Blind phase retrieval and source separation of electromagnetic fields

Blind source separation of two electromagnetic fields is investigated. The difficulty of this task lies in the fact that only the power, which is the square of the sum of the electromagnetic fields, can be directly measured; the cross term of the electromagnetic fields is inevitable, and a strong correlation occurs in blind deconvolution. However, the relative phase is physically different from the field intensities, and, hence, extracting the phase during separation seems inconceivable. Our results demonstrate that the intensities and the relative phase of two electromagnetic waves can be determined with eigenvalue problem formalism even when the mixing processes are completely unknown.     

Letter: Nonlinear Gravitational-Electromagnetic Bending of the Rays of Weak Electromagnetic Waves in the Fields of Pulsars and Magnetars

The eikonal equation is constructed for a weak electromagnetic wave that propagates by the laws of parameterized post-Maxwellian electrodynamics of vacuum in the magnetic dipole and gravitational fields of pulsars and magnetars. An approximate solution has been found for the equation for the rays, along which two mutually perpendicular normal modes of electromagnetic wave are propagating. The ray bending angles and time delay of the first normal mode relatively the second normal mode of the electromagnetic waves polarization states are determined as resultant from the nonlinear effect of the gravitational and magnetic dipole fields of neutron stars on the rays.     

Generalized gauge independence and the physical limitations on the von Neumann measurement postulate

An analysis is presented of the significance and consequent limitations on the applicability of the von Neumann measurement postulate in quantum mechanics. Directly observable quantities, such as the expectation value of the velocity operator, are distinguished from mathematical constructs, such as the expectation value of the canonical momentum, which are not directly observable. A simple criterion to distinguish between the two types of operators is derived. The non-observability of the electromagnetic four-potentials is shown to imply the non-measurability of the canonical momentum. The concept of a mechanical gauge is introduced and discussed. Classically the Lagrangian is nonunique within a total time derivative. This may be interpreted as the freedom of choosing a mechanical (M) gauge function. In quantum mechanics it is often implicitly assumed that the M-gauge vanishes. However, the requirement that directly observable quantities be independent of the arbitrary mechanical gauge is shown to lead to results analogous to those derived from the requirement of electromagnetic gauge independence of observables. The significance of the above to the observability of transition amplitudes between field-free energy eigenstates in the presence (and absence) of electromagnetic fields is discussed. E- and M-gauge independent transition amplitudes between field-free energy eigenstates in the absence of electromagnetic fields are defined. It is shown that, in general, such measurable amplitudes cannot be defined in the presence of externally applied time-dependent fields. Transition amplitudes in the presence of time-independent fields are discussed. The path dependence of previous derivations of E-gauge independent Hamiltonians and/or transition amplitudes in the presence of electromagnetic fields are related to the inherent M-gauge dependence of these quantities in the presence of such fields.     

On the connection between the solutions to the Dirac and Weyl equations and the corresponding electromagnetic four-potentials

In this work we study in detail the connection between the solutions to the Dirac and Weyl equations and the associated electromagnetic four-potentials.First,it is proven that all solutions to the Weyl equation are degenerate,in the sense that they correspond to an infinite number of electromagnetic four-potentials.As far as the solutions to the Dirac equation are concerned,it is shown that they can be classified into two classes.The elements of the first class correspond to one and only one four-potential,and are called non-degenerate Dirac solutions.On the other hand,the elements of the second class correspond to an infinite number of four-potentials,and are called degenerate Dirac solutions.Further,it is proven that at least two of these fourpotentials are gauge-inequivalent,corresponding to different electromagnetic fields.In order to illustrate this particularly important result we have studied the degenerate solutions to the forcefree Dirac equation and shown that they correspond to massless particles.We have also provided explicit examples regarding solutions to the force-free Weyl equation and the Weyl equation for a constant magnetic field.In all cases we have calculated the infinite number of different electromagnetic fields corresponding to these solutions.Finally,we have discussed potential applications of our results in cosmology,materials science and nanoelectronics.     

Parametric resonance in neutrino oscillations in periodically varying electromagnetic fields

It is shown that a parametric resonance may arise in neutrino oscillations in varying electromagnetic fields. For two types of electromagnetic fields—an amplitude-modulated electromagnetic wave and a transverse magnetic field that is constant in time, but which has an amplitude periodically varying in space—the probabilities of the ν _i ? ν _j neutrino transitions are found, and it is shown that the probability amplitudes increase with time for a specific choice of the parameters of external electromagnetic fields.     

Numerical Analysis of Electromagnetic Fields in Multiscale Model

Modeling technique for electromagnetic fields excited by antennas is an important topic in computational electromagnetics, which is concerned with the numerical solution of Maxwell's equations. In this paper, a novel hybrid technique that combines method of moments(MoM) with finite-difference time-domain(FDTD) method is presented to handle the problem. This approach employed Huygen's principle to realize the hybridization of the two classical numerical algorithms. For wideband electromagnetic data, the interpolation scheme is used in the MoM based on the dyadic Green's function. On the other hand, with the help of equivalence principle, the scattered electric and magnetic fields on the Huygen's surface calculated by MoM are taken as the sources for FDTD. Therefore, the electromagnetic fields in the environment can be obtained by employing finite-difference time-domain method. Finally, numerical results show the validity of the proposed technique by analyzing two canonical samples.     

A relation between the dirac field of the electron and electromagnetic fields

There is a point of view from which a field governed by the Dirac equation for the electron is the same as a field governed by the Maxwell-Lorentz equations for electromagnetic fields. This observation suggests the possibility that the two sets of equations are of the same origin.     

Time dependent axially symmetric solutions of the Einstein-Maxwell-Yukawa fields

Extending a technique developed for static fields by Janiset al. [10] to the nonstatic fields two exact solutions in the case of Einstein-Rosen metric for the interacting electromagnetic and zero mass scalar fields have been obtained.     

Bound States in the continuum in photonics

With examples of two parallel dielectric gratings and two arrays of thin parallel dielectric cylinders, it is shown that the interaction between trapped electromagnetic modes can lead to scattering resonances with practically zero width. Such resonances are the bound states in the radiation continuum first discovered in quantum systems by von Neumann and Wigner. Potential applications of such photonic systems include: large amplification of electromagnetic fields within photonic structures and, hence, enhancement of nonlinear phenomena, biosensing, as well as perfect filters and waveguides for a particular frequency, and impurity detection.     

The interaction of three fields in ECE theory: The inverse Faraday effect

The simultaneous interaction of three fundamental fields is illustrated in Einstein Cartan Evans (ECE) theory with reference to the effect of gravitation on the inverse Faraday effect. The three-field interaction in this case is that of the fermionic, electromagnetic and gravitational fields. The interaction of the first two is developed in a well-defined semi-classical approximation of the ECE wave equation and the effect of gravitation incorporated through the index reduced canonical energy momentum density T. The exercise is repeated using the ECE wave equations and a general rule developed for the effect of gravitation on the fermionic, electromagnetic weak and strong fields.     

Hybridization of electromagnetic numerical methods through the G-matrix algorithm

For the sake of numerical performance, we hybridize two common approaches often used in electromagnetic computations, namely the finite-element method and the aperiodic Fourier modal method. To that end, we propose an extension of the classical S-matrix formalism to numerical situations, which requires handling different mathematical representations of the electromagnetic fields. As shown with a three-dimensional example, the proposed G-matrix formalism is stable and allows for an enhanced performance in terms of numerical accuracy and efficiency.     

Stimulation of the stress response by low-frequency electromagneticfields: possibility of direct interaction with DNA

This paper reviews research in our laboratories, which shows that 60-Hz electromagnetic fields stimulate the stress response at field strengths much lower than 0.1 mT (1 Gauss). While research on weak electromagnetic fields has been directed largely toward possible harmful effects, the stimulated expression of stress genes (i.e., synthesis of stress proteins) has many potential therapeutic applications in medicine. To gain insight into the molecular mechanism, we have studied the interactions of fields with well-characterized enzymes, and our findings suggest a coupling of the fields to biological charge transfer reactions. Since, synthesis of stress proteins requires activation of DNA, electromagnetic fields may achieve this by interacting directly with electron currents that flow through the stacked bases within the DNA. Such processes could explain the unusually low thresholds we observe and provide a basis for understanding biological effects of high-frequency electromagnetic fields     

An extension of the plane-symmetric electrovac general solution to Einstein equations

We present the general solution to Einstein-Maxwell equations representing plane-symmetric metrics associated with electromagnetic fields that are not fully plane-symmetric. There are two classes in the general solution, the first approaches Taub's static metric or Kasner's spatially homogeneous one as the electromagnetic field goes to zero, while the second approaches the fiat metric.     

On geometrodynamics and null fields

The possibility of describing null electromagnetic fields by purely metric concepts has recently been subject to some doubt. Following a method devised by Hlavatý, we here investigate the relations that a Riemannian manifold must satisfy in order to correspond to a null electromagnetic field. It is shown that in most cases the fulfilment of five geometrical relations is a necessary and sufficient condition for the existence of a null electromagnetic field. The latter is unique, except for an arbitrary constant phase factor (as in the case of non-null fields). However, in some exceptional cases, there is a larger degree of arbitrariness in the null electromagnetic field that corresponds to a given metric. Such fields (which always possess wave fronts) are not reducible to metric concepts. We then turn to examine how it can occur that null electromagnetic fields require the fulfilment of five relations, rather than three, as non-null ones. In order to settle this question, we make an attempt to consider null fields as a limiting case of non-null ones, by superimposing an arbitrary infinitesimal non-null field on a finite null one. It is then shown that the Rainich vector of such a field does not have a well defined limit, when the perturbing non-null field tends to zero. It is thereby inferred that null electromagnetic fields really have a special status within the frame of geometrodynamics.     

各向同性介质界面本征模分析

分析了两个各向同性材料界面处的本征模,从另一个角度来分析解释了布儒斯特定律.当入射光与界面处的表面模匹配时,入射光的能量就会全部转移到界面的本征场上,如果电磁波在折射介质中为行波,界面的本征场又会在折射介质中激发新的电磁波,形成透射波,也就是布儒斯特定律描述的横电波或者横磁波的全透射现象,这也可以看作是一种光学共振现象.横磁波的全透射现象往往出现在两个具有相同磁导率的介质的界面处,而横电波的全透射现象则往往出现在两个具有相同介电常数的介质的界面处.     

Controlling the XUV transparency of helium using two-pathway quantum interference

Atoms irradiated with combined femtosecond laser and extreme ultraviolet (XUV) fields ionize through multiphoton processes, even when the energy of the XUV photon is below the ionization potential. However, in the presence of two different XUV photons and an intense laser field, it is possible to induce full electromagnetic transparency. Taking helium as an example, the laser field modifies its electronic structure, while the presence of two different XUV photons and the laser field leads to two distinct ionization pathways that can interfere destructively. This work demonstrates a new approach for coherent control in a regime of highly excited states and strong optical fields.     

Verifiable post-Maxwellian effect of the nonlinear electrodynamics in vacuum

The lasing frequencies of a ring laser with counterpropagating electromagnetic waves are calculated for the case when a part of the laser circuit is subjected to a constant electromagnetic field. It is demonstrated that, according to equations of the parametrized post-Maxwellian electrodynamics of vacuum, two waves with different planes of polarization and frequencies should propagate in each direction of the ring laser. The analysis has shown that, with the help of advanced ring lasers and external electromagnetic fields attainable in the laboratory, the post-Maxwellian parameters can be measured with a precision that would be sufficient to verify the most popular theoretical models of the nonlinear electrodynamics of vacuum.