This paper deals with reflection and transmission of a TE plane wave from a one-dimensional random slab with slanted fluctuation by means of the stochastic functional approach. By starting with a generalized representation of the random wavefield from a two-dimensional random slab, and by using a manner for slanted anisotropic fluctuation, the corresponding random wavefield representation and its statistical quantities for one-dimensional cases are newly derived. The first-order incoherent scattering cross section is numerically calculated and illustrated in figures.

This paper deals with reflection and transmission of a TE plane wave from a two-dimensional random slab with slanted fluctuation by means of the stochastic functional approach. Such slanted fluctuation of the random slab is written by a homogeneous random field having a power spectrum with a rotation angle. By starting with the previous paper [IEICE Trans. Electron., Vol. E92-C, no.1, pp.77–84, January 2009], any statistical quantities are immediately obtained even for slanted fluctuation cases. The first-order incoherent scattering cross section is numerically calculated and illustrated in figures. It is then newly found that shift and separation phenomena of the leading or enhanced peaks at four characteristic scattering angles take place in the transmission and reflection sides, respectively.

This paper proposes a further improved technique on the stochastic functional approach for randomly rough surface scattering. The original improved technique has been established in the previous paper [Waves in Random and Complex Media, vol.19, no.2, pp.181-215, 2009] as a novel numerical-analytical method for a Wiener analysis. By deriving modified hierarchy equations based on the diagonal approximation solution of random wavefields for a TM plane wave incidence or even for a TE plane wave incidence under large roughness, large slope or low grazing incidence, such a further improved technique can provide a large reduction of required computational resources, in comparison with the original improved technique. This paper shows that numerical solutions satisfy the optical theorem with very good accuracy, by using small computational resources.

This paper studies reflection and transmission of a TE plane wave from a two-dimensional random slab with statistically anisotropic fluctuation by means of the stochastic functional approach. By starting with a representation of the random wavefield presented in the previous paper [IEICE Trans. Electron., vol.E92-C, no.1, pp.77-84, Jan. 2009], a solution algorithm of the multiple renormalized mass operator is newly shown even for anisotropic fluctuation. The multiple renormalized mass operator, the first-order incoherent scattering cross section and the optical theorem are numerically calculated and illustrated in figures. The relation between statistical properties and anisotropic fluctuation is discussed.

This paper reexamines reflection and transmission of a TE plane wave from a two-dimensional random slab discussed in the previous paper [IEICE Trans. Electron., Vol.E79-C, no.10, pp.1327-1333, October 1996] by means of the stochastic functional approach with the multiply renormalizing approximation. A random wavefield representation is explicitly shown in terms of a Wiener-Hermite expansion. The first-order incoherent scattering cross section and the optical theorem are numerically calculated. Enhanced scattering as gentle peaks or dips on the angular distribution of the incoherent scattering is reconfirmed in the directions of reflection and backscattering, and is newly found in the directions of forward scattering and 'symmetrical forward scattering.' The mechanism of enhanced scattering is deeply discussed.

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 Brewster's angle appears in the coherent reflection.

This paper deals with a TE plane wave reflection and transmission from a one-dimensional random slab by means of the stochastic functional approach. The relative permittivity of the random slab is written by a Gaussian random field in the vertical direction with finite thickness, and is uniform in the horizontal direction with infinite extent. An explicit form of the random wavefield is obtained in terms of a Wiener-Hermite expansion with approximate expansion coefficients (Wiener kernels) under a small fluctuation case. By using the first three terms of the random wavefield representation, the optical theorem is illustrated in figures for several physical parameters. It is then found that the optical theorem holds with good accuracy.

The mean reflection and transmission coefficients of electromagnetic waves incident onto a two-dimensional slightly random dielectric surface are investigated by means of the stochastic functional approach. We discuss the shift of Brewster's scattering angle using the Wiener kernels and numerical calculations. It is also shown that the phase shift at the reflection into Brewster's angle for a flat surface does not depend on the rms height of the surface, but does on the correlation length of the surface.

This paper deals with an orthogonal functional expansion of a non-linear stochastic functional of a stationary binary sequence taking 1 with unequal probability. Several mathematical formulas, such as multivariate orthogonal polynomials, recurrence formula and generating function, are given in explicit form. A formula of an orthogonal functional expansion for a stochastic functional is presented; the completeness of expansion is discussed in Appendix.

The present paper gives a new formulation for rough surface scattering in terms of a stochastic integral equation which can be dealt with by means of stochastic functional approach. The random surface is assumed to be infinite and a homogeneous Gaussian random process. The random wave field is represented in the stochastic Floquet form due to the homogeneity of the surface, and in the non-Rayleigh form consisting of both upward and downward going scattered waves, as well as in the extended Voronovich form based on the consideration of the level-shift invariance. The stochastic integral equations of the first and the second kind are derived for the unknown surface source function which is a functional of the derivative or the increment of the surface profile function. It is also shown that the inhomogeneous term of the stochastic integral equation of the second kind automatically gives the solution of the Kirchhoff approximation for infinite surface.

This paper deals with the scattering of a plane wave from a two-dimensional random thin film. For a Gaussian random disorder, a first order solution is derived explicitly by a probabilistic method. It is then found that ripples appear in angular distributions of the incoherent scattering. Furthermore, the incoherent scattering is enhanced in the directions of backscattering and specular reflection. Physical processes that yield such an enhanced scattering are discussed. Numerical examples of the coherent and incoherent scattering are illustrated in figures.