A. A. Maradudin

A lattice theory of morphic effects in crystals of the diamond structure

Abstract A microscopic theory of the electric field induced infrared absorption by crystals of the diamond structure is presented in this paper, together with a determination of the modifications in the first-order Raman spectra of such crystals induced by externally applied electric fields and stresses. In connection with this, the shifts and splittings of the triply degenerate k = 0 optical mode frequencies in crystals of the diamond structure in the presence of a static electric field or a strain are determined. It is shown that the shifts in frequencies are of second order in the electric field and are of first order in the strain. In both cases the frequency shifts can be expressed in terms of three parameters. Expressions for these parameters are obtained in terms of atomic force constants and derivatives of the electronic polarizability. The magnitudes and signs of the frequency shifts are estimated on the basis of a simple model of diamond-type crystals.

Two-dimensional photonic band structures

Abstract By the use of a position-dependent dielectric constant we have calculated the photonic band structure for electromagnetic waves in a structure that consists of a periodic array of parallel dielectric rods of circular cross section, whose intersections with a perpendicular plane constitute a square lattice. The rods are embedded in a background medium with a different dielectric constant. Two polarizations of the electromagnetic waves are considered, and they are assumed to propagate in the plane perpendicular to the rods. Absolute gaps in the resulting band structures are found for both polarizations, and the properties of these gaps as functions of the ratio of the dielectric constants of the rods and of the background, and of the fraction of the total volume occupied by the rods, are investigated.

Backscattering effects in the elastic scattering of p-polarized light from a large-amplitude random metallic grating

We study the scattering of a p-polarized beam incident onto a random grating whose grooves are perpendicular to the plane of incidence. The scattered field is expressed in terms of the total magnetic field and its normal derivative on the surface of the grating. The integral equations satisfied by these functions are solved numerically for each of several hundred realizations of the surface profile possessing a Gaussian spectrum. The diffuse component of the differential reflection coefficient averaged over these realizations displays a well-defined peak in the retroreflection direction for metallic and perfectly conducting random gratings but not for random gratings on dielectric surfaces.

Nonlinear electromagnetic waves guided by a single interface

Electromagnetic waves guided by the interface between two nonlinear media, and a nonlinear and a linear medium are investigated theoretically and numerically. Both s‐ and p‐polarized waves are analyzed and the guided wave power versus guided wave vector is evaluated for a variety of material conditions. The consequences of two different versions of the uniaxial approximation for the p‐polarized case are compared. The power‐dependent attenuation is approximately evaluated.

Excitation of surface polaritons by end-fire coupling

We calculate the efficiency with which a surface polariton at a metal-dielectric interface is excited when a p-polarized volume electromagnetic wave is incident upon the end face of the metal-dielectric system that is normal to the interface. We find generation efficiencies of approximately 90%

The attenuation of rayleigh surface waves by surface roughness

Abstract This paper presents a calculation of the attenuation length of Rayleigh surface waves in the presence of surface roughness. We consider Rayleigh waves on the surface of a semi-infinite isotropic elastic continuum, and the method we use produces the contribution to the attenuation rate proportional to the square of the rms amplitude of the roughness. We obtain explicit expressions for the contribution to the attenuation rate from roughness-induced scattering into bulk transverse and longitudinal acoustic waves, and into Rayleigh waves. Our derivation makes use of a Greens function method. When the wavelength λ of the Rayleigh wave is long compared to the transverse correlation length a that characterizes the surface roughness, all contributions to the attenuation rate are proportional to the fifth power of the frequency. When λ is comparable to or smaller than a , the attenuation constant varies more slowly with frequency. For a model of the surface roughness, we present numerical calculations of the relative magnitude and frequency dependence of the various contributions to the attenuation rate. The Greens functions used here may be applied to a number of calculations. A derivation of their form is provided in an Appendix.

Leaky surface‐elastic waves on both flat and strongly corrugated surfaces for isotropic, nondissipative media

The dispersion relation for Rayleigh waves propagating across a grating, on the surface of a semi‐infinite, nondissipative, isotropic elastic medium was recently calculated by Rayleigh’s method and equivalently by a formally exact method based on Green’s theorem. Now, using a complex wave‐vector k or complex frequency ω in the present work, we continue the solutions of the dispersion relation into the radiative region of the kω‐plane (i.e., above the bulk transverse sound line) and into the first frequency‐gap on the boundary of the Brillouin zone caused by the grating periodicity. Here the solutions for the surface waves have components that radiate outwardly into the bulk. The acoustic attenuation for the Rayleigh waves, calculated from the imaginary part of complex k, agrees very well with experiment: all the observed peaks, including those missed by previous perturbation scattering theories, are found. Moreover, a branch is found in the dispersion relation, to which a corresponding complex solution is...

Near-field and far-field scattering of surface plasmon polaritons by one-dimensional surface defects

A rigorous formulation for the scattering of surface plasmon polaritons (SPPs) from a one-dimensional surface defect of any shape that yields the electromagnetic field in the vacuum half-space above the vacuum-metal interface is developed by the use of an impedance boundary condition. The electric and magnetic near fields, the angular distribution of the far-field radiation into vacuum due to SPP-photon coupling, and the SPP reflection and transmission coefficients are calculated by numerically solving the k-space integral equation upon which the formulation is based. In particular, we consider Gaussian-shaped defects (either protuberances or indentations) and study the dependence of the above-mentioned physical quantities on their

Out of Plane Propagation of Electromagnetic Waves in a Two-dimensional Periodic Dielectric Medium

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Localization effects in the elastic scattering of light from a randomly rough surface

half-width a and height h. SPP reflection is significant for narrow defects