Showing papers by "A. A. Maradudin published in 1972"

Vibrational Edge Modes in Finite Crystals

Abstract: In addition to surfaces, real crystals have edges, corners, and steps. In this paper we present a theory of long-wavelength acoustic phonons localized at an edge of a cubic elastic medium bounded by two (100) faces. The stress-free boundary conditions on the faces of the semi-infinite medium meeting at the edge are incorporated into the equations of motion of the medium by the device of assuming position-dependent elastic constants. The equations of motion of the medium are solved by expanding each displacement component in a double series of Laguerre functions, which are orthonormal and complete in the region ${x}_{1}\ensuremath{\ge}0$, ${x}_{2}\ensuremath{\ge}0$. The edge modes obtained are wavelike parallel to the edge and decay rapidly with increasing distance into the medium from the edge. For the particular case of an elastically isotropic medium for which the Lam\'e constants $\ensuremath{\lambda}$ and $\ensuremath{\mu}$ are equal, the speed of propagation of the lowest-frequency edge mode is $0.9013{c}_{t}$, where ${c}_{t}$ is the speed of sound of bulk transverse modes and is lower than that of Rayleigh waves, which is $0.9194{c}_{t}$. A variational principle for the speeds of edge modes is also presented.

Electrostatic Edge Modes in a Dielectric Wedge

Abstract: The dispersion relations are obtained for electrostatic modes localized in the vicinity of the edge of a dielectric wedge formed by the intersection of two semi-infinite planes making an interior angle of $2\ensuremath{\alpha}$. The dielectric constant of the medium is assumed to be isotropic. The resulting modes can be classifed as even or odd under reflection in the plane bisecting the wedge. Their frequencies are functions of one continuously varying quantum number. The general results obtained are specialized to yield the dispersion relations for edge optical modes and edge plasmons. Properties of dielectric edge modes are compared and contrasted with corresponding properties of surface modes.

Pseudopotential Calculation of Transverse Effective Charges for III-V and II-VI Compounds of the Zinc-Blende Structure

Abstract: A method is presented for the $\mathrm{ab}$ initio calculation of transverse effective charges for crystals possessing the zinc-blende structure. The method is implemented within the framework of the empirical pseudopotential method, and theoretical results are presented for the transverse effective charges of several III-V and II-VI compounds which yield both the magnitudes and signs of these quantities. The agreement between the theoretical and experimental values for the transverse effective charges is quite good for the III-V compounds, but is poor for the II-VI compounds. Reasons for this disagreement are discussed.

Ionic Brillouin Effect

Abstract: A theory is presented of the inelastic scattering of monochromatic infrared radiation by the long-wavelength acoustic vibration modes of an arbitrary crystal possessing infrared-active optical modes. Central to the theory is a lattice-dynamical calculation of the ionic contribution to the photoelastic constants of a crystal, i.e., the fourth-rank-tensor coefficients which relate the change in the dielectric tensor to the parameters describing a homogeneous deformation of the crystal. The results of this calculation show that the photoelastic tensor is not symmetric in the second pair of indices, in general, in agreement with recent predictions of Nelson and Lax. The general expression for the ionic contribution to the photoelastic tensor has a resonant character for frequencies of the incident light close to the frequencies of the infrared-active optical modes of the crystal. This general expression is specialized to the case of diatomic cubic crystals, and the magnitude of the ionic contribution to the photoelastic constants is estimated for GaAs and KCl on the basis of simple lattice-dynamical models. From these results the scattering efficiencies for these two crystals are determined. It is found for each of these crystals that the integrated scattering efficiency for Stokes (or anti-Stokes) scattering exceeds ${10}^{\ensuremath{-}10}$ ${\mathrm{cm}}^{\ensuremath{-}1}$ ${\mathrm{sr}}^{\ensuremath{-}1}$ for frequencies of the incident light within 5% of the frequency of the transverse-optical mode.