General Case Of Oblique Incidence Research Articles

Diffraction of a scalar plane wave oblique incidence on a flat screen with a one thin slit

In the framework of this work, we discuss the problem of diffraction of a plane and time-harmonic field on a flat screen with a single narrow slit. As a rule, this problem is considered for the case of normal incidence. At the same time, for a number of applied problems, in particular, the absorption of solar radiation by photocells, it is interesting to consider the general case of oblique incidence. In this work, the problem is solved in the Fraunhofer approximation. An analytical dependence of the intensity of the diffracted field on the direction of observation, the slit length, and the wavelength of the incident radiation is obtained.

Detection of spinning objects at oblique light incidence using the optical rotational Doppler effect

The optical rotational Doppler effect of light beams with angular momentum has recently found applications in the remote sensing of spinning objects. However, most of the reported experimental demonstrations rely on the particular condition of normal incidence, while the general case of oblique incidence has not been addressed yet. Herein, we investigate the optical rotational Doppler effect at oblique incidence based on a local scattering model and formulate the quantitative relation between the Doppler frequency shift and the tilt angle. The analytic results indicate that even if the rotational axis of the spinning object is oriented at a specific tilt angle relative to the light propagation direction, the rotational speed can still be extracted from an asymmetrically broadened Doppler signal. The geometric mean value of the extreme frequency shift is a constant despite the variation of the incident angle. An experiment with obliquely incident and superimposed optical vortices is executed to verify our theoretical predictions, achieving a successful detection of the rotational speed at relatively large tilt angles with a relative error less than 2%. The scheme proposed in this study may be useful for practical applications of rotational Doppler effect in remote sensing and metrology.

Plane wave diffraction from a finite soft cone at oblique incidence

The canonical problem of diffraction of the plane acoustic wave on a finite hollow soft cone in the general case of oblique incidence is solved. The corresponding diffraction problem is formulated as a first-kind boundary value problem for the Helmholtz equation with respect to the scattered velocity potential for each perturbed azimuthal harmonic. The diffracted field is presented as a series of eigenfunctions for the subregions formed by the cone. The pertinent diffraction problem is reduced to an infinite system of linear algebraic equations (ISLAE) for each azimuthal harmonic by using the continuity conditions and the orthogonality properties of the associated Legendre functions. The use of the analytical regularization approach transforms the ISLAE to the second kind and allows to justify the truncation method for obtaining the numerical solution in the required class of sequences. The limiting transition to the disc is considered and the simplified regularization operator for this particular case is derived. The low-frequency approximation of the problem is examined and the analytical solution in the explicit form is derived. By means of illustration, we establish the relationship between the wave size of the cone and the order of reduction of the polar and azimuthal harmonics. We examine the scattering features of a finite soft cone as a function of the incident angle. We validate the obtained results by comparing them to the ones known in literature.

Analysis of a Plane Wave-Excited Subwavelength Circular Aperture in a Planar Conducting Screen Illuminating a Multilayer Uniaxial Sample

A spectral domain analysis is presented of a plane wave-excited subwavelength circular aperture in a planar perfectly conducting screen in close proximity to a multilayer stack, which may comprise uniaxially anisotropic slices. The formulation employs the Bethe-Bouwkamp aperture model for the general case of oblique incidence, and it combines the Hankel transform method with a transmission line network analogue of the medium, which facilitates the inclusion of any number of material layers. The electromagnetic fields are expressed in terms of one-dimensional (1-D) Hankel transform integrals, which are efficiently evaluated by a numerical quadrature along a suitably selected path, with convergence acceleration by extrapolation. Sample numerical results are presented to demonstrate the validity of the method and its utility in the modeling of multilayer near-field lenses and aperture-type probes of near-field optical microscopy.

Symmetry Properties of Electromagnetic Planar Arrays in Transfer Matrix Description

We analyze in this paper symmetry properties of planar arrays in the long-wave approximation and for general case of oblique incidence of electromagnetic waves. We introduce the concept of the group of wave vectors for scattering problems in transfer matrix description. Using formalism of magnetic groups we define all the possible symmetries for planar arrays and show how to calculate the structure of 4 × 4 transfer matrix for nonmagnetic and magnetic arrays. We discuss also the reciprocity conditions for the transfer matrices which are different from those in scattering matrix description. Application of the theory is illustrated by some examples.

Transmission of subhertz electromagnetic waves from an inhomogeneous earth’s crust to the atmosphere

For the study of electromagnetic fields generated by precursory effects of earthquakes, the problem of transmission to the atmosphere is investigated for a subhertz plane electromagnetic wave obliquely incident from a homogeneous earth’s crust of semi-infinite extent through an inhomogeneous earth’s crust of finite thickness. To analyze the problem, the inhomogeneous earth’s crust is subdivided into a number of thin homogeneous layers. Then, an easier problem of propagation through a composite multilayered medium replacing the homogeneous and inhomogeneous earth’s crusts and the atmosphere is treated. To confirm the validity of the above formulation, an exponential inhomogeneity for the conductivity of the earth’s crust is considered for a specific example. First, for the case of the inhomogeneous earth’s crust, the overall power transmission coefficient on the earth-atmosphere interface at normal incidence is found to show a broader frequency characteristic and to take a maximum value at a definite subhertz frequency, shifting to a lower frequency. For the general case of oblique incidence as well, these features of the overall power transmission coefficient are retained except in the vicinity of the critical angle of incidence for the H-wave. At the critical angle of incidence, the power flow density carried by a surface wave along the earth-atmosphere interface becomes anomalously large for the H-wave.

On the measurement of the orientational order parameters in biaxial liquid crystals using the polarised infrared technique

The limits of the applicability of the Polarised Infrared (Fourier transform infrared) spectroscopy technique, which is used to measure the order parameters of biaxial liquid crystals, is investigated in detail for different experimental geometries and cell thicknesses. General expressions for the transmittance of the polarised infrared radiation by a biaxial liquid crystal material in planar and homeotropic cells are obtained in the general case of oblique incidence. These expressions are then simplified in the limiting cases of thin and thick cells, and in both cases the relationship is established between the cell transmittance and the components of the imaginary part of the infrared molecular permittivity. It is shown that simple expressions, used in the literature to extract the values of the biaxial order parameters, are valid only for thin cells and in specific geometries when light propagates along one of the optical axes of the material. For thicker cells typical for experimental conditions, approximate expressions are obtained which are to be used to reveal the order parameters of biaxial liquid crystals. Various types of experimental geometries are discussed including those suitable for measurements of the order parameters, and those to be avoided.

Effective antiplane properties in the presence of frictional shear cracks

Cracked solids are viewed as equivalent homogenous media that sustain the propagation of coherent shear horizontal waves in the presence of multiple scattering. Strip‐like cracks are filled with viscous fluid and are randomly distributed. Their faces undergo viscous friction. The effective wave number and shear stiffness are calculated for parallel cracks in terms of the far‐field response of a single crack. Attention is focused on the derivation of this single‐scattering property in the general case of oblique incidence. Effect of the crack density and fluid viscosity on the effective properties is investigated. Simple low‐ and high‐frequency analytical approximations allow a direct assessment of the crack density and fluid viscosity from seismic wave measurements. Knowledge of these parameters facilitates more precise estimation of the crack size in the Earth's crust.

Analysis of the influence of the passive facet of blazed transmission gratings in the intermediate diffraction regime

Blazed diffraction gratings are of enormous practical importance for imaging and analyzing hybrid optical systems. The intermediate diffraction regime is characterized by the transition from the scalar to the rigorous electromagnetic theory. An effect known as shadowing occurs and reduces the diffraction efficiency. Based on rigorous calculations for optimized sawtooth-shaped and binary-multilevel blaze profiles, we deduce a semianalytical model describing the shadowing phenomenon for the general case of oblique incidence. We discuss illumination both from air and from the substrate. Though a multilevel blaze possesses a discrete substructure, our shadowing model remains valid, if substructural effects are neglected. We find that electromagnetic effects due to the passive blaze facet lead to the efficiency reduction, and the blazing efficiency shows a linear dependence on the ratio of blaze wavelength to grating period. Our shadowing model is applied to predict the performance of a Littrow-like blazing condition in transmission geometry as, e.g., for a diffractive solid immersion lens.

Optical characteristics of a multilayer photovoltaic cell for oblique incidence of light

Taking into account the contributions of interference and incoherent multiple reflections of light in the substrate, we have determined the distribution of the absorbed energy density Q in layers of a multilayer photovoltaic cell in the general case of oblique incidence of light on the cell. The relations obtained are expressed in terms of the Fresnel reflection and transmission coefficients for interfaces between media, which for oblique incidence are different for s and p polarization of the incident light. The energy absorbed by an active layer of the cell varies very slightly with the angle of incidence if the maximum in the Q distribution is located at a heterojunction. We carried out a numerical analysis for a five-layer cell based on a copper phthalocyanine-fullerene heterojunction.

Multiple reflection method for electromagnetic waves in layered dielectric structures

Reflection and transmission of a plane electromagnetic wave propagating in a layered dielectric structure with an arbitrary number of layers of various thicknesses are investigated. For the general case of oblique incidence of the wave on this structure, the reflection and transmission coefficients are calculated for both TE and TM waves using a multiple reflection method. An algorithm to apply the obtained formulas for numerical and analytical calculations is suggested.

High-frequency scattering by the edge of a thin dielectric slab loaded by a metallic strip grating

A heuristic diffraction coefficient is presented that is suitable to describe the scattering from the edge of a thin dielectric half-plane, loaded by a metallic strip grating on one of its faces, when the grating period is much smaller than the free-space wavelength. The most general case of oblique incidence is analysed, with the incident plane wave arbitrarily polarised. The direction of the strips can be arbitrarily oriented with respect to the edge of the half-plane. Extensive numerical tests have been performed to verify the effectiveness of the heuristic solution and to check its accuracy through comparisons with reference data.

Conical diffraction from index-matched gratings

We study the diffraction of electromagnetic waves from a periodically corrugated interface between two index-matched dielectrics in the general case of oblique incidence. We show that the eigenmodes of the index-matched grating can be used to provide a strong degree of polarization conversion between p and s modes. The possibility of producing curves of specular reflectivity versus angle of incidence with arbitrarily close resonance peaks is investigated.

Plane wave scattering by slots on a ground plane loaded with semicircular dielectric cylinders in case of oblique incidence and arbitrary polarization

Plane wave scattering by single or double slots loaded with semicircular dielectric cylinders is investigated in the most general case of oblique incidence and arbitrary polarization. To this end, systems of singular integral-integrodifferential equations of the first kind are constructed and discretized on the basis of recently developed algorithms. Several internal tests and extensive comparisons with available results were made in order to validate the numerical codes. Plotted results both for the surface magnetic current densities and the radar cross sections reveal how the scattering properties may be controlled by changing several physical and geometrical parameters of the structure.

Plane-wave scattering by strip-loaded circular dielectric cylinders in the case of oblique incidence and arbitrary polarization

Plane-wave scattering by strip-loaded circular, multilayered dielectric cylinders is investigated in the most general case of oblique incidence and arbitrary polarization. The problem is formulated via systems of singular integral-integrodifferential equations of the first kind which are most efficiently discretized on the basis of previously developed analytical algorithms. Several internal tests along with extended comparisons with available results have been completed to validate the numerical codes. Plotted results for both the induced surface current densities and the total radar cross section reveal how the scattering properties may be controlled by changing several physical and geometrical parameters of the structure.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Rigorous formulation of scattering at a randomly varying impedance plane: general case of oblique incidence

The problem of scattering of electromagnetic plane waves at one-dimensional surfaces (random gratings) is solved in the general case in which the incident wave vector does not lie on the main section of the cylindrical surface (oblique incidence). The scatterer is simulated by a plane boundary characterized by a coordinate-dependent impedance that varies along one of the two coordinates on the surface. This representation could be regarded as a canonical model of one-dimensional surfaces with height corrugations. A rigorous electromagnetic formalism for calculating the fields scattered at the impedance plane is presented. The fields above the scatterer are represented by spectral domain expansions. It is shown that the wave vectors of the scattered waves lie on the surface of a cone containing the direction of specular reflection and whose axis coincides with the direction of the grooves of the random grating. The theory is exemplified by calculating the angular distribution of the mean intensity scattered from an ensemble of surfaces with similar statistical parameters.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Rigorous formulation of scattering and guidance by dielectric grating waveguides: general case of oblique incidence

First a rigorous formulation is presented for the scattering of a uniform plane wave by an infinite dielectric grating waveguide, under the most general condition of oblique incidence. The results are then applied to the analysis of the guidance of waves by the dielectric grating waveguide. By using a simple coordinate rotation, the TE and TM Floquet mode functions determined previously for the special case of principal-plane incidence are combined to treat the general case of oblique incidence. In terms of the coupling between the known Floquet mode functions of both polarizations, the general case of oblique incidence is formulated in an exact fashion, as a three-dimensional boundary-value problem, so that the hybrid nature of waves supported by the structure can be investigated rigorously.

Jones matrix treatment of electromagnetic wave propagation in anisotropic stratified media

Light propagation in anisotropic stratified media may be conveniently described, in the quasi-adiabatic limit, by the so-called Jones matrix formalism. In systems like liquid crystals, the quasi adiabatic limit occurs when the director rotates very slightly over distances of the order of the light wavelength. This limit is of relevant interest in many optical devices. As known, the general solution of the Maxwell's equations in anisotropic stratified media may be obtained by using the 4 × 4 Berreman's matrix method. However, as long as the polarization properties of the light transmitted through the medium are concerned, a much simpler approach is possible, which consists in completely neglecting the solutions of the Berreman's equations corresponding to the waves propagating in the backward direction. In this case, the number of differential equations describing light propagation is reduced from 4 to 2. The 2 × 2 matrix introduced in this approximated fromalism is termed the Jones matrix of the problem. In this paper, we show that in general case of oblique incidence of light is possible to properly transform the original Berreman's matrix into a form suitable for reduction to a 2 × 2 Jones matrix.

Scattering of plane waves by soft obstacles: anomalous diffraction theory for circular cylinders

An anomolous diffraction theory is presented to describe the scattering of plane waves by circular cylinders for the general case of oblique incidence and for both real and complex values of particle refractive index in terms of a single Bessel-like function. By comparison with the formal solution of Maxwell’s equations, it is demonstrated that the simple theory well approximates the extinction and absorption efficiencies, particularly for a normally incident wave on a nonabsorbing or weakly to moderately absorbing particle. It is also shown that the simple theory provides the correct small (i.e., x → 0) and large (i.e., x → ∞) particle limits for extinction and absorption efficiencies despite the original premise that the theory requires x ≫ 1. The simple theory is particularly useful for those types of practical problem that require integration over all particle orientations or integration over a distribution of particle sizes, since these integrations tend to smear out the errors associated with the single particle theory.

ELECTROMAGNETIC COUPLING TO A CONDUCTING BODY OF REVOLUTION WITH A HOMOGENEOUS MATERIAL REGION

ABSTRACT A numerical solution for electromagnetic coupling to a perfectly conducting body of revolution with a loss-free homogeneous material region is developed here. The material region is exposed by a rotationally symmetric aperture in the conducting body. Application of the equivalence principle introduces an unknown electric current on the surface of the conducting body, and both an unknown equivalent electric current and an unknown equivalent magnetic current in the aperture. These currents satisfy the integral equations obtained by annihilating the tangential components of the electric field on the surface of the conducting body and by enforcing continuity of the tangential components of the electric and magnetic fields across the aperture. These integral equations are solved numerically by means of the method of moments. Numerical results for the above mentioned currents are presented for four different conducting bodies, each of which has a dielectric region and is excited by an axially incident plane wave. The computer program that was used to calculate these currents allows for the more general case of oblique incidence.