The Reflection of electromagnetic waves from almost periodic structures

We investigate the reflection of electromagnetic waves from structures charaterized by a spatially varying dielectric permittivity of an almost periodic nature. The reflection from almost periodic structures is compared and contrasted with the reflection from periodic structures. Paradoxically, it is found that almost periodic structures may prove superior to their periodic counterparts when these structures are used as filters. The major portion of this work was performed while the author was with the California Institute of Technology, Pasadena, California 91125, USA     

Interface extinction and subsurface peaking of the radiation pattern of a line source

The radiation pattern of a line source lying along the plane interface of two dielectric half-spaces is calculated. It is found that the pattern at the interface has a null (interface extinction); that the pattern in the upper half-space, whose index of refraction is taken to be less than that of the lower half-space, has a single lobe with a maximum normal to the interface; and that the pattern in the lower half-space (subsurface region) has two maxima (peaks) straddling symmetrically a minimum. Interpretation of these results in terms of ray optics, Oseen's extinction theorem, and the Cerenkov effect are given.     

Waves in an active medium guided by a reactive surface with reactance of gain modulation

The characteristics of surface waves (i) in a passive medium supported by a passive surface with reactance modulation and an active surface with the modulation of either the reactance or the negative resistance, and (ii) in an active medium supported by a passive surface with a reactance modulation are investigated with emphasis on the band regions. The periodic variation is sinusoidal and is in the propagation direction. For a passive medium terminated by a passive surface with a reactance modulation, there are stop bands in frequency for the surface waves and the structure of the first two stop bands is analyzed. For a passive medium terminated by an active surface and for an active medium terminated by a reactance-modulated passive surface, the characteristics of the absolute instabilities occurring in the first-order band are examined. The nature of the convective instability taking place in the second-order band for an active medium terminated by a reactance-modulated surface is discussed. Analytical expressions for the frequency shift of the second-order band are deduced. The Floquet theory is used to obtain the exact dispersion relation in the form of a continued fraction which is analyzed by singular expansions.     

Higher-order wave interactions in a periodic medium

A singular perturbation analysis of the interaction of the fundamental plane wave progressing in the direction of the sinusoidally varying permittivity of an unbounded medium with the first four space harmonics progressing in the reverse direction is carried out. The periodic inhomogeneity introduces self and mutual interaction phenomena. The self interaction, in general, produces a phase shift and causes the mutual interaction to occur for frequencies higher than those predicted by the Bragg condition. The mutual interaction introduces a complex change in the wavenumber resulting in the interacting waves becoming evanescent. Analytical expressions for the frequency shift and the other wave characteristics in the interaction region are deduced. With the increase in the order of the interaction, the frequency shift becomes a more dominant effect than the wave evanescence.     

On electromagnetic waves in chiral media

We analyze the propagation of electromagnetic waves through chiral media, i.e., through composite media consisting of macroscopic chiral objects randomly embedded in a dielectric. The peculiar effects that such media have on the polarization properties of the waves are placed in evidence. To demonstrate the physical basis of these effects, a specific example, chosen for its analytical simplicity, is worked out from first principles.     

Some remarks on the classical electrodynamics of moving media

Extension of Maxwell's electrodynamics of media at rest to moving bodies is hampered by a basic difficulty: how to determine the excitation sources and the fields inside a body which is moving relative to the laboratory where the measurements are performed. In this paper various approaches are analyzed and interpreted from a point of view not previously emphasized, i.e., theoretical results are directly related to the Röntgen-Eichenwald experiments and to the phenomenon of unipolar induction. Practical difficulties associated with possible processes of measurement are pointed out.     

Asymmetric first-order Bragg interactions in an active dielectric waveguide

The asymmetric first-order Bragg interactions in an active planar dielectric waveguide are investigated for the case of even TE modes. Either the index or the gain is assumed to have a sinusoidal variation in the propagation direction. By a singular perturbation procedure using multiple space scales, the coupled-mode equations governing the nature of the Bragg interactions are systematically deduced and the characteristics of this instability are examined. For the gain-modulated waveguide having an average loss, there are two threshold values for the modulation index of the gain, one for absolute instability and the other for traveling wave amplification, and these threshold values are deduced. Representative numerical results are presented to illustrate the characteristics of the Bragg interactions.     

TM-mode coupling in anisotropic optical waveguides caused by periodic variation optic-axis direction

The problem of mode coupling caused by a small periodic variation of the opticaxis direction in an anisotropic optical waveguide is reduced to a pair of coupled differential equations and an expression for the coupling coefficient is given. For a periodically perturbed section of the waveguide the coupled-mode equations are solved subject to suitable boundary conditions, and the coupling between the forward TM mode and the backward TM mode is analysed. A perturbed section of an anisotropic waveguide acts as a frequency selective reflection filter for TM modes only.     

TE-TE mode coupling at oblique incidence in a periodic dielectric waveguide

The characteristics of reflection of a TE mode into another TE mode in a planar dielectric waveguide with a sinusoidally modulated index are investigated for the general case in which the wavevectors are not aligned with the grating vector. A singular perturbation procedure is used to deduce the asymptotically exact coupled mode equations which govern the interaction. An analysis of the coupled-mode equations has shown the existence of the Brewster phenomenon at the angle of incidence θ_iB=45°. For angles of incidence sufficiently greater than the Brewster angle, the reflection coefficient can be considerably larger than that for the normal incidence. In the spectral response curves of the reflection coefficient, a higher maximum and a smaller base bandwidth are possible for the oblique incidence as compared to that for the normal incidence. The angular sensitivity of the reflection characteristics increases as the angle of incidence changes from the normal incidence to the grazing incidence.     

On the application of symmetrization to the transmission of electromagnetic waves through small convex apertures of arbitrary shape

The transmission of an electromagnetic wave through a small aperture in a perfectly conducting screen is examined from the viewpoint of symmetrization.     

An application of isoperimetric inequalities to the transmission of scalar waves through small apertures

Isoperimetric inequalities bound the exact solution of complicated boundaryvalue problems through the use of certain simple geometric quantities. As an example of this concept, we propose bounds on the scalar (acoustic) transmission coeficient which characterizes a small aperture of arbitrary shape. These bounds depend solely on the area and perimeter of the aperture. The plausibility of the bounds is demonstrated through the evaluation of several known solutions. Results are noted for apertures in both flexible and rigid screens and these results are compared and contrasted with those of the corresponding vector (electromagnetic) problem.     

The Green's function moment method

This paper develops a modified moment method for the numerical solution of two “Pocklington Type” integral equations. The first equation arises from the problem of scalar diffraction through a slot; the second from scattering by a straight, thin-wire. Numerical results and comparison with a more conventional method are given.     

Mechanical forces and torques associated with electromagnetic waves

Mechanical forces and torques associated with electromagnetic waves impinging on several objects are computed. The incoming radiation can be linearly or circularly polarized, thus carrying linear and angular momenta. The objects are matched dipoles in several configurations and a metal sphere. Numerous interesting results are obtained.     

The impact of higher-order bragg terms on radar sea return

Summary The possibility that radar sea return observed using aKu band fan beam Doppler airborne scatterometer flown over crude oil artificial spills might have been back-scattered via the second-order Bragg interaction is surmised. An attempt is made to justify the absence of the first-order Bragg term.

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Riassunto Prendendo in considerazione l'effetto dei primi ordini di Bragg e sopprimendo il ter mine di ordine 1, si mostra come l'inesplicato andamento dell'eco del mare in presenza di film di spandimento, rilevato con radar doppler in bandaKu montato su aereo, coincida con misure effettuate altrove in presenza di analogo film. Si propone una teoria secondo cui l'assenza del primo ordine è dovuta ad una carenza dell'onda capillare pertinente.

     

Singularity expansions for cylinders of finite conductivity

A new rigorous differential formulation to compute the scattering matrix of an obliquely oriented cylinder of finite conductivity and arbitrary shape is given. The analytic continuation of the scattering operator is examined in the frequency domain as well as in the propagation constant domain. The corresponding computer program is able to compute the singularity expansion for such a cylinder, as well as the propagating mode along it. Numerical examples are given.     

Symmetry group and natural resonances for a cylinder of finite conductivity

The connection of the natural resonances and the symmetry group of the cross-section of the diffracting-cylinders is established. As is done in spectroscopy, selection rules for the propagation directions of the diffracted field are deduced. Some remarks about the case of propagating modes along a dielectric rod are also made.     

The threshold of subharmonic parametric excitation in the bragg gap of a periodic structure

Methods of excitation of the subharmonic whose frequency lies within the forbidden band gap of a periodic structure are discussed. The dependences of threshold values of in-phase pumping on structure parameters are found.     

Nondiffracting beams in periodic media

We identify nondiffracting beams in two-dimensional periodic systems, exhibiting symmetry properties and phase structure characteristic of the band(s) they are associated with.