Geometrical Optics Approach Research Articles

A geometrical-optics approach for the deflection of a floating flexible platform

In an earlier paper, see [J Fluids Struct 14 (2000) 943], a derivation of an integro-differential equation for the determination of the deflection of a large floating flexible platform, excited by waves, is given. In this paper, we investigate the possibility to derive a short wave formulation for this problem. It will be shown that for a flexible half-plane and a strip in deep water, the integral equation can be used to find such a formulation. The asymptotic results shall be compared with the numerical results obtained earlier.

Enhanced two-layer radiative transfer scheme for a land surface model with a discontinuous upper canopy

This paper describes a radiative transfer scheme in which vegetation canopies are represented by two layers: a more or less discontinuous upper canopy of trees or shrubs and a continuous lower canopy overlying the soil surface. The model employs a modified geometric-optic approach to estimate the probability that incident radiation will intersect one or more trees, and turbid media radiative transfer to estimate attenuation within the trees and in the underlying herbaceous layer. The primary difference between this and earlier models is that the structure of the model makes it suitable across a range of vegetation types, from woodland and forest to savanna and grassland. An empirical method for separation of green leaf and non-green interception and absorption is also presented. The scheme was developed for inclusion in a land surface model requiring short time-step (e.g. 10–30 min) resolution of the interception and absorption of solar energy by the land surface for use in computations of surface energy balance, evapotranspiration and photosynthesis. The model is applied with good results to a series of sites in Niger, West Africa, where detailed radiative transfer and canopy structural measurements were made during the HAPEX-Sahel experiment.

Spatial distribution of fluorescence intensity within large droplets and its dependence on dye concentration

The dependence of fluorescence intensity distributions within droplets on added dye concentration has been calculated by extension of the geometrical-optics approximation and verified by experimental observations. With rising dye concentration, surface plots of the equatorial fluorescence pattern show decreasing relevance of intensity enhancement at focusing points of internal light rays and increasing effects of linear absorption on the characteristic features of the distribution. For comparison with experimentally obtained images of the fluorescence intensity distribution within droplets, a method for calculating volume-integrated intensity distributions was developed in which image distortion at the fluid-air interface is included. A comparison of the calculated and the experimentally determined fluorescence intensity distributions within a droplet confirmed the accuracy of the geometrical-optics approach at high dye concentrations. However, discrepancies from experimental results are visible at low dye concentrations owing to nonlinear optical effects.

A novel optical method in micro drop deformation measurements

A novel method was developed to determine the deformation of a micro drop on a substrate. The principle of the method is based on the scattering of parallel fringes pattern from the deformed droplet. Because only a very few components are needed together with a conventional laser Doppler anemometry (LDA) transmitting unit, the newly developed method is very easy to be implemented. Within the geometrical optics approach, it is possible to reconstruct the profile of a non-spherical micro drop from the scattered interference fringes. The spatial frequency of the fringes was analyzed using fast Fourier transform (FFT). The validation experiments for this method in the determination of micro drop deformation which is affected by gravity, capillary force and surface tension were performed and the results are agreed well with the theoretical analysis.

Geometric Optics Approach to First‐Passage Distributions: Caustic Boundaries and Exponentially Small Eigenvalues

We develop singular perturbation methods for computing the first passage time distribution for one‐dimensional diffusion processes. Detailed results are given for an Ornstein–Uhlenbeck process, and the method is sketched for more general problems. For some parameter values, we find the presence of caustic boundaries; whereas, for other parameter values, there are exponentially small eigenvalues. We use the ray method of geometric optics and asymptotic matching.

Archetypes of nonlinear hydrodynamic structures in optical beams

Processes underlying the formation of appreciably nonuniform structures in optical beams are examined using a hydrodynamics analogy. The influence of the focusing conditions on the characteristics of optical beams in vacuum is considered. Based on the geometric-optics approach, it is demonstrated that the axial distribution of radiation intensity for a focused beam is controlled by the initial transverse distribution of intensity and phase.

Imaging Properties of Hard X-Ray Zone Plates with Corrugated Boundary Roughness

The imaging properties of hard X-ray multilayer zone plates with corrugated roughness along circular zone boundaries are investigated. First, the transmission function for zone plates with the roughness is derived using a geometric optical approach, and based on the Fresnel-Kirchhoff diffraction theory formulas are developed to calculate the point spread function (PSF) efficiently, assuming that the roughness increases with radius. Then, the PSFs for various magnitudes and angular configurations of the roughness are presented, and the imaging properties are discussed particularly in terms of the focusing efficiency (or the Strehl ratio) and the resolution. Tolerances for the maximum magnitude of the roughness, and the relationship between the angular configuration of the roughness and the symmetry of the PSF are also discussed.

Light scattering from a waveguide structure with a sinusoidally corrugated boundary modulated by a weak roughness

Results are reported of the analysis of light scattering from a waveguide structure with a periodically and randomly distorted boundary. The method is based on the assumption of single scattering. The field inside the waveguide is analyzed within the framework of the geometrical optics approach. Results of a computer simulation are presented.

Improvement of sidelobe characteristics of an offset dual reflector antenna with an elliptical beam

After we manufactured an offset dual-shaped reflector antenna with an elliptical beam designed by the geometrical optics approach, we found that the antenna could not provide the desired low sidelobe characteristics. In general, we often encounter the case in which the desired sidelobe characteristics are not attained because of design inaccuracy, reflector surface error, and reflector alignment error after antenna manufacturing. We here propose a newly developed method, called aperture phase distribution control by adjustment of reflector segments (APCAR). This method has been verified through improvement of sidelobe characteristics of the offset dual-shaped reflector antenna with an elliptical beam, whose aperture diameter is 1.3 m × 2.8 m. © 1999 Scripta Technica, Electron Comm Jpn Pt 1, 82(12): 10–19, 1999

Improvement of sidelobe characteristics of an offset dual reflector antenna with an elliptical beam

After we manufactured an offset dual-shaped reflector antenna with an elliptical beam designed by the geometrical optics approach, we found that the antenna could not provide the desired low sidelobe characteristics. In general, we often encounter the case in which the desired sidelobe characteristics are not attained because of design inaccuracy, reflector surface error, and reflector alignment error after antenna manufacturing. We here propose a newly developed method, called aperture phase distribution control by adjustment of reflector segments (APCAR). This method has been verified through improvement of sidelobe characteristics of the offset dual-shaped reflector antenna with an elliptical beam, whose aperture diameter is 1.3 m × 2.8 m. © 1999 Scripta Technica, Electron Comm Jpn Pt 1, 82(12): 10–19, 1999

Phase center of an H-plane sectoral horn between parallel conductor plates

In feeding parallel plate slot arrays with plane waves propagating between parallel conductor plates, a dielectric plate lens or a parabolic cylindrical reflector is often used to generate the plane waves. Such a lens or a reflector requires a point source at its focus, since these lenses are designed by using a geometrical optics approach and actually are fed by H-plane sectoral horns. However, it is impossible to regard the horn as a point source, because its aperture is generally several wavelengths. Thus it is essential to determine the phase center of the sectoral horn in order to put the feeding system to practical use. Moreover, the lens and reflector are usually placed in the Fresnel region of the horn and are designed to operate at the widest feeding angle possible. In this paper a method to determine the phase center of the horn that is applicable in the wide angle Fresnel region is proposed, and several charts for its location are presented. This method is ascertained to be fully practical by means of several numerical and experimental investigations. A trial-fabricated plate dielectric lens and an offset parabolic cylindrical reflector were tested and found to operate approximately in accordance with the principles of geometrical optics, if their focii are arranged on the phase centers given in this paper. © 1998 Scripta Technica, Electron Comm Jpn Pt 1, 82(3): 28–38, 1999

Short-wavelength instability of a vortex in a multipolar strain field

The extension of the elliptical instability to a rotational flow with an n-fold symmetry is considered in this Brief Communication. Based on the geometrical optics approach, the short-wavelength stability analysis of the multipolar strained vortex described by the streamfunction (in polar coordinates) Ψn=r2/2−(p/n)rn cos(nθ) is carried out for n=3,4,5 and p⩾0. Both the growth rate and the wavevector properties of the most unstable wave are computed as a function of the real parameter εn=p(2nC/(n−2))(n−2)/2 which characterizes the geometry of the streamline Ψn=C. For almost circular flows, i.e., in the small εn limit, exact estimates are also obtained by perturbation methods.

On asymptotic values of light fluxes scattered by large spherical particles between two angles

The asymptotical limits for light fluxes scattered by large spherical particles with various refractive indices into a fixed range of scattering angles are obtained. Calculations are performed within the framework of the Mie theory and the geometrical optics approximation. The geometrical optics approach, combined with approximations of the radiative transfer theory, allows one to make quick estimates of reflection and transmission functions of disperse media with large particles. The results obtained can be used for studies of light fields in random media with large particles within the framework of the small-angle and quasi-single-scattering approximations of the radiative transfer theory.

Model for an investigation of radiative transfer in cloudy atmosphere

Parameterization of droplet size distributions using a composition of three gamma functions is suggested to simulate a wide spectrum of cloud droplets including drizzle and rain. It should be stressed out that this parameterization is based on extensive material (accumulated in the Russian Central Aerological Observatory) of aircraft observations in clouds and dependent on the cloud type, temperature and other factors. Effective computation technique using the geometric optics approach for the calculations of the parameters of electromagnetic scattering on spherical polydispersions and the database containing these parameters for a wide set of aerosol and cloud mediums are described. The parameterization, computation technique and the database are applied to create different optical atmospheric models with scattering properties rather close to reality for theoretical investigations of the atmospheric radiative transfer. Some examples of cloud radiation forcing studies are also considered in this paper. Their principal feature was the use of the original effective line-by-line and Monte-Carlo codes to take into account rigorously both the cloud/molecular scattering and a detailed spectral structure of water vapor, ozone, carbon dioxide and oxygen. It has been found: (a) variations of the mean droplet radius depending on the cloud temperature and other factors lead to essential changes in shortwave fluxes (tens of W/m 2), cloud radiation absorption (tens of W/m 2) and the Liquid Water Path (LWP) (by several times); (b) In continental clouds short wave fluxes mainly depend on small droplets. The existence of large (drizzle) drops perturbs slightly the fluxes and rather strongly affects the liquid water path and the cloud radiation absorption; (c) The solar radiation absorption and scattering by cloud media are generally defined only by the extinction coefficient and the effective radius and are slightly affected by other details of cloud size droplet distributions. These statements are in good agreement with other investigations. Thus, these parameterization and database should be good enough for the cloud optical properties simulation in the majority of practical applications. Moreover, the developed codes may be recommended for exact simulation of atmospheric radiative transfer in satellite and full-scale experiments, for testing and improving the radiation codes being used in climate models, etc.

Coherent Phenomenon in Reflection of Radiation by an UnevenMirror

First experimental results are presented for a coherent phenomenon in reflection of radiation by a mirror with a concave round surface. It consists of interference fringes which arise owing to the interaction of rays undergoing different numbers of reflections on the mirror. An analytical theory of the phenomenon is given in the frame of a geometrical optics approach in a small angle approximation. The experimentally measured interference fringes for the visual light of a Ne–He laser reflected by the round part of the mirror are qualitative coincidence with the results of accurate computer calculations performed in the frame of a geometrical optics approach.

Time-resolved analysis of self-heating in power VDMOSFETs using backside laserprobing

A laserprobe technique for characterization of transient self-heating in power devices is proposed and its applicability is demonstrated on VDMOSFETs. The change in the silicon lattice temperature in the device active region under pulsed operation is sensed by an infrared laser beam focused on a single VDMOS cell from the substrate side. The temperature-induced change in the silicon refractive index causes an optical phase change which is detected interferometrically. The transient phase measurements are carried out under various VDMOSFET bias conditions and for heating pulse widths in the μs range. The laser beam modulation is numerically modeled using a solution of the transient heat transport equation and a transmission line approach to model the beam propagation. Calculated optical phase signals show a very good agreement with the experiments. The phase change calculated by using a simple geometric optic approximation was compared with the phase variation obtained by the rigorous transmission line approach. The results show that the geometric optic approach can accurately be used in the analysis of transient self-heating of VDMOSFETs.

Determination of internal radio frequency electric field profiles via millimeter wave reflectometry in the DIII-D Tokamak

Millimeter wave reflectometry was employed to determine radio frequency wave electric field profiles in the DIII-D Tokamak. The method utilizes spatially localized X-mode reflectometer measurements in the 65–73 GHz frequency range to detect coherent fluctuations in magnetic field and density driven at the fast magnetosonic wave (FW) frequency (60 MHz). The FW electric field profiles were determined by adopting a geometric optics approach, which is appropriate for interpreting reflectometer data where the perturbing wavelength is longer than the probing wavelength. Successful measurements from this system were utilized to investigate FW propagation effects on DIII-D. The FW launch directionality necessary for current drive was confirmed at a position toroidally close to the FW antenna.

New regions of transparency for intermediate-frequency waves in an inhomogeneous magnetoactive plasma

It is shown that in an inhomogeneous plasma there exist new regions of transparency which are absent in the traditional geometrical-optics approach. A more general dispersion relation which adequately describes the propagation of electromagnetic waves in these regions is proposed.

Geometric-optical approach to the problem of excitation of a corrugated optical waveguide at near-normal angles of incidence

A simple method is proposed for calculating the efficiency of coupling laser radiation into a corrugated dielectric waveguide when two coupled modes are excited in the second diffraction order. The angular dependences of the coupling-in efficiency are calculated for various corrugation periods.

Propagation properties of tapered graded-index waveguides

Abstract Propagation of light in multimode parabolic-index linear tapers is studied using a geometrical optics approach. Considering a two-dimensional model, ray trajectories are derived analytically for tapers with small angles. Both bound and leaky rays are examined. It is shown that ray trajectories are described by modulated sinusoidal functions with decreasing amplitude and period as light propagates in the direction of decreasing thickness of the taper core, thus gradual concentration of power from the larger area to the smaller one. Radiation loss of tapers when used to connect two multimode optical waveguides with different core areas, and coupling efficiencies when they are used to couple power from collimated-beam and Lambertian light sources to waveguides are determined. Numerical results for ray trajectories illustrating the gradual concentration of light power, radiation loss, coupling efficiency, and improvement in coupling efficiency for collimated-beam illumination and Lambertian sources a...