Lorentz Reciprocity Theorem Research Articles

Radiative absorption, fluorescence, and scattering of a classical dipole near a lossless interface: a unified description

A simple input–output formalism based on the Lorentz reciprocity theorem is presented for the study of a classical radiating dipole near a lossless interface. The problems of dipole absorption, fluorescence, and scattering are considered in a unified description, and the effects of the interface (a simple dielectric here) are shown to be broadly twofold. First, the channeling of radiation into and out of the dipole is modified. Second, the intrinsic dipole polarizability is found to be modified, leading to an effective absorption (or scattering) cross section that depends on the states of both the dipole and the driving field. These results are particularly applicable to studies involving evanescent-wave microscopy.

Analysis of plasmon resonance and surface-enhanced Raman scattering on periodic silver structures

Surface plasmon excitation and surface-enhanced Raman scattering (SERS) are investigated for periodic grating-type substrates such as binary silver gratings and silver gratings on silica. Electromagnetic near fields are calculated by an efficient implementation of a Rayleigh-expansion technique for rectangular-groove gratings. Far-field signals of Raman-active molecules adsorbed at the grating surface are determined by application of the Lorentz reciprocity theorem. SERS enhancement factors are considered for different types of gratings and for structures with different dimensions with respect to both the intensity and angular width of the emitted Stokes light. Thus, consideration of plasmon resonance widths leads to optimum structures for periodic SERS substrates if realistic experimental configurations involving a lens for detection are taken into account. For binary silver gratings, optimum grating depths of more than 80 nm are proposed for SERS measurements in a realistic experimental configuration, whereas maximum SERS signals are emitted into a single direction at shallow gratings with depths between 10 nm and 20 nm. Furthermore, silica gratings with isolated silver layers are superior to binary silver gratings. Due to both the large intensity and angular width of the emitted signals, SERS enhancement factors are additionally increased on such structures.

Eddy current probe impedance due to a flaw: The influence of phase-shifted fields

An approximate formula for the change in impedance of an eddy current two-coil probe situated above a conducting medium with a volumetric flaw is derived in this paper. The primary field is generated by the superposition of two phase-shifted alternating currents of the same frequency. The Lorentz reciprocity theorem and a layer approximation are used to obtain the change in impedance. Numerical results for different values of the phase difference are presented. These results can be used for developing more selective eddy current testing methods.

General constraints on the propagation of complex waves in closed lossless isotropic waveguides

Complex propagation in linear time-invariant lossless isotropic closed waveguides is a theoretically intriguing subject. Complex modes are also practically important in the characterization of discontinuities as they contribute in pairs with complex conjugate (c.c.) propagation constants to local power storage. By the systematic application of Lorentz's reciprocity theorem, we derive the constraints linking complex propagation constant, Poynting's integral, and electromagnetic energy storage per unit length. Previously known conditions are recovered, and novel constraints on the exchange power between the two components of the pairs are derived. It is emphasized that existing relationships individually derived by different methods and scattered in the literature, as well as novel ones, are derived from a single fundamental theorem. This set of constraints is believed to pose the tightest necessary conditions so far for the existence of complex waves.

Coupled-mode analysis of highly asymmetric directional couplers with periodic perturbation

This paper presents an in-depth analysis of highly asymmetric grating assisted directional couplers. The directional coupler consists of a polymer waveguide with dimensions and refractive indices closely matching a single-mode fiber fabricated atop a Ga/sub 0.6/Al/sub 0.4/As/GaAs/Ga/sub 0.4/Al/sub 0.6/As waveguide. The structure is investigated analytically by means of a new orthogonal coupled-mode theory formulated in terms of the Lorentz reciprocity theorem. For the first time, the analysis includes three distinct loss mechanisms, namely, the leakage of power toward the semiconductor substrate, the power lost to radiation modes (mode mismatching), and the grating radiation loss.

Microstripline- and stripline-fed aperture-coupled cylindrical rectangular microstrip antennas

Stripline-fed and microstripline-fed aperture-coupled cylindrical rectangular microstrip antennas are investigated. The equivalence principle is invoked to separate the feedline and the antenna patch with equivalent magnetic currents distribution on the aperture region. The Lorentz reciprocity theorem is applied to find the interactions between the aperture and the feedline. The unknown patch current and aperture field are determined by solving coupled integral equations, which involve spectral-domain Green's functions, using Galerkin procedure. Numerical results of input-impedance and far-field patterns are compared with those for antennas on a planar surface.

On the Eigenfunction Expansions of the Dyadic Green's Functions for Bianisotropic Media

This paper presents a novel approach for constructing the complete eigenfunction expansions of electric and magnetic dyadic Green's functions for general linear bianisotropic media. The eigenfunctions are expressed in terms of linear combinations of commonly employed solenoidal and irrotational vector wave functions. Based on the theory of distributions, the source point singularities required for complete expansions of the dyadic Green's functions are derived directly from Maxwell dyadic equations without any integration. Apart from the singularities, the discontinuities associated with the eigenfunction expansions across the source point are also obtained as by-products. These discontinuity relations constitute the fundamental equations from which the eigenfunction expansions outside the source point can be constructed. This approach is parallel to the utilization of Lorentz reciprocity theorem for relating eigenwaves with sources and it is applicable directly to both nonreciprocal as well as reciprocal media. Furthermore, the discontinuity relations also yield directly the jump conditions for electric and magnetic fields across a current sheet.

Impedance characteristics of a slot antenna fed by a parallel-plate waveguide

A theoretical model to analyze the impedance and radiation characteristics of a slot fed by a parallel-plate waveguide is presented. The slot is excited by a TEM mode propagating between the parallel plates and its effect is simulated by a series impedance in a transmission line. Its value is computed with the use of the Lorentz reciprocity theorem, whereas the radiation pattern is determined from the radiation of an equivalent magnetic current embedded in an infinite conductive surface. Experimental results on a prototype are given to validate the theoretical model. The data fit the predicted results well. © 1997 John Wiley & Sons, Inc. Microwave Opt Technol Lett 14, 126–128, 1997

Offset coupling between Gaussian beam and the fundamental mode of weakly guiding step‐index fibers

The transmitted power coefficient of a harmonically oscillating Gaussian beam into the HE11 mode of a transverse offset weakly guiding fiber of step index profile is represented as an integral of the coupling power density over all the spectral components of the beam. This coupling of a complex power density into the fundamental mode of a fiber which takes into account the Fresnel losses is expressed in closed form by using a vectorial analysis: normal mode method, the field equivalence principle, the Lorentz reciprocity theorem and the translational addition expressions for the cylindrical functions. Numerical results of the transmitted power coefficient are presented for various normalized frequency parameter V, transverse offset R, and different launching distance d.

Internal dynamics of multilevel atoms near a vacuum-dielectric interface.

We show how the internal dynamics of a multilevel atom are modified in the vicinity of the interface between a vacuum and a simple or multilayered lossless dielectric medium. Optical Bloch equations are derived, which take into account the modifications of spontaneous emission rates and energy levels experienced by the atom. van der Waals level shifts are evaluated using the method of images for dielectrics. Spontaneous emission rates and radiation patterns are calculated in a simple way using the Lorentz reciprocity theorem. \textcopyright{} 1996 The American Physical Society.

Coupling characteristics of eccentric arranged dielectric disk and ring

An analysis is presented for a novel coupling configuration in which a circular dielectric disk and ring are arranged eccentrically. Whispering gallery (WG) mode coupling characteristics between the dielectric disk and ring are investigated. In this paper, a coupled-mode equation based on the Lorentz's reciprocity theorem is utilized. Distributed coupling coefficients and electric field distributions around the coupling region are obtained numerically through solving the coupled-mode equation. The theory described in this paper is confirmed by comparing measured electric field distributions with calculated ones. Electromagnetic powers flowed along the disk are also calculated. It is shown that coupling quantity of the eccentric configuration would be easily controlled by changing a radius of the disk or ring. The results obtained here will be used to design a WG mode coupled resonator for millimeter wave integrated circuits.

High-frequency reciprocity-based circuit model for the incidence of electromagnetic waves on general waveguide structures

In the present contribution we construct a high-frequency circuit model for the excitation of eigenmodes in general waveguides due to externally impinging electromagnetic waves. The circuit model, consisting of distributed sources in a transmission line model, is based on Lorentz's reciprocity theorem. The classical quasi-TEM solution of this problem is found as a special case from the full-wave model. The theory is illustrated with numerical examples of electric dipoles radiating above thick coupled lossy microstrip lines. >

The reciprocity and power conservation principles for boundary conditions on a semitransparent surface

Generalized boundary conditions of coupling on a semitransparent surface are valid only if the Lorentz reciprocity theorem and the electromagnetic power conservation principle are satisfied on the surface with these boundary conditions. These criteria are reformulated as relations between the tensors in the boundary conditions. Some known boundary conditions of coupling are considered.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The Lorentz reciprocity theorem and range-dependent propagation modeling

Modeling of electromagnetic propagation in the troposphere has been advanced in the last decade to the point where both the vertical and horizontal variation of refractivity can be accommodated readily. A hybrid ray-optics/parabolic equation model is utilized to predict propagation loss for a range-varying refractive structure to demonstrate the model obeys the Sommerfeld-Pfrang statement of the Lorentz reciprocity theorem. >

On the electromagnetic dyadic Green's functions for planar multi-layered anistropic uniaxial material media

A complete, plane-wave spectral, vector-wave function expansion of the electromagnetic, electric, and magnetic, dyadic Green's function for electric, as well as magnetic, point currents for a planar, anisotropic uniaxial multi-layered medium is presented. It is given in terms ofz-propagating, source-free vector-wave functions, where ž is normal to the interfaces, and it is developed via a utilization of the Lorentz reciprocity theorem. The electromagnetic dyadic Green's function for periodic electric as well as magnetic point current sources is also presented. Some salient features of the Green's dyadics, along with a physical interpretation are also described.

On the dyadic Green's function for a planar multilayered dielectric/magnetic media

A complete plane wave spectral eigenfunction expansion of the electric dyadic Green's function for a planar multilayered dielectric/magnetic media is given in terms of a pair of the (z)-propagating solenoidal eigenfunctions, where (z) is normal to the interface, and it is developed via a utilization of the Lorentz reciprocity theorem. This expansion also contains an explicit dyadic delta function term which is required for completeness at the source point. Some useful concepts such as the effective plane wave reflection and transmission coefficients are employed in the present spectral domain eigenfunction expansion. The salient features of this Green's function are also described along with a physical interpretation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Reciprocity, discretization, and the numerical solution of direct and inverse electromagnetic radiation and scattering problems

The author gives a formulation, based on Lorentz reciprocity, that unifies the finite element method (FEM) and the integral equation models. Wave propagation and scattering problems in electromagnetics have to be addressed with the aid of numerical techniques. Many of these methods can be envisaged as being discretized versions of appropriate weak formulations of the pertinent operator (differential or integral) equations. For the relevant problems as formulated in the time Laplace-transform domain it is shown that the Lorentz reciprocity theorem encompasses all known weak formulations, while its discretization leads to the discretized forms of the corresponding operator equations, in particular to their finite-element and integral-equation modeling schemes. Both direct (forward) and inverse problems are discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Variable geometry capacitive probes for multipurpose sensing

A capacitive array for robotic proximity and feature sensing has been designed, modeled, and tested. The basic probe consists of alternating metallic strip electrodes. One set of strips makes up the drive plate. The other set consists of tiny receivers. Both sum and differential modes of operations are used to allow one to detect proximity and features, respectively. Modeling has encompassed calculation of admittance changes (ΔY) due to the introduction of materials with simple geometric configurations. The theory is developed in detail using the Lorentz reciprocity theorem. The relationship between the spatial frequency of the probe electrodes and the interrogation field penetration is also discussed. Testing has involved scanning a two-port configured probe system over a test piece with known features and flaws. Four capabilities of the probe have been examined: distance ranging, edge detection, field optimization (changing the electric field pattern of the probe to enhance output signal), and complex pattern recognition (filtering). Both dielectric and metal objects have been investigated.

Radiation from oscillating dipoles embedded in a layered system

Maxwell’s equations are solved for the radiation due to a source consisting of an oscillating point dipole located in a layered system. Solutions are developed first for the related problem of the fields generated in the system by a distant dipole source, and the problem of interest is then solved by application of the Lorentz reciprocity theorem. The effects of extremely thin layers are considered in detail. Some of the results are illustrated by calculations of the emission from dipoles located in, or near, a film covering a plane-bounded silver metal substrate. It is found that the surface selection rule for absorption, emission, or Raman scattering is not valid for molecules contained in this film.

Fields in extended cavity lasers

The electromagnetic fields for an extended-cavity laser are described precisely and in detail. The extended-cavity laser consists of a semiconductor laser diode with a partially reflecting coating on one facet and an antireflection coating on the other coupled by radiation through a lensed-fiber, single-mode guide to another partially reflecting coating terminating a narrow-wavelength filter. The formulation is based on the Lorentz reciprocity theorem, the fields are described by angular plane-wave spectra, and the equivalent transmission line representation is used to determine the fields reflected and transmitted by partially reflecting and antireflection coatings. The design of antireflection coatings is considered in detail, and a formula which gives the optimum distance from the diode antireflection coating to an inline lensed fiber is derived.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>