Propagation of electromagnetic waves generated by moving sources in dispersive media

The propagation of electromagnetic waves issued by modulated moving sources of the form j( t,x ) = a( t )e ^{- iw₀ t} [(x)\dot]₀ ( t )d( x - x₀ ( t ) )j\left( {t,x} \right) = a\left( t \right)e^{ - i\omega _0 t} \dot x_0 \left( t \right)\delta \left( {x - x_0 \left( t \right)} \right) is considered, where j(t, x) stands for the current density vector, x = (x ₁, x ₂, x ₃) ∈ ℝ³ for the space variables, t ∈ ℝ for time, t → x ₀(t) ∈ ℝ³ for the vector function defining the motion of the source, ω ₀ for the eigenfrequency of the source, a(t) for a narrow-band amplitude, and δ for the standard δ function. Suppose that the media under consideration are dispersive. This means that the electric and magnetic permittivity ɛ(ω), μ(ω) depends on the frequency ω. We obtain a representation of electromagnetic fields in the form of time-frequency oscillating integrals whose phase contains a large parameter λ > 0 characterizing the slowness of the change of the amplitude a(t) and the velocity [(x)\dot]₀ ( t )\dot x_0 \left( t \right) and a large distance between positions of the source and the receiver. Applying the two-dimensional stationary phase method to the integrals, we obtain explicit formulas for the electromagnetic field and for the Doppler effects. As an application of our approach, we consider the propagation of electromagnetic waves produced by moving source in a cold nonmagnetized plasma and the Cherenkov radiation in dispersive media.     

Electromagnetic field generated by a modulated moving point source in a planarly layered waveguide

In the present work, we consider a modulated point source in an arbitrary motion in an isotropic planarly layered waveguide. The radiation field generated by this source is represented in the form of double oscillatory integrals in terms of the time and the frequency, depending on the large parameter λ. By means of the stationary phase method, we analyze, in the waveguide, the Doppler effect, the retarded time, and the Vavilov–Cherenkov radiation. Numerically, the problem of the moving source is approached by the method of spectral parameter power series.     

Hydrodynamics of modulated finite-amplitude waves in dispersive media

Analytic approaches are developed for integrating the nondiagonalizable Whitham equations for the generation and propagation of nonlinear modulated finite-amplitude waves in dissipationless dispersive media. Natural matching conditions for these equations are stated in a general form analogous to the Gurevich-Pitaevskii conditions for the averaged Korteweg-de Vries equations. Exact relationships between the hydrodynamic quantities on different sides of a dissipationless shock wave, an analog of the shock adiabat in ordinary dissipative hydrodynamics and first proposed on the basis of physical considerations by Gurevich and Meshcherkin, are obtained. The boundaries of a self similar, dissipationless shock wave are determined analytically as a function of the density jump. Some specific examples are considered. Zh. éksp. Teor. Fiz. 115, 1116–1136 (March 1999)     

Electromagnetic momenta and forces in dispersive dielectric media

When the effects of dispersion are included, neither the Abraham nor the Minkowski expression for electromagnetic momentum in a dielectric medium gives the correct recoil momentum for absorbers or emitters of radiation. The total momentum density associated with a field in a dielectric medium has three contributions: (i) the Abraham momentum density of the field, (ii) the momentum density associated with the Abraham force, and (iii) a momentum density arising from the dispersive part of the response of the medium to the field, the latter having a form evidently first derived by Nelson (1991) [8]. All three contributions are required for momentum conservation in the recoil of an absorber or emitter in a dielectric medium. We consider the momentum exchanged and the force on a polarizable particle (e.g., an atom or a small dielectric sphere) in a host dielectric when a pulse of light is incident upon it, including the dispersion of the dielectric medium as well as a dispersive component in the response of the particle to the field. The force can be greatly increased in slow-light dielectric media.     

Electromagnetic fields and potentials generated by massless charged particles

We provide for the first time the exact solution of Maxwell’s equations for a massless charged particle moving on a generic trajectory at the speed of light. In particular we furnish explicit expressions for the vector potential and the electromagnetic field, which were both previously unknown, finding that they entail different physical features for bounded and unbounded trajectories. With respect to the standard Liénard–Wiechert field the electromagnetic field acquires singular δ$\delta$-like contributions whose support and dimensionality depend crucially on whether the motion is (a) linear, (b) accelerated unbounded, (c) accelerated bounded. In the first two cases the particle generates a planar shock-wave-like electromagnetic field traveling along a straight line. In the second and third cases the field acquires, in addition, a δ$\delta$-like contribution supported on a physical singularity-string attached to the particle. For generic accelerated motions a genuine radiation field is also present, represented by a regular principal-part type distribution diverging on the same singularity-string.     

Neutrinos in electromagnetic fields and moving media

The history of the development of the theory of neutrino-flavor and neutrino-spin oscillations in electromagnetic fields and in a medium is briefly surveyed. A new Lorentz-invariant approach to describing neutrino oscillations in a medium is formulated in such a way that it makes it possible to consider the motion of a medium at an arbitrary velocity, including relativistic ones. This approach permits studying neutrinospin oscillations under the effect of an arbitrary external electromagnetic field. In particular, it is predicted that, in the field of an electromagnetic wave, new resonances may exist in neutrino oscillations. In the case of spin oscillations in various electromagnetic fields, the concept of a critical magnetic-field-component strength is introduced above which the oscillations become sizable. In considering neutrino oscillations in moving matter, it is shown within the Lorentz-invariant formalism that the relativistic motion of matter significantly affects the character of neutrino oscillations and can radically change the conditions under which the oscillations are resonantly enhanced. Possible new effects in neutrino oscillations are discussed for the case of neutrino propagation in relativistic fluxes of matter.     

Electromagnetic radiation of a charged tachyon moving in a dispersive medium

At the present time a number of studies [1–6] have considered the possible properties of ultrarelativistic tachyon particles. In particular, [5, 6] were dedicated to analysis of the radiation of charged tachyons in a vacuum. The goal of the present study is to analyze the radiation emitted by charged tachyons in an immobile dispersive medium. We will consider the following problem: a charged particle moves with velocity v in an immobile dispersive medium and at time t=0 decays to neutral particles and a charged tachyon which moves at a velocity v₀. The tachyon in turn, because of collisions with neutral particles of the medium, at time t= forms a charged particle (electron) also moving with velocity v.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 130–134, June, 1978.In conclusion, the author expresses his sincere thanks to Professor Ya. P. Terletskii for his interest and aid in the study.     

Superchiral fields generated by nanostructures and their applications for chiral sensing

Chirality is ubiquitous in natural world. Although with similar physical and chemical properties, chiral enantiomers could play different roles in biochemical processes. Discrimination of chiral enantiomers is extremely important in biochemical, analytical chemistry, and pharmaceutical industries. Conventional chiroptical spectroscopic methods are disadvantageous at a limited detection sensitivity because of the weak signals of natural chiral molecules. Recently, superchiral fields were proposed to effectively enhance the interaction between light and molecules, allowing for ultrasensitive chiral detection. Intensive theoretical and experimental works have been devoted to generation of superchiral fields based on artificial nanostructures and their application in ultrasensitive chiral sensing. In this review, we present a survey on these works. We begin with the introduction of chiral properties of electromagnetic fields. Then, the optical chirality enhancement and ultrasensitive chiral detection based on chiral and achiral nanostructures are discussed respectively. Finally, we give a short summary and a perspective for the future ultrasensitive chiral sensing.     

Near fields and far fields generated by sources in the presence of dielectric structures with cylindrical symmetry

A full-vectorial integral equation method is presented for calculating near fields and far fields generated by sources in the presence of general finite-sized dielectric structures with cylindrical symmetry. The method is relevant for modeling of a class of antenna designs and some optical components with cylindrical symmetry, e.g., vertical-cavity surface-emitting lasers, microdisk lasers, and light-emitting diodes.     

Self-modulation and nonlinear diffraction of strong light fields in dispersive media

The problem of space-time self-modulation of strong laser fields is solved by the method of successive approximations. The nonlinear diffractional and nonlinear dispersive transformations of beam width and pulse duration are studied with emphasis on the reciprocal effects of nonlinear diffraction and dispersion. The effect of incomplete initial time and space coherence on the space-time parameters of a laser field and the conversion of its coherent properties is examined.Moscow State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 35, No. 6/7, pp. 525–532, June–July, 1992.     

On second-harmonic generation in nonuniformly magnetized media

This paper presents a theoretical study of new effects of double-frequency optical signal generation in magnetic media with a nonuniform magnetization distribution. The study is based on the hydrodynamic approximation of the motion of conduction electrons in the field of an electromagnetic wave and equations for the mean electron spin. Within this approach, the mechanisms of the toroidal moment effect, which was experimentally discovered earlier in a system of magnetic particles with a vertical magnetization distribution as well as in a multilayered magnetic system (which is a collinear nonuniform magnetic system), are demonstrated. A new effect that appears due to the presence of equilibrium spin currents in a nonuniform magnetic system is studied in detail. This effect was predicted from the symmetry and can occur only in noncollinearly magnetized media. It is shown that this effect has a resonance nature with a resonance at a pump frequency equal to the plasma frequency of conduction electrons. Estimates of the susceptibility at the double frequency for the parameters of nickel and the typical scale of variation in the magnetization, which is equal to 10 nm, show that the susceptibility near the frequency of the plasma resonance at the chosen parameters is on the order of 10^–9 esu, which holds up a hope of the experimental detection of this effect.