Showing papers on "Reflection coefficient published in 1973"
TL;DR: In this paper, a model of the reflection process is developed that explains all of the observed phenomena, including a shift of the reflected beam from the position predicted by geometrical acoustics, a null or minimum of intensity within the reflected beacon, a 180° phase reversal of the field on either side of the null, a weak trailing field on only one side of a reflected beam and a frequency of least reflection when the solid is lossy.
Abstract: Various phenomena have been observed when a bounded acoustic beam is incident from a liquid onto the surface of a solid at or near the Rayleigh angle. These phenomena include: a shift of the reflected beam from the position predicted by geometrical acoustics, a null or minimum of intensity within the reflected beam, a 180° phase reversal of the field on either side of the null, a weak trailing field on only one side of the reflected beam and a frequency of least reflection when the solid is lossy. By carefully examining the reflection coefficient for angles in the vicinity of the Rayleight angle, and by taking into account the angular spectrum of plane waves that comprise a bounded beam, a model of the reflection process is developed that explains all of the observed phenomena. This model shows that the various critical-reflection effects result from the interference between a geometrically reflected field and the field of a leaky Rayleigh wave, which is excited by the incident beam. Moreover, this model resolves the conflict between various explanations made for these phenomena in the past; in particular, it is found that Schoch's classical description of a laterally displaced reflected beam is valid only for beams having a large width.
339 citations
IBM1
TL;DR: A generalized procedure is presented that permits an accurate description of metal boundaries at optical frequencies and it is found that, with increasing buffer thickness, TM(N) modes undergo a continuous transformation to becomeTM(N+1).
Abstract: A number of analysis techniques aimed at determining the characteristics of optical guided waves propagating in lossy structures are examined. The exact theory is used as a guide to assess the validity of several approximate methods based on two basic approaches: (a) geometrical optics and (b) perturbation calculations. The limitations of the conventional perturbation techniques are specified. We present a generalized procedure that permits an accurate description of metal boundaries at optical frequencies. In this case, TM modes differ from their TE counterparts by a field buildup near conducting walls and by the existence of an additional surface plasma mode. The dependence of attenuation coefficients on film thickness and mode order are discussed. The use of low-index dielectric buffers to reduce ohmic losses is considered. It is found that, with increasing buffer thickness, TM(N) modes undergo a continuous transformation to become TM(N+1).
157 citations
TL;DR: In this article, the effect of variations in the dielectric constant with depth was investigated and the significance of the fading of layer echoes and the possible causes of variations were considered.
Abstract: Radio echo-sounding surveys of Antarctica and Greenland have revealed extensive layering within the ice. Formulae for the effective reflection coefficient, when viewed by a pulsed radar, are derived for isolated or multiple randomly spaced layers. In the latter case the variation in dielectric constant with depth is described by a vertical autocorrelation function and a standard deviation. Some measurements of the reflection coefficient of layers, and the dielectric absorption of ice are given. The significance of the fading of layer echoes and the possible causes of variations in the dielectric constant are considered and some further investigations are suggested. It is concluded that the echo strengths found in the Antarctic may be explained by multiple layering, and that the necessary fractional change in the dielectric constant may be as small as 10−4. It is suggested that this change in dielectric constant may be due to differences in orientation of anisotropic ice crystals.
97 citations
TL;DR: In this paper, the dispersive characteristics of phase velocities of Lamb waves excited by interdigital transducers on unpolarized PZT ceramic plates have been studied, and it is shown that the generation of symmetric mode Lamb waves by their transducers is equivalently represented by a thickness mode transducer of half-wavelength inserted perpendicular to the plate.
Abstract: Propagation characteristics and the equivalent circuit model of delay lines using Lamb waves excited by interdigital transducers on unpolarized PZT ceramic plates have been studied. Dispersive characteristics of phase velocities of Lamb waves excited by the interdigital transducers are in good agreement with the numerical solution from the dispersive equation of phase velocities developed by Worlton. When the product of frequency times plate thickness is below 1.3×106 Hz mm, the zeroth symmetric Lamb wave is strongly excited. The Lamb waves are excited most effectively when the half‐period of interdigital electrode is equal to the wavelength of the Lamb wave. Also, the values of the attenuation coefficient and the reflection coefficient from the edge of the specimen are given. It is shown that the generation of symmetrical‐mode Lamb waves by our transducer is equivalently represented by a thickness mode transducer of half‐wavelength inserted perpendicular to the plate.
50 citations
TL;DR: In this paper, light scattered from oppositely directed surface acoustic waves on ycut zpropagating lithium niobate was frequency analyzed with a high-resolution Fabry-Perot interferometer.
Abstract: Under conditions of continuous acoustic generation, light scattered from oppositely directed surface acoustic waves on y‐cut z‐propagating lithium niobate was frequency analyzed with a high‐resolution Fabry‐Perot interferometer. The following parameters were measured at 105 MHz: acoustic power standing‐wave ratio, reflection coefficient for both sending and receiving transducers, low‐power acoustic damping coefficients, surface wave propagation velocity, and nonlinear harmonic growth. We note that the method used has an advantage over other methods since it is to a large extent independent of the optical quality of the propagation surface.
43 citations
TL;DR: In this paper, the authors proposed a temperature reference for high-precision radiometry, which has an accurately known radiometric temperature, a very low reflection coefficient, and whose geometry is well suited to the calibration of horn antennas.
Abstract: The calibration of microwave radiometers is normally achieved by replacing the antenna with a cooled reference termination and then applying corrections for ohmic and reflective losses of the antenna, and for the nonideality of the reference termination. The uncertainty in this correction is the dominating factor in the precision of many high-quality radiometers, and for some applications it is unacceptably large. An alternative is to point the antenna at a target of known temperature. To the extent that this temperature is known and the target is reflectionless and encompasses the full view of the antenna, the calibration is ex'act and no further corrections are required. A target suitable for high-precision radiometry has been developed that has an accurately known radiometric temperature, a very low reflection coefficient, and whose geometry is well suited to the calibration of horn antennas. The essence of the temperature reference is described. A piece of porous microwave absorber having a convoluted surface for a low reflection coefficient is fitted with a cap of nonporous plastic foam whose mating surface is the inverse of that of the absorber. The microwave-absorbing material is then soaked with the chosen cryogen, the nonporous cap forcing the liquid to conform to the shape of said absorbing material. This procedure 1) ensures that the temperature at which the microwaves are absorbed (and therefore thermally emitted) is exactly that of the cryogen, and 2) avoids the reflection that would be produced by the dielectric discontinuity of a plane surface of cryogen.
40 citations
TL;DR: One-dimensional inverse-scattering theory is applied to the study of the reflection of electromagnetic waves from an inhomogeneous region having a refractive index n(x) = [1-(1/k^{2})q(x)]^{1/2} where k is the free-space wavelength.
Abstract: One-dimensional inverse-scattering theory is applied to the study of the reflection of electromagnetic waves from an inhomogeneous region having a refractive index n(x) = [1-(1/k^{2})q(x)]^{1/2} where k = 2\pi/\lambda , and \lambda is the free-space wavelength. The exact refractive index profile is obtained that will produce a reflection coefficient in which the frequency dependence is described by the Butterworth approximation.
36 citations
TL;DR: In this paper, the performance characteristics of large dual-polarization phased arrays of square waveguides were investigated and a simple design procedure that yields well-matched practical elements with high polarization isolation was developed.
Abstract: Square-waveguide elements capable of radiating and receiving any of four different sets of dual polarizations were considered. Each element may consist of as many as 8 matching sections of square waveguide in tandem. The known solution to a "standard" phased-array problem was used to synthesize the solution for the many-junction element, and a computer program was developed to implement the solution. A systematic investigation of the performance characteristics of large dual-polarization phased arrays of square waveguides was carried out. Coupling between radiated polarizations and active reflection coefficient were computed for two wide-bandwidth (20 and 25 percent of center frequency) designs for dual-linear, dual-circular, and dual-scanned polarization states. A simple design procedure that yields well-matched practical elements with high polarization isolation was developed. Various phenomena peculiar to dual-polarization excitation were identified and are discussed. The theoretical predictions are supported by experimental evidence obtained by means of two infinite-array simulators and a 267-element array.
32 citations
TL;DR: In this paper, a numerical model is presented which describes the strain level build-up in yarns due to multiple strain wave reflections from yarn crossover intersections in a woven fabric subject to ballistic impact.
Abstract: A numerical model is presented which describes the strain level build-up in yarns due to multiple strain wave reflections from yarn crossover intersections in a woven fabric subject to ballistic impact. Crossing yarns present barriers from which strain waves are partially reflected. The maximum yarn strain occurs at the point of impact and decays with distance along the yarn away from this point. The rapidity of decay is governed by the crossover reflection coefficient. Using observations of the deformation cone size of ballistically impacted fabric panels, it is concluded that the reflection coef ficient is small (approximately 0.01). The strain increases with time at different rates for different reflection coefficients until failure at the impact point. Extensions of this model to other fibrous structures are discussed.
31 citations
TL;DR: The local flux-force equations of nonequilibrium thermodynamics in friction coefficient form are integrated for a solvent and a nonelectrolyte solute flowing in a uniform channel between two well-mixed reservoirs to yield global equations of similar form and for which global Onsager reciprocity holds.
30 citations
TL;DR: In this paper, it was shown that the refractive index is a two-valued markovian random function of position, and the distribution of the phase of the reflection coefficient is calculated both analytically and numerically.
Patent•
07 Feb 1973
TL;DR: In this article, the insertion loss between an input port and an output port is proportional to the reflection coefficient of the load connected to a third port, and the constant of proportionality is substantially independent of frequency.
Abstract: A bridge for measuring the reflection coefficient of a twoterminal load, in which the insertion loss between an input port and an output port is proportional to the reflection coefficient of the load connected to a third port, and the constant of proportionality is substantially independent of frequency; includes a balun, a first two-terminal network connected in one arm of the bridge, a second two-terminal network connected in the opposite arm of the bridge, and a resistance equal to the reference resistance in the arm opposite the port to which the load is connected. The impedance of the second network is the inverse, relative to the reference resistance, of the parallel combination of the first network and the additional impedance to ground caused by the connection of the balun.
TL;DR: In this article, the effect of conductive ground reflection was taken into account in the calculation of the penetration and reflection coefficients of the VLF electromagnetic waves incident on to the plane-stratified ionosphere both from below and above.
TL;DR: In this article, the exact wave solution, the Floquet theorem, and the corresponding Brillouin diagram were used to investigate the stop-band characteristics of waves in cholesteric liquid-crystal half-space.
Abstract: The stop-band characteristics of waves in cholesteric-liquid-crystal half-space are investigated using the exact wave solution, the Floquet theorem, and the corresponding Brillouin diagram. The other half-space is filled with a uniform dielectric medium. By appropriate choice of the dielectric constant of the uniform medium and the angle of incidence of the incoming plane wave, the stop band may split into two or three stop bands.
TL;DR: In this article, the problem of a plane wave normally incident on a slab of one-dimensional random medium is studied and the refractive index variations of the random medium are taken to be a stationary Gaussian-Markov process.
Abstract: The problem of a plane wave normally incident on a slab of one‐dimensional random medium is studied. The refractive index variations of the random medium are taken to be a stationary Gaussian‐Markov process. By employing an invariant imbedding technique and by using the Markov property of the refractive index variations, two cascaded diffusion equations are obtained for the probability density function of the reflection coefficient and the field in the slab. These equations are then solved approximately for small refractive index fluctuations and an expression is obtained for mean intensity in the slab interior.
TL;DR: In this article, a self-consistent nonlinear analysis is given for the (one-dimensional) problem of laser interaction with a plasma layer, where the main process considered is the decay of the laser wave into an ion sound wave and a reflected wave.
Abstract: A self-consistent nonlinear analysis is given for the (one-dimensional) problem of laser interaction with a plasma layer. The main process considered is the decay of the laser wave into an ion sound wave and a reflected wave. Nonlinear reflection is shown to be possible even for a linearly transparent layer. The reflection and absorption coefficients are studied as functions of as a function of the level of excitation of the ion sound waves in the plasma. The range of parameters for which the reflection or the heating is maximum is considered.
TL;DR: The thicknesses of UO(2) films from 100 A to 1800 A on uranium substrates were determined from reflectance measurements in the visible region by obtaining the best match of the clorimetric properties of the sample with the colorimetric Properties of a predetermined film thickness calibration curve.
Abstract: The thicknesses of UO2 films from 100 A to 1800 A on uranium substrates were determined from reflectance measurements in the visible region The reflectance measurements on the U–UO2 system were analyzed by two different methods to determine film thicknesses In the first method, film thicknesses were determined by comparing theoretical reflectance calculations with the experimental reflectance measurements In the second method, film thicknesses were determined by obtaining the best match of the colorimetric properties (wavelength, excitation purity, and luminous reflectance) of the sample with the colorimetric properties of a predetermined film thickness calibration curve
TL;DR: It is suggested that a combination of three mirrors as a mode selective laser reflector be used, which should be simpler in construction and should have better mode selective properties.
Abstract: The complex reflectance of a combination of three parallel mirrors with arbitrary distances is computed. If the distance between the mirrors is equal to an integer multiple of a certain wavelength of the incident light, the reflectance of the system has narrow maxima and broad minima as a function of wavelength. This behavior is opposite to a usual two-mirror Fabry-Perot interferometer. It is suggested that such a combination of three mirrors as a mode selective laser reflector be used. Compared with other mode selecting devices this arrangement should be simpler in construction and should have better mode selective properties.
TL;DR: In this paper, a model of the partial-reflection mechanism which employs multiple reflectors as opposed to the single-reflector concept was described. But this model only considers the variation of the reflection coefficient throughout the reflecting volume.
Abstract: Recently published results on D-region partial-reflection amplitude distributions indicate that below 80 km, the distributions are Rayleigh-like in character. Because of this, this paper describes a model of the partial-reflection mechanism which employs multiple reflectors as opposed to the single-reflector concept now in use by most experimenters using the partial-reflection experiment. The particular new feature incorporated by this model is the variation of the reflection coefficient throughout the reflecting volume; previous multiple-reflector models considered only the variation of the differential absorption in the reflecting volume. It is shown, for example, that for 50-μsec pulse lengths, serious errors in electron density can result in the analysis of partial-reflection data for which multiple reflectors are present.
TL;DR: In this article, the nonlinear propagation of an intense (pump) beam of electromagnetic radiation that excites a parametric decay instability in an inhomogeneous plasma is calculated self-consistently.
Abstract: The nonlinear propagation of an intense (pump) beam of electromagnetic radiation that excites a parametric decay instability in an inhomogeneous plasma is calculated self‐consistently. A generalization to an inhomogeneous plasma of the nonlinear absorptive conductivity calculated according to several recent theories for the saturated electron‐ion decay instability in a homogeneous plasma is added to the linear absorptive conductivity in the wave equation. A model is introduced for the qualitative change in the pump dependence of the nonlinear conductivity in the strong pumping limit. The resulting nonlinear wave equation for radiation propagating into a stratified plasma is integrated numerically. Application is made to the anomalous absorption of the modified radiation in ionosphere modification experiments and to absorption of laser radiation in laser‐produced plasmas. The reflection coefficient is computed as a function of incident power. Also computed are waveforms, the Poynting flux, and the ponderomotive force. These are displayed as functions of position in the plasma. A distinct standing‐wave pattern is shown to persist very near the reflection point even in cases of nearly total absorption.
TL;DR: A theoretical study of the radiation and reflection of a electromagnetic surface wave at a guiding structure discontinuity is given in this paper, where a TE surface wave is supported by a dielectric coated conductor which has a contour deformation of the guiding surface.
Abstract: A theoretical study of the radiation and reflection of a electromagnetic surface wave at a guiding structure discontinuity is given in this paper. A TE surface wave is considered. It is supported by a dielectric coated conductor which has a contour deformation of the guiding surface. When the deformation is small, the problem may be treated by the boundary perturbation technique to yield the radiated electromagnetic wave and the reflected surface wave. A numerical example is given to illustrate how the radiation pattern and the reflection coefficient vary for different degrees of surface deformation.
TL;DR: In this paper, the maxima and minima of the power reflection coefficient as a function of the normalized incident wave frequency (Omega ) and the slab velocity (β ) are discussed for slab motion parallel as well as normal to the slab boundaries.
Abstract: The reflection and transmission properties of electromagnetic waves obliquely incident on a relativistically moving uniaxial plasma slab are investigated theoretically and the maxima and minima of the power reflection coefficient as a function of the normalized incident wave frequency ( \Omega ) and the slab velocity ( \beta ) are discussed for slab motion parallel as well as normal to the slab boundaries. One can predict the nature of variation of the reflection coefficient with respect to any parameter from the variation of q' (the root of the dispersion equation) with that parameter. When q' is real and varies rapidly, the oscillations in the reflection coefficient are rapid and when q' differs significantly from the free-space value, the amplitude will be large. In the imaginary range of q' , the reflection coefficient is nonoscillatory. The discussion of the results is facilitated by introducing a parameter p which is a quadratic in \beta . For slab motion parallel to the interface, the two slab velocities for a given p give rise to same reflection coefficient whilst for normal motion the results are significantly different.
TL;DR: In this article, the mutual coupling between two identical parallel-plate waveguides having the same axis of symmetry is investigated and a modified Wiener-Hopf equation is obtained.
Abstract: The radiation field and mutual coupling between two identical parallel-plate waveguides having the same axis of symmetry are investigated. Jones' method of formulation is applied and a modified Wiener-Hopf equation is obtained. Expressions for the radiated field in free space, reflected field in the exciting waveguide, and transmitted field in the coupled waveguide are obtained and the reflected and transmitted fields are expressed in terms of waveguide modes. The reflection coefficient for each mode is represented by three terms, two of which are due to reflections at the open end of the exciting waveguide and are constant along the waveguide. The third term is the contribution from the field scattered by the open end of the coupled waveguide and decays along the waveguide according to the radiation condition. Similarly, the transmission coefficient of each mode is represented by three terms, two of which decay along the coupled waveguide and the third one is constant. The radiation field is also divided into three terms. One of them is due to the radiation from the open end of the exciting waveguide and the other two are the contribution of multiple interactions between the two waveguides. Computed results for the reflection and transmission coefficients and the radiation field are shown for TE/sub 0,1/ excitation and various separation distance of the waveguides. The results for the reflection and transmission coefficients are oscillating functions of period /spl pi/, and approach gradually the well-known final values of a single excited wavegnide.
TL;DR: In this paper, the interaction of an electromagnetic wave with a plane interface between a stationary isotropic medium (dielectric or vacuum) and a homogeneous cold magnetized plasma moving uniformly parallel to the interface is considered for arbitrary angles of incidence.
Abstract: The interaction of an electromagnetic wave with a plane interface between a stationary isotropic medium (dielectric or vacuum) and a homogeneous cold magnetized plasma moving uniformly parallel to the interface is considered for arbitrary angles of incidence. Calculations are presented for the case in which the static magnetic field lies in the interface and is oriented normal to both the plane of incidence and the direction of the streaming motion. It is found that the reflection and the transmission characteristics for an incident E wave are unaffected by the anisotropy and the velocity of the moving medium. Numerical results for the reflection and the transmission coefficients for an obliquely incident H wave have been obtained for several values of the magnetic field and the electron density of the moving plasma half-space. It is found that the moving magnetized plasma medium allows certain stop and pass bands under suitable physical conditions.
TL;DR: In this paper, the power reflection coefficient as a function of the normalized incident wave frequency and slab velocity is shown for electromagnetic waves obliquely incident on an isotropic plasma slab relativistically moving along the slab interface.
Abstract: The oscillations in the power reflection coefficient as a function of the normalized incident wave frequency and slab velocity are shown for electromagnetic waves obliquely incident on an isotropic plasma slab relativistically moving along the slab interface. Both parallel and perpendicular polarizations of the wave are considered.
TL;DR: The maxima and minima of the power reflection coefficient as a function of the normalized slab velocity are also shown for both parallel and perpendicular polarizations of the wave incident on an isotropic plasma slab as discussed by the authors.
Abstract: It is shown that above some critical velocity of the medium moving normal to the interface, the reflected wave actually travels towards the medium over a range of medium velocity. Beyond this range, the incident wave from below never catches the moving medium, but the medium can interact with the portion of an existing plane wave above. The maxima and minima of the power reflection coefficient as a function of the normalized slab velocity are also shown for both parallel and perpendicular polarizations of the wave incident on an isotropic plasma slab.
TL;DR: In this article, the problem of choosing the "physical" path of analytic continuation of the solutions is considered in the case of a wave equation with two poles, and the reflection and transmission coefficients are obtained, as well as the coefficient of transformation of an electromagnetic wave into a plasma wave.
Abstract: The reflection and transmission coefficients are obtained, as well as the coefficient of transformation of an electromagnetic wave into a plasma wave. The problem of choosing the “physical” path of analytic continuation of the solutions is considered in the case of a wave equation with two poles.
TL;DR: The maxima and minima of the power reflection coefficient as a function of the wave frequency of an electromagnetic wave obliquely incident on isotropic and uni-axial plasma slabs are discussed in this paper.
Abstract: The maxima and minima of the power reflection coefficient as a function of the wave frequency of an electromagnetic wave obliquely incident on isotropic and uni-axial plasma slabs are discussed.
TL;DR: In this article, the microwave reflection method suitable for the diagnostics of a plasma column placed transversely across a rectangular waveguide for a TE10 wave was discussed, and the complex reflection coefficient of a discharge Neon diode Philips K50A used as a positive column in the 2-11 Gc/s band was calculated.
Abstract: The paper concerns the microwave reflection method suitable for the diagnostics of a plasma column placed transversely across a rectangular waveguide for a TE10 wave. VSWR and phase measurement results are presented regarding the complex reflection coefficient of a discharge Neon diode Philips K50A used as a positive column in the 2–11 Gc/s band. A reflection coefficient theory of cylindrical dielectric post having two coaxial layers of different dielectric permittivity, has also been presented and checked with measurements on calibrated dielectric rods. A numerical calculation of the complex coefficient of reflection performed in the 2–11 Gc/s band is presented for conventional plasma parameters along with a radial electron density distribution depending on a paraboloidal function. The computed values fit the measurement results within the experimental errors.