits an extra band-gap controlled by the, suitably chosen by design, relative detuning. In more general physics settings, this system represents a discretization scheme for the single-equation-based continuous models in media with transversely modulated linear and nonlinear properties. Continuous wave solutions and the associated modulational instability are fully analytically investigated and numerically tested for focusing and defocusing nonlinearity. The propagation dynamics and the stability of periodic modes are also analytically investigated for the case of zero Bloch momentum. In the band-gaps a variety of stable discrete solitary modes, dipole or otherwise, in-phase or of staggered type are found and discussed.

Quasilinear theory of electron transport by radio frequency waves and nonaxisymmetric perturbations in toroidal plasmas

The use of radio frequency waves to generate plasma current and to modify the current profile in magnetically confined fusion devices is well documented. The current is generated by the interaction of electrons with an appropriately tailored spectrum of externally launched rf waves. In theoretical and computational studies, the interaction of rf waves with electrons is represented by a quasilinear diffusion operator. The balance, in steady state, between the quasilinear operator and the collision operator gives the modified electron distribution from which the generated current can be calculated. In this paper the relativistic operator for momentum and spatial diffusion of electrons due to rf waves and nonaxisymmetric magnetic field perturbations is derived. Relativistic treatment is necessary for the interaction of electrons with waves in the electron cyclotron range of frequencies. The spatial profile of the rf waves is treated in general so that diffusion due to localized beams is included. The nonaxis...

ANALYTICAL SOLUTIONS OF SYSTEMS WITH PIECEWISE LINEAR DYNAMICS

A class of nonautonomous dynamical systems, consisting of an autonomous nonlinear system and an autonomous linear periodic system, each acting by itself at different time intervals, is studied. It is shown that under certain conditions for the durations of the linear and the nonlinear time intervals, the dynamics of the nonautonomous piecewise linear system is closely related to that of its nonlinear autonomous component. As a result, families of explicit periodic, nonperiodic and localized breather-like solutions are analytically obtained for a variety of interesting physical phenomena.

Continuous-wave-controlled steering of spatial solitons

Spatial-soliton interactions with continuous waves (cw’s) are studied, with numerical simulations as well as a quasi-particle perturbation method, and the critical dependency of their features on the parameters of the cw is shown. The intentional mixing of appropriately launched cw’s with spatial solitons is proposed as a technique for the design and implementation of all-optical, dynamically reconfigurable devices.

Canonical perturbation theory for complex electron dynamics in gyrotron resonators

Complex electron dynamics in gyrotron resonators are analyzed in the context of the Hamiltonian formalism. Application of the canonical perturbation theory provides analytical approximate invariants of the electron motion. The latter are used for describing the resonant structure of the electron phase space and the electron rest energies at the output of the cavity. Hysteresis effects are also described through analytic expressions and approximate electron distribution functions are provided. The general case of resonant interaction at an arbitrary harmonic of the electron cyclotron frequency is considered and the effect of a varying frequency mismatch is studied. Also, the case of electron interaction with multiple rf modes is investigated.