Generalized Reciprocity Theorem Research Articles

The radiation from ultrafast point dipoles, moving uniformly near chiral media

The article discusses the features of the radiation of ultrafast point clusters of charged particles moving uniformly near a gyrotropic medium interface. It is shown that some types of electromagnetic radiation – transient and/or Cherenkov radiation – have the characteristics of superchiral fields. Therefore, they can be effectively used to study chiral structures (for example, to detect circular dichroism, the frequency characteristics of refractive indices), various materials, including biomaterials. Ultrafast (relativistic) particles can serve as a «tool» not only for studying the structure of various materials. They can also be used as «generators» of quasiparticles that determine the «dynamic» properties of the materials under study, as well as the features of their interaction with radiation of various nature and response to external influences. In this paper, some types of circularly polarized EM waves propagating in optically active (magnetoactive, naturally active, gyrotropic, and chiral) media are considered. Using the generalized reciprocity theorem for media characterized by the Hermitian permittivity tensor, we consider the transient and Cherenkov radiation excited by a uniformly moving bunch of charged particles when it crosses (or moves along) the interface of media, one of which is an optically active gyrotropic medium. It is shown that the superchiral electromagnetic fields of the transition and Cherenkov radiation of dipoles can serve as a source of chiral collective excitations in magnetoactive and naturally active media. The investigated mechanisms of interaction of electromagnetic radiation with chiral materials (structures and media) are one of the possible physical approaches to solving the problem of the chiral purity of the biosphere and to elucidate the factor of deracemization of the organic primeval environment. A new hypothesis is presented, suggesting that ultra-high-speed clumps of charged particles of cosmic origin can cause deracemization of the prebiosphere.

Theoretical constraints on reciprocal and non-reciprocal many-body radiative heat transfer

We study the constraints on reciprocal and non-reciprocal many-body radiative heat transfer imposed by symmetry and the second law of thermodynamics. We show that the symmetry of such a many-body system in general forms a magnetic group, and the constraints of the magnetic group on the heat transfer can be derived using a generalized reciprocity theorem. We also show that the second law of thermodynamics provides additional constraints in the form of a nodal conservation law of heat flow at equilibrium. As an application, we provide a systematic approach to determine the existence of persistent heat current in arbitrary many-body systems.

Realizing total reciprocity violation in the phase for photon scattering

Reciprocity is when wave or quantum scattering satisfies a symmetry property, connecting a scattering process with the reversed one. While reciprocity involves the interchange of source and detector, it is fundamentally different from rotational invariance, and is a generalization of time reversal invariance, occurring in absorptive media as well. Due to its presence at diverse areas of physics, it admits a wide variety of applications. For polarization dependent scatterings, reciprocity is often violated, but violation in the phase of the scattering amplitude is much harder to experimentally observe than violation in magnitude. Enabled by the advantageous properties of nuclear resonance scattering of synchrotron radiation, we have measured maximal, i.e., 180-degree, reciprocity violation in the phase. For accessing phase information, we introduced a new version of stroboscopic detection. The scattering setting was devised based on a generalized reciprocity theorem that opens the way to construct new types of reciprocity related devices.

Dynamics of a microorganism in a sheared viscoelastic liquid.

In this paper, we investigate the dynamics of a model spherical microorganism, called squirmer, suspended in a viscoelastic fluid undergoing unconfined shear flow. The effect of the interplay of shear flow, fluid viscoelasticity, and self-propulsion on the orientational dynamics is addressed. In the limit of weak viscoelasticity, quantified by the Deborah number, an analytical expression for the squirmer angular velocity is derived by means of the generalized reciprocity theorem. Direct finite element simulations are carried out to study the squirmer dynamics at larger Deborah numbers. Our results show that the orientational dynamics of active microorganisms in a sheared viscoelastic fluid greatly differs from that observed in Newtonian suspensions. Fluid viscoelasticity leads to a drift of the particle orientation vector towards the vorticity axis or the flow-gradient plane depending on the Deborah number, the relative weight between the self-propulsion velocity and the flow characteristic velocity, and the type of swimming. Generally, pullers and pushers show an opposite equilibrium orientation. The results reported in the present paper could be helpful in designing devices where separation of microorganisms, based on their self-propulsion mechanism, is obtained.

Locomotion of a microorganism in weakly viscoelastic liquids.

In the present work we study the motion of microorganisms swimming by an axisymmetric distribution of surface tangential velocity in a weakly viscoelastic fluid. The second-order fluid constitutive equation is used to model the suspending fluid, while the well-known "squirmer model" [M. J. Lighthill, Comm. Pure Appl. Math. 5, 109 (1952); J. R. Blake, J. Fluid Mech. 46, 199 (1971)] is employed to describe the organism propulsion mechanism. A regular perturbation expansion up to first order in the Deborah number is performed, and the generalized reciprocity theorem from Stokes flow theory is then used, to derive analytical formulas for the squirmer velocity. Results show that "neutral" squirmers are unaffected by viscoelasticity, whereas "pullers" and "pushers" are slowed down and hastened, respectively. The power dissipated by the swimming microorganism and the "swimming efficiency" are also analytically quantified.

Author's reply to “Comments on ‘Onsager–Casimir Principle and Reciprocity Relations for Bianisotropic Media’”

Ž . Ž . and it is apparent that 15 18 are equivalent to 3 5 . Therefore, there is no difference between the ‘‘dynamical Ž . constitutive symmetry relations,’’ summarized in 1, eq. 6 , Ž . Ž . and the Lorentz adjointness 3 5 . Since these two set of relations are equivalent, we can conclude that both the Lorentz adjointness relations and the macroscopic generalized reciprocity theorem can be derived, as usual, from the Onsager Casimir principle, even in the most general case of a bianisotropic medium.

Initial strain effects in multilayer composite laminates

A boundary integral formulation for the analysis of stress fields induced in composite laminates by initial strains, such as may be due to temperature changes and moisture absorption is presented. The study is formulated on the basis of the theory of generalized orthotropic thermo-elasticity and the governing integral equations are directly deduced through the generalized reciprocity theorem. A suitable expression of the problem fundamental solutions is given for use in computations. The resulting linear system of algebraic equations is obtained by the boundary element method and stress interlaminar distributions in the boundary-layer are calculated by using a boundary only discretization. The approach is general and it does not require a priori assumptions. Numerical results are presented to show the potential of the proposed approach.

Excitation of the earth-ionosphere irregular waveguide by sources located in an anisotropic ionosphere

Abstract The electromagnetic fields excited in the Earth-ionosphere waveguide by arbitrarily oriented VLF transmitters (electric and magnetic dipoles) located in the ionosphere are treated. The formulation allows for a spherical radially and longitudinally irregular waveguide as well as for an anisotropic ionosphere. The generalized reciprocity theorem is used for the solution of the problem. Numerical techniques have been developed. To illustrate the field features conditioned by the longitudinal irregularities, the diurnal variations of the field components excited at the Earth's surface by the sources located in the low ionosphere and at satellite altitudes have been calculated for some propagation paths.

Electromagnetic-field relationship in anisotropic case with one or both communicating points ground-based

The excitation of a spherical regular (in angular coordinates) anisotropic waveguide by electric and magnetic dipoles located in the ionospheric plasma or in the waveguide cavity is examined. It is shown that between the ionospheric fields of different ground-based sources oriented along the basis vectors of a spherical coordinate system there exists an elementary relationship that follows from the generalized reciprocity theorem and the boundary conditions on the earth's surface. The components of the electromagnetic-field strength of an individual ionospheric radiator on the earth's surface are also simply related. When both communicating points are ground-based, to determine the fields of the radiators it is sufficient to find the radial components of the electric and magnetic fields of radial electric and magnetic dipoles.

A reciprocity formulation for the EM scattering by an obstacle within a large open cavity

A formulation based on a generalized reciprocity theorem is developed for analyzing the external high-frequency EM scattering by a complex obstacle inside a relatively arbitrary open-ended waveguide cavity when it is illuminated by an external source. This formulation is also extended to include EM fields whose time dependence may be nonperiodic. A significant advantage of this formulation is that it allows one to break up the analysis into two independent parts, one dealing with the waveguide cavity shape alone and the other with the obstacle alone. The external scattered field produced by the obstacle (in the presence of the waveguide cavity structure) is given in terms of a generalized reciprocity integral over a surface S/sub T/ corresponding to the interior waveguide cavity cross-section located conveniently but sufficiently close to the obstacle. Furthermore, the fields coupled into the cavity from the source in the exterior region generally need to propagate only one way via the open front end (which is directly illuminated) to the interior surface S/sub T/ in this approach, and not back, in order to find the external field scattered by the obstacle.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An alternative proof of the generalized reciprocity theorem for charge collection

An alternative proof is given of the generalized reciprocity theorem for charge collection discussed by Misiakos and Lindholm [J. Appl. Phys. 58, 4743 (1985)]. The present analysis directly yields an equation for the distribution of the charge collection probability in quasi-neutral regions of a semiconductor device and the associated boundary conditions.

A coupled mode formulation by reciprocity and a variational principle

A coupled mode formulation for parallel dielectric waveguides is presented via two methods: a reciprocity theorem and a variational principle. In the first method, a generalized reciprocity relation for two sets of field solutions (E^{(1)}, H^{(1)}) and (E^{(2)}, H^{(2)}) satisfying Maxwell's equation and the boundary conditions in two different media \epsilon^{(1)}(x,y) and \epsilon^{(2)}(x,y) , respectively, is derived. Based on the generalized reciprocity theorem, we then formulate the coupled mode equations. The second method using a variational principle is also presented for a general waveguide system which can be lossy. The results of the variational principle can also be shown to be identical to those from the reciprocity theorem. The exact relations governing the and the new coupling coefficients are derived. It is shown analytically that our formulation satisfies the reciprocity theorem and power conservation exactly, while the conventional theory violates the power conservation and reciprocity theorem by as much as 55 percent and the Hardy-Streifer theory by 0.033 percent, for example.

Generalized reciprocity theorem for semiconductor devices

A reciprocity theorem is presented that relates the short-circuit current of a device, induced by a carrier generation source, to the minority-carrier Fermi level in the dark. The basic relation is general under low injection. It holds for three-dimensional devices with position dependent parameters (energy gap, electron affinity, mobility, etc.), and for transient or steady-state conditions. This theorem allows calculation of the internal quantum efficiency of a solar cell by using the analysis of the device in the dark. Other applications could involve measurements of various device parameters, interfacial surface recombination velocity at a polycrystalline silicon emitter contact, for example, by using steady-state or transient photon or mass-particle radiation.

A General Reciprocity Theorem for Conducting Media

The paper presents a generalization of Ramo's theorem to conducting media. The generalized reciprocity theorem derived here is valid for configurations consisting of N metallic electrodes of arbitrary shape embedded in any conducting or non-conducting medium, and, furthermore, holds for non-shorted electrodes and for arbitrarily large signals. Its generality makes the theorem potentially applicable in many different areas concerned with measurement, registration, and interpretation of distributions of current in a variety of electronic media such as vacuum, plasmas, electrolytes, biological tissue, semiconductors, and many others. As an example of a typical application the latter part of the paper shows how the generalized theorem can be used for analysis of excessive flicker noise in semiconductors. In this analysis the noise properties of N-terminal devices are described, in particular the dependence of excessive noise on typical semiconductor parameters and geometrical structure.

On the generalized theory of normal mode excitation in electromagnetic and polarized medium waveguides by external sources

A generalized reciprocity theorem valid for electromagnetic waveguides, ferromagnetic media, elastic piezodielectric media, and drifting carrier streams in semiconductors in the presence of mobile carrier collisions with crystal defects is derived. The reciprocity theorem is the basis for obtaining mode orthogonality and normalization relations and excitation equations of normal modes in electromagnetic and polarized medium waveguides. The excitation equations thus obtained are reduced to the form of coupled−mode equations.

Mössbauer diffraction. III. Emission of Mössbauerγrays from crystals. A. General theory

We develop the dynamical theory of the emission of M\"ossbauer $\ensuremath{\gamma}$ rays from crystals. The direct solution of the multiple-scattering equations, valid in the near and far zones, is obtained along with that utilizing the generalized reciprocity theorem. As in the x-ray case, the emission pattern exhibits the Kossel cone structure, but there are interesting new features. Enhanced-intensity "anomalous-emission" Kossel lines are predicted in the early development of a radioactive source as consequence of the fact that the electronic scattering absorption of the lattice is predominantly $E1$, while most M\"ossbauer transitions correspond to the emission of higher-order-multipole waves. In addition, the sensitivity of the M\"ossbauer scattering to the magnetic field and electric-field-gradient tensor at the nucleus gives rise to unique Kossel cones which exhibit the structure of the internal fields. Finally, Faraday effects are important in determining the polarization state of the emitted $\ensuremath{\gamma}$ quanta. Kossel analysis can also be used to determine the phase of the x-ray structure factor of (molecular) crystals. In this paper we develop the general theory describing the optics of M\"ossbauer $\ensuremath{\gamma}$ emission from crystals.

Propagation in a model terrestrial waveguide of nonuniform height - theory and experiment

Propagation of electromagnetic waves in multimode waveguides of variable height is investigated. The model consists of two uniform rectangular waveguides connected by a linearly tapered waveguide section. Using a generalized reciprocity theorem for waveguide junctions, a previous quasi-optic solution of this problem is extended to account for reflected waves. The results have application to the theory of VLF radio propagation when the effective height of reflection of the ionosphere boundary varies along the path. The analytical investigation has been complemented by laboratory measurements taken from a two-dimensional microwave model, and good agreement with calculated results was achieved.

Traveling Wave Slot Antennas

Approximate formulas for the complex propagation constant and characteristic field configuration for dielectric-filled traveling wave slot antennas are obtained by a variational procedure. To set up the variational method, the generalized reciprocity theorem for traveling wave line sources is deduced; it differs considerably from the reciprocity theorem for point sources. A perturbation technique for solving the variational equations is given. Formulas are worked out for rectangular wave guides and good agreement with available measurements is obtained.

Circuit Relations in Radiating Systems and Applications to Antenna Problems

Expressions for the self and mutual impedances within a radiating system are developed by the use of the generalized reciprocity theorem. These expressions are given in terms of the distributions of the electric field intensities along the radiators. A method for the determination of the field intensities is outlined. Formulas for the self and mutual impedances in several types of directional antennas are given. Questions of practical interest in connection with arrays of half-wave dipoles, long parallel wires, and "V" type radiators are discussed. Different types of reflector systems are considered. Curves of the more important relations are shown. The mathematical development is shown in an appendix.