Showing papers by "A. A. Maradudin published in 1999"

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

Abstract: A rigorous formulation for the scattering of surface plasmon polaritons (SPP's) 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 $1/e$ half-width a and height h. SPP reflection is significant for narrow defects $(a\ensuremath{\lesssim}\ensuremath{\lambda}/5,$ for either protuberances or indentations, where $\ensuremath{\lambda}$ is the wavelength of the SPP); maximum reflection (plasmon mirrors) is achieved for $a\ensuremath{\approx}\ensuremath{\lambda}/10.$ For increasing defect widths, protuberances and indentations behave differently. The former give rise to a monotonic increase of radiation at the expense of SPP transmission for increasing defect half-width. However, indentations exhibit a significant increase of radiation (decrease of SPP transmission) for half-widths of the order of or smaller than the wavelength, but tend to total SPP transmission in an oscillatory manner upon further increasing the half-width. Both the position of the maximum radiation and the oscillation period depend on the defect height, which in all other cases only affects the process quantitatively. Light emitters might thus be associated with either wide indentations or protuberances with widths that are of the order of or smaller than the wavelength.

Reflection and transmission of waves in surface-disordered waveguides

Abstract: The reflection and transmission amplitudes of waves in disordered multimode waveguides are studied by means of numerical simulations based on the invariant embedding equations. In particular, we analyze the influence of surface-type disorder on the behavior of the ensemble average and fluctuations of the reflection and transmission coefficients, reflectance, transmittance, and conductance. Our results show anomalous effects stemming from the combination of mode dispersion and rough-surface scattering: For a given waveguide length, the larger the mode transverse momentum is, the more strongly is the mode scattered. These effects manifest themselves in the mode selectivity of the transmission coefficients, anomalous backscattering enhancement, and speckle pattern both in reflection and transmission, reflectance and transmittance, and also in the conductance and its universal fluctuations. It is shown that, in contrast to volume impurities, surface scattering in quasi-one-dimensional structures (waveguides) gives rise to the coexistence of the ballistic, diffusive, and localized regimes within the same sample.

Interaction of Rayleigh waves with randomly distributed oscillators on the surface.

Abstract: The attenuation of Rayleigh waves due to their interaction with resonating structures randomly distributed on the surface of a semi-infinite elastic medium is calculated along with the Rayleigh wave frequency. The resonating structures are modeled by single oscillators coupled to the displacement field at the surface of the elastic medium. Using the coherent potential approximation, the dependence of the frequency and damping constant of the Rayleigh waves on wave vectors are determined for various values of the concentration of oscillators on the surface.

Stability of stationary gap solitary waves at periodically modulated surfaces.

Abstract: Nonlinear optical waveguides with periodically modulated surfaces or interfaces can support stationary localized waves, often called gap solitons, with frequencies lying in the stop gaps of the spectrum of linear excitations. They are solutions of evolution equations that have been derived for instantaneous Kerr-type, thermal (diffusive) as well as instantaneous resonant and nonresonant second-order nonlinearity. A numerical linear stability analysis is carried out for some examples of these gap solitary wave solutions based on discretization of the spatial coordinate. In addition to numerical instabilities, which are a consequence of discretization and which pose a problem to numerical integration schemes, weak physical instabilities have been found, which correspond to radiation away from the solitary wave. The growth rates are strongly dependent on the boundary conditions imposed at the edges of the spatial domain. Growth rates and radiation frequencies have also been computed for an infinite spatial domain. The influence of the diffusion length on the instability has been investigated.

The design and fabrication of one-dimensional random surfaces with specified scattering properties

Abstract: We describe methods for designing and fabricating one-dimensional random surfaces that scatter light uniformly within a specified range of scattering angles, and produce no scattering outside this range. These methods are tested by means of computer simulations. Preliminary experimental results are presented.

Kinetic Instability of Semiconductor Alloy Growth

Abstract: A kinetic theory of the instability of homogeneous alloy growth with respect to fluctuations of alloy composition is developed. The growth mechanism studied is the step-flow growth of an alloy from the vapor on a surface vicinal to the (001) surface of a cubic substrate. The epitaxial growth implies that the adsorbed atoms migrate on the surface during growth of each monolayer, and that their motion is “frozen” after the completion of the monolayer. Frozen fluctuations in all completed monolayers create, via the composition-dependent lattice parameter, an effective potential which influences the surface migration of adatoms. The migration consists of diffusion and strain-induced drift in the effective potential. For temperatures lower than a certain critical temperature Tc, strain-induced drift dominates diffusion and results in the kinetic instability of the homogeneous alloy growth. In the linear approximation in the fluctuation amplitude, the instability means the exponential increase of the fluctuation amplitude with the thickness of the epitaxial film. It is shown that the critical temperature of kinetic instability Tc, increases with the increase of elastic effects. The wave vector kc of the most unstable mode of composition fluctuations is determined by the interplay of anisotropic elastic interaction and anisotropic diffusion on a stepped vicinal surface. The direction of the wave vector kc differs from the lowest-stiffness direction of the crystal, and any direction of kc is possible.