Geometrical Optics Waves Research Articles

Scattering of waves by a soft–hard half-plane between isorefractive medium

The scattering of plane waves by a soft–hard half-plane residing between isorefractive medium is studied. The scattered geometrical optics fields are obtained by subtracting the initial geometrical optics fields from the total geometrical optics waves. The diffracted fields are determined by considering the structure of the scattered geometrical optics waves. The uniform expressions for the diffracted fields are derived. The behaviour of the total waves is investigated numerically.

Interaction of electromagnetic waves with a resistive half-plane

The interaction process of electromagnetic waves by a resistive half-plane is investigated. The scattered geometrical optics fields are obtained by subtracting the incident field from the total geometrical optics waves. The physical optics integral of the scattered waves is derived with the aid of the scattered geometrical optics fields. The edge diffracted waves are derived from the physical optics integral by the edge point technique. A correction field is added to the diffracted fields in order to obtain a solution that satisfies the resistive boundary conditions on the surface of the half-screen. The uniform diffracted fields are expressed in terms of the Fresnel function and the resultant field representations are compared with the literature numerically.

Scattering by a conductive half-screen between isorefractive media.

The scattering process of electromagnetic waves by a conductive half-plane, located between isorefractive media, is investigated. First, the conductive sheet at the interface of isorefractive media is considered. The reflection and transmission coefficients of the plane are evaluated. The diffracted fields by the half-plane are obtained with the aid of a relation between the diffracted and scattered geometrical optics waves. The resultant field expressions are numerically examined.

The physical optics integral on the scatterer's unlit surface

The scattering integrals of the modified theory of physical optics are redefined according to the illuminated and unlit surfaces of the scattering object. With this aim the canonical problem of wedge diffraction is taken into account. It is shown that the new scattering integral contain two geometrical optics and diffracted fields. One of the geometrical optics waves is the reflected field component that propagates in the real space. The other one transmits to an imaginary space through the scattering surface and does not have any influence in the real space. The diffracted waves exist in the real space and satisfy the related boundary condition on the scattering surfaces. The resultant field expressions are compared with the exact series solution of the problem numerically.

Diffraction of waves by a perfectly conducting half-plane between two dielectric media

The scattered fields by a perfectly conducting half-plane, located at the interface of two dielectric media, are investigated. The diffracted fields are defined with novel reflection and transmission coefficients that are functions of the observation distance and angle. These coefficients reduce to the constant reflection and transmission coefficients of the geometrical optics wave. The unknown quantities in the coefficients of the diffracted waves are determined according to the boundary conditions on the half-plane and the interface of the dielectric media. The resultant field expressions are investigated numerically and the behavior of the scattered and diffracted waves are studied.

The MTPO/Malyughinetz hybrid method for the scattering analysis of parabolic impedance reflectors

The scattering process of cylindrical waves, radiated by a line source, from a parabolic reflector is investigated with the MTPO/Malyughinetz hybrid method. The geometrical optics and diffracted waves are evaluated asymptotically from the radiation integral. The scattered, diffracted and geometrical optics waves are plotted numerically for different impedance values.

FRINGE WAVES IN AN IMPEDANCE HALF-PLANE

The uniform expressions of scalar fringe waves which are based on the physical theory of difiraction (PTD) were obtained for the impedance half plane in terms of the Fresnel integrals. Asymptotic and uniform forms of the fringe flelds were compared. The radiated flelds of the fringe expressions were analyzed numerically. Physical optics (PO) is based on the integration of surface currents which are induced by the incident flelds. This concept is valid and accurate for metallic scatterer surfaces and gives exact geometric optics (GO) waves in the high frequencies. There are lots of studies in the literature about the application of the PO method (1{3). The edge difiracted flelds which are found from the contribution of the PO surface integral are not correct. In addition PO currents just consider the illuminated part of the scatterer and ignore the shadow regions. The physical theory of difiraction (PTD) method was proposed by Uflmtsev to overcome the flrst defeat (4). The PTD consists of two main parts. The flrst part is the uniform part which is obtained from the PO and the second part is the contribution of the non-uniform or fringe part. The fringe part is the result of the fringe currents. It is pointed out that the fringe currents are obtained by dividing the induced surface currents into two parts. The flelds, radiated by the fringe currents, can be found by subtracting of uniform part from the exact solution. The method is widely used in the literature for investigation of the scattering problems (5{8). Using the uniform fringe flelds instead of the non-uniform version is more reliable. Non- uniform fringe flelds can be obtained by the subtraction of asymptotic

SCATTERING BY AN IMPEDANCE HALF-PLANE: COMPARISON OF THE SOLUTIONS OF RAMAN/KRISHNAN AND MALIUZHINETS/SENIOR

There are three approaches for the solution of the difiraction problem of plane waves by an impedance half-plane in the literature. The difiracted fleld expressions, obtained by the related methods, are compared numerically. The examination of the scattered fleld shows that the most reliable solution is the fleld representation of Raman and Krishnan. Since the difiracted flelds of Senior and Maliuzhinets do not compensate the discontinuities of the geometrical optics waves at the transition regions. The difiraction problem of waves by a conducting half-plane is a canonical problem of the difiraction theory. The flrst rigorous solution of this problem was put forward by Sommerfeld (1). He deflned a spectrum integral of plane waves and chose the amplitude function according to an extended space that has a period of 4…. The evaluation of the complex integral yielded to the uniform expressions of the scattered flelds in terms of the Fresnel functions. The method of Sommerfeld was applied to more general case of the conducting wedge by Carslaw (2). The impedance surfaces are more realistic in the modeling of the scatterers since an object does not generally re∞ect all of the incoming energy. The flrst solution of the difiraction problem of waves by a non-perfectly re∞ecting half-screen was obtained by Raman and Krishnan (3). They applied the uniform solution of Sommerfeld to the problem by using the re∞ection coe-cient from a whole impedance

Fronts in randomly advected and heterogeneous media and nonuniversality of Burgers turbulence: Theory and numerics

A recently established mathematical equivalence-between weakly perturbed Huygens fronts (e.g., flames in weak turbulence or geometrical-optics wave fronts in slightly nonuniform media) and the inviscid limit of white-noise-driven Burgers turbulence-motivates theoretical and numerical estimates of Burgers-turbulence properties for specific types of white-in-time forcing. Existing mathematical relations between Burgers turbulence and the statistical mechanics of directed polymers, allowing use of the replica method, are exploited to obtain systematic upper bounds on the Burgers energy density, corresponding to the ground-state binding energy of the directed polymer and the speedup of the Huygens front. The results are complementary to previous studies of both Burgers turbulence and directed polymers, which have focused on universal scaling properties instead of forcing-dependent parameters. The upper-bound formula can be heuristically understood in terms of renormalization of a different kind from that previously used in combustion models, and also shows that the burning velocity of an idealized turbulent flame does not diverge with increasing Reynolds number at fixed turbulence intensity, a conclusion that applies even to strong turbulence. Numerical simulations of the one-dimensional inviscid Burgers equation using a Lagrangian finite-element method confirm that the theoretical upper bounds are sharp within about 15% for various forcing spectra (corresponding to various two-dimensional random media). These computations provide a quantitative test of the replica method. The inferred nonuniversality (spectrum dependence) of the front speedup is of direct importance for combustion modeling.

Cosmology with a dark refraction index

We review Gordon's optical metric and the transport equations for the amplitude and polarization of a geometrical optics wave traveling in a gravity field. We apply the theory to the Friedmann-Lemaitre-Robertson-Walker cosmologies by associating a refraction index with the cosmic fluid. We then derive an expression for the accumulated effect of a refraction index on the distance-redshift relations and fit the Hubble curve of current supernova observations with a nonaccelerating cosmological model. We also show that some observational effects caused by inhomogeneities, e.g., the Sachs-Wolfe effect, can be interpreted as being caused by an effective index of refraction, and hence this theory could extend to other speed of light communications such as gravitational radiation and neutrino fluxes.

A comparison of the results of a numerical simulation and an approximate calculation of the statistical characteristics of radio waves in a layer with random inhomogeneities of dielectric permittivity

We consider the formation algorithm for a random inhomogeneity field of dielectric permittivity of a medium that is used in simulations of the statistical characteristics of a wave that has propagated through a randomly inhomogeneous layer. We carry out a comparison of the statistical characteristics of a geometrical-optics wave, obtained via a numerical simulation, with the results of calculations of these characteristics by approximate formulae obtained using perturbation theory. It is pointed out that the applicability limits of the perturbation method, when solving geometrical-optics equations in a randomly inhomogeneous medium, depend on the formulation (one- or two-point) of the trajectory problem. It is shown that a calculation of the spatial correlation function of the field can be carried out using the perturbation method, even in the case of relatively strong fluctuations of dielectric permittivity. This is due to the fact that, in the region where this function differs markedly from zero, the correlation function of the eikonal obtained by the perturbation method is sufficiently accurate, and amplitude fluctuations are small.

A uniform physical optics analysis of scattered electromagnetic field by the edge of concave conducting surface

A physical optics approximation is discussed for the analysis of the scattered electromagnetic field when a cylindrical wave radiated from a line source is incident near the edge of a concave conducting surface with its radius of curvature slowly varying as a function of position. By analyzing approximately the integral of the scattered electromagnetic field expressed in terms of the physical optics current, a uniform asymptotic solution is derived by superposition of the geometrical optics wave and the edge diffraction wave. The diffraction coefficient for the edge diffraction wave is expressed in terms of the Fresnel function, while the expressions on the reflection boundary (RB) side and the shadow boundary (SB) side have symmetry. The argument of the Fresnel function uses a new representation containing information on the radius of curvature of the wave front of the diffracted wave and the location of the caustic, or the radius of curvature of the wave front of the incident wave, so that a scattered field continuous on the RB and SB is formed. The effectiveness of the uniform asymptotic solution is numerically clarified by comparison with the rigorous solution obtained by the Wiener–Hopf method and the reference solution obtained by direct numerical integration of the integral on the scattered field. The results are compared with analytical results based on the physical optics approximation published elsewhere. The causes of the difference from the present results are discussed. © 2000 Scripta Technica, Electron Comm Jpn Pt 2, 83(6): 32–42, 2000

A uniform physical optics analysis of scattered electromagnetic field by the edge of concave conducting surface

A physical optics approximation is discussed for the analysis of the scattered electromagnetic field when a cylindrical wave radiated from a line source is incident near the edge of a concave conducting surface with its radius of curvature slowly varying as a function of position. By analyzing approximately the integral of the scattered electromagnetic field expressed in terms of the physical optics current, a uniform asymptotic solution is derived by superposition of the geometrical optics wave and the edge diffraction wave. The diffraction coefficient for the edge diffraction wave is expressed in terms of the Fresnel function, while the expressions on the reflection boundary (RB) side and the shadow boundary (SB) side have symmetry. The argument of the Fresnel function uses a new representation containing information on the radius of curvature of the wave front of the diffracted wave and the location of the caustic, or the radius of curvature of the wave front of the incident wave, so that a scattered field continuous on the RB and SB is formed. The effectiveness of the uniform asymptotic solution is numerically clarified by comparison with the rigorous solution obtained by the Wiener–Hopf method and the reference solution obtained by direct numerical integration of the integral on the scattered field. The results are compared with analytical results based on the physical optics approximation published elsewhere. The causes of the difference from the present results are discussed. © 2000 Scripta Technica, Electron Comm Jpn Pt 2, 83(6): 32–42, 2000

Far-field analysis of the Malyuzhinets solution for plane and surface waves diffraction by an impedance wedge

The basic problem of determining the far-field scattered from the edge of a wedge of exterior angle 2 Φ with arbitrary impedance conditions on either face is considered. An accurate solution in the form of a Sommerfeld integral obtained by Malyuzhinets is evaluated for kr≫1. A fairly complete discussion of the far-field response is provided, including uniform and non-uniform asymptotic approximations. The far-field is split into edge-diffracted, surface, and geometrical optics waves, including multiply reflected components. The edge-diffracted field is defined by the diffraction coefficient, which we show has a simple factorisation: D= u 0( φ) u 0( φ 0) F Φ ( φ, φ 0), where φ and φ 0 are the source and observation directions, u 0( φ) is the value of the wave function at the edge for a plane wave of unit amplitude incident from the direction φ, and F Φ ( φ, φ 0) involves only trigonometric functions. We demonstrate that the monostatic tip diffraction from a wedge of arbitrary angle can be made to vanish by appropriate choice of the surface impedance. The unique value of impedance is always real, and an explicit formula is given for its evaluation. New results are presented for the reflection and transmission of surface waves on an impedance wedge, including simple approximations for an internal wedge with small Φ. Finally, a complete uniform description of the far-field is given in the format of the Uniform Asymptotic Theory of Diffraction.

A method of calculating the field of a point source in a waveguide

In the paper a representation is obtained of the field of a point source in a waveguide with quadratic dependence of the index of refraction in the form of a sum of normal, geometrical-optics waves and a remainder. Sufficient conditions on the number of separate normal and geometrical-optics waves are found. The remainder is expressed by a simple formula.