Diffraction by a Corrugated Interface. Complete Transformation of an Incident Wave to the Diffraction Lobe

Using the simplest (sinusoidal) corrugation profile in the approximation of absence of losses in the material as an example, we study the regimes of complete transformation of an incident wave to the diffraction lobe by a corrugated metal surface or a corrugated interface of two dielectric media. A numerical-intuitive pattern of appearance and evolution of such regimes with increasing corrugation amplitude is revealed. It is shown that the regimes of complete transformation of an incident wave to the diffraction lobe are possible in both the case of autocollimation and the case of a considerable deviation from it. The examination is based on a numerical method of solving the integral equation by means of a specially created interactive processing system in Visual Fortran.     

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.     

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.     

Total anti-specular reflection at an undulating dielectric interface

We have studied the diffraction of electromagnetic waves at a corrugated interface between two dielectrics by rigorously solving the integral equation for scattered waves. We show that total anti-specular reflection is possible when the radiation is incident from the denser dielectric, and we find the parameters for a corrugated surface needed to observe this phenomenon.Institute of Applied Physics, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 3, pp. 351–362, March, 1994.     

Simulation of a periodic dielectric corrugation with an equivalent anisotropic layer

A periodic, corrugated, dielectric layer is simulated by an anisotropic dielectric layer of equal thickness. The tensor elements of the equivalent dielectric layer are given in terms of the permittivity of the dielectric material, the period of the surface corrugation, and the width of the corrugations. The validity of this technique is verified by comparing the reflection coefficient of the equivalent layer with that of the corresponding corrugated layer using the moment method. Employing a multiple layer approach, the technique is extended to handle periodic surfaces with arbitrary cross sections which can be used to design millimeter wave dielectric plate polarizers and absorbers.     

Anisotropic Interface Roughness Scattering in a Lateral Superlattice

A novel interface roughness due to the perturbation of the periodic interface structure is studied theoretically for a lateral superlattice realized by an interface corrugated quantum well. It is found by numerical simulation that the correlation function for interface roughness can be well modeled by a sinusoidal function with an exponential decay in the direction of corrugation. Such a feature makes the correlation function far from a Gaussian function which is extensively used as a theoretical approximation of the correlation function for interface roughness. With such a correlation function, the influence of interface roughness scattering on electronic transport in the lateral superlattice is investigated. Consequently, it gives rise to a high anisotropy of electronic transport both in the absence and presence of a magnetic field, by which the relevant experiments can be well explained.     

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.     

Anisotropic Interface Roughness Scattering in a Lateral Superlattice

A novel interface roughness due to the perturbation of the periodic interface structure is studied theoretically for a lateral superlattice realized by an interface corrugated quantum well. It is found by numerical simulation that the correlation function for interface roughness can be well modeled by a sinusoidal function with an exponential decay in the direction of corrugation. Such a feature makes the correlation function far from a Gaussian function which is extensively used as a theoretical approximation of the correlation function for interface roughness. With such a correlation function, the influence of interface roughness scattering on electronic transport in the lateral superlattice is investigated.Consequently, it gives rise to a high anisotropy of electronic transport both in the absence and presence of a magnetic field, by which the relevant experiments can be well explained.     

Chiral planar waveguide for guiding single-mode backward wave

Single-mode backward wave is shown to be guided in a planar dielectric waveguide with a strong chiral core. The significant difference of such a waveguide from the traditional one is the guidance of single-mode backward wave, without using negative permittivity and/or negative permeability. In the design, we generalize the idea of total internal reflection to the chiral medium and make a numerical analysis on the reflection with oblique incidence. We deduce rigorously a general solution of incident wave on the boundary of two arbitrary chiral magneto-electric media. We observe that the impedance matching can eliminate the coupling between two eigenwaves in chiral media. With strong chiral core and the matched impedance with cladding, one eigenwave becomes a backward wave and can be guided without transferring to the other eigenwave. If a single-mode propagation condition is satisfied, we will get single-mode backward guided wave. A special interface has been designed to prevent the forward wave entering the waveguide from the source.     

Reflection and transmission of circularly polarized waves in nonlinear dielectrics

A time-sinusoidal circularly polarized plane standing wave solution is obtained for isotropic lossless dielectric media with arbitrary nonlinearity. The spatial variation of the standing wave depends on the nonlinearity and is found by solving a problem of centralforce motion in which the electric complementary energy density furnishes the potential and the spatial coordinate has the role of time. Two special nonlinear dielectric response laws-cubic and quintic-are treated, and explicit solutions for the spatial variation of the wave amplitude and phase are obtained in terms of elliptic functions and elliptic integrals, respectively. The standing-wave solution is applied to give steady state solutions of two reflection/transmission problems (a) reflection from, or resonance modes between, ideally conducting planes and (b) reflection and transmission at a plane interface between two nonlinear dielectric media.     

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.     

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.     

The scattering of atoms from a corrugated wall model with the GR method in the system He/LiF(001)

In this communication we present a new method, called GR, to calculate the diffraction probabilities of atomic beams from a hard corrugated surface model. The method is applied to the system He/LiF(001). We show that the method gives a convergent solution, within 10^?4 in unitarity, when β₀ ? 0.12, where β₀ is the dimensionless total corrugation amplitude. This limit suggests that the method converges for “any” crystallographic surface of interest. The agreement between the experimental data and the calculated curves is good. From this agreement we conclude that the surface corrugation for He/LiF(001) is cosine-like and the “best” corrugated surface is given.     

Investigation of interface roughness cross-correlation properties of optical thin films from total scattering losses

The interface roughness and interface roughness cross-correlation properties affect the scattering losses of high-quality optical thin films. In this paper, the theoretical models of light scattering induced by surface and interface roughness of optical thin films are concisely presented. Furthermore, influence of interface roughness cross-correlation properties to light scattering is analyzed by total scattering losses. Moreover, single-layer TiO₂ thin film thickness, substrate roughness of K9 glass and ion beam assisted deposition (IBAD) technique effect on interface roughness cross-correlation properties are studied by experiments, respectively. A 17-layer dielectric quarter-wave high reflection multilayer is analyzed by total scattering losses. The results show that the interface roughness cross-correlation properties depend on TiO₂ thin film thickness, substrate roughness and deposition technique. The interface roughness cross-correlation properties decrease with the increase of film thickness or the decrease of substrates roughness. Furthermore, ion beam assisted deposition technique can increase the interface roughness cross-correlation properties of optical thin films. The measured total scattering losses of 17-layer dielectric quarter-wave high reflection multilayer deposited with IBAD indicate that completely correlated interface model can be observed, when substrate roughness is about 2.84 nm.     

Self-processing solgel material for one-step fabrication of micrometer-period sinusoidal phase gratings using the Lloyd's mirror scheme

A novel self-processing silica-zirconia hybrid solgel material has been developed and employed in one-step fabrication of micrometer-period sinusoidal phase gratings. In the process, the gratings with a sinusoidal profile were corrugated on the surface of the solgel film by UV exposure using the Lloyd's mirror setup. No further development or etching step is needed to reveal the sinusoidal profile because the corrugation is formed due to the self-processing property of the solgel material, which is robust enough to be used as an end product. The period, amplitude, diffraction efficiency of the +/-1 order, and surface roughness of one of the fabricated gratings are 0.99 microm, 330 nm, 30.56%, and 1.27 nm, respectively. The new self-processing material is practical and promising for fabrication of micro-optical elements.     

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.     

Design Method for Optical Waveguide Filters Having Corrugation Structures by Corrugation Width Modulation

A method to design a corrugated optical waveguide filter by modulating the corrugation width profile is proposed. This method is based on combined applications of the Fourier transformation and the F-matrix formalism. The method achieves the spatial profile of the corrugation width required to design a filter with any specified spectral profile of the reflection coefficient. The idea of the technique is that the spatial variation of the effective refractive index can be transformed, with the help of the F-matrix formalism, to variation of the corrugation width while maintaining a constant amplitude of the refractive index variation. Two examples are given applying the technique to the design of optical waveguide filters with reflectivity profiles of two- and four-rejection bands.     

Reflected image of a strongly focused spot

We describe the reflection of a strongly focused beam from an interface between two dielectric media. If the beam is incident from the optically denser medium, the image generated by the reflected light is strongly aberrated. This situation is encountered in high-resolution confocal microscopy and data sampling based on solid immersion lenses and oil immersion objectives. The origin of the observed aberrations lies in the nature of total internal reflection, for which there is a phase shift between incident and reflected waves. This phase shift displaces the apparent reflection point beyond the interface, similarly to the Goos-H?nchen shift.