Nonlinear surface waves in one-dimensional photonic crystals containing left-handed metamaterials

In this review we consider the propagation of nonlinear waves in magnetically structured plasmas. We start from studying nonlinear surface waves on magnetic interfaces and give a derivation of the equation governing propagation of these waves in incompressible plasmas. We present the results of a numerical solution of this equation. Then we discuss various generalizations of this equation.We proceed to study slow nonlinear waves in magnetic slabs. We present the Benjamin-Ono equation describing nonlinear slow sausage surface waves in magnetic slabs, and discuss its solutions in the form of algebraic solitons. Then we consider nonlinear slow body waves and write down the governing equation for these waves. We discuss its numerical solution which shows that the evolution of an initial perturbation results in a gradient catastrophe.After that we consider nonlinear slow sausage surface and slow body waves in magnetic tubes, which are similar to the corresponding counterparts in magnetic slabs. We present a system of two equations describing both types of waves. We briefly discuss the derivation of the Leibovich-Roberts equation for slow sausage surface waves from this system of equations, and present the results of its numerical study. Then we give a brief description of the derivation of the governing equation for slow body waves, which is very similar to its counterpart for slow body waves in magnetic slabs and has very similar properties. We complete this part of the review with presenting the governing equation for non-axisymmetric surface waves in a thin magnetic tube in an incompressible plasma.In the last part of the paper we consider the damping of nonlinear waves in weakly dissipative magnetically structured plasmas. We briefly discuss the application of the obtained results to the problem of heating of the solar corona.KeywordsSurface WaveSolitary WaveSolar PhysMagnetic TubeKink ModeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Excitation of nonlinear surface waves is studied at the SBN-75 crystal — air interface. The SBN-75 crystal is characterised by the diffusion-type photorefractive nonlinearity, the surface wave being excited in the surface layer and the depth of its penetration into the crystal being determined by the nonlinear crystal parameters. Because of a large refraction coefficient in SBN-75, the penetration depth of the surface wave into the air is small; therefore, the nonlinear surface wave is localised in the surface crystal layer several micrometers in thickness. The oscillating intensity distribution of the surface wave at the output end of the crystal is measured. The oscillation period is determined by the angle of incidence of the exciting beam. The nonlinear wave is excited not only at the crystal — air interface but also in the case when the active surface of the crystal is covered by an electrode, for example, an aquadag layer. This circumstance opens up a possibility of studying new properties of the surface waves when an external electric field is applied to the crystal.

This paper focuses on the study of linear and non-linear surface and internal waves, in a complete setting, using a two-layer model of a stratified fluid. The respective Korteweg-de Vries evolutionary equations have been obtained, analysed, and compared with the ‘rigid lid’ model data. Boussinesq-type equations have been derived for the interacting modes pertaining to one type and to different types. It is shown that in addition to the known mechanisms of interaction between internal and surface waves, interaction between long non-linear baroclinic modes and barotropic modes, propagating in the same direction, is likely in such a system.

A hybrid numerical method for the prediction of free surface flows including both nonlinear wave and viscous effects is presented. In this method, a zonal approach that combines a potential flow method for fully nonlinear free surface waves and a Reynolds-averaged Navier-Stokes (RANS) method for turbulent incompressible flow is used. The potential flow equation is solved in the far field to provide the nonlinear waves generated by the body motion. The RANS method is used in the near field to resolve the turbulent boundary layer and wake flows around the body. Extensive results are presented for a submerged hydrofoil with and without the presence of free surface waves. The coupled RANS and potential flow method successfully resolves the body boundary layer, the viscous wake, and the nonlinear free surface waves. The results clearly demonstrate the feasibility of the coupling approach and therefore enables the use of a rather small RANS solution domain for efficient and accurate resolution of free surface flows including both the viscous and nonlinear wave effects.

We study the electromagnetic surface waves localized at an interface separating a homogeneous dielectric medium and a semi-infinite one-dimensional photonic crystal made of alternative left-handed metamaterial and right-handed material. An analytical direct matching procedure within the Kronig-Penney model was applied to analyze the dispersion properties of the localized surface states. We show that the presence of metamaterial in the photonic crystal structure can support the surface waves with a backward energy flow and allows a flexible control of dispersion properties of the surface modes. The surface states can be either forward or backward waves depending on the physical parameters of the photonic crystal, physical parameters of the cap layer, the position of the surface plane, and incident angle of the incoming beam.

Stationary TE nonlinear surface waves at the interface separating two nonlinear diffusive Kerr-like media are computed for differing diffusion mechanisms and diffusion lengths. The stability of the surface waves on each branch of stationary solutions is determined by launching the appropriate wave and following its evolution, using the beam-propagation method. The stability criteria follow those determined earlier [ J. Opt. Soc. Am. B5, 559 ( 1988)] for non-diffusive Kerr media. The critical power necessary for observing surface waves is determined and shown to depend on the nature of the diffusion process. Analysis supports the observed numerical behavior of the diffusion coefficient at the interface as a function of increasing diffusion length.

We study the polarization properties of the light field under a dynamic ocean surface using realistic linear and nonlinear ocean surface waves. The three‐dimensional polarized radiative transfer of the dynamic ocean–atmosphere system is considered using a Monte Carlo vector radiative transfer simulation for arbitrary depth. The program is validated with measurement data taken in Hawaii during the Radiance in a Dynamic Ocean project. The main focus of this study is the influence of the wind‐driven ocean waves on the polarization patterns and statistics at different optical depths under various conditions of light wavelength and solar incidence. Of special interest is the effect of the nonlinearity of the surface waves on the polarization statistics. To facilitate the study, phase‐resolved direct simulations of the linear and nonlinear surface wavefields are performed using a high‐order spectral method. The results show that the time‐averaged degree of polarization within the Snell's window is dependent on the mean square slope of the ocean surface. Higher mean square slope, or wind speed, leads to a smaller degree of polarization. At the same time, the variability of the degree of polarization has a strong dependence on the surface roughness. A rougher ocean surface induces higher variability of the degree of polarization. The effect of wave nonlinearity can be neglected for the mean value of polarization, but is manifested in the variability of the degree of polarization, with a general increase in the variance with increasing wave nonlinearity. The present findings provide possible mechanisms for characterizing the dynamic ocean surface based on underwater polarized light measurements.

The paper is concerned with the propagation characteristics of TE surface waves in a planer wave-guide structure of a lateral antiferromagnetic -non magnetic superlattices (LANS)film bounded by a nonlinear dielectric cover and a left handed substrate (LHM). In (LHM) substrate both permittivity and magnetic permeability are negative in definite frequency range. We study nonlinear dispersion properties of the TE surface waves and illustrate power flow variation with the wave index when both permittivity and magnetic permeability are negative. We found that surface waves are backward traveling and the wave power variation with the wave index shows bistability behavior.

A promising direction in the tailored control of quantum materials is the modification of their structure-function relationship via engineered laser-driven shock waves. In order to inform how the laser excitation should be tailored to optimize the effect of the shock waves, a model is desired for strongly focused nonlinear surface waves in crystals. A model was developed previously in the paraxial approximation for weakly diffracting nonlinear surface wave beams in isotropic solids [Shull et al., JASA 97, 2126 (1995)]. Harmonic generation and shock formation were investigated numerically in that work for sources with uniform amplitude distributions, with analytical solutions for the fundamental and second harmonic obtained for weakly focused Gaussian beams. Here, numerical results are reported for shock formation in focused nonlinear surface waves obtained using a model unrestricted by the paraxial approximation in order to accommodate strong focusing in isotropic solids. Removal of the restriction to isotropic solids is work in progress based on representation of the wave field in terms of its angular spectrum and a model for planar nonlinear surface waves in crystals [Hamilton et al., JASA 105, 639 (1999)]. [Work supported by the IR&D Program at Applied Research Laboratories.]

The analysis of band structure of one-dimensional (1-D) photonic crystal containing dispersive and non-linear dispersive materials has been presented. The band spectra for the different combination of photonic crystals have been calculated by the well-known plane wave expansion method. The effect of the dispersive and non-linear materials on the band structures has been determined. The third-order nonlinearity has been considered in the non-linear material, and Lorentz–Drude model has been taken for dispersive material. The band gaps of considered photonic crystal are affected by the nonlinearity in the presence of dispersive material like gold. We have observed that the normalized frequency difference between photonic bands decreases on increasing intensity of input beam. This work may be useful in optical switching devices.

It is known [1,2] that an electromagnetic wave can propagate along the planar interface of two linear dielectric media. The strengths of both electric and magnetic field vanish as |x|→ ∞. This is the reason why these waves were called surface waves. It can be shown that such a surface wave exists only if a magnetic field strength vector is parallel to the interface plane, i.e. it is a TM-wave (sometimes it is called a p-polarised wave). If the dielectric permeability of one of the media is a square-law function of electrical field strength, then both propagation of TM wave and the TE wave are possible [3–9]. Such waves were named either non-linear surface waves or non-linear surface polaritons.

Effect of surface scratches on the characteristics of nonlinear Rayleigh surface waves in glass

Processes of localization of field excitations in the form of nonlinear surface waves that propagate along the interface between linear and nonlinear media are considered. The existence conditions of nonlinear surface waves, which are determined by the ratio between the linear characteristics of the media, the Kerr nonlinearity coefficient, and the intensity of interaction of the wave with the interface, are analyzed. The dependences of the energy flux carried by nonlinear surface waves are calculated and analyzed. Two approaches are proposed to selection of the control parameters for determining the energy flux, which are the position of the maximum field perturbation in the nonlinear halfspace and the field amplitude at the interface. Estimates of the fluxes are found in different limiting cases, which correspond to small-amplitude field perturbations and to weak or strong interaction of a nonlinear surface wave with the interface between the media. It is shown that, in the case of small-amplitude field perturbations and the weak interaction of the wave with the interface, the flux in the linear halfspace is directly proportional to the interaction intensity of the wave with the interface, while that in the nonlinear halfspace is inversely proportional to the interaction intensity.

The impact of subsurface currents induced by internal waves on nonlinear Stokes surface waves is theoretically analyzed. An analytical and numerical solution of the modulation equations are found under the conditions close to the group velocity resonance. It is shown that smoothing of the down current surface waves is accompanied by a relatively high-frequency modulation while the profile of the opposing current is reproduced by the surface wave’s envelope. The possibility of generation of an internal wave forerunner, that is a modulated surface wavepacket, is established. Long surface waves can form the wave modulation forerunner ahead of the internal wave, while the relatively short surface waves create the trace of the internal wave. Modulation of surface waves by the periodic internal wave train may have the characteristic period less than the internal wave period and be no uniform while crossing the current zone. Surface wave excitation by internal waves, observable at their group resonance is efficient only on the opposing current.

In recent studies with nonlinear Rayleigh surface waves, harmonic generation measurements have been successfully employed to characterize material damage and microstructural changes, and found to be sensitive to early stages of damage process. A nonlinearity parameter of Rayleigh surface waves was derived and frequently measured to quantify the level of damage. The accurate measurement of the nonlinearity parameter generally requires making corrections for beam diffraction and medium attenuation. These effects are not generally known for nonlinear Rayleigh waves, and therefore not properly considered in most of previous studies. In this paper, the nonlinearity parameter for a Rayleigh surface wave is defined from the plane wave displacement solutions. We explicitly define the attenuation and diffraction corrections for fundamental and second harmonic Rayleigh wave beams radiated from a uniform line source. Attenuation corrections are obtained from the quasilinear theory of plane Rayleigh wave equations. To obtain closed-form expressions for diffraction corrections, multi-Gaussian beam (MGB) models are employed to represent the integral solutions derived from the quasilinear theory of the full two-dimensional wave equation without parabolic approximation. Diffraction corrections are presented for a couple of transmitter-receiver geometries, and the effects of making attenuation and diffraction corrections are examined through the simulation of nonlinearity parameter determination in a solid sample.