Controlling electromagnetic surface waves with conformal transformation optics

Gaussian beam migration (GBM), as it is implemented today, efficiently handles isotropic inhomogeneous media. The approach is based on the solution of the wave equation in ray‐centered coordinates. Here, I extend the method to work for 2-D migration in generally anisotropic inhomogeneous media. Extension of the Gaussian‐beam method from isotropic to anisotropic media involves modification of the kinematics and dynamics in the required ray tracing. While the accuracy of the paraxial expansion for anisotropic media is comparable to that for isotropic media, ray tracing in anisotropic media is much slower than that in isotropic media. However, because ray tracing is just a small portion of the computation in GBM, the increased computational effort in general anisotropic GBM is typically only about 40%. Application of this method to synthetic examples shows successful migration in inhomogeneous, transversely isotropic media for reflector dips up to and beyond 90°. Further applications to synthetic data of layered anisotropic media show the importance of applying the proper smoothing to the velocity field used in the migration. Also, tests with synthetic data show that the quality of anisotropic migration of steep events in a medium with velocity increasing with depth is much more sensitive to the Thomsen anisotropy parameter ε than to the parameter δ. Thus, a good estimate of ε is needed to apply anisotropic migration with confidence.

The attenuation vector plays an important role in investigating waves propagating in dissipative, isotropic or anisotropic media. It is defined as the imaginary part of the complex-valued traveltime gradient. The real part of the complex-valued traveltime gradient is referred to as the propagation vector. In this paper, simple expressions for the attenuation vector are derived for seismic body waves propagating in heterogeneous, weakly dissipative, anisotropic media. The ray-theory perturbation method is used, in which the dissipative medium is considered to be a small perturbation of a perfectly elastic medium. The general perturbation procedure proposed by Klimeš (2002) is very suitable for this purpose, as it does not require ray tracing in dissipative media; the computation of rays in the reference perfectly elastic medium, followed by quadratures along them, is quite sufficient. It is shown that the waves propagating in a heterogeneous, weakly dissipative, anisotropic or isotropic medium are, in general, inhomogeneous. This means that their attenuation vector is not parallel to the propagation vector. This holds even for waves generated by a point-source in a homogeneous anisotropic weakly dissipative medium. An exception is a wave generated by a point-source in a homogeneous isotropic dissipative medium, where the generated wave is homogeneous. Thus, the commonly used concept of homogeneous waves can be applied neither to heterogeneous nor to anisotropic dissipative media. The situation is different for plane waves propagating in homogeneous dissipative isotropic or anisotropic media. In this case, the homogeneity or inhomogeneity of the plane wave may be chosen freely. Besides the attenuation vector, we also study the complex-valued ray-velocity vector. In heterogeneous media, the complex-valued ray-velocity vector is generally inhomogeneous, that is, its real and imaginary parts are not parallel. It is also shown that twice the scalar product of the attenuation vector with the ray-velocity vector in the reference medium yields 1/Q, where Q is the position- and direction-dependent quality factor. Quality factor Q does not depend on the inhomogeneity of the wave under consideration and offers a convenient measure of intrinsic material dissipation.

In this paper, we investigated the propagation of surface waves in a nonhomogeneous rotating fibre-reinforced viscoelastic anisotropic media of higher order of nth order including time rate of strain. The general surface wave speed is derived to study the effect of rotation on surface waves. Particular cases for Stoneley, Love and Rayleigh waves are discussed. The results obtained in this investigation are more general in the sense that some earlier published results are obtained from our result as special cases. Also results for homogeneous media can be deduced from this investigation. For order zero our results are well agreed to fibre-reinforced materials. Also by neglecting the reinforced elastic parameters, the results reduce to well known isotropic medium. It is also observed that, surface waves cannot propagate in a fast rotating medium. Comparison was made with the results obtained in the presence and absence of rotation and parameters for fibre-reinforced of the material medium Numerical results are given and illustrated graphically. The results indicate that the effect of rotation and parameters for fibre-reinforced of the material are very pronounced.

Electromagnetic ultrasound surface wave generated by combination of double magnets and the snake-shaped coil is widely used in the aluminum plate surface flaw detection. The electromagnetic ultrasonic transducer model is investigated and the theory analysis of electromagnetic ultrasound surface wave and numerical simulation of EMAT physical mechanism are discussed in this paper. Based on ANSYS, the 3-D finite element model of electromagnetic ultrasonic transducer is established, furthermore the relationship between magnet field, Lorentz force and surface wave generated on aluminum plate is concluded by applying electromagnetic structural coupling in this model. The consistency of electromagnetic ultrasonic theory and simulation results provides the theoretic basis for the parameters of electromagnetic ultrasonic transducer and facilitates the structural design and optimization of electro-magnetic ultrasonic transducer surface wave devices.

Nearly all dip‐moveout correction (DMO) implementations to date assume isotropic homogeneous media. Usually, this has been acceptable considering the tremendous cost savings of homogeneous isotropic DMO and considering the difficulty of obtaining the anisotropy parameters required for effective implementation. In the presence of typical anisotropy, however, ignoring the anisotropy can yield inadequate results. Since anisotropy may introduce large deviations from hyperbolic moveout, accurate transformation to zero‐offset in anisotropic media should address such nonhyperbolic moveout behavior of reflections. Artley and Hale’s v(z) ray‐tracing‐based DMO, developed for isotropic media, provides an attractive approach to treating such problems. By using a ray‐tracing procedure crafted for anisotropic media, I modify some aspects of their DMO so that it can work for v(z) anisotropic media. DMO impulse responses in typical transversely isotropic (TI) models (such as those associated with shales) deviate substantially from the familiar elliptical shape associated with responses in homogeneous isotropic media (to the extent that triplications arise even where the medium is homogeneous). Such deviations can exceed those caused by vertical inhomogeneity, thus emphasizing the importance of taking anisotropy into account in DMO processing. For isotropic or elliptically anisotropic media, the impulse response is an ellipse; but as the key anisotropy parameter η varies, the shape of the response differs substantially from elliptical. For typical η > 0, the impulse response in TI media tends to broaden compared to the response in an isotropic homogeneous medium, a behavior opposite to that encountered in typical v(z) isotropic media, where the response tends to be squeezed. Furthermore, the amplitude distribution along the DMO operator differs significantly from that for isotropic media. Application of this anisotropic DMO to data from offshore Africa resulted in a considerably better alignment of reflections from horizontal and dipping reflectors in common‐midpoint gather than that obtained using an isotropic DMO. Even the presence of vertical inhomogeneity in this medium could not eliminate the importance of considering the shale‐induced anisotropy.

Dynamic stiffness of three-dimensional anisotropic multi-layered media based on the continued-fraction method

Foreword. I: Theoretical problems concerning propagation of surface wave in elastic anisotropic media. On the role of anisotropy in crystalloacoustics V.I. Alshits. Surface waves of non-Rayleigh type S.V. Kuznetsov. Nonlinearity in elastic surface waves acts nonlocally D.F. Parker. Explicit secular equations for surface waves in an anisotropic elastic half space from Rayleigh to today T.C.T. Ting. II: Bending and edge waves in plates and shells. 'Nongeometrical phenomena' in propagation of elastic surface waves V.M. Babich, A.P. Kiselev. Complex rays and internal diffraction at the cusp edge M. Deschamps, O. Poncelet. Edge waves in the fluid beneath an elastic sheet with linear nonhomogeneity R.V. Goldstein, A.V. Marchenko. On continuum modelling of wave propagation in layered medium: bending waves K.B. Ustinov. Edge-localised bending waves in anisotropic media: energy and dispersion III: Experimental, numerical and semi-analytical methods for analysis of surface waves. Surface electromagnetic perturbations induced by unsteady-state subsurface flow P.M. Adler, V.M. Entov. Resonant waves in a structured elastic halfspace M.V. Ayzenberg-Stepanenko. Mumerical analysis of Rayleigh waves in anisotropic media A.V. Kaptsov. Guided waves in anisotropic media: applications R.A. Kline. A general purpose computer model for calculating elastic waveguide properties, with application to Non-Destructive Testing M.J.S. Lowe, P. Cawley, B.N. Pavlakovic. The influence of the initial stresses on the dynamic instability of an anisotropic cone Y.R. Rossikhin, M.V. Shitikova. Embedding theorem and mutual relation for the interface and shear wavespeeds I.V. Simonov. IV: Applications of surface waves to analysis of fracture and damage. The non-uniqueness of constant velocity crack propagation K.B. Broberg. Embedding formulae for planar cracks R.V. Craster, A.V. Shanin. Wave propagation and crack detection in layered structures E.V. Glushkov, N.V. Glushkova, A.V. Ekhlakov. Author Index.

Temporal changes in seismic anisotropy can be interpreted as variations in the orientation of cracks in seismogenic zones, and thus as variations in the stress field. Such temporal changes have been observed in seismogenic zones before and after earthquakes, although they are still not well understood. In this study, we investigate the azimuthal polarization of surface waves in anisotropic media with respect to the orientation of anisotropy, from a numerical point of view. This technique is based on the observation of the signature of anisotropy on the nine-component cross-correlation tensor (CCT) computed from seismic ambient noise recorded on pairs of three-component sensors. If noise sources are spatially distributed in a homogeneous medium, the CCT allows the reconstruction of the surface wave Green's tensor between the station pairs. In homogeneous, isotropic medium, four off-diagonal terms of the surface wave Green's tensor are null, but not in anisotropic medium. This technique is applied to three-component synthetic seismograms computed in a transversely isotropic medium with a horizontal symmetry axis, using a spectral element code. The CCT is computed between each pair of stations and then rotated, to approximate the surface wave Green's tensor by minimizing the off-diagonal components. This procedure allows the calculation of the azimuthal variation of quasi-Rayleigh and quasi-Love waves. In an anisotropic medium, in some cases, the azimuth of seismic anisotropy can induce a large variation in the horizontal polarization of surface waves. This variation depends on the relative angle between a pair of stations and the direction of anisotropy, the amplitude of the anisotropy, the frequency band of the signal and the depth of the anisotropic layer.

MESH GENERATION BY CONFORMAL AND QUASICONFORMAL MAPPINGS

With the use of the exact expression for the local propagation matrix that was obtained by Wöhler et al. [ J. Opt. Soc. Am. A5, 1554 ( 1988)], we show explicitly that the Berreman 4 × 4 propagation matrix method for layered inhomogeneous anisotropic media reduces to the Abelés 2 × 2 propagation matrix method for layered inhomogeneous isotropic media when the anisotropic medium becomes isotropic. The optical properties of isotropic and anisotropic media have been extensively studied, and a number of schemes for the computation of the optical effects of layered inhomogeneous media have been proposed. Propagation matrix methods have been shown to be particularly useful for studying the reflection and the transmission of electromagnetic waves by layered inhomogeneous isotropic and anisotropic media.1–5 Generally, the Abelés 2 × 2 matrix method is used for layered inhomogeneous isotropic media,1,2,4,5 and the Berreman 4 × 4 matrix method is used for layered inhomogeneous anisotropic media.3 The 4 × 4 matrix method is more general than the 2 × 2 matrix method and is applicable to problems involving media of low optical symmetry.

The self-focusing effect of optical beams has been a popular topic of study for quite a while, but such a nonlinear phenomenon at microwave frequencies has never been realized, partially due to the underdevelopment of nonlinear material. In this research, self-focused electromagnetic (EM) surface waves are demonstrated on a circuit-based, power-dependent impedance surface. The formation of a self-focused beam is investigated using a series of discrete-time simulations, and the result is further validated in measurement. It is experimentally observed that, in contrast to the normal scattering of low-power surface waves, high-power waves propagate through the surface while maintaining narrow beam width, and even converge extremely tightly to create a hot spot with higher power. The result is essentially a nonlinear effect of the surface that compensates for the natural tendency of surface waves to diffract. This intriguing experiment can be extended to various potential EM applications such as power-dependent beam steering antennas and nonlinear microwave propagation or dissipation.

Propagation of different electromagnetic surface waves (SW) is recognized as one of the most possible cause of undesirable plasma periphery heating, strengthening interaction between plasma column and walls of fusion device, impurity generation. This is found out clearly in experiments with ion cyclotron heating [1]. On the other hand in order to supply periodical operation of fusion devices, one can clean the devices inner surface. One of the prospective methods that can be used for this procedure is application both ion and electron cyclotron hardwares (without dismantling the whole device) for sustaining gas discharge, which can remove different contaminations from the chamber wall. The urgency of researches into parametric instability of SW at harmonics of cyclotron frequencies is caused as well by wide application of SW in various plasma technologies [2]. The present paper is devoted to development theory of parametric instability of slow surface Xand O-modes at electron cyclotron frequency for the model of semi-bounded plasma. Surface electron cyclotron O-modes (SECOM) were found theoretically [3] to propagate along plane plasmadielectric interface, when an external constant magnetic field is parallel to the plasma boundary and penetration depth of the modes is approximately equal to their wavelength. SECOM frequencies decrease if their wave number grows, their damping is determined by both collision (interaction between plasma particles) and kinetic (interaction between particles and plasma interface) mechanisms. Dispersion properties of surface electron cyclotron X-modes (SECXM) were studied theoretically in [4]. Unlike the SECOM they are unidirectional modes, their propagation coincides with direction of Larmor rotation of electrons on the plasma surface. They can propagate even along plasma-metal interface that makes them especially dangerous for destroying walls of fusion chambers. Sets of equations for these Xand O-modes are obtained by application of non-linear boundary conditions for their tangential magnetic field. Non-linear boundary conditions, which describe discontinuity of tangential component of their magnetic field are formulated by the aid of conception of existence of surface electric current, which is induced by the mentioned above external alternation electric field on the plasma interface. The reduced sets of equations for the Xand O-modes wave packets are obtained in approximation that the packets are composed by the main harmonic and two nearest satellite harmonics. EPJ Web of Conferences DOI: 10.1051/

The combined effect of metamaterials (MTMs) and nonlinear ferroelectric layers in guiding electromagnetic wave has been studied. The dispersion relation for the electromagnetic surface wave (EMSW) which is TE mode of propagation has been derived and numerically solved. Moreover, the power for the propagating wave at the interface has been presented. The effect of the nonlinear term is explicitly studied. Results show that EMSW depends on the nonlinear term.

This paper presents a novel two-dimensional (2-D) partial Maxwell fish-eye (PMFE) lens with the capability of wide-angle beam scanning inspired by the Gutman lens and Eaton lens, which is obtained by cutting a part from the 2-D Maxwell fish-eye (MFE) lens along a straight line. In terms of the refractive index profile, the MFE lens is similar to the Gutman lens near the center and the Eaton lens near the edge, respectively. We demonstrate the potential of the PMFE lens in wide-angle beam scanning based on its Gutman-like focusing and Eaton-like rotating characteristics corresponding to different feed points. As an example, a fully metallic PMFE lens antenna in the Ka-band composed of a bed of nails and a series of linearly arranged waveguide feeders is designed and experimentally verified. The measured results reveal wide-angle scanning ranges, especially about ±90° at 36 GHz, low reflections and low mutual couplings. The frequency scanning due to the dispersion of the lens is also discussed.

We consider the problem of constructing quasi-conformal mappings between surfaces by solving Beltrami equations. This is of great importance for shape registration.In the physical world, most surface deformations can be rigorously modeled as quasi-conformal maps. The local deformation is characterized by a complex-value function, Beltrami coefficient, which describes the deviation from conformality of the deformation at each point.We propose an effective algorithm to solve the quasi-conformal map from the Beltrami coefficient. The major strategy is to deform the conformal structure of the original surface to a new conformal structure by the Beltrami coefficient, such that the quasi-conformal map becomes a conformal map. By using holomorphic differential forms, conformal maps under the new conformal structure are calculated, which are the desired quasi-conformal maps.The efficiency and efficacy of the algorithms are demonstrated by experimental results. Furthermore, the algorithms are robust for surfaces scanned from real life, and general for surfaces with different topologies.KeywordsQuasic-Conformal MapBeltrami EquationRiemannian MetricUniformization