Diffraction by a corrugated interface of media: The influence of the corrugation shape and losses in the medium on total transformation regimes

We study regimes of total reflection of a plane wave to the diffraction lobe in the case where the wave is incident on a corrugated metal surface or a corrugated interface of two dielectric media. The purpose is to analyze the influence of both the corrugation shape and losses in the medium on the characteristics of the regimes of total reflection to the diffraction lobe. We consider a number of corrugation profiles differing from the sinusoid by the resonance-region width and the presence of additional elements, namely, (i) the profiles having pair resonance regions with scale of the order of the wavelength, for which qualitatively new diffraction regimes compared with those observed for the sinusoidal interface can be realized due to interaction of waves, and (ii) the profiles comprising small-scale deviations, which can be a model of actual gratings. To study the influence of losses in the problem of scattering from a corrugated interface of dielectrics, the dielectric permittivity is assumed complex. We compare the obtained results with data for a sinusoidal profile and loss-free media. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 5, pp. 391–405, May 2006.     

Reflection and transmission of SH-waves at a corrugated interface between two semi-infinite anisotropic magnetoelastic half-spaces

An analysis has been carried out for reflection and transmission of a plane SH-wave incident at a corrugated interface between two anisotropic magnetoelastic half-spaces. Rayleigh’s method of approximation is applied to derive the reflection and transmission coefficients for first order approximation of corrugation. The expressions for reflection and transmission coefficients for first order approximation of corrugation are obtained in closed form for a special type of interface. It is found that these coefficients are proportional to the amplitude of corrugation and are functions of magnetoelastic properties of materials of the half-spaces as well as the angle of incidence. Special cases are deduced for anisotropic and isotropic materials for particular case of corrugation. Numerical computations are performed for a specific model of two different anisotropic magnetoelastic media. The effects of anisotropic magnetoelastic coupling parameter, the angle at which wave crosses the magnetic field, frequency factor, wave length of corrugation, and the amplitude of corrugation are shown through figures.     

Diffraction of homogeneous and inhomogeneous plane waves on a doubly corrugated liquid/solid interface

This paper extends the theory of the diffraction of sound on 1D corrugated surfaces to 2D corrugated surfaces. Such surfaces, that are egg crate shaped, diffract incoming sound into all polar directions, which is fundamentally different from 1D corrugated surfaces. A theoretical justification is given for extending the classical grating equation to the case of incident inhomogeneous waves, for 1D corrugated surfaces as well as for 2D corrugated surfaces. Even though the present paper presents a theory which is valid for all angles of incidence, special attention is given to the particular case of the stimulation of surface waves by normal incident sound. The most interesting conclusion is that, depending on the frequency and the incident inhomogeneity, Scholte-Stoneley waves and leaky Rayleigh waves can be generated in different directions. This effect might be of particular interest in the development of surface acoustic wave devices and the basic idea of this steering effect can be of importance for planar actuators.     

Dispersive characteristics of surface plasmon polaritons on negative refractive index gratings

The dispersive characteristics of surface plasmon polaritons (SPPs) supported by a periodically corrugated boundary between vacuum and a negative refractive index, isotropic material were studied theoretically by numerical solution of a dispersion equation. SPP dispersion curves were correlated with the optical response of the corrugated boundary in frequency regions where SPPs can be excited by a normally incident plane wave. Abrupt reflectivity variations, characterized by the presence of a near unity maximum and an almost zero minimum, were found in regions where the boundary without corrugation exhibits low reflectivity and rather featureless reflectivity curves.     

Stimulated Cherenkov radiation of a relativistic electron beam moving over a periodically corrugated surface (quasi-optical theory)

The propagation of waves over periodically corrugated surfaces and their excitation by relativistic electron beams are investigated within the framework of a quasi-optical approach. The dispersion equation is derived for normal waves under the assumption of a small (in the scale of the period and wavelength) corrugation depth, based on which two limiting cases are identified. In the first limiting case, the wave frequency is far from the Bragg resonance, and the propagation of waves can be described in terms of the impedance approximation, in which the fundamental spatial harmonic slows down. In the second limiting case realized at frequencies close to the Bragg resonance, the field is represented as two counterpropagating quasi-optical wave beams coupled on a corrugated surface and forming a normal surface wave. When interacting with an electron beam, convective instability, which can be used to realize amplifier regimes, corresponds to the first case, and absolute one, which is applied in surface-wave oscillators, corresponds to the second case. The developed theory is used to determine basic characteristics of amplifier and oscillator schemes: the growth rates, the energy exchange efficiency, and the formation of a self-consistent spatial structure of the radiated field. The practical realization of relativistic submillimeter amplifiers and surface-wave oscillators is shown to hold promise.     

Diffraction and Spectral Characteristics of Chiral Layer

Diffraction problems for the E- and H-polarized plane waves incident on a chiral magneto-dielectric layer are solved. The spectral characteristics (complex natural frequencies and oscillations) of the layer are investigated. A comparative analysis of diffraction and spectral characteristics is made. The phenomenon of the quasi-complete wideband cross-polarization transformation of plane waves by a chiral layer is found. The conditions for complete cross-polarization transformation of a plane wave normally incident on a chiral layer are determined.     

Method of Designing a Corrugated Optical Waveguide Filter

The method of designing a corrugated optical waveguide filter is proposed to yield an arbitrary spectral profile of the reflection coefficient. It gives the functional dependence of the corrugation depth on distance along the wave propagation direction. The basis of the theory of the method is a combination of the effective index approach and the Fourier transformation technique. It represents the spectral profile of the reflection coefficient approximately to Fourier transformation of the spatial profile of the effective refractive index. Examples are presented to illustrate how to apply the technique.     

Elastic wave propagation in sinusoidally corrugated waveguides

The ultrasonic wave propagation in sinusoidally corrugated waveguides is studied in this paper. Periodically corrugated waveguides are gaining popularity in the field of vibration control and for designing structures with desired acoustic band gaps. Currently only numerical method (Boundary Element Method or Finite Element Method) based packages (e.g., PZFlex) are in principle capable of modeling ultrasonic fields in complex structures with rapid change of curvatures at the interfaces and boundaries but no analyses have been reported. However, the packages are very CPU intensive; it requires a huge amount of computation memory and time for its execution. In this paper a new semi-analytical technique called Distributed Point Source Method (DPSM) is used to model the ultrasonic field in sinusoidally corrugated waveguides immersed in water where the interface curvature changes rapidly. DPSM results are compared with analytical solutions. It is found that when a narrow ultrasonic beam hits the corrugation peaks at an angle, the wave propagates in the backward direction in waveguides with high corrugation depth. However, in waveguides with small corrugation the wave propagates in the forward direction. The forward and backward propagation phenomenon is found to be independent of the signal frequency and depends on the degree of corrugation.     

Total Transformation of an Electromagnetic Wave Incident on a Corrugated Boundary between Transparent Dielectrics to a Transmitting Wave of the (-1)st-Order Harmonic

We present the results of a theoretical and experimental study of a new phenomenon of total transformation of an electromagnetic wave incident from a dielectric on a corrugated boundary between two transparent dielectrics to a transmitting wave of the (-1)st-order harmonic propagating in the other dielectric. The theoretical study is based on numerical solution of the full-wave equations for electromagnetic field. The experimental study is made using a Teflon prism with a corrugated surface located in a two-mirror resonator.     

Analysis of the methods proposed for computing the scattering of atoms from a hard corrugated surface model of He/LiF (001)

It appears that the scattering of atoms on crystal surfaces is accounted for by a corrugated infinite wall model of the surface. To determine the “corrugation function” which represents best the experimental scattering intensities, it is necessary to choose among many possible versions, the simplest and most effective computational method of the theoretical scattering amplitudes. It is the purpose of this paper to analyze the relative merits of three particular versions which we call HDM, NHM and GR, and which are described in section 3. This comparison is carried out on the He/LiF(001) system for variable incident wave vector (k) and orientation (θ_i) as well as a number of Fourier components (ζ_G) used to describe the “corrugation function”. We conclude that the GR method presents advantages over the other two: (i) it reduces the computer time necessary for the HDM and NHM methods, (ii) converges and computes to within 10^?4 in unitarity the scattering amplitudes in a larger range of energies as well as angular and corrugation parameters, and (iii) it presents a great simplicity and the corrugation is very handy. The size of that range depends on the computer facilities used. In our case, the GR method works for any calculation in which kC₀ < 9 and $\text{C}{}_0\text{< 0.35}\text{A}\text{?}$ (where k is the incident wave vector and C₀ twice the amplitude of the corrugation). These characteristics prove to make the GR method a good tool for the study of surface crystallography by parametrization of the surface corrugation.     

Diffraction of helium from a stepped surface: Cu(117) — An experimental study

The scattering of an helium nozzle beam (incident energy 21 and 63 meV) from a copper (117) stepped surface has been studied for crystal temperature ranging from 70 to 773 K. The diffraction pattern from the step array is readily seen. The influence of residual impurity on the surface is carefully discussed. Special attention has been paid to the influence of experimental factors upon peak shapes. True peak amplitudes are deduced. The peak intensities versus temperature and versus incidence angle has been measured. Extrapolation of the intensities to 0 K allows a direct comparison of the data with the prediction of a hard corrugated wall model. A corrugation profile is given which fits quite well the data. Clear evidence for resonances with bound states has been found. Three energy levels of the potential well are thus determined (5.9,4.0, 2.1 meV) which agrees with a Morse or a 3–9 potential.     

The determination of the He-Cu interaction potential by atomic beam scattering

Experimental results on the intensity of helium diffraction peaks for the scattering from Cu(110) and for the selective adsorption from Cu(113) and Cu(115) are reported. The usual hard corrugated wall potential is definitely unable to fit the data. While the corrugated Morse potential, recently proposed by Armand and Manson, gives a very much better agreement. The corrugation is found to be dependent upon incident energy, in good agreement with the prediction of Hamann's calculation     

The theory of planar Bragg resonators

The reflecting properties of one-dimensional planar Bragg gratings are studied. A coupled resonator model for studying the diffraction of electromagnetic waves in an arbitrarily corrugated waveguide is suggested. It is based on exact relationships that follow from the two-dimensional boundary-value problem stated in terms of the Helmholtz equation. The specific relationships for the rectangular corrugation of the grating-forming plates are presented. The reflection coefficients of the Bragg gratings vs. corrugation length and incident radiation frequency are calculated. An analytical solution for the “narrow” corrugation is obtained.     

Diffusive transport in highly corrugated channels

Diffusion in waveguides with spatially modulated profiles is an important topic in modern electromagnetics and optics. Wave dynamics in the high-frequency asymptotics are governed by classical ray dynamics which can be characterised by looking at the diffusion of particles throughout the channel. We study the transport of particles (rays) in a channel with a sinusoidal profile at different values of the corrugation amplitude. We find that below a certain corrugation level the transport is ballistic, beyond this threshold, a diffusion-like behaviour emerges in the asymptotic limit of large times. In this regime particle transport slows down due to the trapping mechanism in the corrugated regions of the channel. We use the analogy with correlated random walks to discuss the observed transport regimes.     

Reflection gratings as polarization converters

An experimental and theoretical modelling study of corrugated gold surfaces, where the refractive index of the upper medium is varied to change the effective wavelength of the incident radiation, is presented. For certain corrugation amplitudes we show that it is possible to convert nearly 100% of plane polarized light incident normal to the average plane of the grating surface into the orthogonal polarization. Investigations of the incident radiation's E-fields immediately above the corrugated surface show that the physical origin of this phenomenon rests with the phase retardation introduced by reflection. It is found that optimum polarization conversion occurs when the component of the optical E-field parallel to the grating wavevector is retarded by 180° with respect to the component parallel to the grooves.     

Narrow-band terahertz Bragg reflectors based on coupling of propagating and quasi-critical waves

We consider a planar system of narrow-band Bragg reflectors in which the transformation of an incident wave into a counterpropagating wave occurs via the excitation of a quasi-critical mode. The period of the structure with a new modification of Bragg mirrors is approximately twice as large as that in the traditional case, in which direct coupling between two counterpropagating waves takes place. Analysis of modified Bragg structures based on the method of coupled waves, in which high-frequency fields are quasi-optical beams, demonstrates the effectiveness of the proposed system of reflectors for the spacing between corrugated plates from 10 to 15 wavelengths λ. These conclusions were confirmed by direct numerical simulation. Such a superdimensionality is sufficient for using modified Bragg reflectors in high-power long-pulse free-electron lasers operating at short-wave frequency ranges up to the terahertz range.     

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).     

Frequency upshifting of electromagnetic radiation via obliqueincidence on an ionization front

Frequency upshifting of electromagnetic radiation impinging on a relativistically moving ionization front is theoretically investigated. Unlike previous works in this field treating the case of normal incidence and qualitatively similar case of oblique incidence of a transverse electric polarized wave, oblique incidence of a transverse magnetic polarized wave on the front is considered. The peculiarities of the case under consideration are connected with the generation of Langmuir waves behind the front and Brewster's phenomenon. We present a complete analysis of the incident wave transformation including analysis of the frequencies and amplitudes of the waves excited ahead of and behind the front. Special emphasis is made on energy transformation in the case when a wave packet is incident on the front. In particular, we show that even for negligible angles of incidence, energy losses via transformation into Langmuir waves may be very high (up to ~60%). In general, generation of Langmuir waves may play a significant role in the plasma-based radiation sources with relativistic ionization fronts