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 studies the scattering of a TM plane wave from a perfectly conductive sinusoidal surface with finite extent by the small perturbation method. We obtain the first and second order perturbed solutions explicitly, in terms of which the differential scattering cross section and the total scattering cross section per unit surface are calculated and are illustrated in figures. By comparison with results by a numerical method, it is concluded that the perturbed solution is reasonable even for a critical angle of incidence if the surface is small in roughness and gentle in slope and if the corrugation width is less than certain value. A brief discussion is given on multiple scattering effects.

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 energy conservation law and the optical theorem in the grating theory are discussed: the energy conservation law states that the incident energy is equal to the sum of diffracted energies and the optical theorem means that the diffraction takes place at the loss of the specularly reflection amplitude. A mathematical relation between the optical theorem and the energy conservation law is given. Some numerical examples are given for a TM plane wave diffraction by a sinusoidal surface.