High frequency fields in the presence of a curved dielectric interface

A high-frequency line source in a dielectric medium that is separated by a concave cylindrical boundary from an exterior medium with lower dielectric constant generates a variety of wave phenomena which have been explored extensively. This problem is reexamined here with a view toward clarifying relevant reflection and transmission characteristics within the framework of ray optics, with emphasis on the more complicated transmitted field. The exterior domain is divided into illuminated and shadow regions separated by the transmitted tangent ray launched by a ray incident at the critical angle. Conventional ray optics is valid far from the tangent ray shadow boundary on the illuminated side. The shadow boundary is surrounded by transition regions wherein Fock type integrals and Weber functions yielding local lateral waves provide alternative representations. On the shadow side, not too far from the shadow boundary, the field can be interpreted via "tunneling" and subsequent radiation along a ray from a virtual caustic to the observer. The tunneling is associated with the initial evanescent decay of the transmitted field excited by a totally reflected incident ray. However, deeper inside the shadow, this mechanism is inapplicable, and the field is expressed either in terms of the Fock integrals or a creeping wave-type residue series. The results are presented in a format that permits insertion into a geometrical theory of diffraction (GTD) user's manual.     

Rays, Beams, and Modes Pertaining to the Excitation of Dielectric Waveguides

The two-dimensional problem of excitation of an inhomogeneous dielectric layer by a Gaussian beam is considered, with emphasis on useful representations that treat the field either in terms of multiple reflections or in terms of guided modes. A recently developed method is employed whereby the beam fields are generated from line source fields by assigning a complex value to the source coordinates. When applied to the asymptotic solution for the line source field, this procedure furnishes a simple and quantitative relation between line-source-excited ray optics and paraxial beam optics. It also clarifies the role of lateral ray and beam shifts for reflection at a boundary with incidence-angle-dependent reflection coefficient, especially when multiply reflected fields are converted into modal form. Results are given for beams which are reflected at both boundaries, reflected at one boundary and refracted before reaching the other boundary, and trapped by refraction without reaching either boundary. In the first case, conversion to modal form is more convenient at large distances whereas in the latter case, paraxial beam tracking is preferable.     

Radiation from a uniaxially anisotropic plasma half space

A line source of magnetic currents is located in a half space with uniaxially anisotropic dielectric constant, with the optic axis inclined at an arbitrary angle to the interface. This two-dimensional, scalar diffraction problem is solved by Fourier integral techniques, and the solution is examined in the asymptotic range of large distance from the source. The radiation field comprises incident, reflected and refracted ray contributions whose properties are determined from a study of the refractive index curves for the medium. In addition, there may exist a lateral wave which is excited by a critically refracted incident ray, and which sheds energy back into the anisotropic medium by refraction. If the medium is a plasma with an externally impressed infinite dc magnetic field, and if the source oscillates below the plasma frequency, there exist shadow regions from which the direct and reflected rays are excluded but which can be penetrated by the lateral waves.     

Fundamental and Higher Mode Inversion of Dispersed GPR Waves Propagating in an Ice Layer

Dispersion of ground-penetrating radar (GPR) waves can occur when they are trapped in a layer. In this paper, we analyze the modal propagation of GPR pulses through a layer of ice that is overlying water. Dispersed transverse electric (TE) waves that are trapped in the waveguide have larger amplitudes than the critically refracted waves that travel through air, whereas the transverse magnetic (TM) critically refracted waves traveling through air are more dominant than the trapped dispersed TM waves. This can be explained by the leaky waveguide behavior of the ice layer. The reflection coefficients for the waves incident on the ice-water interface show that the TM modes are more leaky than the TE modes. Still, clear dispersion is observed in both cases, which depends on the permittivity and thickness of the ice. Similar to inversion of dispersed Rayleigh waves, these parameters can be estimated by calculating phase-velocity spectra, picking dispersion curves, and inverting the dispersion curves using a combined local and global minimization procedure. Synthetic data show several higher order modes of which separate and combined inversions return the input modeling parameters accurately. Experimental data acquired on a frozen lake show strong dispersion for the TE and TM modes. The phase-velocity spectra of the field data show three TE and four TM modes of which separate and combined inversion of different modes return similar values for the ice thickness and known permittivity of ice. Due to the more leaky behavior of the TM modes, the TE inversion is better constrained and more suitable for inversion.     

Propagation of radio waves past a coast line with a gradual change of surface impedance

The amplitude and phase of a radio ground wave are calculated for an oblique crossing of a flat-lying coast line. The surface impedance is allowed to change in a continuous and gradual manner in the vicinity of the coast line. The earlier results for an abrupt boundary are recovered as the width of the transition zone is reduced to zero. In general, it is found that the presence of the transition region will not produce a significant modification of the transmitted field. On the other hand, the reflected waves and the behavior of the field near the coast line are profoundly influenced by the width of the transition. In particular, certain singular behavior of the field associated with an abrupt boundary is virtually eliminated when the transition zone has a finite width.     

Ray-Optical Calculation of Edge Diffraction in Unstable Resonators

A previously developed ray-optical theory for calculation of modal reflection and coupling coefficients due to edge discontinuities in homogeneously or inhomogeneously filled parallel-plane waveguides is generalized to waveguides with nonplanar boundaries. Treated in particular are the reflections from the open ends of a bilaterally truncated waveguide whose convex walls are confocal hyperbolas. This open configuration serves as a model for unstable optical resonators with cylindrical mirrors. The ray optically determined modal reflection and coupling coefficients for mirrors with large Fresnel number are shown to reduce to those in a previously employed local parallel-plane approximation when the Fresnel numbers are moderate. The analysis quantifies proposed ray-optical models for explaining the influence of edge diffraction on the behavior of the resonant modes.     

On superluminal tunneling

Photonic tunneling is currently of theoretical and applied interest. In a previous review, faster-than-light (i.e. superluminal) photonic tunneling was discussed (Progr. Quantum Electron. 21 (1997) 81). Recently, superluminal photonic pulse transmission and reflection have been measured at microwave and infrared frequencies. It seems clear that superluminal photonic and electronic devices will become a reality in the near future.

In the present report, we introduce new experimental and theoretical data on superluminal tunneling and reflection. Data of reflection by barriers have evidenced the nonlocal nature of tunneling. Asymmetric barriers have revealed a strange asymmetric reflection behavior in time.

The principle of causality is not violated by a superluminal speed even though the time duration between cause and effect can be shortened compared with a luminal interaction exchange. An empirical relationship independent of the barrier system is found for the photonic tunneling time. This relation seems to be universal for all kind of tunneling processes in the case of single opaque barriers. We show that the superluminal velocity can be applied to speed up photonic modulation and transmission as well as to improve microelectronic devices.     

Electromagnetic scattering from an inhomogeneous object by raytracing

A shooting and bouncing ray (SBR) formulation is presented for treating the electromagnetic scattering from electrically large, inhomogeneous objects. A dense grid of rays representing the incident plane wave is shot toward the inhomogeneous objects. At the scatterer boundary, reflected rays and refracted rays are generated due to the discontinuity of the medium parameters. The trajectory, amplitude, phase and polarization of the rays inside the inhomogeneous object are traced based on geometrical optics. Whenever the rays cross the scatterer surface, additional reflected/refracted rays are generated and are tracked. This is repeated until the intensities of the refracted/reflected rays become negligible. The contributions of the existing rays to the total scattered field are calculated using the equivalence principle in conjunction with a ray-tube integration scheme. The ray formulation is applied to calculate the backscattering from cylinders and spheres and good agreement with the exact series solutions is observed in the high-frequency range. In addition, the backscattering mechanisms in penetrable objects are interpreted in terms of simple ray pictures     

High-frequency (whispering-gallery mode)-to-beam conversion on a perfectly conducting concave-convex boundary

When a well-confined high-frequency (HF) whispering-gallery (WG) mode launched from the concave side of a concave-convex perfectly conducting boundary propagates toward the convex side, it becomes successively less confined and eventually detaches completely to form a radiated beam field. Detailed characterization of the intricate WG mode-to-beam conversion (here considered for the two-dimensional case) poses a challenging problem in HF wave propagation and asymptotics. This paper begins with a review of the accomplishments and shortcomings in previous investigations that dealt with the analytic-asymptotic aspects as well as the construction of numerical reference solutions to validate the HF approximations. We then develop algorithms based upon the earlier results, but with inclusion of new refinements. These yield a comprehensive asymptotic theory for the induced surface currents on the boundary as well as the near and far fields generated by them, well-matched to the WG mode detachment phenomenology and numerically accurate when compared with reference data obtained from a new hybrid analytic-numerical code. The asymptotic analysis makes use of Kirchhoff, physical optics, and spectral integral representations, WG modes on the concave side, modal ray tracing, replacing modal and/or ray caustics by equivalent induced source distributions, creeping waves on the convex side, etc., with self-consistent blending of nonuniform and locally uniform asymptotics through transition regions where transformations of the affected wavefields occur.     

Ray analysis of two-dimensional radomes

The fields transmitted from a line source through a two-dimensional curved dielectric layer of variable thickness are constructed by geometric-optical ray tracing that accounts for multiple reflections on the concave side, where the source is located, as well as for reflections between the layer boundaries. Moreover, internally trapped rays, excited by evanescent tunneling, are included when source and observer are near the layer boundaries but laterally displaced along it. By applying Poisson summation to the ray series, the multiple reflected contributions, for weakly tapered configurations, can be summed to yield trapped and leaky local modes guided along the layer, as well as a "collective" ray field that incorporates a plane layer transmission coefficient, with curvature and slope corrections, instead of the conventional coefficients for individual boundaries. Detailed calculations are performed for the special cases of a circularly curved layer of constant thickness and a tapered layer with nonparallel plane boundaries. For the former, the various ray-optically derived solutions agree completely with those obtained from a rigorous analysis. For the latter nonseparable configuration, no rigorous solution is available. With direct summation of conventional ray fields taken as a reference, extensive numerical results demonstrate the economies effected by the collective ray formulation and the importance of including the curvature or slope corrections in the equivalent slab transmission coefficients.     

Application of the impedance sheet concept to thin periodically varying dielectrics

The impedance sheet concept used to predict the transmission and reflection properties of thin dielectrics is extended to determine the transmission and reflection properties of thin periodically varying dielectrics. For plane-wave incidence, the effect of the periodic interface is to generate a higher order modal distribution on both sides of the boundary. It is shown that situations exist where the higher order modes can be strongly excited, and in fact can carry more power than the dominant transmitted mode. The frequency response of the dielectric is obtained and shown to be quite different than the homogeneous thin dielectric except at lower frequencies.     

Hybrid ray-mode parametrization of high frequency propagation in anopen waveguide with bilinear transverse bilinear transverse refractiveindex: numerical results and quality assessment

Numerical reference solutions are generated by summing a large number of trapped and leaky modes, and are then examined to identify observables. After confirming qualitatively that the much simpler and efficient ray parametrization models are the basic features of the observed signal, quantitative evaluations are performed to assess the capability of the hybrid ray-mode algorithm to recover all relevant features of the reference field with adequate accuracy and numerical efficiency. Such features include uniform corrections near isolated ray caustics, replacement of illegitimate ray fields (and their pileup of caustics in the surface boundary layer) by a few surface guided modes, and mode cluster substitution for the transitional ray field that grazes the profile slope discontinuity, and therefore splits into two beam-like fields refracted out of, and back into, the duct. For the development of the parametrizations see ibid., vol.39, no.6, p.780-8 (1991)     

Measurement of the core diameter of multimode graded-index fibers: A comparison of transmitted near-field and index profiling techniques

The core diameters of six graded-index fiber from four different fiber manufacturers were compared using the transmitted near-field (TNF), the refracted near-field (RNF), and the transverse-interferometric (TI) measurement methods. This study was part of an effort to develop a standardized, industry-wide definition of core diameter and to determine the precision of interlaboratory core-diameter measurements using different measurement techniques. For fibers with smooth index-of-refraction profiles, all three methods were in good agreement (< 1.0-mum difference). Substantial differences between the transmitted near field and the two profiling methods (RNF and TI) were observed for fibers having step structure near the core-cladding boundary. In an attempt to resolve these differences, splice-loss measurements were used as an indicator of diameter differences. These experiments suggested that curve-fitting routines should be applied to the two profiling methods. A comparison of the curve-fitted profile data with measured transmitted near-field data at points 2 percent above the baseline produced values for the diameters which agreed to within 1 μm for all of the fibers measured.     

Refraction of a uniform plane wave incident on a plane boundary between two lossy media

The expressions describing the modified propagation constants of the refracted nonuniform transmitted field, produced by a uniform plane wave incident on a plane boundary between two lossy media, are presented. Some examples under which the modified propagation constants must be used are illustrated to determine the limitations.     

Optical fiber characterization by simultaneous measurement of thetransmitted and refracted near field

An experimental setup is presented which permits, in a routine way for R&D purposes, simultaneous measurement of the transmitted near field at 1300 nm and 1550 nm, and the refracted near field at 820 nm. A new method for the calibration of the refractive index is proposed. The obtained accuracy for the refractive index is dn±0.0002. The reproducibility of measurements of geometrical parameters like the mode field diameter, the core and cladding diameters, and concentricity error, is ±0.1 μm. Measurements of the mode field as a function of polarization state for four different hi-bi fiber are presented     

Transmission into staggered parallel-plate waveguides

The modal field transmitted into a staggered parallel-plate waveguide when illuminated by a line source is studied. To widen the limited applicability of existing ray methods, an aperture field integration (AFI) method is developed, in which the field in the waveguide aperture is first calculated by high-frequency techniques (uniform asymptotic theory (UAT) and spectral theory of diffraction (STD)) and then decomposed into modal fields via the Fourier analysis. For problems in which the exact Wiener-Hopf and/or the ray solutions are available, AFI gives excellent numerical results. New results are staggered waveguides which find application in the analysis of a waveguide lens.     

Electromagnetic transmission of an oblique waveguide array

Transverse magnetic (TM) and transverse electric (TE) wave transmissions of an oblique parallel-plate waveguide array is studied. The scattered wave is represented in terms of continuous and discrete modes based on the Fourier transform and series, respectively. The tangential field continuities at the boundary are enforced to obtain simultaneous equations for the discrete modal coefficients. Residue calculus is utilized to transform the radiation field and reflection coefficient into numerically efficient forms. Numerical computations are performed to illustrate the behavior of wave radiation and reception by an oblique waveguide array.     

Scattering and radiation from a slitted parallel-plate withrectangular grooves: TE-wave

TE-wave scattering and radiation from a slitted parallel-plate waveguide with rectangular grooves is considered. The Fourier transform and the mode matching are used to represent the scattered field in terms of the continuous and discrete modes. The simultaneous equations for the discrete modal coefficients are obtained by matching the boundary conditions. The fast-converging series solutions are presented to evaluate the far-zone radiation, reflection, and transmission coefficients. The numerical computations illustrate the angular behavior of far-zone radiation in terms of the slit size, groove size, and operating frequency. The antenna radiation pattern of the slitted parallel-plate is measured and compared with theory     

Efficient reflection and transmission dyad multiplication for 3D geometrical optics

Electromagnetic fields are often calculated in indoor environments using geometrical optics and ray tracing. When a ray is reflected from a panel or transmitted through a panel, a ray-fixed coordinate system is used to decompose the field into transverse electric (TE) and transverse magnetic (TM) components, and 2/spl times/2 dyads are used to calculate the reflection and the transmission. The paper develops an efficient arrangement of the multiplications associated with multiple reflections and transmissions along a ray path to reduce the overall count of floating-point operations.     

Ray analysis of modal reflection for three-dimensional open-endedwaveguides

An efficient high-frequency ray analysis, which combines the geometrical theory of diffraction (GTD) with the equivalent current method, is used for evaluating modal reflection at the open ends of three-dimensional waveguides. After reviewing a method used for the two-dimensional case and introducing some extensions necessary for evaluating modal reflection of open-ended three-dimensional waveguides, the modal reflection coefficients are then given for open-ended circular and rectangular waveguides. Numerical results calculated using these expressions agree favorably with those obtained by a different analytical technique and by experiment