Phenomenological theory of multimode surface waves for plane structures

The authors present a rigorous uniform theory of diffraction (UTD) solution of the diffraction by a coated convex cylinder simulated with generalized impedance boundary conditions (GIBC). In addition, a uniform asymptotic solution is obtained which remains valid when the observation point is in the close vicinity of the cylinder. An important aspect of this work is the use of second-order GIBCs which are characterized by the inclusion of second-order field derivatives in their definition. Because of this, they are less local, leading to an improved simulation (with respect to the standard impedance boundary conditions) of the coating. The improved accuracy of the GIBC simulation is demonstrated, and it is shown how the presented UTD solution can be extended to treat multilayered coated cylinders. >

In this paper, we are interested in using impedance boundary conditions ( IBCs) to model the scattering from a vibrating object which can be considered a perturbation problem where the perturbation (and the corresponding IBC) varies with time. One of the most basic objects for which a scattering solution can be obtained is an infinite PEC cylinder. Using the exact solution for a circular cylinder, the IBCs needed to model the scattering from a perturbed PEC cylinder are derived for both the TM and TE polarizations. It is shown that the standard IBC (SIBC) is accurate to first order for the TM case, but a second generalized IBC (GIBC) is needed to provide first order accuracy for the TE case. Results from a moments method (MoM) implementation of the IBCs are presented.

ABSTRACTWe show how a Trefftz Discontinuous Galerkin (TDG) method for the displacement form of the Helmholtz equation can be used to approximate problems having a generalized impedance boundary condition (GIBC) involving surface derivatives of the solution. Such boundary conditions arise naturally when modeling scattering from a scatterer with a thin coating. The thin coating can then be approximated by a GIBC. A second place GIBCs arise is as higher order absorbing boundary conditions. This paper also covers both cases. Because the TDG scheme has discontinuous elements, we propose to couple it to a surface discretization of the GIBC using continuous finite elements. We prove convergence of the resulting scheme and demonstrate it with two numerical examples.

Summary Hamilton’s wave theory is used to study the effect on seismic surface wave propagation of lateral variations in the composition of the crust and mantle. For cases with small lateral variations the distortion of the propagation paths from the great circle paths is determined by a perturbation method. Moreover, surface wave paths from the Mid-Atlantic Ridge toward the NORSAR and LASA arrays are computed by numerical integration of the ray equations. The computed wave paths agree well with existing observations. The model of the surface wave velocity distribution used in this study cannot, however, explain all the observed multipathing effects. Studies by several authors have shown that the lateral variations in the structure of the Earth’s crust and upper mantle may lead to large distortions of the propagation paths for seismic surface waves. Notably among these works are the works by Evernden (1953, 1954) and the works by Capon (1970, 1971). These works show that surface waves are refracted or reflected at the continental margins and at major geological structures. The oceanic ridge systems are an example to the latter. Estimates of the propagation path for surface waves are presented in the work cited above. Apart from this and a study by Julian (1972) little has been done in order to compute the propagation paths for surface waves. In various branches of Physics, Hamilton’s wave theory (or the eikonal approximation) has successfully been used to study wave propagation in heterogeneous media. Within the theory of seismic surface waves the method has received less attention although the applicability of it has been demonstrated in an elegant study by Backus (1962). The application of this theory to surface wave propagation in cases with lateral variation in the structure of the crust and upper mantle deserves more exploration. A fundamental assumption in Hamilton’s wave theory is that the physical parameters which are important for the wave propagation vary only by a small fraction of their values over a distance comparable to a wavelength. The theory has therefore very misleadingly been referred to as a short wavelength approximation. The propagation of seismic surface waves are for example fundamentally effected by the value of the physical parameters in a surface layer with thickness comparable to the wavelength. Therefore the lateral variations of the parameters describing the wave motion may be smaller for long waves than for short waves. This is confirmed by the observations

The authors present generalized surface impedance conditions that improve medium characterization. One of the most common conditions that is often used to simulate a dielectric coating is the standard impedance boundary condition, and the improved boundary condition discussed can be viewed as a generalization of this, distinguished by the presence of higher-order derivatives of the field. By virtue of the derivatives, the conditions are less local in character, and the additional degrees of freedom can be used to better simulate the material properties of a surface. Following a review of the standard impedance condition, the new conditions are introduced. Several forms are presented, each with coefficients which are functions of the geometry and material properties of the surface. The applications of these to a variety of scattering problems are then discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In this paper we consider the electromagnetic scattering problem by an obstacle characterised by a Generalized Impedance Boundary Condition in the harmonic regime. These boundary conditions are well known to provide accurate models for thin layers or imperfectly conducting bodies. We give two different formulations of the scattering problem and we provide some general assumptions on the boundary condition under which the scattering problem has at most one solution. We also prove that it is well-posed for three different boundary conditions which involve second order surface differential operators under weak sign assumptions on the coefficients defining the surface operators.

Dynamics of surface and internal long waves generated by atmospheric pressure disturbances

This work is devoted to theoretical study of surface plasmon polariton propagation on metal or metamaterial – dielectric interfaces where media can possess optical or magnetooptical activity or cubic nonlinearity. On the interface of gyrotropic media surface wave changes its polarization and profile as well as in case of interface of media with cubic nonlinearity. Surface wave propagation constant can be modified by magnetization leading to magnetooptical intensity effect. The properties of plasmons in gratings are also considered including excitation, dispersion and existence of various types of modes. The theory of surface wave and pulsed beam diffraction in gyrotropic, nonlinear and layered media is developed. We also present waveguide for surface waves based on layered metamaterial – dielectric interfaces suppressing diffraction spreading.

We investigate the localization properties of surface waves created at the interface between a truncated 1D photonic crystal and homogeneous medium in the presence of a chiral cap layer using the transfer matrix method. The numerical results show that the interface can support surface waves with both transverse electric and transverse magnetic polarizations. We demonstrate that the surface waves can be engineered by varying the chirality parameter of the cap layer, which plays an important role in controlling and localization of surface states. It is shown that the effect of a chirality parameter on surface waves with transverse electric polarization is more remarkable compared with surface waves with transverse magnetic polarization. In addition, the effect of thickness and material type of the cap layer and the termination layer of a photonic crystal on surface waves is investigated. The results show that these parameters have considerable effect on modification of surface states. These findings may open new opportunities in the design of cavity-based devices such as high-Q sensors and perfect absorbers.

Tunable surface waves supported by graphene-covered left-handed material structures

It has been shown in recent years ((5)–(8), (10)) that it is possible to obtain closed form solutions for the time harmonic wave equation when a linear combination of the wave function and its normal derivative is prescribed on the surface of a wedge. Boundary-value problems of this type occur in the problem of diffraction by a highly conducting wedge or by a wedge whose surfaces are thinly coated with dielectric. In certain circumstances such surfaces can support surface waves and one important aspect of the solution of the boundary-value problem is the determination of the amplitude of the surface wave excited.

We consider the inverse scattering problem of determining the shape of an impenetrable two-dimensional obstacle with a generalized impedance boundary condition from near-field measurements. We propose the reverse time migration method where the imaging functional is defined as the imaginary part of the cross-correlation. Our analysis shows that, on the one hand, the imaging functional has contrast at the boundary of the scatterer and decays outside the scatterer; On the other hand, the imaging functional is always positive thus may have better stability properties. These imply that the approach has powerful imaging quality which is confirmed in our numerical experiments.

Rigorous uniform geometrical theory of diffraction (UTD) diffraction coefficients are presented for a convex coated cylinder simulated with generalized impedance boundary conditions. In particular, ray solutions are obtained which remain valid in the transition region and reduce uniformly to those in the deep lit and shadow regions. These involve new transition functions in place of the usual Fock‐type integrals, characteristic to the impedance cylinder. A uniform asymptotic solution is also presented for observations in the close vicinity of the cylinder. As usual, the diffraction coefficients for the convex cylinder are obtained via a generalization of the corresponding ones for the circular cylinder.

Surface Waves in Cubic Elastic Materials

The aim of this paper is to investigate surface waves in anisotropic fibre-reinforced solid elastic media. First, the theory of general surface waves has been derived and applied to study the particular cases of surface waves — Rayleigh, Love and Stoneley types. The wave velocity equations are found to be in agreement with the corresponding classical result when the anisotropic elastic parameters tends to zero. It is important to note that the Rayleigh type of wave velocity in the fibre-reinforced elastic medium increases to a considerable amount in comparison with the Rayleigh wave velocity in isotropic materials.