Focusing of two-dimensional electromagnetic waves through a plane interface
01 May 1998-Pure and Applied Optics: Journal of The European Optical Society Part A (IOP Publishing)-Vol. 7, Iss: 3, pp 603-625
TL;DR: In this article, the focusing of two-dimensional (2D) electromagnetic waves through a plane interface was studied and the exact solution for the transmitted field due to an arbitrary 3D incident wave was derived in the Kirchhoff approximation.
Abstract: We study the focusing of two-dimensional (2D) electromagnetic waves through a plane interface. Starting from the exact solution for the transmitted field due to an arbitrary three-dimensional (3D) incident wave, we derive solutions for focused 3D waves in the Kirchhoff approximation. Then we construct corresponding solutions for focused 2D electromagnetic waves and study in detail the focusing properties of a TM field numerically and analytically.
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TL;DR: In this paper, boundary integral analysis is applied to the analysis of diffraction from both conductive and dielectric diffractive optical elements, and the boundary element method is used to solve the boundary integral equations and validate its implementation by comparing with analytical solutions.
Abstract: We apply boundary integrals to the analysis of diffraction from both conductive and dielectric diffractive optical elements. Boundary integral analysis uses the integral form of the wave equation to describe the induced surface distributions over the boundary of a diffractive element. The surface distributions are used to determine the diffracted fields anywhere in space. In contrast to other vector analysis techniques, boundary integral methods are not restricted to the analysis of infinitely periodic structures but extend to finite aperiodic structures as well. We apply the boundary element method to solve the boundary integral equations and validate its implementation by comparing with analytical solutions our results for the diffractive analysis of a circular conducting cylinder and a dielectric cylinder. We also present the diffractive analysis of a conducting plate, a conducting linear grating, an eight-level off-axis conducting lens, an eight-level on-axis dielectric lens, and a binary dielectric lens that has subwavelength features.
154 citations
TL;DR: In this paper, the authors derived integral representations suitable for studying the focusing of electromagnetic waves through a plane interface into a uniaxial crystal and derived explicit expressions for the dyadic Green's functions associated with the transmitted fields.
48 citations
TL;DR: Experimental results for focusing of a three-dimensional electromagnetic wave through a plane interface into two different uniaxial crystals, a positive MgF2 crystal and a negative LiNbO3 crystal are presented.
35 citations
TL;DR: It is shown that the transmitted beam corresponding to an incident 2-D TM Gaussian beam with its main propagation direction along the interface normal is tilted inside the crystal by the same angle as is the transmitted axial ray that corresponds to a normally incident ray.
Abstract: We study the transmission of a two-dimensional (2-D) TM Gaussian beam through a plane interface between an isotropic medium (e.g., air) and a uniaxially anisotropic crystal. The optic axis of the crystal is taken to be in the plane of incidence but is arbitrarily oriented relative to the interface normal. We show that, in the paraxial approximation, a nontruncated transmitted 2-D TM Gaussian beam inside a uniaxial crystal can be expressed in a form similar to that of a scalar Gaussian beam that propagates in a homogeneous medium. We also show that the transmitted beam corresponding to an incident 2-D TM Gaussian beam with its main propagation direction along the interface normal is tilted inside the crystal by the same angle as is the transmitted axial ray that corresponds to a normally incident ray.
30 citations
TL;DR: From exact solutions for the reflected fields resulting when a plane TE or TM wave is incident on the plane interface, it can be inferred that the reflected field contains both a TE and a TM component, which gives a change in polarization that can be utilized to determine the properties of the biaxial medium.
Abstract: Exact solutions are obtained for the reflected and transmitted fields resulting when an arbitrary electromagnetic field is incident on a plane interface separating an isotropic medium and a biaxially anisotropic medium in which one of the principal axes is along the interface normal. From our exact solutions for the reflected fields resulting when a plane TE or TM wave is incident on the plane interface, it can be inferred that the reflected field contains both a TE and a TM component. This gives a change in polarization that can be utilized to determine the properties of the biaxial medium. The time-harmonic solution for the reflected field is in the form of two quadruple integrals, one of which is a superposition of plane waves polarized perpendicular to the plane of incidence and the other a superposition of plane waves polarized parallel to the plane of incidence. The time-harmonic solution for the transmitted field is also in the form of two quadruple integrals. Each of these is a superposition of extraordinary plane waves with displacement vectors that are perpendicular to the direction of phase propagation.
27 citations
References
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TL;DR: In this article, an investigation of the structure of the electromagnetic field near the focus of an aplanatic system which images a point source is made, and the results are illustrated by diagrams and in a tabulated form based on data obtained by extensive calculations on an electronic computor.
Abstract: An investigation is made of the structure of the electromagnetic field near the focus of an aplanatic system which images a point source. First the case of a linearly polarized incident field is examined and expressions are derived for the electric and magnetic vectors in the image space. Some general consequences of the formulae are then discussed. In particular the symmetry properties of the field with respect to the focal plane are noted and the state of polarization of the image region is investigated. The distribution of the time-averaged electric and magnetic energy densities and of the energy flow (Poynting vector) in the focal plane is studied in detail, and the results are illustrated by diagrams and in a tabulated form based on data obtained by extensive calculations on an electronic computor. The case of an unpolarized field is also investigated. The solution is riot restricted to systems of low aperture, and the computational results cover, in fact, selected values of the angular semi-aperture a on the image side, in the whole range 0 ≤ α ≤ 90°. The limiting case α → 0 is examined in detail and it is shown that the field is then completely characterized by a single, generally complex, scalar function, which turns out to be identical with that of the classical scalar theory of Airy, Lommel and Struve. The results have an immediate bearing on the resolving power of image forming systems; they also help our understanding of the significance of the scalar diffraction theory, which is customarily employed, without a proper justification, in the analysis of images in lowaperture systems.
2,636 citations
TL;DR: A simple model is developed, based on the diffusion approximation to radiative transfer theory, which yields analytic expressions for the pulse shape in terms of the interaction coefficients of a homogeneous slab.
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TL;DR: In this article, a solution to an inverse scattering problem that arises in the application of holography to the determination of the three-dimensional structure of weakly scattering semi-transparent objects is presented.
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TL;DR: The reconstruction algorithm is derived for parallel beam transmission computed tomography through two-dimensional structures in which diffraction of the insonifying beam must be taken into account and is applicable to diffraction tomography within either the first Born or Rytov approximations.
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TL;DR: To the knowledge, the images are the first experimental reconstruction based on data collected in the frequency domain, and it is shown that this method is sensitive to the optical properties of the heterogeneity.
Abstract: We present images of heterogeneous turbid media derived from measurements of diffuse photon-density waves traveling through highly scattering tissue phantoms. To our knowledge, the images are the first experimental reconstruction based on data collected in the frequency domain. We demonstrate images of both absorbing and scattering heterogeneities and show that this method is sensitive to the optical properties of the heterogeneity. The algorithm employs a differential measurement scheme that reduces the effect of errors resulting from incorrect estimation of the background optical properties. The relative advantages of sources with low and high modulation frequency are discussed within this context.
494 citations