Showing papers on "Plane wave published in 1973"

Wave propagation in the two temperature theory of thermoelasticity

Abstract: Within the framework of a linear two-temperature theory two separate wave propagation problems are investigated. Interest is directed to wave speeds, travelling discontinuities in the two temperatures and the strain, and long and short time approximations.

Attenuation and phase rotation of radio waves due to rain: Calculations at 19.3 and 34.8 GHz

Abstract: Computations are made of the forward- and back-scattering intensities of oblate spheroidal raindrops at 19.3 and 34.8 GHz, assuming plane waves at normal incidence to the drop axis. Two kinds of polarization are considered in the incident field: one is parallel to drop axis; the other is perpendicular. Numerical values of these basic scattering intensities are listed in tables. Forward-scattering intensities are then used for determining the effective propagation constants of rain-filled space. From these propagation constants, attenuations and phase rotations for parallel and perpendicular polarizations are computed for several rain rates. One significant conclusion is that the difference between phase rotations in the two polarizations at 19.3 GHz becomes very large as the rain rate increases, whereas that at 34.8 GHz is bounded in a very small range throughout all possible rain rates.

Power Deposition in a Spherical Model of Man Exposed to I-20-MHz Electromagnetic Fields

Abstract: The induced fields and the associated power deposition in mail exposed to HF electromagnetic (EM) fields have been investigated theoretically using spherical models. The induced electric fields inside the model exposed to either plane wave or near fields can be described adequately by a combination of quasi-static electric and magnetic induction solutions. It is shown that for field impedances less than 1200/spl pi//spl Omega/ the magnetically induced energy absorption predominates. Therefore, H fields must be measured to obtain any estimate of the hazards due to HF exposure. For a 70-kg model of man exposed to a plane wave field, the theory indicates that the time-average power absorption per unit volume is less than 2.5x10/sup -3/ mW/g for each milliwatt per square centimeter incident at 20 MHz and below. This suggests that the thermal safe-exposure levels for the HF band are many orders of magnitude in excess of the 10-mW/cm/sup 2/ level recommended for the microwave region.

Energy and plane waves in linear viscoelastic media

Abstract: The mathematical framework for describing plane waves in elastic and linear anelastic media is presented. Theoretical results suggest that the nature of plane waves in anelastic materials is distinctly different from the nature of plane waves in elastic materials. In elastic media the only type of inhomogeneous plane wave (P or S) that can propagate is one for which planes of constant phase are perpendicular to planes of constant amplitude. However, in anelastic media this is the only type of inhomogeneous wave that cannot propagate. For an inhomogeneous P or S plane wave the particle motion is elliptical, the velocity is less than that of a corresponding homogeneous wave, the maximum attenuation is greater than that of a corresponding homogeneous wave, and the direction of maximum energy flow is not the direction of phase propagation. Expressions for the energy flux, energy densities, dissipated energy, stored energy, and Q−1 are derived from an explicit energy conservation relation, valid for an arbitrary steady state viscoelastic radiation field. Each energy expression is valid for homogeneous or inhomogeneous P or S plane waves in elastic or linear anelastic media.

Natural-mode representation of transient scattered fields

Abstract: Electromagnetic scattering from a perfectly conducting body of finite extent is considered from an integral equation point of view. It is shown that the operator inverse to the integral operator of the magnetic field formulation is an analytic operator-valued function in the complex frequency plane except at certain points (the natural frequencies) where it has poles. Furthermore, a representation of the inverse operator in terms of the natural frequencies and the nontrivial solutions of the homogeneous integral equation is given. Explicit expressions for the scattered field in terms of exponentially damped sinusoidal oscillations are given for the special case where the incident wave is a delta-function plane wave and the inverse operator has only simple poles.

Asymptotic theory for inhomogeneous waves

Abstract: The conventional asymptotic theory for propagation of high-frequency fields is based on a local description in terms of homogeneous plane waves A(r) exp [ik_{0}S(r)] , where k_{0} is the (large) free space wavenumber, A(r) is a spatially dependent amplitude, and the phase S(r) is real. The conventional theory does not accommodate the more general class of fields that behave locally like inhomogeneous plane waves with complex phase S(r)= R(r) + iI(r) , where R determines the propagation of the equiphase surfaces and I describes the attenuation. This paper develops an asymptotic theory for inhomogeneous wave fields in lossless media, to be termed evanescent fields. Such fields are encountered, for example, in connection with Gaussian beams and with phenomena on the exterior of surface wave structures or on the dark side of caustics. The scalar wave equation is used to derive eikonal and transport equations for S and A , respectively, and it is shown how the latter equations may be integrated with the aid of trajectories tangent to the direction of ablaR , which differs slightly from that for the local power flow. Detailed application of the theory is made to two-dimensional scattering of a weakly evanescent incident plane wave by a curved boundary in a homogeneous medium. The phase propagation paths for the reflected field are determined explicitly and are found to possess curvature and points of inflection; these characteristics are shown to be predictable from basic attributes of evanescent wave propagation. For the special case of a circular cylinder, the subsequently constructed reflected field is found to agree with the asymptotic expansion of the rigorous solution, thereby confirming the validity of the theory for weakly evanescent fields. The rigorous solution, valid for arbitrary evanescent decay and obtained from known results for ordinary plane wave scattering by analytic continuation of the incidence angle to complex values, reveals that both the reflected and creeping wave fields should be viewed in a restrictive manner when the evanescent decay is large. However, for weak evanescent decay, these fields retain their customary significance and permit their construction by local evanescent field tracking. It is interesting to observe that in contrast to the nonevanescent case, the creeping waves provide a field contribution exceeding that of the incident or reflected waves in certain portions of the illuminated region.

Optical Properties of Cholesteric Liquid Crystals

Abstract: A general theory of wave propagation in helical structures is developed. It is shown that this problem is quite similar to the well-known wave propagation in solid crystal lattices. If energy dissipation is neglected there are shown to exist frequency bands for wave propagation without attenuation separated by frequency bands where waves are damped out and cannot propagate. Formally, the waves have the form of Bloch waves ${e}^{i\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}.\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}}u(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$, having the character of plane waves modulated by a function $u(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ which is periodic with the structure. Based on this theory, for reflection of light by homogeneously ordered cholesteric liquid crystals the following results are obtained: For incident light parallel to the helical axis there exists only one band of selective reflection. For obliquely incident light, however, an infinite series of higher-order reflection bands occur. Each reflection band is split into two branches. The angular dependence of the reflection bands and the sequence of the higher-order reflections on the wavelength scale bear a certain analogy to Bragg reflection.

Plane-Wave Representations for Scalar Wave Fields

Abstract: The theory of the representation of wave fields in terms of superpositions of monochromatic plane waves is presented for fields satisfying the inhomogeneous scalar wave equation The discussion includes expansions of the type originally used by E T Whittaker involving only homogeneous plane waves, and of the type introduced by H Weyl involving both homogeneous and inhomogeneous plane waves Expressions for the plane-wave amplitudes for both types of representations are obtained in terms of the source function, and precise conditions under which each expansion is valid are given It is shown that when both types of expansions are valid, the superposition of inhomogeneous plane waves in the Weyl-type representation is equal to the superposition of the homogeneous plane waves that propagate into a specific half-space in the Whittaker-type representation It is shown also that in restricted space-time regions only a certain subset of the plane waves in the Whittaker-type expansion contribute to the field This result leads to a simple expression for the field valid at large distances from the source

Planar leaky light-guides and couplers

Abstract: A quantitative theory of light propagation in a dielectric slab guide with general cladding media is presented. It is based on a plane wave which bounces in a zigzag fashion along the guide as a result of total or partial reflections at the two surfaces of the film. Two mechanisms are considered which contribute to the attenuation of the guide: losses due to absorption in the slab and cladding materials, and radiation losses if the guide is a leaky one. We point out the significance of the Goos-Hanchen effect for all questions relating to the power flow in the slab guide. The theory is illustrated by discussing dispersion and attenuation of guides with various low-index and high-index claddings, operating above and below cutoff. The low-index leaky guide is considered particularly in detail. Its high attenuation by leakage can be reduced to practically acceptable values (<1d B/cm) by increasing the film thickness to ≳ 40λ. One application of this guide is in the leaky wave coupler. This coupler may be viewed as a prism-film coupler simplified by omission of the gap. It offers a new approach to the problem of broad-band coupling to thin-film light guides.

Transverse surface waves on a piezoelectric material carrying a metal layer of finite thickness

Abstract: Theory of the propagation of a surface wave related both to Bleustein‐Gulyaev waves and Love waves is developed. The wave has unidirectional particle motion perpendicular to the direction of propagation and parallel to the surface of a piezoelectric material which is covered with a finite‐thickness layer of an isotropic conducting material. An equation relating phase velocity to material costants is solved in closed form for a piezoelectric material of class 6mm, and conditions for the existence of various modes are presented. Piezoelectricity allows a nonleaky but dispersive wave to exist under conditions is which no love wave is possible, namely, when the shear wave velocity in the layer is greater than that in the substrate. Numerical results are presented for aluminium, gold, and zinc layers on PZT 4 ceramic.

Flux density for ray propagation in geometrical optics

Abstract: A general formula is derived that specifies the illumination (flux density) over an arbitrary receiver surface when light rays are reflected by or refracted through a curved surface. The direction of the deflected ray and its intersection with the receiving surface, used with the equation for the surfaces, lead to a transformation that maps an element of deflecting area onto the receiving area, by means of the jacobian determinant. A formula for the flux density along a ray path follows as a special case. An equation for the caustic surface is obtained from the latter. As an example radiation flux-density contours are calculated for a plane wave reflected from a sphere. Flux density and the caustic surface are calculated for a plane wave reflected onto a plane from a concave spherical lens and also for a plane wave refracted onto a plane through a hemisphere.

Twist reflector design using E-type and H-type modes

Abstract: A complete solution of plane wave scattering from a twist reflector of infinite extent for arbitrary incidence is presented. The solution is accomplished through the use of an E -and H -type modal representation of the fields in the twister and free space regions. The equivalent circuits for strip and parallel plate twister gratings are derived by transforming E and H mode results [5] to appropriate type mode parameters. The modal reflection coefficients \Gamma' and \Gamma'' are determined from these equivalent circuit parameters and together with the use of a type mode description of the incident and reflected fields lead to two simple conditions for an optimum design; one geometric, namely \tan \phi = \sec \theta and one electrical, \Gamma"/\Gamma' = - 1 . The computed performance of this optimum twist reflector in terms of a cross-polarized suppression ratio versus incidence angle for various planes of incidence represents the best that can be done with any physical structure. A design procedure including design formulas and curves is given from which twist reflector dimensions can be determined. Experimental verification for two specific implementations, parallel plates and parallel strips twist reflectors, is described.

Scalar waves in the mixmaster universe. I. The Helmholtz equation in a fixed background

Abstract: Solutions to the scalar wave equation in a fixed mixmaster background are presented. Separability conditions on the Laplace-Beltrami equation are related to the complete sets of invariant operators of the symmetry group S${\mathrm{O}}_{3}$. Solutions to the Helmholtz equation are equivalent to the quantum-mechanical problem of asymmetric rotors. The wave functions in the mixmaster space are the asymmetric-top wave functions. In Euler angle variables, they are expanded in terms of the symmetric-top wave functions (the wave functions in Taub space) possessing definite ($J, K, M$) symmetries, with a coupling in the intrinsic magnetic quantum number $K$; the case with $M=0$ can be expressed as a product of the Lam\'e functions in elliptic coordinates. Invariance of the mixmaster space under the four - group characterizes the wave functions into four symmetry species and causes the factorization of the energy matrix into four submatrices. Eigenvalues and expansion coefficients for the wave functions are calculated for some low-lying levels.

Experimental analysis of spherical wave propagation

Abstract: Analyses coupling in-material stress and particle velocity gage measurements with the equations of hydrodynamic flow are presently used for determining stress-volume paths during transient one-dimensional plane wave propagation in solids. In this work a method is described that allows analysis of attenuating experimental wave profiles of arbitrary shape in spherically symmetric flow. The method is applied to radial stress and particle velocity data for spherically divergent wave propagation in Westerly granite. The resulting relations among pressure, volume, and deviatoric stress are compared and are found to be consistent with other available data on Westerly granite. It is concluded that the analysis promises to be a useful tool for relating observed wave structure to physical processes occurring in the material and for developing better constitutive relations to predict the transient dynamic behavior of material.

Plane waves at small arrays

Abstract: The resolving power of a seismic array is defined in terms of the array response function and via the classical uncertainty principle. Using the theory of maximum likelihood wavenumber spectra (Capon, 1969), we show for the case of two correlated plane waves that arbitrarily high resolution is achievable in the limit as the background white noise tends to zero. This extends Barnard’s (1969) result to the case of correlated plane waves. The increased resolution arises from the additional assumption that the data are plane waves over all space, and not zero off the array as the classical result assumes. It is found that a sample rate (in time) large compared to the Nyquist rate, is needed in the case of a short time gate at a small array. Cross‐power spectral matrices are estimated at 4 hz from 1 sec of computer generated data consisting of two correlated plane waves in white noise. These spectral matrices are then used to generate maximum likelihood wavenumber spectra. The two plane waves are resolved at v...

Depolarization of electromagnetic waves excited by distributions of electric and magnetic sources in inhomogeneous multilayered structures of arbitrarily varying thickness. Generalized field transforms

Abstract: A suitable basis for the full wave expansion of electromagnetic fields in inhomogeneous multilayered structures of arbitrarily varying thickness is presented in this paper. To this end, we formulate appropriate sets of transform pairs for the transverse electric and magnetic fields. Since arbitrary distribution of electric and magnetic sources are considered, the complete expansion must be composed of both vertically and horizontally polarized waves. Each set of generalized transforms, for the vertically and horizontally polarized waves, consists of two infinite integrals (continuous spectrum) which correspond to the radiation and the lateral wave terms as well as a finite number of terms (discrete spectrum) which correspond to the surface waves. For a general three‐dimensional distribution of sources in any of the structure's layers, the transverse electric and magnetic fields are in general two component vector functions. Thus, the transform pairs involve vector rather than scalar functions. Exact boundary conditions are employed in the analysis rather than approximate surface impedance boundary conditions. When the boundary media of the structure are regarded as perfect electric or magnetic walls, or are characterized by surface impedances, the fields are expressed exclusively in terms of infinite sets of waveguide modes.

Depolarization of electromagnetic waves excited by distributions of electric and magnetic sources in inhomogeneous multilayered structures of arbitrarily varying thickness. Full wave solutions

Abstract: Full wave solutions to the problem of depolarization of electromagnetic waves excited by general three‐dimensional distributions of electric and magnetic sources in inhomogeneous multilayered structures of arbitrarily varying thickness are derived. Generalized field transforms that provide an appropriate basis for the expansion of transverse electromagnetic fields are employed to convert Maxwell's equations into a set of coupled first order ordinary differential equations for the forward and backward, vertically and horizontally polarized wave amplitudes. The continuous parts of the complete wave spectrum correspond to the radiation and lateral wave terms while the discrete part of the wave spectrum corresponds to the surface wave or trapped waveguide modes. Exact boundary conditions are imposed at all the interfaces of the structure and the solution is not restricted by the surface impedance concept. When the bounding media of the structure are characterized by perfect electric or magnetic walls, the fields are expressed exclusively in terms of waveguide modes. On the other hand, if the electromagnetic parameters are functions of one coordinate variable, the solutions are expressed exclusively in terms of an infinite integral—the radiation term. The solutions are shown to satisfy the reciprocity relationships.

Seismic waves due to a shear fault in a semi-infinite medium

Abstract: In order to clarify basic characteristics of seismic waves in the near-field as well as in the far-field, exact solutions for free surface displacements generated from a shear fault with an arbitrary orientation in a semi-infinite medium are obtained in a cylindrical coordinate system. First, taking the free surface effects into account, expressions for Laplace transforms of displacements with respect to time are derived, and secondly exact transient solutions are obtained by using the Cagniard's method which gives the inverse Laplace transforms in a very ingenious manner when the source time function is of the ramp type. In sections 2, 3 and 4, mathematical expressions are derived, and the results and interpretations of numerical computations for a point source are presented in section 5. Basic characteristics of each phase are summarized as follows: P pulse has basically a rectangular form. The initial pulse amplitudes in a semi-infinite medium are, even in rather near-field, close to those in an infinite medium with correction of surface effects due to plane wave incidence. SP pulse, which radiates from the source as S phase, is incident onto the free surface with a critical angle and then is propagated along the surface with the speed of P-wave velocity, has a relatively large amplitude in the near-field and cannot be neglected when the wave form on the free surface is discussed. This pulse is observed when the epicentral distance is greater than the critical distance. S pulse forms are quite different at epicentral distances less than and greater than the critical distance. S pulse beyond the critical distance has logarithmic infinities at the arrival time of S phase, tS, and tS+t0, t0 being the rise time of the source function. Therefore a plane-wave correction can-not be applied successfully as in the case of an onset of the P pulse. The Rayleigh pulse is well developed when the epicentral distance is about five to ten times as large as the focal depth and its form is not very much affected by the rise time of the source function. For surface focus, S pulse has no logarithmic infinity but the Rayleigh pulse has infinities at the arrival time tR and tR+t0. It is shown that the solutions for a moving source can be obtained by numerical integrations of the solutions for the point source. This case will be dealt with in a subsequent paper.