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.     

A theoretical study of surface plasmon cross coupling in asymmetric corrugated metal films

We investigate numerically the transmission properties of a thin sinusoidally corrugated metal film bounded by two different dielectrics in the context of the experiment of Gruhlkeet al (1986). We study the dominant contributions from both the propagating and evanescent plane waves. A comparison with the experimental results reveals that the decisive role in cross coupling is played by the evanescent waves emitted by the molecular dipole. We extend our studies to different corrugation amplitudes and widths to show their effect on transmission.     

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.     

Beaming of light and enhanced transmission via surface modes of photonic crystals

We report beaming and enhanced transmission of electromagnetic waves by use of surface corrugated photonic crystals. The modes of a finite-size photonic crystal composed of dielectric rods in free space have been analyzed by the plane-wave expansion method. We show the existence of surface propagating modes when the surface of the finite-size photonic crystal is corrugated. We theoretically and experimentally demonstrate that the transmission through photonic crystal waveguides can be substantially increased by the existence of surface propagating modes at the input surface. In addition, the power emitted from the photonic crystal waveguide is confined to a narrow angular region when an appropriate surface corrugation is added to the output surface of the photonic crystal.     

Roughness-trapped shear horizontal surface acoustic waves

Shear horizontal surface acoustic waves do not exist on the flat surface of a semi-infinite elastic medium. It has been shown by several authors recently that such waves can exist on a periodically corrugated, planar surface. We show here on the basis of the Rayleigh method that shear horizontal surface acoustic waves exist on a randomly rough planar surface of an isotropic elastic medium. These waves are only weakly localized to the surface and they have a lifetime that is long due to their roughness-induced scattering into other surface acoustic waves and into bulk waves.     

Premixed flame response to oscillatory pressure waves

We numerically investigate the interaction of sinusoidal pressure waves and slightly corrugated premixed flames. Work up to now has demonstrated the well-known Rayleigh–Taylor instability by imposing a single pressure ramp function onto a corrugated premixed flame. This paper considers sinusoidal oscillations of pressure. Such inputs are important since observations of large-scale experiments suggest that the presence of acoustic waves might be expected to have a significant influence on the propagation of the flame. The numerical experiments reported in this paper show that oscillatory pressure waves of the order of 800 Hz can have a magnifying effect on the wrinkling of the flame, due to the effect of Rayleigh–Taylor instabilities, hence increasing the overall mass burning rate, and that a sinusoidal pressure wave interacting with a premixed flame causes the flame to increase its wrinkling with every cycle in pressure. The result of great interest is that this growing process reaches a maximum after a few cycles, creating a dynamic equilibrium in which the final time-averaged mass burning flux is larger compared to that of the initial flame. It is also shown that the final mass burning flux increases with amplitude of the pressure wave, and increases with increasing frequency over the range explored.     

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.     

On generation of electromagnetic waves in the terahertz frequency range in a multilayered open dielectric waveguide

We show that it is possible to produce terahertz wave generation in an open waveguide, which includes a multilayer dielectric plate. The plate consists of two dielectric layers with a corrugated interface. Electrons, drifting in the potential well, interact with the non-uniform electric field which is induced near the dielectric interface by the natural wave of the waveguide. The corrugated period and parameters of the electronic system are chosen in order to ensure the most effective interaction of electrons with a wave. Generation of electromagnetic waves is achieved by converting the electrons? energy into the electromagnetic wave energy.     

Extremely long range surface polaritons in a thin corrugated metal film

The essential increase of propagation length of a long range surface plasmon polariton in a thin symmetrically corrugated plasmon-carrying film embedded in a dielectric medium is theoretically predicted. The calculations are based on the differential formalism for the system of Maxwells equations where the solution for electromagnetic fields is written as a superposition of partial plane waves in the presentation of a curvilinear non-orthogonal coordinates system for simplifying the boundary conditions. The spectral and angular dependencies of p-polarized light transmittance/reflectance demonstrate that the in-plane shift between both profiles of corrugated film drastically changes the surface plasmon polariton propagation length from minimum of the asymmetric profile to maximum of the symmetric one. The obtained results were qualitatively explained using the model of weakly coupled photonic wells.     

Intensity fluctuations of randomly scattered waves considered as local time

The concept of local time of a stochastic process is available for the study of intensity fluctuations in randomly scattered waves. A result of Jakeman on rays scattered by a corrugated surface of brownian slope is deduced from the Ray-Knight theorem on brownian local time.     

Threshold gain analysis of second order distributed feedback lasers based on [2-methoxy-5-(2′-ethylhexyloxy)-1,4-phenylenevinylene]

We present a theoretical study of the threshold analysis of second order surface emitting distributed feedback lasers based on the polymer [2-methoxy-5-(2′-ethylhexyloxy)-1,4-phenylenevinylene] (MEH-PPV). A coupled mode formalism that includes radiation modes is used to describe the propagation of the waves in the periodically corrugated region. A detailed calculation of the threshold gain of the laser that includes the effects of the radiation modes is described.     

Ohmic quality of resonators shaped by corrugated guide sections at frequencies near bragg stop bands

The effect of ohmic loss decrease in corrugated waveguide is studied for the case of period, equal to half of longitudinal wave length (so called π-type oscillations). As demonstrated, in periodical guide there are π-type waves with ohmic quality growing approximatelly as a cube of guide radius, which looks very attractive for different applications.     

Excitation of eigenmodes at gyroelectromagnetic gratings in conical mounting

We study the diffraction of electromagnetic waves at periodically corrugated isotropic–gyroelectromagnetic surfaces, in the index-matching situation, when the plane of incidence forms an arbitrary angle with the main section of the grating (“conical mounting”). It is shown that, under these conditions, eigenmodes can be excited at certain angles of incidence, which can be calculated. We analyze the variation of the position of the anomalies when the orientations of the plane of incidence and of the optic axis are varied. We also show the dependence of the maximum reflected power as a function of the groove height-to-period ratio.     

Peculiarities of electron-beam interaction with waves in partially plasma-filled corrugated waveguide

It is shown when the cross-section of a waveguide is partially filled by magnetized plasma, slow and fast E-waves can exist simultaneously at the same frequency, which is lower than the plasma frequency. In the case of spatially periodic corrugation of the waveguide wall, the waves can be coupled, forming new waves with hybrid properties in a certain frequency range. The interaction of an electron beam with the hybrid waves differs from the interaction with a slow plasma wave in a waveguide with smooth walls or with the wave in an evacuated corrugated waveguide. For example, when two waves traveling in the same direction are coupled, the increments of the hybrid waves have values on the order of but somewhat smaller than those of the increment of a slow plasma wave in a smooth waveguide.Moscow Radio-Engineering Institute, Academy of Sciences of the USSR. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 34, No. 7, pp. 825–836, July, 1991.     

Observation of electron diffraction due to a reflection grating in an electron wave transistor

We investigate quantum transport in the presence of an electron reflection grating fabricated in an electron wave transistor structure. The grating is made up of a periodically corrugated potential wall by which the electron waves are coherently scattered. We observe a number of peaks with respect to the gate voltage in the low-temperature conductance measurements. The conductance oscillations are attributed to the electron diffraction effect, and the peak positions agree well with those predicted by the Fraunhofer diffraction condition.     

The use of polarized bounded beams to determine the groove direction of a surface corrugation at normal incidence,the generation of surface waves and the insonification at Bragg-angles

Zero order reflected sound from a singly corrugated interface between a solid and a liquid, insonified from the solid side by circular polarized shear waves, can become almost perfect linearly polarized in a direction parallel or perpendicular to the corrugations, depending on the frequency, and can therefore reveal the direction of the corrugations. When narrow bounded beams, formed by a summation of infinite plane waves, are diffracted at certain frequencies, depending on the angle of incidence, or vice versa, one can predict phenomena like backscattering at Bragg-angle incidence and also the creation of Scholte-Stoneley waves.     

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.     

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.     

Microwave reflection properties of grooved metallic mirrors

Maxwell's equations are solved using finite difference equations to obtain the near and the far field distribution of electromagnetic waves in front of corrugated mirrors. We treat the case of perpendicular incidence to obtain both the phaseshift between TE- and TM-modes in polarisation twisters and mode converters as well as the amplitude of the electromagnetic field.     

The sharpness-induced mode stopping and spectrum rarefication in waveguides with periodically corrugated walls

Abstract

Starting from the rigorous excitation equation, the propagation of waves through a 2D waveguide with the periodically corrugated finite-length insert is examined in detail. The corrugation profile is chosen to obey the property that its amplitude is small as compared to the waveguide width, whereas the sharpness of the asperities is arbitrarily large. With the aid of the method of mode separation, which was developed earlier for inhomogeneous-in-bulk waveguide systems [Waves Random Media 2000; 10: 395], the corrugated segment of the waveguide is shown to serve as the effective scattering barrier whose width is coincident with the length of the insert and the average height is controlled by the sharpness of boundary asperities. Due to this barrier, the mode spectrum of the waveguide can be substantially rarefied and adjusted so as to reduce the number of extended modes to the value arbitrarily less than that in the absence of corrugation (up to zero), without changing considerably the waveguide average width.