Ray-optical Techniques Research Articles

Short-wavelength radiation of a charge moving in the presence of a dielectric prism

The radiation of a charge moving in the presence of a large (compared with the wavelengths under consideration) dielectric prism of two different configurations is studied: case (I), a charge moving in the channel, and case (II), a charge moving along the prism’s face. The approximate method that combines an exact solution of certain “key problems” (without the external boundaries of the object) and the ray-optics technique for the field outside the prism is used. A general analytical solution of the problems is obtained, a particular case of small angles is considered, and an algorithm for computation of the radiation field is developed. The computed results are visualized in plots of the spectral density of radiation on the plane parallel to the external face of the prism. In case (I), the radiation is found to be more intensive and has a single maximum in the central plane. In case (II), the radiation can have a single maximum in the central plane (for relatively low velocities) or two lateral maxima (for an ultra-relativistic velocity).

MODELLING OF SHADOWING LOSS DUE TO HUGE NON-POLYGONAL STRUCTURES IN URBAN RADIO PROPAGATION

AtilimUniversityDepartmentofElectricalandElectronicsEngineeringIncek,Ankara,TurkeyE. YazganHacettepeUniversityDepartmentofElectricalandElectronicsEngineeringBeytepe,Ankara,TurkeyAbstract—Raytracingalgorithmsrelyontwodimensionalorthreedimensional database. They use ray optical techniques referred toas the uniform theory of diffraction (UTD) using building databasegivenaspolygons. Buildinggeometriescanalsobemodelledashavingnon-planar geometries, and this would be important in modeling ofshadowinglossduetocurvedstructuresinurbanradiopropagation.To demonstrate modelling of buildings as non-polygonal geometries,a particular building composition involving 3D cruved geometries ischosen, and shadowing loss for this building composition is studiedvia UTD ray tracing. Building structure considered in this studyinvolves main canonical shapes of non-planar geometries includingcone,cylinderandsphere. Singleandmultipleinteractionofsurfacediffractions,effectofcreepingwavesaretakeninto considerationintheanalysis.

Built‐up terrain wave propagation by Fourier split‐step parabolic wave equation‐ray optical techniques

Fourier split‐step (FSS) solutions of the parabolic wave equation (PWE) represent wave fields in terms of plane wave decompositions. However, those field solutions are usually only valid in the air space above built‐up terrain, whereas field predictions for modern wireless systems often require knowledge of the fields on a street level. Since FSS PWE solutions with large step sizes are not applicable for field computations between irregular scattering obstacles such as buildings, this problem is overcome by a two‐step approach combining the FSS solution of the PWE with ray optical techniques to compute the fields at ground level in wooded and urbanized areas. To account for the great variety of propagation effects in a statistical sense, direct rays, reflected rays, diffracted rays and attenuated rays at typical receiver locations are included into the considerations. Comparisons to a wide variety of measured data show that this two‐step approach produces better results than state of the art semiempirical field prediction techniques.

Analysis of Coupling Coefficient in a Laterally Tapered Waveguide Distributed Feedback Laser Using Ray Optics Technique

Based on ray optics technique we have analyzed the first-order backward coupling coefficient in a laterally tapered distributed feedback (DFB) laser diode. These tapered structures are designed to realize narrow beam divergence, low threshold current and high longitudinal mode selectivity. The coupling coefficient, κ, for three different laterally tapered waveguide distributed feedback laser diodes have been studied. It has been found that without changing the grating period and the material properties, the coupling coefficient can be altered by modifying the taper profile and waveguide dimensions while satisfying the adiabatic single-mode condition.

A quality measure for ray-tracing algorithms

The paper focuses on the validation of ray-optical techniques as tools fur predicting wide-band radio propagation, in the case of indoor environments. A novel approach to address the topic is proposed: it is based on a likelihood test between the simulations and the measures appropriately treated with a super-resolution technique.

Optical selection, manipulation, trapping, and activation of a microgear structure for applications in micro-optical–electromechanical systems

The optical processes involved in laser trapping and optical manipulation are explored theoretically and experimentally as a means of activating a micrometer-size gear structure. We modeled the structure by using an enhanced ray-optics technique, and results indicate that the torque present on the gear can induce the gear to rotate about the gear-arm plane center with light as the driving energy source. We confirmed these findings experimentally by using gears manufactured with conventional semiconductor techniques and from a layer of polyimide. It is expected that such a simple gear design activated by use of light could lead to an entire new class of micro-optical-electromechanical systems.

Performance analysis of radar antenna systems

If modern airborne radar systems are to function properly, the radar antenna radiation patterns must meet certain specifications. Until recently, most radar antennas were designed and tested in a clean antenna environment, i.e., there is no near field scattering from host structures or radome effects. However, these higher order effects are the matter of increasing concern with added performance demands in the ever-increasing jammer and clutter interference environments. We investigated the capabilities and limitations of currently available analysis techniques and computer codes for installed performance of airborne radar antenna systems. Then we developed an extended ray-optical technique that could predict total installed performance of airborne radar antenna systems, i.e., the near field scattering from aircraft structures and radome effects. The new analysis technique utilized a ray-tracing method in both airframe and radome simulation. Thus, it can efficiently predict the total installed performance of large radar antenna systems on an aircraft structure.

Ray optics determination of the DFB coupling coefficient for trapezoidal gratings

A ray optics technique is used to derive a closed-form expression for the first-order coupling coefficient of trapezoidal gratings in a generic five-layer separate confinement heterostructure distributed feedback (DFB) laser configuration for transverse electric (TE) mode. Expressions for a rectangular grating with the duty cycle of 0.5 and a symmetric triangular grating are also obtained as special cases of our general expressions. Based on the comparison of the coupling coefficient calculated by the ray optics technique with those calculated by the extended additional layer method, we show that the ray optics technique is very useful to calculate the coupling coefficient for most cases of realistic grating depths and profiles used in multilayer DFB devices without using any numerical techniques.

Radiation patterns of line sources mounted in a multi-dielectric substrate medium

The far-field of line sources lying between the slabs of a multi-dielectric substrate are presented. Such a configuration is usual in the technology of microstrips as well as in remote sensing. The electric field in the 2-D wave equation is expressed as a Fourier integral of the potentialV(y, h). The coefficients of the solution are found from the boundary conditions at the interfaces of the substrate. The main conclusion is the similarity between the patterns from a line source and a complex array of sources in free space. The ray optical techniques due to multi-reflection and refraction fail for more than three substrates, while our procedure can be applied for any set of lossless or lossy substrates.

Analysis of planar waveguide grating couplers with double surface corrugations of identical period

Planar waveguide grating couplers with double surface corrugations of identical period are analyzed by using the ray-optics technique and by using the rigorous diffraction grating theory. The ray-optics technique offers physical insight and renders simple analytical expressions for conditions of optimum output coupling.

Ray optics determination of the DFB coupling coefficient in separate confinement and multiquantum-well laser structures

A ray optics technique is used to derive a closed-form expression for the first-order backward coupling coefficient /spl kappa/ in a generic five-layer separate confinement distributed feedback laser configuration with sinusoidal, triangular, or rectangular gratings. The expression is applicable to multiquantum-well structures as well as strong coupling configurations, and can be evaluated without using any numerical techniques. For the weak perturbation configurations normally encountered in such devices, the ray optics /spl kappa/ values are in good agreement with those obtained using the standard overlap integral technique.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Distributed feedback coupling coefficient in diode lasers with metallized gratings

First-order distributed-feedback (DFB) evanescent coupling effects are investigated in heterojunction diode laser structures with integrated, metallized diffraction gratings. A closed-form expression for the DFB coupling coefficient kappa is derived using a ray optics technique. The expression can be evaluated easily since it depends only on the laser wavelength, the grating depth, and the parameters of the metallized planar waveguide. The validity of the expression is established by using a truncated Floquet-Bloch approach to compute kappa .< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Diffraction by a prism

Diffraction of electrically polarized plane waves by a dielectric prism (or wedge) of arbitrary apex angle and refractive index in the range of commonly used dielectric materials is treated by a combined analytical-computational approach. Ray-optical techniques are supplemented by the null-field method (or extended boundary condition). Straightforward modal concepts lead to a system of linear algebraic equations, which, after truncation, are solved by matrix inversion. The field diffracted at the apex is shown by example to be (virtually) entirely outgoing. The accuracy of the computed results is assessed in several ways. Comparison is made of the approach introduced here with two other methods, the first restricted to right-angled prisms and the second valid only for refractive indices moderately close to unity; the numerical agreement is encouraging.

Comparison of Wave and Ray Techniques for Solution of Graded Index Optical Waveguide Problems

Transit times and eigenvalue equations found using ray-optics methods are compared with the exact wave-equation solution results. Geometric optics gives excellent accuracy for commonly used values of the dimensionless waveguide parameter V. Even when the effects of dispersion are included, the WKB condition gives exactly the same transit times as the more physically intuitive ray-optics technique.

Radiation from a line charge source located near an air-piezoelectric interface

The ray optical solution to the problem of a time harmonic line charge source radiating acoustic energy into a semi-infinite piezo-electric half space is outlined. This ray optical technique differs from the approach employed in recent publications [1], [2], and leads to a better understanding of bulk-wave radiation in SAW devices. PZT ferroceramic materials have been chosen for this study and numerical results are obtained and given.

Wavefunctions for prisms

Abstract Iterative formulae are presented for the expansion coefficients for a set of basic wavefunctions due to sources situated on the plane of symmetry of a prism of arbitrary angle and refractive indox (which can be complex). The treatment applies to the diffraction of an electrically polarized wave by a dielectric wedge. The formulae are shown to be computationally convenient. The basic wavefunctions can be built up into wavefunctions due to localized sources. The analysis can be related straightforwardly to situations of technical interest if the faces of the prism are in tho far field of the source. It is suggested that the method introduced here would be useful for checking the accuracy of ray-optical techniques in the vicinity of tho apex of a prism. The method is shown to support a previous contention that free modes cannot exist in a penetrable prism.

Ray Methods for Trapped and Slightly Leaky Modes in Multilayered or Multiwave Regions

Ray-optical techniques presented previously by the authors for study of mode propagation in homogeneously filled waveguides are extended to accommodate multilayered regions and regions capable of supporting multiple wave species. Emphasis is placed on a self-consistent ray treatment which illustrates alternative methods for dealing with ray coupling at boundaries and with the presence of multiple wave types, either in a single layer or in adjacent regions. Both closed and open structures are analyzed, with discussion of the latter limited to modes with small leakage due either to duct inhomogeneities or to curvature. Examples include layered dielectric waveguides with a straight or circular axis, and compressible plasma waveguides which are illustrative of media wherein two wave species (electromagnetic and electroacoustic) can propagate.

Application of the ray-optical technique to dielectric-loaded rectangular waveguides

Abstract : The propagating electric fields in rectangular waveguides loaded by a homogeneous dielectric layer are evaluated using the ray-optical technique. The accuracy of the asymptotic solution is investigated and the results are shown to be in good agreement with the exact LSE sub mn-mode solution. It is concluded that, with this critical evaluation, more reliance can be placed on the accuracy of the method for other schemes for which no exact solutions are available for comparison. (Author)

Ray-optical techniques applied to antenna admittance theory

It is demonstrated that the admittance of thick tubular antennas can be accurately computed by using a ray-optical technique for finding the reflection from the end. The theory gives good results for a radius as small as 0.2 of a wavelength. The results are compared with a numerical solution by Chang [1].

Ray Optics-A Novel Approach to Scattering by Discontinuities in a Waveguide

Waveguide discontinuities are analyzed conventionally by techniques utilizing the induced field in the vicinity of the discontinuity for calculation of the distant reflected and transmitted field in the various modes. Evaluation of the induced field constitutes the major difficulty in the problem. By an alternative and novel approach explored in this paper, scattering by a discontinuity in a waveguide is deduced from a knowledge of its far zone (asymptotic) scattering properties in free space. In contrast to "small obstacle" techniques wherein similar concepts are utilized for isolated scatterers whose size is small compared to the free-space wavelength, the present procedure accommodates also large discontinuities such as strips, apertures, bifurcations, changes in cross section, etc. The description of various scattering processes is carried out naturally in terms of ray optics which provides at each stage of the calculation an interpretation of the associated physical mechanism. The procedure is illustrated for apertures, strips, and bifurcations in a parallel plane waveguide for which comparisons with exact solutions can be made. It is found that while the ray-optical technique is best suited to the high-frequency (multimode) regime far from modal cutoffs, it is capable of providing remarkable accuracy even in the range of propagation of only the dominant mode.