Showing papers by "A. A. Maradudin published in 1981"

Surface Polaritons On Large-amplitude Gratings

Abstract: We present numerical studies of the dispersion relation for surface polaritons that propagate on the surface of a model free-electron metal upon which a periodic grating has been impressed. The calculations are based on the integral equation formulation of the boundary-value problem, as discussed earlier by Toigo, Marvin, Hill, Celli, and others. We employ the "extinction theorem" scheme, which yields convergent results for values of the ratio $\frac{{\ensuremath{\zeta}}_{0}}{a}$ far in excess of 0.072, where the Rayleigh-Fano method fails when applied to the scattering of a scalar wave from a hard wall with profile given by ${\ensuremath{\zeta}}_{0}cos(\frac{2\ensuremath{\pi}x}{a})$. We give results for the dispersion relation for two grating profiles, the sinusoidal and the symmetric sawtooth forms.

Vibration modes of a two-dimensional Wigner lattice coupled to ripplons on a liquid-helium surface

Abstract: We present a theory of the vibration modes of a two-dimensional Wigner lattice coupled to ripplons on a liquid-helium surface based on the use of thermodynamic Green's functions. Starting from the phonon-ripplon Hamiltonian proposed by Fisher, Halperin, and Platzman, the effects of the electron-ripplon interaction (and hence the effects of the temperature and pressing electric field) on the frequencies of the coupled phonon-ripplon modes are obtained from the poles of the Green's function for the phonons of the Wigner lattice. The nature of these poles is determined by the phonon self-energy, which clearly displays the resonant coupling between the phonons and the ripplons. Our theory gives a first-principles derivation of the weights of the ripplon-induced resonances. We present approximate analytical results for the frequencies of the coupled modes. Our results are in qualitative agreement with the experiments of Grimes and Adams and the theory of Fisher et al. However, we do not find justification for the quantitative agreement with experiment that has been reported by Fisher et al. This discrepancy has to do with the fact that we show that the aforementioned weights are not given in terms of an effective Debye-Waller factor for the 2D Wigner lattice, but rather in terms of an exponential whose argument originates from the difference in electron displacement correlation functions given by $〈\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{u}}({l}_{1};{t}_{1})\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{u}}({l}_{2};{t}_{2})〉\ensuremath{-}〈{(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{u}})}^{2}〉$. This being the case, the normal modes of the phonon-ripplon Hamiltonian have frequencies whose values are somewhat smaller than the frequencies of the resonances measured by Grimes and Adams.

Surface plasmons on a large-amplitude grating

Abstract: Dispersion relations are obtained by two different methods for surface plasmons (in the nonretarded limit) propagating on the surface of a dielectric medium on which a large-amplitude grating has been ruled. The first method is based on the Rayleigh hypothesis; the second method is based on the extinction-theorem form of Green's theorem. It is found that there is an infinite number of branches of the surface-plasmon dispersion curve. Numerical solutions of the dispersion relations are obtained in the case that the dielectric medium is a free-electron metal for two surface profiles: a sinusoidal profile and a symmetric sawtooth profile. For the former profile, results are obtained for corrugation strengths far exceeding the value for which the Rayleigh hypothesis ceases to be valid.