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 Wood's anomaly appears in the angular distribution of scattering even when the surface has zero average.     

Reflection and refraction of surface acoustic waves by a periodic domain structure

Reflection and refraction of surface acoustic waves by a periodic domain structure formed in lithium niobate is studied. A second harmonic generation is observed. A mechanism underlying the linear and nonlinear interactions of acoustic waves with a periodic domain structure is proposed.     

Double-resonant extremely asymmetrical scattering of electromagnetic waves in periodic arrays separated by a gap

Two strong simultaneous resonances of scattering – double-resonant extremely asymmetrical scattering (DEAS) – are predicted in two parallel, oblique, periodic Bragg arrays separated by a gap, when the scattered wave propagates parallel to the arrays. One of these resonances is with respect to frequency (which is common to all types of Bragg scattering), and another is with respect to phase variation between the arrays. The diffractional divergence of the scattered wave is shown to be the main physical reason for DEAS in the considered structure. Although the arrays are separated, they are shown to interact by means of the diffractional divergence of the scattered wave across the gap from one array into the other. It is also shown that increasing separation between the two arrays results in a broader and weaker resonance with respect to phase shift. The analysis is based on a recently developed new approach allowing for the diffractional divergence of the scattered wave inside and outside the arrays. Physical interpretations of the predicted features of DEAS in separated arrays are also presented. Applicability conditions for the developed theory are derived.     

Wave scattering from a periodic random surface generated by a stationary binary sequence

This paper studies the scattering of a TE plane wave from a periodic random surface generated by a stochastic binary sequence using a stochastic functional method. The scattered wave is first expressed as a product of an exponential phase factor and a periodic stationary process. The periodic stationary process is then expressed by a harmonic series representation, that is a 'Fourier series' with 'Fourier coefficients' given by mutually correlated stationary processes. These stationary processes are regarded as stochastic functionals of the binary sequence and they are represented by orthogonal binary functional expansions with band-limited binary kernels. The binary kernels are determined up to the second order from the boundary condition. Then, several statistical properties of the scattering are calculated numerically and illustrated in figures. It is found that, in the binary case, the second-order scattering cross section has a subtractive term and becomes much smaller than the first-order one.     

Reflection and scattering of spin waves by surface roughness of a ferromagnet

Abstract

A detailed theory of volume spin wave reflection from the randomly rough surface of a ferromagnet is presented. The contribution to damping of the reflected wave is calculated. This contribution is due to the scattering of the initial volume wave into secondary surface and volume spin waves. The value of damping is proportional to the correlation length and the square of the roughness amplitude. Numerical calculations of the attenuation rate as a function of the angle of incidence and the ratio between the surface anisotropy and the wavenumber are provided. They yield the angle of incidence where the attenuation has a maximum. In analogy to optics, this angle is similar to the Brewster angle. Numerical estimations of damping and a comparison of its value with the ferromagnetic resonance linewidth are also made. Finally, the results of the calculation of the scattering of surface exchange spin waves by surface roughness are presented and discussed.     

Low-frequency scattering of acoustic waves by a bounded rough surface in a half-plane

The problem of the scattering of harmonic plane waves by a rough half-plane is studied here. The surface roughness is finite. The slope of the irregularity is taken as arbitrary. Two boundary conditions are considered, those of Dirichlet and Neumann. An asymptotic solution is obtained, when the wavelength lambda of the incident wave is much larger than the characteristic length of the roughness iota, by means of the method of matched asymptotic expansions in terms of the small parameter epsilon= 2piiota/lambda. For the Dirichlet problem, the solution of the near and far fields is obtained up to O(epsilon2). The far field solution is given in terms of a coefficient that have a simple explicit expression, which also appears in the corresponding solution to the Neumann problem, already solved. Also the scattering cross section is given by simple formulas to O(epsilon3). It is noted that, for the Dirichlet problem, the leading term is of order epsilon3 which, by contrast, is different from that of the circular cylinder in full space, that is, of order epsilon(-1) (log epsilon)(-2). Some examples display the simplicity of the general results based on conformal mapping, which involve arcs of circle, polygonal lines, surface cracks and the like.     

Grazing-angle scattering of waves in infinitely wide periodic gratings

The approximate method of analysis of grazing-angle scattering (GAS), based on allowance for the diffractional divergence of the scattered wave, is justified and extended to GAS in infinitely wide, slanted, periodic gratings. The analysis has revealed an unusual and strong dependence of the pattern of GAS on small variations of mean structural parameters at the grating boundary. Several times increase of already resonantly large scattered wave amplitudes can be achieved in this case. Sharp resonance-like maximums on the angular dependence of the scattered wave amplitude are predicted inside the grating. The theory is extended to the case of GAS of optical modes guided by a slab with a semi-infinite periodic groove array. Physical interpretation of the obtained results is presented.     

Grazing-angle scattering of electromagnetic waves in periodic Bragg arrays

A new powerful approximate approach for the theoretical analysis of Bragg scattering in oblique strip-like periodic arrays with the scattered wave propagating almost parallel to the array boundaries – grazing-angle scattering (GAS) – is introduced and justified. This approach is based on allowance for the diffractional divergence of the scattered wave by means of the parabolic equation of diffraction and Fourier analysis. The divergence is demonstrated to be an intrinsic physical cause of GAS. Detailed theoretical analysis of steady-state GAS is carried out for bulk and guided optical modes. It is demonstrated that the most interesting feature of GAS in arrays of width that is greater than a critical width is a unique combination of two strong simultaneous resonances with respect to frequency and angle of scattering. In such wide arrays, GAS is demonstrated to be not only unusually sensitive to angle of scattering, but also to small variations of array width and grating amplitude. Entire concentration of the resonantly strong scattered wave inside the array is shown to be possible. A relationship between GAS, conventional Bragg scattering, and extremely asymmetrical scattering (i.e. where the scattered wave propagates parallel to the array boundaries) is analysed. Applicability conditions for the used approximations and obtained results are derived and discussed.     

Nonresonant mechanism of scattering of electromagnetic waves by sea surface: Scattering by steep sharpened waves

We develop an asymptotic theory of nonresonant backscattering of electromagnetic waves in the X-band by the ocean surface. Small-height (5÷20 cm) breaking surface waves with sharpened edges are assumed to be the main cause of nonresonant scattering. Using the methods of physical optics and geometrical theory of diffraction, we calculate the contribution of breaking sharpened waves to the scattering cross section for two orthogonal polarizations of electromagnetic scattering. It is shown that the main contribution to the backscattering is from the mirror reflection from the leading edge of such a wave, and the sharpness of the wave edge leads to the fact that the backscattering cross section of horizontally polarized radiation can exceed that of the vertically polarized radiation. Institute for Space Research, Russian Academy of Sciences, Moscow, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 3, pp. 240–254, March 1999.     

Nonlinear periodic waves on the charged surfactant-covered surface of a viscous fluid

The profile of a periodic capillary-gravitational wave propagating over the surfactant-covered surface of a fluid is found in the second-order approximation in initial deformation amplitude. It is shown that the surfactant film appreciably affects the intensity of nonlinear interaction between harmonics constituting the nonlinear wave.     

Nonlinear periodic waves on the charged surface of a viscous finite-conductivity fluid

The profile of a periodic capillary-gravitational wave propagating over the surface of a viscous finite-conductivity fluid is found in a second-order approximation in initial deformation amplitude. When the finiteness of the rate with which the potential of the fluid smoothes out as capillary-gravitational waves travel over its free surface is taken into account, the intensity of nonlinear interaction between the waves changes. This intensity is found to depend on the electric charge surface density, conductivity of the fluid, and wavenumbers. The finiteness of the potential smoothing rate influences the nonlinear interaction between the waves nonmonotonically.     

Bragg interaction of surface magnetostatic waves with a periodic granular HTSC structure

The Bragg interaction of surface magnetostatic waves with periodic granular HTSC structure has been investigated. The dispersion equation for the coupled waves has been obtained. Resonant absorption of waves near the critical temperature involving the granular structure of the superconductor has been found. The possibility of using the observed effect for making frequency-selective structures and high-speed bolometric photodetectors is shown. Tomsk University. Radio Electronic and Control Systems. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 94–98, October, 1997.     

Nonlinear periodic waves on the charged free surface of a perfect fluid

Analytical expressions for the profile of a nonlinear wave and for a nonlinear correction to its frequency are derived in the fourth-order approximation in amplitude of a periodic traveling wave on a uniformly charged free surface of an infinitely deep perfect incompressible fluid. It is found that corrections to the amplitude and frequency of the nonlinear wave are absent if the problem is solved under the initial condition that provides the constancy of the first-order amplitude and wavelength in time. Nonlinear analysis of conditions for instability of the fluid free surface against the surface charge shows that the critical charge density and wave-number of the least stable wave are not constant (as in the linear theory) and decrease with growing amplitude of the wave.     

On geometric optics and surface waves for light scattering by spheres

A geometric optics approach including surface wave contributions has been developed for homogeneous and concentrically coated spheres. In this approach, a ray-by-ray tracing program was used for efficient computation of the extinction and absorption cross sections. The present geometric-optics surface-wave (GOS) theory for light scattering by spheres considers the surface wave contribution along the edge of a particle as a perturbation term to the geometric-optics core that includes Fresnel reflection–refraction and Fraunhofer diffraction. Accuracies of the GOS approach for spheres have been assessed through comparison with the results determined from the exact Lorenz–Mie (LM) theory in terms of the extinction efficiency, single-scattering albedo, and asymmetry factor in the size–wavelength ratio domain. In this quest, we have selected a range of real and imaginary refractive indices representative of water/ice and aerosol species and demonstrated close agreement between the results computed by GOS and LM. This provides the foundation to conduct physically reliable light absorption and scattering computations based on the GOS approach for aerosol aggregates associated with internal and external mixing states employing spheres as building blocks.     

Double-resonant extremely asymmetrical scattering of electromagnetic waves in non-uniform periodic arrays

A new type of Bragg scattering – double-resonant extremely asymmetrical scattering (DEAS) of optical waves in oblique, non-uniform, periodic Bragg arrays is analysed theoretically and numerically. Steady-state DEAS is demonstrated to occur in the extremely asymmetrical geometry where the scattered wave propagates parallel to the front array boundary. The non-uniform array is represented by two joint uniform, strip-like, periodic arrays with different phases (and amplitudes) of the grating. DEAS is characterised by a unique combination of two simultaneous resonances with respect to frequency and phase variation at the interface between the joint arrays. As a result, a strong resonant increase in the scattered wave amplitude compared with the amplitude of the incident wave is predicted and investigated theoretically. The amplitude of the incident wave inside the array is also shown to increase resonantly in the middle of the array where the step-like variation in the phase of the grating takes place. The effect of different widths of the joint arrays, and magnitudes of the grating amplitudes on DEAS is analysed. Physical explanations of this type of scattering, based on the diffractional divergence of the scattered wave from one of the joint arrays into another, are presented.     

Propagation of surface acoustic waves in a piezoelectric medium with a periodic groove structure

A system of equations is formulated to describe the propagation of surface acoustic waves in a piezoelectric substrate whose surface has a periodic structure formed by transverse grooves. Dependences of the reflection coefficient and the wave velocity on the geometry of the periodic structure (the width and the depth of the grooves) are obtained in a wide range of variation of these parameters for five different orientations in various piezoelectric crystals (quartz, lithium niobate, lithium tantalate, and langasite).     

周期结构表面散射系数测试及修正方法*

无规入射散射系数是描述结构声反射特性的重要参数,在周期结构等典型扩散体的声学设计和室内声场模拟中具有重要的作用。本文给出了混响室法测试无规入射散射系数的原理,对正弦型周期结构进行了实验测试,并针对测试中存在的缺陷,提出了一种考虑空气间隙吸声的修正方法,经验证具有较好的修正效果。