Self-trapped nonlinear matter waves in periodic potentials

We demonstrate that the recent observation of nonlinear self-trapping of matter waves in one-dimensional optical lattices [Th. Anker, Phys. Rev. Lett. 94, 020403 (2005)10.1103/PhysRevLett.94.020403] can be associated with a novel type of broad nonlinear state existing in the gaps of the matter-wave band-gap spectrum. We find these self-trapped localized modes in one-, two-, and three-dimensional periodic potentials, and demonstrate that such novel gap states can be generated experimentally in any dimension.     

Linear and nonlinear waves in crystals with charged dislocations

Based on the principle, a set of equations describing ultrasonic wave propagation in a dielectric crystal with charged dislocations has been derived. The linear dispersion relation has been derived, and the ultrasonic wave velocity and absorbance have been determined. In the case of the nonlinear ultrasonic wave, equations for its amplitude damping and phase variation have been obtained.     

Linear and nonlinear dust lattice waves in plasma crystals

Linear and nonlinear studies of dust lattice waves in a dusty plasma crystal have been carried out on the basis of the Schrödinger equation which is deduced from Poisson's equation for small dust grain potentials. The spatial distribution of the potential in the dust-lattice includes the effect of the whole system of the dust particles. Such a self-consistent analysis gives a dispersion relation for the dust lattice wave, which is different from the expression found earlier. The frequency of the lattice oscillation increases considerably for large grain charges. Furthermore, it is found that an ideal lattice can only exist if the dusty plasma parameters satisfy a definite relationship between the dusty plasma Debye radius, the inter-grain separation, and the grain size. Finally, accounting for the weak nonlinearities, we also derive a Korteweg-de Vries (KdV) equation for the nonlinear dust lattice waves in the long wavelength approximation (kd≪1), where k is the wave number and d the inter-grain spacing.     

Linear and nonlinear magnetohydrodynamic waves in twisted magnetic flux tubes

Dynamics of axisymmetric Alfvén and slow magnetoacoustic waves in weakly twisted magnetic flux tubes is considered. Linear dispersion relations for the waves are derived and analyzed in the presence of the twisting. The weakly nonlinear dynamics is shown to be governed by the Korteweg-de Vries equation. Nonlinear slow body waves appear as a narrowing of tube in a low β plasma and widening of tube, when β ⪢ 1. Nonlinear Alfvén torsional waves appear as a widening (β > 1) and narrowing (β < 1) of tube, accompanied by the local increase of the tube twisting.     

Fringe waves in wedge diffraction

Explicit expressions for the non-uniform currents of the physical theory of diffraction are derived in terms of Fresnel functions for wedge diffraction by taking into account the surface integrals of the modified theory of physical optics. The obtained fringe waves are compared numerically by the asymptotic representations, found in the literature.     

Pulsed nonlinear surface wavesand soliton emission at nonlinear graded index waveguides

Pulsed beam propagation at nonlinear ion-exchange waveguides has been analysed. Critical values of input power and film thickness to obtain emission and excitation of nonlinear surface pulses have been calculated by means of a variational approach in the dispersionless approximation. The analytical expressions obtained can be used as a qualitative guide for deeper computational exploration of the propagation problem and show a good agreement with the numerical simulations presented.     

On the nonlinear energy transfer in the unidirected adiabatic surface waves

The results of numerical simulation of the adiabatic evolution of waves are presented. The model is based on the fully nonlinear 1D equations of potential waves written in conformal coordinates. It is shown that a wave spectrum is subject to strong fluctuations. Most of such fluctuations are reversible, however a residual effect of the fluctuations causes downshifting of the spectrum. The rate of downshifting depends on nonlinearity.     

The nonlinear self-defocusing electromagnetic surface waves in a metalised ferrite film

The dispersion relations for TE s-polarized nonlinear electromagnetic surface waves guided by a metallised ferrite film, surrounded by a nonlinear self-defocusing dielectric cover with intensity dependent refractive indices have been computed. Numerical results are also illustrated to show the propagation characteristics for different values of the film thickness, and at a fixed value of the dielectric-ferrite interface nonlinearity. It has been found that the surface waves exist in both directions of propagation, where the external field is applied. The propagation of these waves is non-reciprocal, and has a resonant interaction in the reverse direction. The power flow carried by the structure has also been calculated for different values of the slab thickness. The non-reciprocity has also been obsorved, and the power flow level can been controlled by the film thickness. of semi-infinite gyromagnetic and nonlinear media². If we increase the operating frequency, the power flow level changes at a fixed film thickness, for 0 and for 0 as in Figs.4. There exist a limited eigenvalues (solutions) with f=17.8GHz for 0, and for different values of the operating frequency for 0. So the eigenvalues and the power flow level can be varied as the operating frequency is tunned. At f=17.8GHz for 0, as in fig.4b, to some value of the power flow there correspond two propagation wave index, which are being related to bistable states of nonlinear surface. All the above mentioned behaviours exhibit the characteristics of microwave switches, isolators, and limiters and could be used in some experimental applications in Microwave Engineering Technology. The other parameters effects as the magnetic field, magnetization, types of ferrite etc. on the dispersion characteristics and the power flow are now under consideration.     

Optically S-polarized surface waves in symmetrical nonlinear sensors: Thermal effects

A surface wave in a planar nonlinear waveguide is a current problem that has several applications in modern electronics and optics such as optical sensors design. The effect of thermal stress on the optical performance of a nonlinear symmetrical sensor is studied. The mathematical forms of the dispersion equation and thermal-stress sensitivity are analytically derived and plotted numerically. It is found that the thermal sensitivity of the sensor can be controlled by tuning the core size, by changing the loading materials, and by carefully selecting the materials.     

New nonlinear magnetostatic surface waves in a ferromagnetic (YIG)

The general propagation characteristics of magnetostatic surface waves guided by a single interface of a semi-infinite nonlinear dielectric cover and a ferromagnetic substrate (YIG) have been derived. The nonlinear dielectric cover has intensity dependent refractive indices. The magnetostatic approximation is considered and retardation is ignored in describing the electromagnetic fields in the structure. The used magnetostatic approximation is leading to new waves and might be called nonlinear magnetostatic surface waves. The propagation of these waves is non-reciprocal in contrast to the linear magnetostaic surface waves, which had been only found in the negative direction of propagation.     

Surface acoustic waves in an elastic wedge media

We consider surface acoustic waves in an elastic wedge media. It is established that the investigated waves substantially differ from known ones. For example, the movement of surface Rayleigh wave in the direction to the edge leads to a change of its structure, accompanied by the splitting of the initial wave to two separate modes and radiation of shift and longitudinal waves. Along the edge of the wedge the surface wave is strongly localized in the transverse direction. Are discussed the properties of the wedge antisymmetric normal waves, propagating parallel to the edge of the wedge.     

Linear and nonlinear intersubband optical absorption and refractive index change in asymmetrical semi-exponential quantum wells

Linear and nonlinear intersubband optical absorption and refractive index change in asymmetrical semi-exponential quantum wells are theoretically investigated within the framework of the compact–density–matrix approach and iterative method. The wave functions are obtained by using the effective mass approximation. The energy levels are obtained by numerical method. It is found that the optical absorption coefficients and refractive index changes are strongly affected not only by σ   and _U0$U_0$, but also by the incident optical intensity.     

Linear gravitational waves

The equations for a weak gravitational field are investigated without the usual simplifications; attention is paid to the difference between gravitational and electromagnetic waves.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 98–101, February, 1982.     

Excitation of surface waves near the boundary of nonlinear induced inhomogeneities

Trapping the inclined beam in a surface wave with a powerful reference beam at another frequency in defocusing media with cubic or cascade quadratic nonlinearity is investigated for the first time. The results from numerical simulations of the dynamics of flat and cylindrical surface wave formation are presented. Gaussian, Hyper-Gaussian, slit, and tube reference beams are considered.     

Basic properties of nonlinear surface charge waves at a plasma boundary

The nonlinear properties of surface charges are here analyzed under ideal conditions. We thus deduce a new single equation from the wellknown equations which govern the cold electron plasma motion. Simple formulas that describe the propagation of surface charge perturbations along the plasma boundary are also found.     

Air-coupled detection of nonlinear Rayleigh surface waves to assess material nonlinearity

This research presents a new technique for nonlinear Rayleigh surface wave measurements that uses a non-contact, air-coupled ultrasonic transducer; this receiver is less dependent on surface conditions than laser-based detection, and is much more accurate and efficient than detection with a contact wedge transducer. A viable experimental setup is presented that enables the robust, non-contact measurement of nonlinear Rayleigh surface waves over a range of propagation distances. The relative nonlinearity parameter is obtained as the slope of the normalized second harmonic amplitudes plotted versus propagation distance. This experimental setup is then used to assess the relative nonlinearity parameters of two aluminum alloy specimens (Al 2024-T351 and Al 7075-T651). These results demonstrate the effectiveness of the proposed technique – the average standard deviation of the normalized second harmonic amplitudes, measured at locations along the propagation path, is below 2%. Experimental validation is provided by a comparison of the ratio of the measured nonlinearity parameters of these specimens with ratios from the absolute nonlinearity parameters for the same materials measured by capacitive detection of nonlinear longitudinal waves.