Energy transfer to an anharmonic diatomic system

We model an anharmonic diatomic molecule using deformed creation and annihilation operators such that the energy spectrum generated by a Hamiltonian of the harmonic oscillator's form written in terms of deformed operators is similar to that of a Morse potential. We construct an approximate time evolution operator and evaluate transition probabilities which are compared with those obtained by an expansion in a basis of Morse eigenfunctions. The algebraic results compare favorably with the numerical results.     

The lattice dynamics of an anharmonic crystal

The theory of the physical properties of an anharmonic crystal is discussed by using the thermodynamic Green's functions for the phonons. A perturbation procedure is developed to obtain the Green's functions and it is shown that for some purposes a quasi-harmonic approximation is useful, in which the frequencies of the normal modes are those determined by infra-red or neutron spectrometry. The thermodynamic, elastic, dielectric and scattering properties of an anharmonic crystal are discussed in terms of the Green's functions, and detailed expressions are given for the more important contributions. Detailed numerical calculations are presented of the thermal expansion, dielectric properties and shapes of some of the inelastically scattered neutron groups, for sodium iodide and potassium bromide. The calculations, which give reasonable agreement with experiment, show that even at quite low temperatures, the lifetimes of some of the normal modes can be quite short. By using the quasi-harmonic approximation it is shown that the large temperature dependence of the normal modes in a ferroelectric crystal can be treated adequately.     

Gap solitons in an extended anti-directional coupler

A nonlinear solitary wave in an inhomogeneous medium formed by two tunnel-coupled waveguides is considered. One of the waveguides is manufactured from an ordinary dielectric, while the second has negative refraction. The results from numerical simulations demonstrate the high stability of gap solitons with respect to collisions. It is discovered that for low relative velocities of two colliding solitons, a longlived coupled state of these solitons can be formed.     

First order phase transition in an anharmonic ising lattice

Criteria are derived for the existence of a first order phase transition in a compressible anharmonic Ising lattice. The analysis is based on a variational calculation and on the assumption that a compressible harmonic Ising lattice does not show a first order transition. A first order transition can occure only if the lattice and magnetic Grüneisen constants have the same sign and if the pressure is below some critical value. At this pressure the transition changes from first to second order. The results are applied to ammonium cloride exhibiting an order disorder transition of this type.     

Gap solitons in metamaterials

Electromagnetic localization and the existence of gap solitons in nonlinear metamaterials, which exhibit a stop band in their linear spectral response, is theoretically investigated. For a self-focusing Kerr nonlinearity, the equation for the electric field envelope with carrier frequency in the stop band—where the magnetic permeability µ(?) is positive and the dielectric permittivity ε(?) is negative—is described by a nonlinear Klein-Gordon equation with a dispersive nonlinear term. A family of standing and moving localized waves for both electric and magnetic fields is found, and the role played by the nonlinear dispersive term on solitary wave stability is discussed.     

Gap polariton solitons

We report the existence, and study mobility and interactions of gap polariton solitons in a microcavity with a periodic potential, where the light field is strongly coupled to excitons. Gap solitons are formed due to the interplay between the repulsive exciton-exciton interaction and cavity dispersion. The analysis is carried out in an analytical form, using the coupled-mode (CM) approximation, and also by means of numerical methods.     

Surface lattice solitons

We study theoretically nonlinear surface waves in optical lattices and show that solitons can exist at the heterointerface between two different semi-infinite 1D waveguide arrays, as well as at the boundaries of a 2D nonlinear lattice. The existence and properties of these surface soliton solutions are investigated in detail.     

Disordered lattice solitons

We study the properties of a nonlinear Schr?dinger equation in the presence of a disordered potential modeling a waveguide array. We find that, for both signs of the nonlinearity, there is a large number of soliton families each one possessing different quantitative properties. However, all these families can be categorized to only a few classes with the same qualitative properties. Highly confined solitons exist in each waveguide of the lattice. In addition, solitons families originate from each Anderson mode. Resonant interactions between a soliton and an Anderson mode can take place, leading to broadening of the soliton profile.     

Multicolor lattice solitons

We report on the existence of multicolor solitons supported by periodic lattices made from quadratic nonlinear media. Such lattice solitons bridge the gap between continuous solitons in uniform media and discrete solitons in strongly localized systems and exhibit a wealth of new features. We discovered that, in contrast to uniform media, multipeaked lattice solitons are stable. Thus they open new opportunities for all-optical switching based on soliton packets.     

Dynamics of kicked matter-wave solitons in an optical lattice

We investigate effects of the application of a kick to one-dimensional matter-wave solitons in a self-attractive Bose-Einstein condensate trapped in an optical lattice. The resulting soliton’s dynamics is studied within the framework of the time-dependent nonpolynomial Schrödinger equation. The crossover from the pinning to quasi-free motion crucially depends on the size of the kick, strength of the self-attraction, and parameters of the optical lattice.     

Dipole solitons in an optical lattice with longitudinal modulation

In this paper, we numerically demonstrate the (1+1)-dimensional dipole solitons can exist in a new Kerr-type optical lattice with longitudinal modulation that fades away and boosts up alternately. The solitons whose two dipoles simultaneously located at one lattice site and at two adjacent lattice sites are investigated, respectively. The results show that, in the two cases, the dipole solitons can be stably trapped in this kind of lattice by properly adjusting lattice parameters and soliton parameters when the repulsive force of dipoles balances the centripetal force resulting from the lattice potential effect on dipole solitons. In addition, the trapping of dipole solitons with an incident angle or the initial center position is discussed.     

Gap solitons in waveguide arrays

Bright and dark spatial gap solitons are demonstrated in waveguide arrays. These gap solitons travel across the array at zero transverse velocity, in complete analogy with stationary (immobile) temporal gap solitons. Furthermore, the launching configuration for observing these stationary gap solitons is shown to be the analog of an "ideal experiment" for observing stationary temporal gap solitons, never observed so far. A clear distinction is established between the family of Floquet-Bloch solitons in general and discrete solitons in particular, and the limiting case of gap solitons.     

Dissipative photonic lattice solitons

We show that discrete dissipative optical lattice solitons are possible in waveguide array configurations that involve periodically patterned semiconductor optical amplifiers and saturable absorbers. The characteristics of these low-power soliton states are investigated, and their propagation constant eigenvalues are mapped on Floquet-Bloch band diagrams. The prospect of observing such low-power dissipative lattice solitons is discussed in detail.     

Multiband vector lattice solitons

We predict multiband vector solitons in nonlinear periodic systems, using photonic lattices as a prime example. The solitons consist of two optical fields arising from different bands of the transmission spectrum, which involve both bound state and radiation mode components.     

Long-range effects on superdiffusive algebraic solitons in anharmonic chains

Studies on thermal diffusion of lattice solitons in Fermi-Pasta-Ulam (FPU)-like lattices were recently generalized to the case of dispersive long-range interactions (LRI) of the Kac-Baker form. The variance of the soliton position shows a stronger than linear time-dependence (superdiffusion) as found earlier for lattice solitons on FPU chains with nearest-neighbour interactions (NNI). Since the superdiffusion seems to be generic for nontopological solitons, we want to illuminate the role of the soliton shape on the superdiffusive mechanism. Therefore, we concentrate on an FPU-like lattice with a certain class of power-law long-range interactions where the solitons have algebraic tails instead of the exponential tails in the case of FPU-type interactions (with or without Kac-Baker LRI).Despite of structurally similar Langevin equations which hold for the soliton position and width of the two soliton types, the algebraic solitons reach the superdiffusive long-time limit with a characteristic t^3/2 time-dependence much faster than exponential solitons. The soliton shape determines the diffusion constant in the long-time limit that is approximately a factor of π smaller for algebraic solitons. Our results appear to be generic for nonlinear excitaitons in FPU-chains, because the same superdiffusive time-dependence was also observed in simulations with discrete breathers.     

Two-dimensional optical lattice solitons

We study various families of two-dimensional discrete or lattice solitons, and show that they are possible only when their power level exceeds a critical threshold. In addition, we show that gap-lattice solitons exist only when the lattice possesses a complete 2D band gap. Our results suggest that these conditions are universally valid, irrespective of the nature of the nonlinearity or the specific structure of the index lattice. The analysis explains fundamental aspects of behavior of two-dimensional discrete solitons that have been very recently observed in photosensitive optical crystals.     

Vector solitons in the dynamics of anharmonic monatomic lattices

It is shown that three types of solitary acoustic waves can develop in anharmonic crystal lattices corresponding to the three branches of acoustic phonons. A system of three nonlinear Schrödinger equations is derived to describe this situation. For greatly different group velocities, the interaction between solitons reduces collisions between them. When the group velocities of the different acoustic modes in a lattice are close to one another, bound states of the corresponding types of solitary waves occur. Bound states of this sort are vector solitons, whose polarization varies along the pulse. If the transverse acoustic modes are degenerate in velocity, the situation is extremely similar to the propagation of pulses in optical fibers.