Showing papers on "Physical optics published in 1970"

Theory of Prism–Film Coupler and Thin-Film Light Guides

Abstract: A prism–film coupler has been discussed recently by Tien, Ulrich, and Martin as a device to couple efficiently a laser beam into thin-film dielectric light guides. This coupler also allows an accurate measurement of the spectrum of propagating modes from which the refractive index and the thickness of the film can be determined. We present here a theory of the prism–film coupler. The physical principles involved are illustrated by a method that combines wave and ray optics. We study the modes in the thin-film light guide and their modification by the effect of coupling. We also calculate the field distributions in the prism and the film, the power transfer between the prism and the film, and derive a condition of optimum operation. In one example, 81% of the laser power can be fed into any desired mode of propagation in the film.

Kinematic wave theory

Abstract: In the kinematic theory of wave propagation (e. g. geometrical optics) a quantity J is needed in the calculation of wave intensity either through transport equations or the principle of conservation of wave action. This quantity is a spatial Jacobian with respect to a parameter space and represents a volume element convected with the rays. To avoid its direct computationas a Jacobian, derived ray equations are obtained whose solutions lead to alternative ways of calculating J . This approach is specialized to cases involving Snell’s law (with cylindrical and spherical as well as planar symmetry) and non-dispersive propagation. The behaviour of the theory under Lorentz transformations is shown.

Geometrical Optics of Parabolic Index-Gradient Cylindrical Lenses

Abstract: The first-order imaging properties of dielectric rods with refractive index decreasing quadratically with distance from the axis are analyzed from the viewpoint of gaussian ray optics. Cardinal-point locations vary with rod length, but the usual object–image relationships are then still applicable. Several ray diagrams are shown; one of the examples is a contact magnifier.

Unacceptable height correlation coefficients and the quasi-specular component in rough surface scattering

Abstract: The purpose of this note is to put to rest once and for all the use of an erroneous result derived from the linear (or exponential) height correlation coefficient in the physical optics formulation of rough surface scatter. The form of the correlation coefficient near the origin must be quadratic so that the physical optics integral can be evaluated asymptotically. Hence, the theoretical shape of the quasi-specular component for backscatter is not due to the nature of the correlation coefficient but to the form and behavior of the probability density function for the surface slopes evaluated for tilts near their mean values, the horizontal.

The geometric optics contribution to the scattering from a large dense dielectric sphere

Abstract: An analysis is presented for calculating the backscattered fields of an electromagnetic plane wave by lossless dielectric spheres of arbitrary density. This method involves the Watson transformation which serves to split the exact Mie solution, given as an infinite series, into the geometrical optics fields and the diffracted fields. The former comes from the illuminated region of the sphere and may be obtained from the geometrical optics method. The latter comes from the shadow region and consists of two different types of surface waves. One is a "creeping wave" analogous to that of perfectly conducting spheres. The other is a wave which enters the sphere and emerges as a surface wave in the shadow region. This wave is unique to dielectric spheres and is the stronger of the two surface waves. In the widely used geometric optics methods it is assumed that the optics fields are the dominant contributors even though stationary rays which are not in the direction of backscatter must be added in to give a degree of agreement with the exact Mie series results. In this paper we derive the optics fields and show that they differ in some respects from those obtained by the geometric optics method. They are smaller than heretofore assumed and contribute negligibly to the backscatter in this particular range of ka (4-20). Using our rigorous approach we can show the diffracted fields to be the major contributors to the total backscatter. Numerical results for the backscattering cross sections using diffracted and optics fields, and optics fields alone will be presented for relative index of refraction of 1.6. The agreement between our results (diffracted and optics) and exact results from the Mie series is excellent. A subsequent paper will be concerned with the diffracted fields.

The Apparent Temperature and Emissivity of Natural Surfaces at Microwave Frequencies.

Abstract: : The effect of surface roughness on the emissivity of natural surfaces has attained considerable importance in the fields of passive microwave remote sensing of environment and planetary surface emissions. Between the plane surface model and the Lambert surface model, which describe the two extreme cases of a perfectly flat surface and a very rough surface respectively, two statistical surface models have recently been considered: the geometric optics type surface and the physical optics type surface. The paper examines the behavior of the microwave emissivity of some natural surfaces as a function of nadir angle and polarization. This examination includes a comparison between measured and calculated values of the apparent temperature of the ocean surface at 19.4 and 37 GHz.

Imaging properties of diffraction gratings

Abstract: For almost a century now diffraction gratings are being used as the dispersing element in spectroscopic systems. In the greater majority of cases this grating is of the reflecting type, which (among others) has the advantage that the radiation to be analysed need not pass absorbing material as is the case with prisms and transmission gratings. It is therefore possible to study a large part of the electromagnetic spectrum on account of the reflecting properties of the coatings available. As reflection gratings are widely applied, many papers have appeared, describing various aspects of spectral image formation by such gratings. In this thesis we shall restrict ourselves to the properties of grating systems as seen from the viewpoint of the geometrical aberration theory. We have excluded any questions of physical optics such as, for instance, diffraction due to the finite width of the grating and the intensity distribution over the spectral orders (blaze). Also matters as ruling errors and ghosts will not be considered here.

Energy flow: Wave motion and geometrical optics

Abstract: Energy distribution for solutions of the wave equation in the presence of a reflecting body can be investigated with varying degrees of refinement by using quadratic inequalities, Huyghens principle and geometrical optics. The relations between these properties and their validity in general cases is discussed and some of the simpler proofs outlined.

Propagation of light beams in continuously focusing lens-like media

Abstract: A method is presented which allows a wave optical calculation of the Gaussian light beam in continuously focusing lenslike media. It is based on a formal quantum theory of physical optics. An example is worked out.

Scattering by a periodic surface

Abstract: : Numerical procedures are developed for the digital solution of the integral equations for the currents induced in a perfectly conducting, two dimensional periodic surface when a plane electromagnetic wave is incident. Data are obtained for the surface and far fields for a variety of sinusoidal surfaces for plane waves of either polarization at oblique as well as normal incidence, and the results are compared with the predictions of physical optics.

Effects of roughness on emissivity of natural surfaces in the microwave region

Abstract: : The effect of surface roughness on the emissivity of natural surfaces has attained considerable importance in the fields of passive microwave remote sensing of environment and planetary surface emissions. Between the plane surface model and the Lambert surface model, which describe the two extreme cases of a perfectly flat surface and a very rough surface respectively, two statistical surface models have recently been considered: the geometric optics type surface and the physical optics type surface. The paper examines the behavior of the microwave emissivity of some natural surfaces as a function of nadir angle and polarization. This examination includes a comparison between measured and calculated values of the apparent temperature of the ocean surface at 19.4 and 37 GHz. (Author)

Geometrical Optics: An Introduction

Abstract: (1970). Geometrical Optics: An Introduction. Optica Acta: International Journal of Optics: Vol. 17, No. 5, pp. 396-396.

Radiative properties of rough surfaces

Abstract: Most studies on surface roughness effects are based on geometrical optics. This analytical investigation treats the surface roughness effects from wave optics considerations, thus accounting for the interference of waves. The rough surface is sinusoidal, infinite in extent and it is irradiated by plane monochromatic waves. The scattering of electromagnetic waves by the rough surface is determined by the direct solution of Maxwell's equations instead of the commonly used Huygens-Kirchhoff approximation (Beckmann's reflectance). Consequently, the solution is not restricted to small wavelength to roughness ratios; furthermore, polarization effects can be accounted for. The results indicate that the transmittance of the rough surface exhibits a maximum near the point where the wavelength of the surface roughness is the same as the wavelength of the radiation. The interval around this point is called transition region because the surface changes from specular to diffuse. The radiative properties are influenced by both the pitch and amplitude of the roughness. The results approach Fresnel's law when the pitch and amplitude of the surface become small compared to the wavelength of the radiation. Similarly, the surfaces become specular even at larger pitch if the amplitude of the roughness is small. It is also shown that Beckmann's reflectance relation is the limiting case of the reflectance obtained by the direct solution of Maxwell's equations. In addition, numerical results are presented on the effective properties of rough dielectric plates with various refractive indices and optical thicknesses.

Diffraction Fringes of Ripple in Ferromagnetic Thin Films

Abstract: The intensity distribution of ripple structure in ferromagnetic thin films is discussed on the basis of wave optics in the defocused mode of Lorentz microscopy. The ripple angle for a 90% Ni-Fe evaporated thin film was determined to be about 7° experimentally on the basis of the Fresnel diffraction fringes observed.

The calculation of corrections to geometrical optics: II. An electromagnetic problem☆

Abstract: THE calculation of the first correction to geometrical optics in a problem on the reflection of a plane electromagnetic wave from an ideally conducting surface of revolution was carried out in [1]. The first correction for an arbitrary smooth surface has been calculated in [2], the result being presented in a rather clumsy form. The second correction to geometrical optics has not as yet been written out but in explicit form exactly as it is needed for calculating the current amplitude. This paper gives the calculations for the first and second corrections to the geometrical optics value of the electric field and current on an arbitrary smooth ideally conducting surface. The method of calculation is the same as in [3].

The Physics of Moire Fringes.

Abstract: Describes the formation and properties of moire fringes, with particular emphasis on the important part played by wave optics. It is hoped that this coupled with the suggested experiments and demonstrations might form a useful addition to the usual course in physical optics.