Wave Propagation In Stratified Media Research Articles

Ab initio spatial coupled-mode theory of Fano resonances in optical responses of multilayer interference resonators

To reveal origins of resonance characteristics of multilayer interference structures, we developed an ab initio spatial coupled-mode theory using the approximations of general electromagnetic theory of wave propagation in stratified media. In contrast to the conventional coupled-mode theory, the coefficients of developed coupled-mode models, which describe the Fano resonance behavior of interference field enhancement, are given by analytical functions of structural and optical parameters of the resonance systems. The results of analytical modeling of low- and high-loss resonator systems supporting waveguide, Fabry-P\'erot, symmetric, and antisymmetric plasmonic normal modes agree very well with electromagnetic numerical simulations. We demonstrate also that the conventional spatial phenomenological coupled-mode theory is accurate only for low-loss structures.

Shear surface wave propagation in stratified media with slip interfaces

Shear surface wave propagation in stratified media with slip interfaces

Shear surface wave propagation in stratified media with slip interfaces

The surface shear wave propagation is studied in elastic semi-spaces separated by elastic layer with an imperfectly bonded interface between layer and semi-spaces. The dispersion equations are obtained analytically describing the surface wave phase speed. Based on the dispersion equation analysis it is shown that the interface imperfectness sufficiently decreases the phase speed and can increase the number of shear wave modes too.

Sweeping preconditioners for stratified media in the presence of reflections

In this paper we consider sweeping preconditioners for time harmonic wave propagation in stratified media, especially in the presence of reflections. In the most famous class of sweeping preconditioners Dirichlet-to-Neumann operators for half-space problems are approximated through absorbing boundary conditions. In the presence of reflections absorbing boundary conditions are not accurate resulting in an unsatisfactory performance of these sweeping preconditioners. We explore the potential of using more accurate Dirichlet-to-Neumann operators within the sweep. To this end, we make use of the separability of the equation for the background model. While this improves the accuracy of the Dirichlet-to-Neumann operator, we find both from numerical tests and analytical arguments that it is very sensitive to perturbations in the presence of reflections. This implies that even if accurate approximations to Dirichlet-to-Neumann operators can be devised for a stratified medium, sweeping preconditioners are limited to very small perturbations.

Electromagnetic beam propagation in nonlinear media

We deduce a complete wave propagation equation that includes inhomogeneity of the dielectric constant and present this propagation equation in compact vector form. Although similar equations are known in narrow fields such as radio wave propagation in the ionosphere and electromagnetic and acoustic wave propagation in stratified media, we develop here a novel approach of using such equations in the modeling of laser beam propagation in nonlinear media. Our approach satisfies the correspondence principle since in the limit of zero-length wavelength it reduces from physical to geometrical optics.

High-order thin layer method for viscoelastic wave propagation in stratified media

Wave propagation in stratified media has wide applications in petroleum exploration, geophysical inversion, nondestructive evaluation of highway and airport pavement structures, countermine technology, structural health monitoring, and vehicle weigh-in-motion systems. A high-order thin layer method is developed to improve the accuracy and robustness of thin layer method for analyzing viscoelastic wave propagation in stratified media. It approximates the stiffness matrix involving transcendental functions by truncating the Taylor series of the stiffness matrix to the fourth order term. A generalized eigenvalue problem is then formulated, which allows an efficient numerical algorithm to be designed in a computer program DynaThinLayer. The high-order thin layer method is compared to the thin layer method, the stiffness matrix method and the exact Zoeppritz method in terms of accuracy and efficiency. It is shown that the high-order method requires the same level of computation time as does the thin layer method, but the former produce more accurate result than the latter. The computation time of the high-order thin layer method increases linearly when the number of layers increases. The new method is most applicable to situations where a large number of layers is involved or to situations where some natural layers have large thickness.

10.1007/s11449-008-3012-7

The propagation and scattering of light in stratified media are considered. Based on the Maxwell equations, the present approaches to the solution of these problems are formulated in a unified way. The particular features of the wave propagation in stratified media are discussed. Scalar and vector fields are considered. Media with small-and large-scale regular inhomogeneities are examined. The construction of the Green’s function of the wave equation in a spatially homogeneous medium is discussed. Stratified isotropic and anisotropic media are analyzed. The scattering of light in a stratified medium is studied with emphasis on the Kirchhoff method, as this makes it possible to obtain calculation formulas in a form convenient for comparing the theory with the experiment. The propagation of waves in photonic crystals and the formation of forbidden zones in such objects are briefly considered.

Homogenization of integro-differential equation of Burgers type

Non-linear partial differential equation of Burgers type with integral term is considered. Its coefficients are rapidly oscillating functions. The equation describes wave propagation in stratified media with relaxation. Existence and uniqueness of solution is proved. Homogenized equation with constant coefficients is constructed. Convergence of exact solution to homogenized problem solution is proved.

Excitation of s-polarized surface electromagnetic waves in inhomogeneous dielectric media

We consider a model of an inhomogeneous dielectric slab first studied by Shvartzburg, Petite and Auby [J. Opt. Soc. Am. B 16, 966 (1999)] and several variations of that model and study the excitation of s-polarized surface electromagnetic waves on the surface of inhomogeneous dielectric media. Using the invariant imbedding theory of wave propagation in stratified media, we calculate the reflectance and the absorptance of an s wave incident obliquely on a dielectric slab in the Otto configuration, as a function of incident angle and frequency. We also calculate the spatial distribution of the electric field intensity in the inhomogeneous region. We find that in all cases we have considered, s-polarized surface waves are excited at certain incident angles and frequencies. We discuss the physical mechanism of the surface wave generation and the possibility of experimental observations of these effects.

Propagation and scattering of light in stratified media

The propagation and scattering of light in stratified media are considered. Based on the Maxwell equations, the present approaches to the solution of these problems are formulated in a unified way. The particular features of the wave propagation in stratified media are discussed. Scalar and vector fields are considered. Media with small-and large-scale regular inhomogeneities are examined. The construction of the Green’s function of the wave equation in a spatially homogeneous medium is discussed. Stratified isotropic and anisotropic media are analyzed. The scattering of light in a stratified medium is studied with emphasis on the Kirchhoff method, as this makes it possible to obtain calculation formulas in a form convenient for comparing the theory with the experiment. The propagation of waves in photonic crystals and the formation of forbidden zones in such objects are briefly considered.

Recursive Stiffness Matrix Method for Wave Propagation in Stratified Media

A stable recursive stiffness matrix method is described for wave propagation in a layered elastic medium. The 4 × 4 global stiffness matrix for a stratified medium is recursively calculated from the layer stiffness matrices. The layer stiffness matrix has only six different elements, which are given in closed form. For general buried sources, a simple formulation has been developed to calculate the response for arbitrary positions of the receivers. Based on this method, characteristic equations for surface and guided modes in stratified media have also been obtained. The algorithm is unconditionally stable and retains the simplicity and flexibility of the transfer matrix method. Manuscript received 8 June 2001.

Low and High Energy Resolvent Estimates for Wave Propagation in Stratified Media and Their Applications

Low and High Energy Resolvent Estimates for Wave Propagation in Stratified Media and Their Applications

Modular method for calculation of transmission and reflection in multilayered structures

We describe a new modular method for the calculation of wave propagation in stratified media based on the direct use of reflection and transmission coefficients. Within this reflection from the left, transmission, and reflection from the right (LTR) method we define addition and multiplication operators that enable the theoretical construction of any multilayered structures from substructures. This modular concept allows for the design and analysis of complex multilayer structures for optical devices.

Modelling surface waves in anisotropic structures I. Theory

Surface-wave theory in generally-anisotropic laterally-homogeneous media is partially reformulated in order to obtain intuitively-expected extensions of classic body-wave ideas such as Maslov plane-wave summation, the geometrical-ray/WKBJ limit and source-receiver reciprocity. This is done using the ‘reversal’ symmetry of Chapman [Chapman, C.H., 1994. Reflection/transmission coefficient reciprocities in anisotropic media. Geophys. J. Int. 116, 498–501] to generalize the point-source treatment of Kennett [Kennett, B.L N., 1983. Seismic Wave Propagation in Stratified Media. Cambridge Univ. Press, Cambridge, UK] to a stack of anisotropic layers with complex elastic parameters, lateral slowness and frequency. The 2D-integral representation over horizontal slownesses is reduced by residues to a 1D integral over each mode's slowness or dispersion curve at fixed frequency and this may be considered a 1D Maslov summation over local plane waves tangential to the phase front. The residue calculation involves a modified form of the usual variational principle, in which the Lagrangian now contains reversed modes. The 1D slowness integral may be reduced by stationary-phase arguments to the geometrical-ray or WKBJ limit, provided the dispersion-surface curvature does not vanish. This limit satisfies reciprocity, as the reversal symmetry shows. Dimples on the dispersion surface will correspond to folds on the phase front and multiple arrivals. An appendix contains a discussion of orthogonality of the surface-wave modes in relation to the various wave-equation symmetries.

Multistatic scattering from bottom targets in the presence of anisotropically rough interfaces

The performance of active, multistatic sonar systems can be enhanced significantly, if the 3-dimensional environmental physics is incorporated into the processing. Thus fundamental understanding of the difference between target scattering and bottom reverberation could provide the basis for advanced, multistatic clutter reduction. Strong bottom interaction is the most distinct acoustic feature in shallow-water environments. Consequently, bottom roughness becomes the major reverberation mechanism limiting sonar system performance. To investigate the three-dimensional spatial characteristics of multistatic target scattering and bottom reverberation, a unified numerical model is being developed. It combines existing theoretical models for scattering from shells of finite length, anisotropic interface scattering and seismo-acoustic wave propagation in stratified media. The model generates Monte Carlo statistics for multistatic target scattering in the presence of a strongly reverberant, rough elastic bottom. The effects of anisotropic statistics of the bottom roughness on the multistatic field are investigated, and the significance of the geometric and acoustic properties of target is addressed. [Work supported by ONR.]

Time domain analysis of electromagnetic wave propagation in stratified media

We investigate the plane-wave solution of Maxwell's equations for a stratified medium characterized by a slowly varying index n(z) . The study is carried out in the time domain. We show that the transmitted wave from a source generates reflected wavelets which are propagated in the opposite direction. The reflected wave may be interpreted as the propagation medium response to the source excitation. The medium is thus characterized by a transfer function and an impulse response exclusively dependent on the propagation velocity. Conversely, knowing the impulse response makes estimating the index n(z) possible.

Eigenfunction expansions for elastic wave propagation problems in stratified media $R^{3}$

This paper provides eigenfunction expansions associated with the stationary problems for elastic wave propagation in stratified media $R^{3}$. The eigenfunction expansion is given in terms of generalized eigenfunctions corresponding to incident, reflected, refracted and Stoneley waves.

Scale effects on velocity dispersion: From ray to effective medium theories in stratified media

Wave propagation in stratified media may be explained by ray theory, effective medium theory, or scattering theory depending on the scales of wavelength and layer spacing. To effectively integrate and use seismic data at different frequencies and widely varying scales, it is essential to understand the domain of applicability of long and short wavelength behavior and the transition between them. A joint experimental and theoretical study was conducted to investigate velocity behavior at the transition from ray theory to effective medium theory in stratified media. Velocity measurements were performed at 50 and 500 kHz on periodic media composed of steel and plastic discs. The ratio of wavelength to layer spacing, λ/d, spanned more than two orders of magnitude between 0.1 and 50, and the volume fraction of steel ranged from 9 to 89 percent by volume. Our results confirm that velocities in stratified media depend on composition and are controlled by the ratio of wavelength to layer spacing. Velocities in the short wavelength limit are generally faster than velocities in the long wavelength limit. We find that transition from ray to effective medium approximations occurs over a narrow range of λ/d at a value of approximately 10. The amount of velocity change increases with impedance contrast, but the value of λ/d at the transition is generally independent of the composition of the stratified medium. Our numerically simulated waveforms are in close agreement with the experimentally observed delayed first arrival in the long wavelength limit and with the reduced amplitudes at the transition from short to long wavelength regime.

Reflection and transmission of surface waves in laterally varying media

SUMMARY The T-matrix description of surface wave scattering is viewed in a reflection/transmission context reminiscent of problems involving elastic wave propagation in stratified media. This approach exploits the orthogonality properties of the surface wave basis functions and permits a description of surface wave propagation in environments exhibiting a degree of quasi-concentric multilayering about a vertical axis. In the first case we consider a multilayered environment where the individual layers are laterally homogeneous and where the layer boundaries need not be circularly cylindrical. The reflection/transmission treatment incorporates all higher order scattering processes and may be used to examine both scattering from multilayered obstacles and the outward evolution of a wavefield from a source acting along the vertical coordinate axis. We then examine the form taken by the reflection/transmission matrices where arbitrary lateral variations in material properties are confined to a broad cylindrical band surrounding the vertical axis. The total response is assembled by considering the band as a succession of infinitesimally thin, heterogeneous shells in welded contact. This treatment relies on the use of invariant embedding techniques and the expansion of the Green's function for a stratified medium in terms of surface wave basis functions. It is demonstrated that the theory is the 3-D extension of coupled mode techniques used to model surface wave propagation in strictly 2-D waveguides. The theory is applied to investigate the effect of near-source, continuously varying heterogeneity on surface wave radiation patterns in the far-field. The general character of the transmitted wavefield agrees with that expected from arguments based on geometrical optics. Despite the suggestive behaviour of the surface wave basis functions in the near-field, wavetype coupling by continuously varying heterogeneity is not especially efficient in this regime. This implies that large transverse components of displacement frequently observed on regional seismograms from explosive sources are the result of other mechanisms, for example abrupt changes in structure or anisotropy.

Scattering matrix method for propagation of radiation in stratified media: attenuated total reflection studies of liquid crystals

We present a new scattering matrix formalism for the modeling of electromagnetic wave propagation in stratified media. It is computationally efficient and stable and is well suited to the layer geometry that is characteristic of stratified materials. It is applied successfully to the modeling of total attenuated reflection in nematic liquid crystals with beyond-critical-angle incidence when the conventional transfer matrix methods normally fail.