Alexei A. Maradudin

Surface acoustic waves on real surfaces

A survey is given of recent work on acoustic excitations localized in the vicinity of a rough surface. The rough surfaces considered, which would all be planar in the absence of the roughness, are of three kinds: (a) a planar surface with an isolated protuberance on it; (b) a periodically corrugated surface; and (c) a randomly rough surface. The first kind of roughness gives rise to surface shape resonances, i.e. to modes that are spatially localized in the vicinity of the surface perturbation and that are characterized by discrete frequencies. Waves localized to the surface can propagate across surfaces of the second and third kinds. The effects of the roughness on their dispersion curves are described. Experimental results bearing on the theoretical results obtained are presented.

Photonic Band Structures of Two-Dimensional Dielectric Media

When a quantum or a classical wave propagates in a periodic structure in any number of spatial dimensions, the dispersion curves that relate the frequencies of the wave to the wave vector characterizing its propagation possess an infinite number of branches. These branches form bands that are separated by frequency gaps at points of symmetry in the corresponding Brillouin zones. In some cases an absolute gap occurs, viz. a frequency range in which no waves can propagate that exists for all values of the wave vector in the Brillouin zone, and gives rise to a gap in the density of states of the waves propagating through these structures.

Surface Acoustic Waves on Nonlinear Substrates

The nonlinearity of the substrate on which a surface acoustic wave propagates causes acoustical rectification of the surface wave, harmonic generation and nonlinear mixing of surface waves, and the acoustoelastic effect. It gives rise to weakly nonlinear surface acoustic waves, and to associated surface acoustic solitary waves. The spatial dispersion required for the existence of the latter is introduced by coating the substrate by a thin film with different material properties. Explicit conditions for the formation of envelope solitons are presented, as well as for self‐focusing of the surface acoustic waves. The nonlinearity can also cause Love waves to become leaky with an amplitude‐dependent damping constant. Finally, a periodic corrugation of the surface of a nonlinear elastic substrate is used to introduce spatial dispersion into the system. An amplitude dependence of the stop bands for the propagation of weakly nonlinear surface acoustic waves across the resulting periodic structure, and an amplitu...

Optical Interactions at Rough Surfaces

A discussion is given of optical interactions at three types of rough planar surfaces: (a) a deterministic, nonperiodic surface; (b) a deterministic, periodic surface; and (c) a randomly rough surface. The scattering of p-polarized light from an isolated ridge or groove on an otherwise planar metal surface is studied, and the efficiency of exciting surface polaritons in this fashion is estimated. A strong enhancement of the electric field within the grooves of a perfectly conducting lamellar grating illuminated by s-polarized light is demonstrated. Then the Goos-Hanchen effect for a p-polarized, bounded (Gaussian) light beam incident from the vacuum side onto a random metal grating is investigated. The resulting lateral displacement of the reflected beam is negative, and is larger than when the metal surface is flat. Finally, the diffuse component of the light scattered from a two-dimensional, randomly rough metal surface is calculated. This diffuse component is shown to exhibit a maximum in the anti-specular direction (opposition effect) that can be associated with the localization of surface polaritons by the random roughness of the surface. Experimental results showing this opposition effect are presented.

Multiple-Scattering Effects in Angular Intensity Correlation Functions

The majority of the existing theoretical and experimental studies of multiplescattering effects in the scattering of light from a randomly rough surface have been devoted to the reflectivity or transmissivity of such a surface or to its mean differential reflection or transmission coefficients, i.e. to the first and second moments of the scattered or transmitted field. Recently, however, attention has begun to be directed to the theoretical1-20 and experimental9,10,18,21-23 study of multiplescattering effects in higher moments of the scattered field, in particular in angular intensity correlation functions. These correlation functions describe how the speckle pattern, formed by the interference of randomly scattered waves, changes when the angles of incidence and scattering are varied.

Multiple-Scattering Phenomena in the Second-Harmonic Generation of Light Reflected from and Transmitted Through Randomly Rough Metal Surfaces

Theories of multiple-scattering effects in the second-harmonic generation of light reflected from clean randomly rough metal surfaces and reflected from and transmitted through randomly rough metal surfaces in Kretschmann attenuated total reflection geometry are outlined. Both weakly rough and strongly rough surfaces are considered, the former by perturbative approaches, the latter by numerical simulations. Comparisons of theoretical results with experimental data for second-harmonic generation on clean random metal surfaces are presented.

Scattering of an Obliquely Incident Surface Plasmon Polariton from Sub-Micron Metal Grooves and Ridges

The reduced Rayleigh equation for the scattering of a surface plasmon polariton incident non-normally on a one-dimensional ridge or groove on an otherwise planar metal surface is solved by a purely numerical approach. The solution is used to calculate the transmission, reflection, and out-of-plane scattering coefficients of the surface plasmon polariton. The angular dependence of the out-of-plane scattering is found to have a conical nature.

The Design of Randomly Rough Surfaces That Scatter Waves in a Specified Manner

It is our aim in this chapter to provide an introduction to a form of the inverse problem in rough surface scattering, and methods for its solution, that differs somewhat from the usual form of this problem. In the usual formulation of this problem scattering data, such as the angular and polarization dependence of the intensity of the scattered field, are provided by experimentalists, and the surface profile function, or some statistical properties of it, such as the power spectrum of the surface roughness, or just the rms height of the surface, is extracted from these data. The type of inverse problem we consider here is how to design a one-or two-dimensional randomly rough surface that scatters in a specified manner a wave or a beam incident on it. We consider two different cases: (i) the scattered field is required to have a prescribed angular dependence of its mean intensity; and (ii) it is required to have a specified wavelength dependence of its mean intensity at a fixed scattering angle. Applications of each of these types of surfaces will be presented.

Multiple-Scattering Effects in the Second Harmonic LightGenerated at Randomly Rough Metallic Interfaces

We study theoretically the generation and scattering of second harmonic light at randomly rough metallic interfaces. For surfaces with relatively large roughness and slopes, we find that the angular distribution of the scattered light at the harmonic frequency displays well-defined minima in the backscattering direction, and show that this effect is due to destructive interference between waves that have been multiply scattered in the valleys of the surface. It is also shown that the complex amplitudes obtained at the frequency 2ω when the positions of the source and detector are exchanged exhibit some degree of anticorrelation.

Photonic Band Structures of Systems with Components Characterized by Frequency-Dependent Dielectric Functions

The great majority of the existing calculations of photonic band structures have been limited to periodic structures, either discrete or continuous, fabricated from a dielectric characterized by a positive, real, frequency-independent dielectric constant ∊ A , embedded in a dielectric matrix characterized by a dielectric constant ∊ B that is also, positive, real, and frequency-independent [1]. The restriction to components characterized by such dielectric constants seems overly restrictive, since one can envision periodic two-and three-dimensional structures fabricated from metal wires or metal particles, or from rods and particles of polar semiconductors or ionic crystals, all of which are characterized by frequency-dependent dielectric functions, that can be negative in certain frequency ranges. It might be expected that the dispersion curves for electromagnetic waves propagating through such systems (their photonic band structures) may display interesting features, especially in the frequency ranges in which the dielectric functions of the embedded components are negative.