Weak Corrugation Research Articles

Ray theory of the Love wave interactions

A ray theory is developed for the treatment of three types of Love wave problems. First, the characteristics of the Love wave are analyzed by the ray technique. Second, for a film with an appropriate weak harmonic corrugation on one of its surfaces, a ray treatment of the first-order coupling between the two Love waves is given. Third, for a film with a suitable weak harmonic corrugation of its free surface, the second-order coupling between the Love wave and the bulk elastic wave in the substrate is investigated using the ray procedure. In all cases, the ray method yields asymptotically exact results for small relative corrugation depths.

Coupling of Love waves with the bulk elastic waves in the substrate

In an elastically isotropic thin film having a free surface with a weak periodic corrugation, deposited on a semi-infinite substrate of another elastically isotropic material, the interaction between the Love wave guided along the film and the horizontal shear bulk elastic wave propagating in the substrate is investigated for the propagation directions lying in a plane perpendicular to the film and containing the grating vector. The transport equation for the guided Love wave incorporating the effect of the coupling with the bulk elastic wave is deduced. The theory is applied to obtain the characteristics of the output coupler in which the Love wave guided along the film radiates a bulk elastic wave in the substrate as well as those of an input coupler in which a bulk elastic wave incident on the grating region of the film launches the Love wave along the film. Energy conservation principle and the reciprocity between the output and the input couplers are examined.

Rotationally mediated selective adsorption in rigid rotor/rigid surface scattering

We present a detailed investigation of a new effect in molecule/surface scattering, rotationally mediated selective adsorption, which has been first observed by Cowin et al. (J. Chem. Phys. 75 (1981) 1033) in rotationally inelastic HD/Pt (111) scattering. It is due to resonance between an asymptotically closed rotational channel and a vibrational bound state of the molecule/surface system. Exact close-coupling and diffractionally sudden calculations are performed for HD scattered from a rigid, flat and weakly corrugated surface. Both variation of the collision energy and variation of the incident angle are considered. In the latter case we include the averaging over the collision energy of the initial beam and compare qualitatively our results with the experiment. Taking into account the resonances below they j = 0 → 1 threshold we are able to explain all of the experimentally observed resonances and to assign them with the appropriate rotational-vibrational quantum numbers. The largest deviation between experimental and theoretical resonance angles is ~ 1.6° at a collision energy of E = 109 meV. An interesting interference effect is found in the case of weak surface corrugation. Although the diffractionally sudden approximation generally gives only poor results, it also reproduces this effect and provides a simple explanation of it in terms of the Breit-Wigner representation of the S-matrix.

Rotationally mediated selective adsorption in rigid rotor/rigid surface scattering

Abstract We present a detailed investigation of a new effect in molecule/surface scattering, rotationally mediated selective adsorption, which has been first observed by Cowin et al. (J. Chem. Phys. 75 (1981) 1033) in rotationally inelastic HD/Pt (111) scattering. It is due to resonance between an asymptotically closed rotational channel and a vibrational bound state of the molecule/surface system. Exact close-coupling and diffractionally sudden calculations are performed for HD scattered from a rigid, flat and weakly corrugated surface. Both variation of the collision energy and variation of the incident angle are considered. In the latter case we include the averaging over the collision energy of the initial beam and compare qualitatively our results with the experiment. Taking into account the resonances below they j = 0 → 1 threshold we are able to explain all of the experimentally observed resonances and to assign them with the appropriate rotational-vibrational quantum numbers. The largest deviation between experimental and theoretical resonance angles is ~ 1.6° at a collision energy of E = 109 meV. An interesting interference effect is found in the case of weak surface corrugation. Although the diffractionally sudden approximation generally gives only poor results, it also reproduces this effect and provides a simple explanation of it in terms of the Breit-Wigner representation of the S -matrix.

Propagation of surface electromagnetic waves along a corrugated interface between two media

An analysis is made of the problem of propagation of surface electromagnetic waves (SEW's) along a corrugated interface between two media. The problem is solved in the weak corrugation approximation. The SEW loss factor due to emission and the coefficient of coupling between the two SEW's under conditions of resonant conversion are obtained as a function of the parameters of the corrugation and the media.

Mode coupling of guided elastic waves in wire with weak surface corrugation

This analytical study aims to explain the experimental result of the mode coupling of elastic waves in a long circular wire by means of the surface corrugations of the wire. It is assumed herein that the wire is made of ideally homogeneous, isotropic, linearly elastic material and its free surface is subjected to weak and continuous corrugation. On the basis of the weakness of corrugation, the multiple scales are introduced to formulate the problem in a perturbation scheme. It is found, as expected, that the mode coupling does occur as the result of scattering from the corrugated surface at a certain frequency where the two modes have the same phase velocity. Coupled-mode equations which govern the amplitude variation in the coupling are then derived systematically from the compatibility condition. The coupling coefficients depend on the modes involved, the geometrical characteristics of the surface corrugation, and the material constant of the wire. The resultant variation of amplitudes well characterizes the pulse distortion observed in the experiments.

Effect of periodic surface corrugation on the propagation of Rayleigh waves

The Rayleigh wave interaction in an elastically isotropic half space having a free surface with weak sinusoidal corrugations in one direction is investigated for the case of propagation normal to the length of the corrugations. Simple and asymptotically exact analytical expressions are deduced with the help of a singular perturbation procedure for the characteristics of the wave interaction. The theory is applied to obtain the characteristics of the selective reflection of a Rayleigh wave incident on a moderately long periodic array of shallow grooves etched on the free surface. The results obtained from the present asymptotic theory are compared with those previously deduced from an empirical equivalent network approach and a phenomenological coupled mode theory.

Threshold and Lennard-Jones resonances and elastic lifetimes in the scattering of atoms from crystalline surfaces

In this paper we apply the GR method for solving the scattering equations of atoms from a hard corrugated surface, on accelerated particles above a hard corrugated surface and a hard corrugated surface with an attractive well. The solutions are given for the Rayleigh hypothesis that under the range of corrugation presented in this paper leads to the exact ones. Threshold resonances are studied observing that the appearance and disappearance of beams must be for a general theory with vertical tangent. The structure of the Lennard-Jones resonances given for the model mentioned above. For the first time it is stressed that Lennard-Jones resonances are not observed in metal surfaces in general, and, accordingly, they are unobserved in compact metallic surfaces. This is correlated with the fact that diffraction has not been observed. Both facts are due to the very weak corrugation of the gas-metal interaction potential. According to our results, the Lennard-Jones resonances in metals present greater difficulties to be observed experimentally. We also note that the absence of diffraction in compact metal surfaces is because they are almost plane and not because of the Debye-Waller effect. Finally, we have calculated the lifetimes of the atoms at the crystal surfaces. These are larger, the smaller the incident energy and the larger the corrugation. But the lifetimes are particularly large at resonance condition (10 −11 s).

Surface roughness effects on energy losses of fast electrons crossing metallic samples

The unevenness of the surface of a metallic sample affects the surface plasmon spectrum and thence the energy losses of fast charged particles crossing the sample. A theory of this effect is presented in which the metal is characterized by a simple local dielectric constant and the interaction with the probe particle is treated semi-classically. By a classical Green’s function method, a closed expression is obtained for the loss spectral profile as a function of the momentum transfer, without assumption on the roughness shape. The geometry of a rough surface is then considered in detail. The loss spectral profile is calculated for some examples of weak periodic corrugations. For a general weak roughness, the width and the mean shift of the loss profile are given in terms of the roughness correlation function. Finally, the case of strong roughnesses is examined for small and large values of the momentum transfer.