Ben Z. Steinberg

On the use of wavelet expansions in the method of moments (EM scattering)

An approach which incorporates the theory of wavelet transforms in method-of-moments solutions for electromagnetic wave interaction problems is presented. The unknown field or response is expressed as a twofold summation of shifted and dilated forms of a properly chosen basis function, which is often referred to as the mother wavelet. The wavelet expansion can adaptively fit itself to the various length scales associated with the scatterer by distributing the localized functions near the discontinuities and the more spatially diffused ones over the smooth expanses of the scatterer. The approach is thus best suited for the analysis of scatterers which contain a broad spectrum of length scales ranging from a subwavelength to several wavelengths. Using a Galerkin method and subsequently applying a threshold procedure, the moment-method matrix is rendered sparsely populated. The structure of the matrix reveals the localized scale-fitting distribution long before the matrix equation is solved. The performance of the proposed discretization scheme is illustrated by a numerical study of electromagnetic coupling through a double-slot aperture. >

Spectral analysis of focus wave modes

The focus wave mode (FWM), which is a time-dependent beam field that propagates at the speed of light without dispersion and retains its shape in space, is an interesting wave object with possible implications for synthesizing focused fields under transient conditions. To explore this potential, it is necessary to understand fully the properties of this wave field. It is already known that the FWM is a homogeneous solution of the wave equation, which is related in a special way to the field of a source moving on a complex trajectory parallel to the real axis of propagation. This suggests that there may be a connection between the FWM and the conventional free-space Green’s function. It is shown here that the FWM is related, in fact, to a source-free combination of causal and anticausal free-space Green’s functions and that one can formulate a bilateral transform pair relating these solutions. This new representation is then analyzed by using the spectral theory of transients to establish the properties of the FWM in terms of a distribution of transient plane waves. The spectral decomposition in the spatial wave-number domain reveals that the FWM is synthesized by both forward- and backward-propagating plane waves that are restricted to the visible spectrum. Asymptotic considerations show that the dominant mechanism is constructive interference of the backward-propagating waves. Taken together, the Green’s-function and spectral approaches grant further insight into the physical and spectral properties of the FWM. The conclusions cast doubt on the possibility of embedding the FWM within a causal excitation scheme.

Phase-space beam summation for time-dependent radiation from large apertures : continuous parameterization

We extend the study of alternative phase-space formulations of time-harmonic radiation from extended but truncated aperture source distributions to the time domain. Included are nonwindowed continuous forms spanning the space–time (configuration) domains, wave-number-frequency (spectrum) domains, and windowed (local beam-type) continuous forms. Synthesized in the frequency domain by nonwindowed or windowed Fourier transforms, field synthesis in the time domain involves nonwindowed or windowed radon transforms combined with the theory of analytic signals. Because the properties of suitable wave objects used in the analysis and synthesis of the field are strongly tied to relevant configurational and spectral parameters, the incorporation of these aspects into the various formats is referred to as phase-space parameterization. In the continuous parameterization the resulting time-dependent field radiated from the aperture is expressed as a superposition of pulsed beams whose phase-space parameters are their initiation time, initiation location, and initial direction. The properties of these formulations are discussed in detail, within a rigorous format and also with more physically transparent asymptotic approximations. As in the time-harmonic case, major stress is placed on localization in the phase space, which is achievable with various alternatives, and on the corresponding implications. Specific examples include analytic δ windows that yield as propagators complex-source pulsed beams, and numerical implementation of field synthesis for nonfocused and focused pulsed aperture distributions.

Rotation-induced superstructure in slow-light waveguides with mode-degeneracy: optical gyroscopes with exponential sensitivity

We study wave propagation in a rotating slow-light structure with mode degeneracy. The rotation, in conjunction with the mode degeneracy, effectively induces superstructure that significantly modifies the structures dispersion relation. It is shown that a rotation-dependent stop band is formed in the center of the slow-light waveguide transmission curve. A light signal of frequency within this stop band that is excited in a finite-length section of such a waveguide decays exponentially with the rotation speed and with the coupled resonator optical waveguides total length or total number of degenerate microcavities. This effect can be used for optical gyroscopes with exponential-type sensitivity to rotation.

Phase-space beam summation for time-harmonic radiation from large apertures

Analytical modeling of high-frequency time-harmonic and transient radiation from extended aperture sources and of propagation of the resulting fields through perturbing environments is facilitated by simultaneous use of configurational (space-time) and spectral (wave number–frequency) information for suitably defined synthesizing wave objects. Such a bilateral approach can be embodied within a configuration-spectrum phase space. The present investigation deals with radiation from extended aperture sources, with emphasis on alternative uses of the phase space at high frequencies, on promising wave objects as basis elements for field synthesis, and on extraction of physical information from exact wave solutions by asymptotic methods. Of special interest are beam-type wave objects that exhibit localization in the phase space because localized wave fields have favorable propagation characteristics in complex external environments. In this paper, alternative phase-space parameterizations are applied to time-harmonic plane aperture distributions and to the corresponding fields radiated into a homogeneous half-space. The parameterizations include nonwindowed continuum versions, in which localization occurs asymptotically through constructive interference; windowed continuum versions, in which localization is embedded inherently; and windowed discretized versions, in which the basis elements are situated on a self-consistent configuration–wave number lattice. By analysis and illustrative examples, it is shown how these alternative formulations are interrelated, how the localization around well-defined regions in the phase space takes place in each formulation, and how these localization properties, through the beam propagators, influence the synthesis of the radiation field. Transient phenomena will be addressed in separate publications.

Spectral analysis of complex-source pulsed beams

By assigning complex values to the source coordinates and pulse-initiation time of the time-dependent Green function in free space, one may generate a field solution that behaves like a propagating pulsed beam. Although the conventional pulsed line source response is known in closed form, the complex extension cannot be performed directly thereon because of the nonanalytic behavior of the causal field. The analytic continuation is carried, out here by spectral analysis and synthesis, utilizing the recently formulated spectral theory of transients. This approach not only guarantees uniqueness but also elucidates the spectral content of the resulting waveform, which is composed of contributions from singularities in the complex spectral wave-number plane. By similar analytic extension of time-dependent Green functions for more complicated environments, one may construct directly the transient field produced in these environments by the incident pulsed beam.

Magnetized Spiral Chains of Plasmonic Ellipsoids for One-Way Optical Waveguides

When a linear chain of plasmonic nanoparticles is subject to longitudinal magnetic field, it exhibits optical Faraday rotation. If the magnetized nanoparticles are plasmonic ellipsoids arranged as a spiral chain, the interplay between the Faraday rotation and the geometrical spiral rotation (structural chirality) can strongly enhance nonreciprocity. This interplay forms a waveguide that permits one-way propagation only, within four disjoint frequency bands, two bands for each direction.

Splitting of microcavity degenerate modes in rotating photonic crystals—the miniature optical gyroscopes

A manifestation of the Sagnac effect in a rotating photonic crystal that contains a microcavity with degenerate modes is explored. It is shown that generally rotation can cause the resonance frequency to split into M different frequencies, where M is the order of the stationary-system mode degeneracy. The results are derived using a new rotation-induced eigenvalue theory that holds for any two-dimensional or three-dimensional rotating microcavity with mode degeneracy. Comparison with exact numerical simulations of the rotating system is provided. Miniature optical gyroscopes are discussed.

Longitudinal chirality, enhanced nonreciprocity, and nanoscale planar one-way plasmonic guiding

(Received 24 January 2012; revised manuscript received 26 June 2012; published 16 July 2012)When a linear chain of plasmonic nanoparticles is exposed to a transverse dc magnetic field, the chain modesare elliptically polarized in a single plane parallel to the chain axis; hence, a new chain mode of longitudinalplasmon rotation is created. If, in addition, the chain geometry possesses longitudinal rotation, e.g., by usingellipsoidal particles that rotate in the same plane as the plasmon rotation, strong nonreciprocity is created. Thestructure possesses a new kind of chirality—longitudinal chirality—and supports one-way guiding. Since allparticles rotate in the same plane, the geometry is planar and can be fabricated by printing leaflike patches on asingle plane. Furthermore, the magnetic field is significantly weaker than in previously reported one-way guidingstructures. These properties are examined for ideal (lossless) and lossy chains.DOI: 10.1103/PhysRevB.86.045120 PACS number(s): 41

Electromagnetic complex source pulsed beam fields

Vector electromagnetic pulsed beam fields are constructed by using current dipoles located at complex coordinate points. As in the scalar case, the direction, collimation, and directivity of the field are determined essentially by the imaginary displacement of the source coordinate. The vector fields also depend on the polarization of the dipole with respect to the beam axis. The properties of the field for two special cases in which the dipole is directed either along or transverse to the beam axis are examined analytically and numerically. The general polarization case is thereby considered as a superposition of these two special cases. As expected, the strongest radiation is achieved when the dipole is directed transverse to the beam axis. >