Yasuhiko Tamura

Mass operator for wave scattering from a slightly random surface

Abstract This paper deals with the mass operator representing multiple-scattering effects in the theory of wave scattering from a slightly random surface. By means of the stochastic-functional approach, a recurrence equation for the mass operator is obtained in the form of an iterative integral. However, its solution oscillates in a non-physical manner against the number of iterations. Next, the recurrence equation may be regarded as a nonlinear integral equation, when the number of iterations goes to infinity. An analytical solution of the nonlinear integral equation is presented for a special case in which the roughness spectrum is the Dirac delta function. Then, the nonlinear integral equation is solved numerically for the Gaussian roughness spectrum by iteration, starting from such an analytical solution. It is shown that only a few iterations are required to obtain the mass operator, even when the correlation distance is small. Effects of the mass operators on the coherent reflection coefficient and ...

Diffraction Amplitudes from Periodic Neumann Surface: Low Grazing Limit of Incidence (II)

This paper deals with the singular behavior of the diffraction of transverse magnetic (TM) waves by a perfectly conductive triangular periodic surface at a low grazing limit of incidence. The wave field above the highest excursion of the surface is represented as a sum of Floquet modes with modified diffraction amplitudes, whereas the wave field inside a triangular groove is written as a sum of guided modes with unknown mode amplitudes. Then, two sets of equations are derived for such amplitudes. From the equation sets, all the amplitudes are analytically shown to vanish at a low grazing limit of incidence. From this fact, it is concluded analytically that no diffraction takes place and only reflection occurs at a low grazing limit of incidence for any period length and any triangle height. This theoretical result is verified by a numerical example.

Enhanced scattering from a thin film with one-dimensional disorder

This paper deals with a TE plane wave scattering from a thin film with one-dimensional disorder by means of the stochastic functional approach. The thin film is one-dimensionally inhomogeneous in the horizontal direction with infinite extent, and is homogeneous in the vertical direction with finite thickness. Based on an approximate wavefield representation in terms of a Wiener–Hermite expansion in a preceding paper (Tamura et al., 2004, Waves in Random Media, 14, 435–465), the first- and second-order incoherent scattering cross-sections are presented in explicit forms and scattering properties are discussed. The scattering properties vary entirely with the film thickness. In a case where the thickness is smaller than a few wavelengths in the thin film, enhanced scattering and associated enhanced scattering may appear as sharp peaks or dips on the second-order incoherent scattering distribution if the thin film has guided wave modes. When the thickness becomes sufficiently larger than the wavelength inside the film, a new enhanced scattering phenomenon appears as gentle peaks on the second-order incoherent scattering distribution in four special directions. Such four directions are the directions of forward scattering, specular reflection, backscattering, and the symmetrical direction of forward scattering with respect to the normal of the film surface.The first-order incoherent scattering occurs distinctly in four such directions. Such enhanced scattering is independent of the existence of the guided wave modes inside the thin film, and deeply relates to the structure of the thin film with one-dimensional disorder that has infinite correlation in the vertical direction. For SiC and glass thin films having one-dimensional disorder with a Gaussian correlation and three types of exponential correlation, the first- and second-order incoherent scattering cross-sections are illustrated in figures. The narrow enhanced scattering peaks appear for the glass film in a thin case. The gentle enhanced peaks turn up for both the SiC and glass films in a thick case. Furthermore, the optical theorem is calculated for several cases. It is then found that the error of the optical theorem decreases and the performance of the wavefield is improved by taking into account the second-order incoherent scattering.

Wave reflection and transmission from a thin film with one-dimensional disorder

Abstract This paper deals with a TE plane wave reflection and transmission from a thin film with one-dimensional disorder by means of the stochastic functional approach. The relative permittivity of the thin film is written by a Gaussian random field in the horizontal direction with infinite extent, and is uniform in the vertical direction with finite thickness. Arandomwavefield is obtained in terms of a Wiener–Hermite expansion representation with approximate expansion coefficients (Wiener kernels) under a small fluctuation case. For a SiC thin film and a glass thin film having one-dimensional disorder with Gaussian correlation or an exponential correlation, numerical examples of the first-order incoherent scattering cross section and the optical theorem are illustrated in the figures. It is then found that ripples and four major peaks appear in angular distributions of the incoherent scattering. Such four peaks may occur in the directions of forward scattering, specular reflection, backscattering and in the symmetrical direction of forward scattering with respect to the normal to surface of the thin film. Physical processes that yield such ripples and peaks are discussed.

Scattering of a plane wave from a periodic random surface: a probabilistic approach

Abstract This paper deals with a probabilistic formulation of the wave scattering from a periodic random surface. When a plane wave is incident on a random surface described by a periodic stationary stochastic process, it is shown by a group-theoretic consideration that the scattered wave may have a stochastic Floquet form, i.e. a product of a periodic stationary random function and an exponential phase factor. Such a periodic stationary random function is then written by a harmonic series representation similar to a Fourier series, where Fourier coefficients are mutually correlated stationary processes instead of constants. The mutually correlated stationary processes are represented by Wiener - Hermite functional series with unknown coefficient functions called Wiener kernels. In case of a slightly rough surface and TE wave incidence, low-order Wiener kernels are determined from the boundary condition. Several statistical properties of the scattering are calculated and illustrated in figures.

TM plane wave scattering and diffraction from a randomly rough half-plane: (part II) An evaluation of the diffraction kernel

In a previous paper (part I), it has been shown that a random wavefield from a randomly rough half-plane for a TM plane wave incidence is written in terms of a Wiener-Hermite expansion with three types of Fourier integrals. This paper studies a concrete representation of the random wavefield by an approximate evaluation of such Fourier integrals, and statistical properties of scattering and diffraction. For a Gaussian roughness spectrum, intensities of the coherent wavefield and the first-order incoherent wavefield are calculated and shown in figures. It is then found that the coherent scattering intensity decreases in the illumination side, but is almost invariant in the shadow side. The incoherent scattering intensity spreads widely in the illumination side, and have ripples at near the grazing angle. Moreover, a major peak at near the antispecular direction, and associated ripples appear in the shadow side. The incoherent scattering intensity increases rapidly at near the random half-plane. These new phenomena for the incoherent scattering are caused by couplings between TM guided waves supported by a slightly random surface and edge diffracted waves excited by a plane wave incidence or by free guided waves on a flat plane without any roughness.

Scattering and diffraction of a plane wave from a randomly rough strip

Abstract This paper deals with plane wave scattering and diffraction from a randomly rough strip using a combination of three tools: the perturbation method, the Wiener-Hopf technique and a group-theoretic consideration based on the shift-invariant property of the homogeneous random surface. The D a -Fourier transformation associated with the shift invariance is defined instead of the conventional complex Fourier transformation. For a slightly rough case, Wiener-Hopf equations for the zero-, first- and second-order perturbed fields are derived. They are reduced to a common Wiener-Hopf equation, an exact solution of which is obtained formally by means of the Wiener-Hopf technique. Using the inverse D a -Fourier transformation, the scattered wavefield is obtained as a stochastic field. When the strip width is large compared with the wavelength, a uniformly asymptotic representation of the scattered far field is obtained by the saddle point method. For a Gaussian roughness spectrum, several numerical results...

TM Plane Wave Reflection and Transmission from a One-Dimensional Random Slab

This paper deals with a TM plane wave reflection and transmission from a one-dimensional random slab with stratified fluctuation by means of the stochastic functional approach. Based on a previous manner [IEICE Trans. Electron. E88-C, 4, pp. 713-720, 2005], an explicit form of the random wavefield is obtained in terms of a Wiener-Hermite expansion with approximate expansion coefficients (Wiener kernels) under small fluctuation. The optical theorem and coherent reflection coefficient are illustrated in figures for several physical parameters. It is then found that the optical theorem by use of the first two or three order Wiener kernels holds with good accuracy and a shift of Brewsters angle appears in the coherent reflection.

Scattering and diffraction of a plane wave by a randomly rough half-plane*

Abstract The scattering and diffraction of a TE (transverse electric) plane wave by a randomly rough half-plane are studied by a combination of three techniques: the Wiener-Hopf technique, the small perturbation method and a probabilistic method based on the shift-invariance of a homogeneous random function. By use of the Da-Fourier transformation based on the shift-invariance, it is shown that the scattered wave is written by an inverse Fourier transformation of a homogeneous random function with a complex parameter. For a small rough case, such a random function with a complex parameter is expanded in a perturbation series and then the first-order solution is obtained exactly in an integral form. The first-order solution involves two physical processes such that the edge-diffracted wave is scattered by the randomly rough plane and the scattered wave, due to roughness, is diffracted by the half-plane. The solution is transformed into a sum of the Fresnel integrals with complex arguments, an integral alon...

Diffraction and scattering of TM plane waves from a binary periodic random surface

This paper deals with the diffraction and scattering of a TM plane wave from a binary periodic random surface generated by a stationary binary sequence using the stochastic functional approach. The scattered wave is represented by a product of an exponential phase factor and a periodic stationary process. Such a periodic stationary process is regarded as a stochastic functional of the binary sequence and is expressed by an orthogonal binary functional expansion with band-limited binary kernels. Then, hierarchical equations for the binary kernels are derived from the boundary condition without approximation. We point out that binary kernels obtained by a single scattering approximation diverge unphysically when the periodic random surface is zero on average, thus the effects of multiple scattering should be taken into account. The expressions of such binary kernels are obtained using the multiply renormalizing approximation. Then, statistical properties such as differential scattering cross-section and the optical theorem are numerically calculated with the first two order binary kernels and illustrated in the figures. It is found that the incoherent Woods anomaly appears in the angular distribution of scattering even when the surface has zero average.