Effect of Slab Interfaces on Diffraction of Visible Light by a Thick Volume Grating

Abstract

A theory of visible light diffraction by a volume grating is given for the case when reflection at slab interfaces cannot be neglected. A method of approximate solution of the second-order coupled-wave equations, applicable over a wide range of the grating vector orientation, is proposed. An appropriate boundary-value problem is discussed and solved in the two-wave approximation. The results are analytical and expressed in matrix notation suitable for both transmission and reflection diffraction gratings. Particular attention is given to the diffraction regime that arises in a slanted grating under the total internal reflection of the diffracted wave (TIRDW). Strong transmission anomalies occurring in the vicinity of the TIRDW threshold are established and analysed.     

Reflection and Transmission Coefficients in Uniaxial Crystals

Abstract

In this work we present a detailed deduction of the general solution of the boundary conditions for an isotropic medium-uniaxial birefringent crystal interface. The reflection and transmission coefficients are defined with reference to a polarization perpendicular or parallel to the incidence plane of the incident ray. The explicit expressions and curves of these coefficients are obtained as functions of the incidence angle, and they are discussed comparing them with the isotropic case.     

Astigmatic foci along a skew ray

Abstract

A method for astigmatism calculations along any skew ray is presented. This is useful in the case of extremely wide angle optical systems (and not only imaging systems), where skew ray aberrations are most dominant, but it is essential in the case of systems which are not rotationally symmetric, where all the rays may be skew. Equations relating the position of the astigmatic foci before and after refraction or reflection are derived from the analysis of infinitesimal wave fronts in the immediate neighbourhood of the point of incidence of any ray, but particularly the central ray of any pencil on an optical surface. The method is then illustrated and checked with representative numerical examples.     

Indicating Surface of Natural Reflectance

Abstract

To study the behaviour of anisotropic media in reflection when illuminated by natural light, an ‘indicating surface of natural reflectance’ is defined. The use of such a surface is proposed, and its statistical parameters are given. The expressions that relate these parameters to the refractive indices of the incident medium and to the principal indices of the medium under observation have been deduced for the case of uniaxial media. Those corresponding to uniaxial transparent substances are presented here.     

Reflection and non-specular effects of 2D gaussian beams in interfaces between isotropic and uniaxial anisotropic media

Abstract

In the present paper bidimensional Gaussian linearly polarized beams, which are incident on an interface between an isotropic medium and a non-absorbing non-magnetic uniaxial crystal are considered. The relation between the reflection coefficients and the non-specular effects are studied. The expressions for the first order effects in the case of a beam linearly polarized in a plane perpendicular to the one containing the crystal optical axis and the normal to the interface are analytically determined. Two highly symmetric geometries are analysed and the results are compared to those obtained with isotropic interfaces.     

Wave four-vectors for the electromagnetic waves in relatively moving dielectric media

Abstract

The wave four-vectors are deduced for the general case where the reflection and transmission of a plane electromagnetic wave are at the interface between a stationary dielectric medium and a dielectric medium moving with an arbitrary velocity. It is demonstrated that the frequency shift in the reflected wave not only depends on the velocity v of the moving medium but also markedly depends on the refractive index n ₁ of the incident medium; the frequency shift in the transmitted wave varies with n ₁ and the refractive index n ₂ of the moving medium, as well as on v Total reflection not only occurs when n ₁ > n ₂ but also may occur when n ₁ ≤ n ₂ if 0 < v/c < 1. The law of reflection, the Snell law and the equivalent refractive index of the moving medium are discussed according to the wave four-vectors as well.     

Explicit expressions for spectral remittances of axially excited chiral sculptured thin films

Abstract

A theory of reflection and transmission of normally incident plane waves to a chiral sculptured thin film (CSTF) is presented. It is based on a coupled wave approach, in which the handedness-reversing reflections at the medium's interfaces are combined with the handedness-preserving distributed reflection inside the CSTF. Explicit formulas for the various reflection and transmission coefficients are derived. The method is shown to provide acceptable quantitative agreement with the exact full electromagnetic analysis.     

An Application of the 4 × 4 Matrix Formalism to the Polar Magnetic Kerr Effect

Abstract

Expressions for the elements of a 2 × 2 matrix describing the reflection of polarized light at oblique incidence from a surface with an applied magnetic field that is perpendicular to the plane of the surface are derived using the 4 × 4 matrix formalism. This reflection matrix can be used to calculate the changes in polarization of light reflected from such a surface. The formalism also provides insight into the behaviour of the classical electromagnetic fields within the reflecting material.     

Nonholonomic relation between the polarization state of light and the angle of twist of a single-mode optical fiber with linear birefringence

The relation between the polarization state of light in a twisted single-mode optical fiber possessing linear birefringence and the twist angle of the fiber is considered for the case of a fiber stretched in a straight line. It is shown that this reflection is of a nonholonomic character. Pis’ma Zh. Tekh. Fiz. 24, 22–25 (June 12, 1998)     

The information content of weakly scattered fields: Implications for near-field imaging of three-dimensional structures

Abstract

The structural information carried by the homogeneous and evanescent components of the scattered field is investigated for the case of a single plane wave, either homogeneous or evanescent, incident on a weakly scattering three-dimensional medium. For homogeneous plane wave incidence, it is shown that, unlike the one-to-one mapping that exists in the case of scattering from thin (i.e. two-dimensional) structures, the evanescent components of the scattered field are related to the three-dimensional Fourier transform of the dielectric susceptibility through a generalized Radon transform. For evanescent plane wave incidence, a reciprocal relationship exists between the homogenous components of the scattered field and the three-dimensional Fourier transform of the susceptibility. Inversion techniques are outlined for these two cases, as well as other experimental modalities, which explicitly require, except for separable media, complete (i.e. multiple view) measurement data. These results have direct bearing on total internal reflection microscopy (TIRM), and they yield insight into the limitations of more general near-field imaging techniques.     

Electromagnetic Wave Reflection and Transmission at a Chiral-dielectric Interface

Abstract

Reflection and transmission of electronmagnetic waves at a chiral-dielectric interface are analysed for normal and oblique incidence and for critical angles. Graphs of the reflection and transmission coefficients are given for various parameters of the two media as a function of the angle of incidence. The results of the analysis and the behaviour of the graphs are discussed and conclusions are drawn from this discussion.     

Beam reflection from multilayers with periodic and fractal distributions

Abstract

An impedance model is used to solve the reflection problem from a multilayer with periodic and Cantor bar fractal distributions. It is based on the calculation of the input surface impedance of such a structure. The method consists of replacing the multilayer reflection problem by a simple reflection problem on a single surface. This approach has the additional advantage that only the fields above the surface should be taken into account. Numerical calculation leads to an iterative method which can be implemented for each polarization mode. The results for the input impedance function of the system and for the reflectance are presented for different iteration states. Also to quantify the comparison between both types of structures we introduce a self-similarity function which correlates orders or states of the same type.     

Interference Phenomena in Waveguides with Two Corrugated Boundaries

Abstract

Waveguide structures with two corrugated interfaces are considered. It is shown theoretically and experimentally that these structures can form the basis for a highly-efficient unidirectional grating coupler for slab waveguides. The anomalous light reflection from waveguides with two corrugated boundaries is also considered. The possibility of using corrugated waveguides for frequency stabilization of a semiconductor laser is demonstrated.     

Interference by multiple reflections in crystal plates of point group symmetries C 3 v,C 4 v,C 6 v

Crystals of symmetry point groups C _3v , C _4v , C _6v possess an antisymmetric tensor of linear spatial dispersion (LSD) and thus they do not rotate the plane of light polarization. The antisymmetric LSD (ALSD) influences the polarization of the electromagnetic eigenmodes of the crystal and it may be studied through reflection only. In this paper we study the interference by multiple reflection in anisotropic crystal plates of the aforementioned point groups (the optical axis is perpendicular to the plane of incidence). The amplitudes of the reflected and transmitted electromagnetic beams are calculated both in the case of single reflection and in the case of multiple reflection. Differential reflection methods have been proposed and analysed in the case of elliptically and linearly polarized incident beams. The dependences of the multiple reflection intensity and of the differential reflected and transmitted signals on the angle of incidence is calculated for the crystals Ag₃AsSe₃, ZnO and CdS. It is shown that in the case of total reflection in an anisotropic plate surrounded by an optically denser medium the effects of the ALSD on reflection are enhanced several times.     

Reprocessibility of Dichromated Gelatin Reflection Gratings

Abstract

The reprocessibility of dichromated gelatin reflection gratings is studied. Reflection gratings developed in six slightly different ways are reprocessed after three years storage. Reflection (diffraction) efficiencies are strongly decreased during storage. After reprocessing reflection efficiencies are close to the original reflection efficiencies. Restoration is better when the original reflection efficiency (RE) is not very high (RE <90%). When, the plates, which are rapidly dehydrated during development procedure, are reprocessed using slow dehydration, reflection efficiencies have often been even better after reprocessing than one day after exposure and the original development procedure.     

Reflection and Transmission of Plane Waves at the Planar Interface of a General Uniaxial Medium and Free Space

Abstract

A general uniaxial medium is characterized by its permittivity and permeability tensors having the same preferred axis. The plane wave reflection and transmission characteristics of a planar interface between free space and a general uniaxial medium have been obtained; since application as a polarizer is envisioned, the preferred axis lies in a plane parallel to the interface. Application of the Brewster law, as well as conditions for total reflection are explored.     

Remote Field Eddy Current Technique: Phantom Exciter Model Calculations

Abstract

High resolution results of finite element calculations for remote field eddy current “phantom exciter” simulations of slit defect interactions using single through wall transit are presented. These show that fine circumferential slits cause almost no field perturbations in the case of nonferromagnetic tubes but big perturbations in ferromagnetic tubes where high magnetic H fields occur in the slits. Defect-induced magnetic field perturbations must therefore be considered in addition to eddy current perturbations when ferromagnetic materials are inspected, particularly in the case of fine slits orthogonal to the magnetic field direction. Additional details seen are the funnelling of energy into slits in ferromagnetic pipes and precursor disturbances of fields approaching defects. It is suggested that these are due to the reflection of the electromagnetic waves dictates by boundary conditions at the near side defect boundary.     

The Use of Annular Pupil Plane Filters to Tune the Imaging Properties in Confocal Microscopy

Abstract

We consider the use of pupil plane filters to modify the imaging properties of confocal optical systems. We specialize to the annular filter as it is useful in itself and as part of a more complex filter. We show, inter alia, that by changing the size of the annular obscuration we can tune the strength of the optical sectioning. The question of spherical aberration is considered and it is found both theoretically and experimentally that the effects are reduced in the annular case. We also discuss the problem of where best to place the filters in reflection systems where different filter functions are required for the two imaging lenses. The use of filters in both bright-field and fluorescence imaging modes is considered.     

Monitoring the deposition of an interference film by differential reflection of light

The change in the reflection (differential reflection) of light from an interference film as a result of the deposition of an ultrathin layer on it is investigated. Formulas describing the differential reflection around the reflectivity minima and maxima of the film are obtained by a perturbation method. It is shown that these formulas and the corresponding differential measurements can be used for an easy and unambiguous determination of the thickness and refractive index not only of ultrathin surface layers but also of the interference films themselves. The proposed method is especially convenient for monitoring the deposition of thin-film structures. Pis’ma Zh. Tekh. Fiz. 24, 78–86 (October 26, 1998)