Showing papers on "Reflection (physics) published in 1977"
01 Jan 1977
947 citations
TL;DR: In this article, a necessary step in the implementation for layered media displaying transverse isotropy is the computation of reflection and transmission coefficients at the interface between two such layers, as well as the corresponding surface conversion coefficients.
Abstract: It has become necessary in seismology to consider more complicated models of the Earth9s structure in order to obtain synthetic seismograms that are more consistent with actual field data. Gassmann (1964) and Postma (1955) have presented results dealing with travel-time methods in anisotropic media—in particular, transversely isotropic media. Kinematic properties alone, however, are not enough to conclusively interpret seismic records. Consequently, dynamic properties must be considered producing a need for synthetic seismograms. One of the most efficient methods for obtaining synthetic seismograms is through the use of asymptotic ray theory (Hron and Kanasewich, 1971; Hron, 1973; Hron, Kanasewich and Alpaslan, 1974). A necessary step in the implementation for layered media displaying transverse isotropy is the computation of reflection and transmission coefficients at the interface between two such layers. Reflection coefficients for a free interface and the corresponding surface conversion coefficients must be computed, as well. Theoretical formulas for reflection, transmission, and surface conversion coefficients corresponding to the zero-order approximation of asymptotic theory are presented for the above-mentioned media.
229 citations
TL;DR: In this paper, the authors extended the coupled mode equations to include radiation and other partial wave coupling effects in distributed feedback (DFB) and distributed Bragg reflector (DBR) lasers, as well as orthogonal radiating couplers.
Abstract: The familiar coupled mode equations are extended in a self-consistent fashion to include radiation and other partial wave coupling effects in distributed feedback (DFB) and distributed Bragg reflector (DBR) lasers, as well as orthogonal radiating couplers. This general formulation takes into account the joint interaction of the two coherent contradirectional guided waves with arbitrarily shaped gratings. In addition to the modified coupled mode equations, which contain added constants characterizing the interactions, expressions for radiated waves are also obtained. A particular waveguide geometry is studied in detail. The interaction constants are evaluated for all Bragg orders up to the fourth and various blazing angles. Then the equations are solved for both a DBR and DFB laser. In the former case it is shown that the reflection is smaller than that computed without the interaction constants. Furthermore, reflection is asymmetrical relative to the Bragg condition. The DFB laser is shown to have an asymmetrical longitudinal mode structure even for symmetrical boundary conditions and to have only slightly higher thresholds than previously calculated.
224 citations
TL;DR: In this paper, a formulation for calculating the energy division among plane waves generated by plane waves incident on a boundary between generally anisotropic media is derived for P, SV and SH waves incident from an isotropic half-space on an orthorhombic olivine halfspace.
Abstract: Summary. A formulation is derived for calculating the energy division among waves generated by plane waves incident on a boundary between generally anisotropic media. A comprehensive account is presented for P, SV and SH waves incident from an isotropic half-space on an orthorhombic olivine half-space, where the interface is parallel to a plane of elastic symmetry. For comparison, a less anisotropic medium having transverse isotropy with a horizontal axis of symmetry is also considered. The particle motion polarizations of waves in anisotropic medium differ greatly from the polarizations in isotropic media, and are an important diagnostic of the presence of anisotropy. Incident P and SV waves generate quasi-SH waves, and incident SH waves generate quasi-P and quasi-SV waves, often of considerable relative magnitude. The direction of energy transport diverges from the propagation direction.
193 citations
TL;DR: In this paper, the concept of the "image ray" is introduced for simulating time migrated reflections, and the Kirchhoff summation method is used to systematically sum signals into the apex of the approximation hyperboloid even though the kirchhoff integral is not strictly valid.
Abstract: Using an elementary theory of migration one can consider a reflecting horizon as a continuum of scattering centres for seismic waves. Reflections arising at interfaces can thus be looked upon as the sum of energy scattered by interface points. The energy from one point is distributed among signals upon its reflection time surface. This surface is usually well approximated by a hyperboloid in the vicinity of its apex. Migration aims at focusing the scattered energy of each depth point into an image point upon the reflection time surface. To ensure a complete migration the image must be vertical above the depth point. This is difficult to achieve for subsurface interfaces which fall below laterally in-homogeneous velocity media. Migration is hence frequently performed for these interfaces as well by the Kirchhoff summation method which systematically sums signals into the apex of the approximation hyperboloid even though the Kirchhoff integral is in this case not strictly valid. For a multilayered subsurface isovelocity layer model with interfaces of a generally curved nature this can only provide a complete migration for the uppermost interface. Still there are various advantages gained by having a process which sums signals consistently into the minimum of the reflection time surface. The position of the time surface minimum is the place where a ray from the depth point emerges vertically to the surface. The Kirchhoff migration, if applied to media with laterally inhomogeneous velocity, must necessarily be followed by a further time-to-depth migration if the true depth structure is to be recovered. Primary normal reflections and their respective migrated reflections have a complementary relationship to each other. Normal reflections relate to rays normal to the reflector and migrated reflections relate to rays normal to the free surface. Ray modeling is performed to indicate a new approach for simulating seismic reflections. Commonly occuring situations are investigated from which lessons can be learned which are of immediate value for those concerned with interpreting time migrated reflections. The concept of the ‘image ray’ is introduced.
161 citations
TL;DR: The general theory of viscoelasticity, which accounts for elastic as well as anelastic linear behavior of materials, predicts that two types of S waves propagate in an elastic earth materials as discussed by the authors.
Abstract: The general theory of viscoelasticity, which accounts for elastic as well as anelastic linear behavior of materials, predicts that two types of S waves propagate in anelastic earth materials. The particle motion for an inhomogeneous plane S wave of type I is elliptical in the plane defined by the directions of propagation and attenuation, while the particle motion for an inhomogeneous plane S wave of type II is linear perpendicular to this plane. The general theory predicts that an S -wave incident upon a plane boundary perpendicular to the plane defined by the directions of propagation and attenuation generates S waves only of the same type. General characteristics of the type-II S waves reflected and refracted at plane anelastic boundaries are:
1. (a) velocities and maximum attenuations which depend on the angle of incidence and frequency,
2. (b) maximum energy flow at a different velocity and in a different direction than phase propagation,
3. (c) energy flow across the boundary due to interaction of the incident and reflected waves.
The general theory predicts these characteristics for the waves whenever a plane type-II S wave interacts with a plane anelastic boundary such as a soil-bedrock, crust-mantle, or core-mantle interface. None of these characteristics are predicted for the plane SH waves described by elasticity theory.
116 citations
TL;DR: In this article, a new pair of second-order coupled-mode equations are derived, solved, and applied to the case of reflection and transmission by a spatially modulated slab medium.
Abstract: A new pair of second-order coupled-mode equations are derived, solved, and applied to the case of reflection and transmission by a spatially modulated slab medium. The derivation is compared with those that arrive at first-order coupled-mode equations. The solutions of the second-order coupled-mode equations are facilitated by reducing them to two uncoupled Helmholtz equations. The solutions of the boundary-value problem for a slab medium are analytical and expressed in closed form. They are confirmed by the rigorous modal theory in the limit of small modulation strength. At the Bragg angle of incidence, energy conservation is shown to be preserved for all modulation strengths.
90 citations
TL;DR: In this article, the three-dimensional current system over an enhanced conductivity strip identified with an auroral arc is calculated for the case of magnetospheric plasma convection across this strip.
88 citations
01 Jan 1977
86 citations
Patent•
22 Apr 1977TL;DR: In this article, a telecentric lens is used as the scanning lens in this scanning device, and the original point of deflection of the above-mentioned light beam coincides with the center of the pupil of this lens.
Abstract: Disclosed in this specification is a scanning device which scans an object having a flat reflection surface and an inclined reflection surface with an inclination relative to the flat reflection surface such as, for example, a mask and a wafer to be used in manufacturing IC, LSI, etc., with light beam, and detects only the reflected light from the inclined reflection surface with a light detector. In order to make it possible to detect only the reflected light from the inclined reflection surface with the light detector, a telecentric lens is used as the scanning lens in this scanning device, and the original point of deflection of the above-mentioned light beam coincides with the center of the pupil of this telecentric lens. In addition, a filter is disposed on the pupil surface to intercept light from the flat reflection surface.
74 citations
TL;DR: In this article, the authors extend the diffraction results for coincident source and receiver locations to the case of arbitrary source/receiver locations, which can be used to study normal-moveout effects and can thus be used for study migration before and after common-depth-point stacking as well as to study common depth-stacking itself.
Abstract: The author’s earlier diffraction paper (Trorey, 1970) for coincident source and receiver locations is extended to the case of arbitrary source and receiver locations. The extension requires no additional assumptions and, as in the earlier paper, is in closed form suitable for calculations. The new results permit modeling of normal‐moveout effects and can thus, for example, be used to study migration before and after common‐depth‐point stacking as well as to study common‐depth‐point stacking itself. In general, the point source/receiver response of an arbitrary subsurface with arbitrary source/receiver locations can be calculated.
TL;DR: In this article, the reflectance of a single-layer gradient refractive-index antireflection film was measured in the visible regime at off-normal incidence (to 70°) using polarized light.
Abstract: Normal incidence measurements of single-layer gradient refractive-index antireflection films, produced by a chemical etch-leach process on glass sensitized by a phase-separating heat treatment, indicate very low reflection over a broad wavelength regime, 0.35–2.5 μm. First-surface measurements of the reflectance of the gradient index films have now been made, in the visible regime, at off-normal incidence (to 70°) using polarized light. These measurements show that significant reflection reduction is obtained even at high angles of incidence—5.7% reflectance from the filmed glass at 70° compared to 16.4% for the unfilmed glass. Furthermore, although the films exhibit a weak wavelength dependence at high angles, they continue to be effective over a broad spectral region. The optical properties observed are in good agreement with computations based on a gradient refractive-index film with a step at the air-film interface. The optical properties of the film offer considerable advantage over conventional interference films in many applications.
TL;DR: In this paper, a theory for mode conversion and tunneling in a warm, collisionless, toroidal plasma near the first ioncyclotron harmonic frequency when the waves are propagating perpendicular to the static magnetic field is presented.
Abstract: A theory is presented describing mode conversion and tunneling in a warm, collisionless, toroidal plasma near the first ion‐cyclotron harmonic frequency when the waves are propagating perpendicular to the static magnetic field. The coupling region may be characterized by a fourth‐order differential equation with one turning point. Employing the method of Laplace integrals and the method of matched asymptotic expansions, transmission, reflection, and conversion coefficients are calculated assuming a fast wave is incident from either side of the coupling region. For a fast wave incident from the low magnetic field side, transmission, reflection, and conversion occur, while for a fast wave incident from the high magnetic field side, only transmission and conversion occur with no reflection, independent of the thickness of the tunneling layer, which implies complete conversion of the fast wave to the slow wave as the tunneling layer becomes thick. The problem of cavity resonance is discussed.
TL;DR: In this paper, the effect of the dominant mode shape with frequency and mode conversion along the horn taper and at waveguide transitions at the horn input on return loss and radiation patterns is investigated.
Abstract: Microwave antennas are often required to carry signals simultaneously over a broad range of frequencies–e.g., the combined td-2 and th common carrier bands encompass a total frequency ratio of about 1.8 to 1 as do the combined 18- and 30-GHz bands. To achieve these bandwidths, an efficient broadband feed horn is required. The corrugated (hybrid-mode) horn is a leading candidate, but it is not immune to some cross-polarization coupling, input reflection, and pattern asymmetry. These problems are introduced mainly by two phenomena: variation of the dominant mode shape with frequency and mode conversion along the horn taper and at waveguide transitions at the horn input. Simple formulas for computing the magnitude of these phenomena and their effects on return loss and radiation patterns are given.
TL;DR: In this paper, the authors used the poles and zeroes of the infinite plane wave amplitude reflection coefficient to derive a theoretical prediction of the nonspecular reflection effects which have been observed for an ultrasonic beam incident on an isotropic solid plate in a liquid.
Abstract: Poles and zeroes of the infinite plane wave amplitude reflection coefficient are used to derive a theoretical prediction of the nonspecular reflection effects which have been observed for an ultrasonic beam incident on an isotropic solid plate in a liquid. It is shown that there are two types of nonspecular reflections, and they can be characterized in terms of a single parameter which requires a knowledge of the imaginary part of a pole of the infinite plane wave reflection coefficient. Theoretical predictions of nonspecular reflection intensities are presented. Finally, it is shown that the reflection characteristics for high-frequency beams incident on thick plates are the same as those expected for the reflection from a single liquidisolid interface, i.e., two infinite half-spaces. T INTRODUCTION HEORETICAL and experimental aspects of beam displacement phenomena have been actively studied since 1947 when Coos and Hanchen [ l ] demonstrated that a beam of light is displaced from the expected geometrically reflected beam upon reflection from the interface between two transparent media. In 1950 Schoch predicted [2] and later experimentally verified [3 J the beam displacement effect for an acoustic beam incident on a liquid/solid (L/S) interface. Schoch’s theory predicted that an incident bounded acoustic beam would be nonspecularly reflected in that the reflected beam would be displaced laterally along the interface while the reflected beam profile retained the same general shape as the incident beam profile. analysis of nonspecular reflection phenomena has been used Although the basic framework of Schoch’s theoretical Manuscript received May 17, 1976. This work was supported by the L. E. Pitts was with the Department of Physics, Georgetown UniverOffice of Naval Research, U.S. Navy. sity, Washington, DC 20057. He is now with the Department of Physics, Mary Washington College, Fredericksburg, VA 22401. sity, Washington, DC 20057. He is now with the Schlumberger-Doll Research Center, Ridgefield, CT 06877. sity, Washington, DC 20057. T. J. Plona was with the Department of Physics, Georgetown UniverW. G. Mayer is with the Department of Physics, Georgetown Univerby later authors [4] , [ 5 ] , his theory did not account for two experimentally observed phenomena: 1) the reflected sound field for certain bounded acoustic beams has a point of null sound intensity which is not present in the incident sound beam and 2) the main portion of the reflected sound field is accompanied by a sound field which becomes weaker as it extends for a considerable distance along the interface, away from the incident beam. This field is called the “trailing sound field.” Assuming an incident beam which is approximately Gaussian, a schematic example of these two phenomena is shown in Fig. 1. have since been reconciled by Bertoni and Tamir [5]. A principle difference between Schoch’s analysis and that of Bertoni and Tamir is that the latter has emphasized the use of complex poles of the plane wave amplitude reflection coeffiThese discrepancies between Schoch’s theory and experiment
TL;DR: Interference fringes arise from the constructive and destructive interference of the multicomponents of light beams generated from partial reflection of the incident light beam at the first and second surfaces of a transparent sample having plane parallel surfaces as mentioned in this paper.
Abstract: Rich colors decorating oil slicks on water are interference fringes. These fringes arise from the constructive and destructive interference of the multicomponents of light beams generated from partial reflection of the incident light beam at the first and second surfaces of a transparent sample having plane parallel surfaces. Fringes are reflection (or transmission) maxima and minima and appear when the wavelength of the incident light, the angle of incidence, or film thickness is changed. Interference fringes are very useful since advantage can be taken of them in many applications, including measurement of film thickness and refractive index n1; constructions of interference filters, cold mirrors, and high Q optical cavities; and modulation of light, to name a few.
TL;DR: In this paper, a prominent bright spot over 2 km in extent which occurs beneath the flat-lying sediments of the Gulf of Oman abyssal plain has been interpreted as due to gas accumulations.
01 Oct 1977
TL;DR: In fact, a considerable number of family sociologists are arguing for the abandonment of the concept of "family power" for a more empirically grounded nomenclature as discussed by the authors.
Abstract: W ithin the sociology of the family, the concept of "family power" has increasingly come to play a major role in interactional analyses of the nuclear family unit. Skolnick and Skolnick (1971), in their directional essay entitled "Rethinking the Family," have stated, "Perhaps the surest key to understanding the problems of the nuclear family is the concept of power" (1971: 21). However, research involving family power dimensions has seemingly plateaued with few recent conceptual or methodological innovations. In fact, a considerable number of family sociologists are arguing for the abandonment of the concept of "family power" for a more empirically grounded nomenclature. This article proposes to examine the present status of the family power literature and to offer suggestions for a redirection of future theory and research.
TL;DR: The origin and nature of radio-echo internal reflections is the subject of much debate as mentioned in this paper, and the results of single and multiple-layer reflection coefficients indicate that the observed reflection strength may result from reflections from many thin layers but the zone of thin layers may best be approximated by replacing the zone with a single thicker layer with average dielectric properties.
Abstract: The origin and nature of radio-echo internal reflections is the subject of much debate. Calculations of single- and multiple-layer reflection coefficients for dielectric changes in the ice sheet indicate that the observed reflection strength may result from reflections from many thin layers but the zone of thin layers may best be approximated by replacing the zone with a single thicker layer with average dielectric properties. Calculation of reflections from density changes, dust and dirt bands and anisotropy of ϵ indicate density variations as the most likely cause of the internal layering in the uppermost kilometer of ice sheets. Comparison of the depth of internal reflections at “Byrd” station, Antarctica, with the physical properties of the ice measured in a deep core hole at that location support this conclusion.
TL;DR: In this paper, the reflection of an elastic wave by a rough stress-free surface with a periodic profile has been investigated rigorously, and the problem is formulated in terms of an integral equation for the particle displacement at a single period of the boundary surface.
Abstract: The reflection of an elastic wave by a rough stress‐free surface with a periodic profile has been investigated rigorously. The problem is formulated in terms of an integral equation for the particle displacement at a single period of the boundary surface. Numerical results pertaining to the reflection of either an incident P wave or an incident SV wave for a sinusoidal profile are presented.
TL;DR: In this paper, the reflection of plane waves by a layered cylindrical shell in water is investigated theoretically, and the solution as a function of frequency is examined for several combinations of inner and outer layers.
Abstract: The reflection of plane waves by a layered cylindrical shell in water is investigated theoretically. Either or both of the two layers of elastic material may be absorptive. The solution as a function of frequency is examined for several combinations of inner and outer layers.
TL;DR: In this article, the authors used ray invariants to derive analytical solutions for the horizontal projections of ray paths for many types of basins, troughs, seamounts, and ridges.
Abstract: Horizontal curvature of long‐range underwater sound rays can be caused by repeated reflection from a sloping or undulating sea bed. This paper uses ray invariants to derive analytical solutions for the horizontal projections of ray paths for many types of basins, troughs, seamounts, and ridges. The isovelocity invariants for elevation angle and ray heading are extended to cover a basin with rotational symmetry as well as a trough of constant cross section, and the additional effects of refraction in a stratified medium are considered. Rough figures for the geometrical spreading loss and reflection loss at the edge of a basin are derived.
TL;DR: In this article, it was shown that the fringes of the fine structure are arranged in a Rydberg series having the constant 1/16 Rydenbergs and terminating at the energy of emergence.
Abstract: LEED calculations are presented which indicate that the emergence of a non-specular beam is accompanied with a surface resonance fine structure in the intensity of the specular beam. It is shown that the fringes of the fine structure are arranged in a Rydberg series having the constant 1/16 Rydbergs and terminating at the energy of emergence. The resonances are caused by reflections of electrons between the image potential before the metal surface on one side and the bulk of the metal on the other. The resolving power required for recording the fine structure is discussed and the calculated fine structure is compared with three electron scattering experiments.
TL;DR: In this article, a homomorphic system is used to map the convolution of a source function with the impulse response of the earth into the sum of the log spectra of the source function and the earth's response.
Abstract: A homomorphic system is used to map the convolution of a source function with the impulse response of the earth into the sum of the log spectra of the source function and the earth’s response. If the source function is considered stationary and the earth’s response spatially nonstationary, by averaging the log spectra of several reflection records, the log spectrum of the source function will be enhanced and the log spectrum of the earth’s response will average out. An inverse homomorphic system maps the average log spectrum to an estimate of the source function. The source function is then deconvolved from reflection records. Application of log spectral averaging as a method of deconvolution to a seismic reflection profile obtained in a shallow water‐geologically complex area indicates the homomorphic technique to be an effective method for suppressing the air gun bubble pulse oscillation.
Patent•
06 Sep 1977
TL;DR: In this paper, Krautkramer et al. measured the deflection of a workpiece surface from accoustic energy at 1 to 10 Hz by measuring optical interference by optical interference.
Abstract: 1488536 Measuring deflection by optical interference KRAUTKRAMER GmbH 24 Nov 1975 [4 Dec 1974] 48172/75 Heading G1A Apparatus for sensing the deflection of a workpiece surface 5 resulting from accoustic energy applied thereto comprises laser 1 whose beam 9 after reflection from surface 5 is split by beamsplitter 2 into portions 9a, 9b which positionally coincideon sensor 7, portion 9b being delayed due to the distance 11 Surface 5 is subjected to accoustic energy at 1 to 10 Hz The strength of the signal from photo-cell 7 depends on the phase difference of 9a to 9b, which varies according to the deflection of surface 9 during the delay time For the phase difference over the photo-cell of diameter d to be constant, the angle between portions 9a and 9b at the photo-cells <#/2/d For this the distance from surface 5 to splitter 2 is at least 5S for a diameter of 1 cm, or a telescope lens system with an aperture at the common focal point is interposed between 5 and 2 or mirror 10 and 2 The delay path may be folded by a pair of facing mirrors Length S may be modualted Piezoelectrically at a frequency f 1 higher than the accoustic frequency f 2 , so that the optimum path period occurs several times within the vibration period and the photo-cell output is at frequency f 1 modulated by f 2 The broken lines of Fig 6 show the light beam of a second interferometer used to maintain a constant length S If the distance of the delay path S via mirrors 2a, 18a, 18b and 2b alters, illumination at photo-cell 19 alters, giving a signal via amplifier 20 and filter 21 to Piezo-electric element 24a causing the motion of mirrors 24b to restore the illumination of photo-cell 19 Alternatively S may be kept constant by the Piezo-electric means moving mirror 18 relative to a fixed reference
TL;DR: In this paper, a general theory for the electromagnetic fields of dipoles in stratified isotropic media is outlined, and recursive relations are developed to propagate the Hankel-domain field coefficients to other layers or to the half spaces.
Abstract: A general theory for the electromagnetic fields of dipoles in stratified isotropic media is outlined. The stratified model consists of a stack of layers sandwiched between two semi-infinite media. Either an electric or a magnetic dipole can be placed at any position in the stack, or in the upper or lower half-space. Dipoles can be electric or magnetic and can be oriented horizontally or vertically. The fields in the layer containing the source are given in terms of reflection coefficients, impedance and admittance terms, and wavenumber ratios. Recursion relations are developed to propagate the Hankel-domain field coefficients to other layers or to the half spaces. This allows the observation point to be placed anywhere except at the source. Numerical checks show that the derived algebra is at least self-consistent.
21 Jun 1977
TL;DR: In this paper, the design of a completely quasi-optical 1.5 mm aircraft radiometer receiver is discussed in detail and the radiometer beam switching is described as well as a reflection isolator utililizing a reciprocating mirror.
Abstract: The design of a completely quasi-optical 1.5 mm aircraft radiometer receiver is discussed in detail. The radiometer beam switching is described as well as a reflection isolator utililizing a reciprocating mirror. A quasi-optical local oscillator injection system using a Folded Fabry-Perot resonator is described and receiver performance levels given.
TL;DR: In this article, the reflection of an acoustic plane wave by an infinitely long elastic cylinder of infinite length was calculated and measured, and the results were compared with experimental data taken using finite cylinders immersed in water.
Abstract: The reflection of an acoustic plane wave by an elastic cylinder of infinite length, which may absorb energy, is calculated and measured. Computations of reflection by an infinitely long elastic cylinder as a function of frequency and angle, are compared with experimental data taken using finite cylinders immersed in water. Good agreement is obtained.
TL;DR: In this paper, it was shown that the predicted focal shift associated with total internal reflection follows from the ray model of the Goos-Hanchen shift if the variation of the GOH with angle is taken into account.
Abstract: The recently predicted focal shift associated with total internal reflection is shown to follow from the ray model of the Goos-Hanchen shift if the variation of the Goos-Hanchen shift with angle is taken into account.
TL;DR: In this article, the reflection and surface-to-bulk wave conversion of a Rayleigh wave incident at a single shallow groove on an elastically isotropic substrate have been studied for various rectangularlike and trough-like groove profiles.
Abstract: The reflection and surface‐to‐bulk wave conversion of a Rayleigh wave incident at a single shallow groove on an elastically isotropic substrate have been studied for various rectangularlike and troughlike groove profiles. It is found that the maximum value of the amplitude reflection coefficient is insensitive to the groove profile, and that the groove width producing maximum reflection or zero reflection of the incident surface wave is independent of the profile for all rectangularlike grooves. In all cases, both P and SV bulk waves are excited, with the latter carrying most of the bulk‐wave power. While the angular distribution of the bulk‐wave power patterns is strongly dependent on the groove width for a given profile, it is surprisingly insensitive to the profile for a given width. The fraction of the total incident power which is converted to bulk waves has been calculated.