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A Lagrangian is defined that governs the dynamics of a classical electron with spin, moving under the influence of electromagnetic forces. The Euler-Lagrange equations associated with this Lagrangian for space-time position x exp-alpha provide a generalization of the Lorentz force law. The remaining Euler-Lagrange equations lead directly to the (generalized) Frenkel (1926)-Thomas (1927)-BMT (1959) equations.
In this semi-tutorial paper, we revisit the interference phenomena caused by pairs of copropagating or counter-propagating transverse electromagnetic waves by letting the host medium be absorbing. We first consider plane waves in an unbounded medium, summarize the standingwave solution of the Maxwell equations, and discuss specific effects caused by nonvanishing absorption. We then consider the superposition of plane and spherical waves in the context of fartfield electromagnetic scattering by a particle. To this end we modify the classical Jones lemma by allowing nonzero absorption in the host medium and consider its most obvious consequences such as forward- and backscattering interference. The physical similarity of the two scenarios (superpositions of plane waves and superpositions of plane and spherical waves) is discussed.
Nanostructured devices that exploit the hybrid-polariton resonances arising from coupling among photons, phonons, and plasmons are subjects of research directed toward the development of infrared-spectroscopic sensors for measuring extremely small quantities of molecules of interest. The spectroscopic techniques in question are surface enhanced Raman scattering (SERS) and surface enhanced infrared absorption (SEIRA). An important intermediate goal of this research is to increase the sensitivity achievable by these techniques. The basic idea of the approach being followed in this research is to engineer nanostructured devices and thereby engineer their hybrid-polariton resonances to concentrate infrared radiation incident upon their surfaces in such a manner as to increase the absorption of the radiation for SEIRA and measure the frequency shifts of surface vibrational modes. The underlying hybrid-polariton-resonance concept is best described by reference to experimental devices that have been built and tested to demonstrate the concept. The nanostructure of each such device includes a matrix of silicon carbide particles of approximately 1 micron in diameter that are supported on a potassium bromide (KBr) or poly(tetrafluoroethylene) [PTFE] window. These grains are sputter-coated with gold grains of 40-nm size (see figure). From the perspective of classical electrodynamics, in this nanostructure, that includes a particulate or otherwise rough surface, the electric-field portion of an incident electromagnetic field becomes concentrated on the particles when optical resonance conditions are met. Going beyond the perspective of classical electrodynamics, it can be seen that when the resonance frequencies of surface phonons and surface plasmons overlap, the coupling of the resonances gives rise to an enhanced radiation-absorption or -scattering mechanism. The sizes, shapes, and aggregation of the particles determine the frequencies of the resonances. Hence, the task of designing a nanostructure to exhibit the desired radiation-absorption properties translates, in large part, to selecting particle sizes and shapes to obtain the desired enhanced coupling of energy from photons to plasmons and phonons. To broaden the spectral region(s) of enhanced absorption, one would select a distribution of particle sizes and shapes.
Radiation absorption and scattering by small spherical solid carbon particles in wavelength range 0.2 to 40 mu calculated by classical Mie theory
Many properties of gaseous systems such as electromagnetic absorption and emission, sound dispersion and absorption, may be elucidated if the nature of collisions between the particles in the system is understood. A procedure for the calculation of the classical trajectories of two interacting diatomic molecules is described. The dynamics of the collision will be assumed to be that of two rigid rotors moving in a specified potential. The actual outcome of a representative sample of many trajectories at 298K was computed, and the use of these values at any temperature for calculations of various molecular properties will be described. Calculations performed for the O2 microwave spectrum are given to demonstrate the use of the procedure described.
Detailed properties of the classical hydromagnetic Alfven wave and the fire-hose instability, driven by an excess in the parallel energy are well understood in the nonrelativistic regime. In this brief communication, the analysis is extended to the fully relativistic regime. The analysis is carried out for fully relativistic bi-Maxwellian distributions of electrons and ions (or positrons). It is shown that the relativistic effect has a nonnegligible effect on the wave and stability properties of the low-frequency modes under certain conditions.
Radiation absorption and scattering by small spherical solid carbon particles in wavelength range 0.2 to 40 mu calculated by classical Mie theory
This study is concerned with the problem of electromagnetic wave propagation in a magneto-plasma filled coaxial structure. The problem is formulated using the classical boundary value problem approach. A numerical investigation shows the existence of propagating slow modes, backward modes, a quasi-TEM mode, and waveguide-type modes in a magneto-plasma filled coaxial structure. Dispersion curves for these different modes are presented. Measurements have been made of electromagnetic propagation in a coaxial electrode structure filled with longitudinally magnetized plasma. The annular plasma region had a 9.55 cm outer diameter, a 3.82 cm inner diameter and was approximately 60 cm long. A magnetic field of 300 gauss was employed. Electromagnetic wave frequencies were in the range .5 to 2.4 GHz. The plasma was generated by a continuous glow discharge. The resulting dispersion curves closely follow the predicted curves for the quasi-TEM mode.
A brief historical review of conformal mapping and its applications to problems in fluid mechanics and electromagnetism is presented. The use of conformal mapping as a grid generator is described. The philosophy of the 'closed form' approach and its application to a Neumann problem is discussed. Karman-Trefftz mappings and grids for ablated, three dimensional bodies are also discussed.
A rigorous discussion is presented of the classical motion of a relativistic electron in a magnetic field and the resulting electromagnetic radiation when radiation reaction is important. In particular, for an electron injected with initial energy gamma(0), a systematic perturbative solution to the Lorentz-Dirac equation of motion is developed for field strengths satisfying gamma(0) B much less than 6 x 10 to the 15th G. A particularly accurate solution to the electron orbital motion in this regime is found and it is demonstrated how lowest-order corrections can be calculated. It is shown that the total energy-loss rate corresponds to what would be found using the exact Larmor power formula without including radiation reaction. Provided that the particle energy and field strength satisfy the same contraint, it is explicitly demonstrated that the intuitive prescription for calculating the time-integrated radiation spectrum described above is correct.
Based on a theoretical model of the propagation of electromagnetic waves through a hypersonically induced plasma, it has been demonstrated that the classical radiofrequency communications blackout that is experienced during atmospheric reentry can be mitigated through the appropriate control of an external magnetic field of nominal magnitude. The model is based on the kinetic equation treatment of Vlasov and involves an analytical solution for the electric and magnetic fields within the plasma allowing for a description of the attendant transmission, reflection and absorption coefficients. The ability to transmit through the magnetized plasma is due to the magnetic windows that are created within the plasma via the well-known whistler modes of propagation. The case of 2 GHz transmission through a re-entry plasma is considered. The coefficients are found to be highly sensitive to the prevailing electron density and will thus require a dynamic control mechanism to vary the magnetic field as the plasma evolves through the re-entry phase.
Thomson theory of arbitrarily intense elliptically polarized plane electromagnetic wave scattering by free electrons, solving electron equations of motion
Following preliminary investigations of the low frequency electric and magnetic fields that may exists in the Earth-ionospheric cavity, measurements were taken with state-of-the art spectrum analyzers. As a follow up to this activity, an investigation was initiated to determine sources and values for possible low frequency signal that would appear in the cavity. The lowest cavity resonance is estimated at about 8 Hz, but lower frequencies may be an important component of our electromagnetic environment. The potential field frequencies produced by the electron were investigated by a classical model that included possible cross coupling of the electric and gravitation fields. During this work, an interesting relationship was found that related the high frequency charge field with the extremely low frequency of the gravitation field. The results of numerical calculations were surprisingly accurate and this area of investigation is continuing. The work toward continued development of a standardized monitoring facility is continuing with the potential of installing the prototype at West Virginia State College early in 1990. This installation would be capable of real time monitoring of ELF signals in the Earth-ionoshpere cavity and would provide some directional information. A high gain, low noise, 1/f frequency corrected preamplifier was designed and tested for the ferrite core magnetic sensor. The potential application of a super conducting sensor for the ELF magnetic field detection is under investigation. It is hoped that a fully operational monitoring network could pinpoint the location of ELF signal sources and provide new information on where these signals originate and what causes them, assuming that they are natural in origin.
Sensors based on quantum mechanical properties of electromagnetic radiation and matter offer unique capabilities and performance sometimes difficult to achieve using classical approaches. This report assesses the suitability of quantum sensing for current and future NASA needs, with a specific focus on NASA’s Science Mission Directorate (SMD). Measurement and sensing needs across NASA SMD are reviewed as a driver for the possible incorporation of existing quantum sensors into the NASA portfolio and the development of next-generation quantum sensors. A range of quantum sensing modalities is then described and the current state of the art for each sensor is presented. Current research and development activities on quantum sensing within NASA are compared with the range of activities ongoing throughout the broader scientific community, both within the United States and internationally. In conclusion, there is considerable advantage to be gained by NASA from quantum sensors through the growth of internal programs and collaboration with outside entities.
I will discuss two types of one-dimensional photonic bandgap (PBG) effects that can arise in systems of coupled spherical resonators: (1) nearly-free-photon Fabry-Perot photonic bands that arise in quarter-wave concentrically stratified spheres and, (2) tight- binding photonic bands that arise in weakly-coupled mutually-resonant spheres as a result of whispering-gallery mode splitting. These effects can be derived directly from Mie theory, in a more straightforward manner, by exploiting an analogy with stratified planar systems. For odd numbers of mutually-resonant lossless coupled ring resonators, the circulating intensity can increase exponentially with the number of resonators, which can potentially be exploited for the development of advanced sensors. For even numbers of resonators, mode splitting and classical destructive interference lead to a cancellation of absorption and slow light on-resonance, reminiscent of electromagnetic induced transparency. The analogy between these coherent photon trapping effects and population trapping in an atomic system will be explored.
An attempt to bridge the gap between classical and quantum mechanics and to explain the Casimir effect is presented. The general nature of chaotic motion is discussed from two points of view: the first uses catastrophe theory and strange attractors to describe the deterministic view of this motion; the underlying framework for chaos in these classical dynamic systems is their extreme sensitivity to initial conditions. The second interpretation refers to randomness associated with probabilistic dynamics, as for Brownian motion. The present approach to understanding evanescent radiation and its relation to the Casimir effect corresponds to the first interpretation, whereas stochastic electrodynamics corresponds to the second viewpoint. The nonlinear behavior of the electromagnetic field is also studied. This well-understood behavior is utilized to examine the motions of two orbiting charges and shows a closeness between the classical behavior and the quantum uncertainty principle. The evanescent radiation is used to help explain the Casimir effect.
A classical model for laser action is discussed, in which an active medium consisting of anharmonic oscillators interacts with an electromagnetic field in a resonant cavity. Comparison with the case of a medium consisting of harmonic oscillators shows the significance of nonlinearities for producing self-sustained oscillations in the radiation field. A theoretical model is presented for the pressure dependence of the intensity of a gas laser, in which only velocity-changing collisions with foreign gas atoms are included. A collision model for hard sphere, repulsive interactions was derived. Collision theory was applied to a third-order expansion of the polarization in powers of the cavity electric field (weak signal theory).
A modification of the classical Rayleigh technique utilizing the fast Fourier transform, developed into the so-called Rayleigh-FFT method for electromagnetic scattering, is shown to obtain valid scattering results from arbitrary irregular periodic structures composed of a rough layer over a rough half-space. The considerable usefulness of the Rayleigh approach is thus established, and Beckmann's (1968) contention (that the convergence of the method is reasonably rapid only if the roughness is very slight) is refuted.