Exponential beams of electromagnetic radiation

We show that in addition to well known Bessel, Hermite-Gauss, and Laguerre-Gauss beams of electromagnetic radiation, one may also construct exponential beams. These beams are characterized by a fall-off in the transverse direction described by an exponential function of rho. Exponential beams, like Bessel beams, carry definite angular momentum and are periodic along the direction of propagation, but unlike Bessel beams they have a finite energy per unit beam length. The analysis of these beams is greatly simplified by an extensive use of the Riemann-Silberstein vector and the Whittaker representation of the solutions of the Maxwell equations in terms of just one complex function. The connection between the Bessel beams and the exponential beams is made explicit by constructing the exponential beams as wave packets of Bessel beams.Comment: Dedicated to the memory of Edwin Powe

Maxwell equations in matrix form, squaring procedure, separating the variables, and structure of electromagnetic solutions

The Riemann -- Silberstein -- Majorana -- Oppenheimer approach to the Maxwell electrodynamics in vacuum is investigated within the matrix formalism. The matrix form of electrodynamics includes three real 4 \times 4 matrices. Within the squaring procedure we construct four formal solutions of the Maxwell equations on the base of scalar Klein -- Fock -- Gordon solutions. The problem of separating physical electromagnetic waves in the linear space \lambda_{0}\Psi^{0}+\lambda_{1}\Psi^{1}+\lambda_{2}\Psi^{2}+ lambda_{3}\Psi^{3} is investigated, several particular cases, plane waves and cylindrical waves, are considered in detail.Comment: 26 pages 16 International Seminar NCPC, May 19-22, 2009, Minsk, Belaru

Generalized Gravi-Electromagnetism

A self consistant and manifestly covariant theory for the dynamics of four charges (masses) (namely electric, magnetic, gravitational, Heavisidian) has been developed in simple, compact and consistent manner. Starting with an invariant Lagrangian density and its quaternionic representation, we have obtained the consistent field equation for the dynamics of four charges. It has been shown that the present reformulation reproduces the dynamics of individual charges (masses) in the absence of other charge (masses) as well as the generalized theory of dyons (gravito - dyons) in the absence gravito - dyons (dyons). key words: dyons, gravito - dyons, quaternion PACS NO: 14.80H

Spherical harmonic decomposition applied to spatial-temporal analysis of human high-density EEG

We demonstrate an application of spherical harmonic decomposition to analysis of the human electroencephalogram (EEG). We implement two methods and discuss issues specific to analysis of hemispherical, irregularly sampled data. Performance of the methods and spatial sampling requirements are quantified using simulated data. The analysis is applied to experimental EEG data, confirming earlier reports of an approximate frequency-wavenumber relationship in some bands.Comment: 12 pages, 8 figures, submitted to Phys. Rev. E, uses APS RevTeX style

Helicity, polarization, and Riemann-Silberstein vortices

Riemann-Silberstein (RS) vortices have been defined as surfaces in spacetime where the complex form of a free electromagnetic field given by F=E+iB is null (F.F=0), and they can indeed be interpreted as the collective history swept out by moving vortex lines of the field. Formally, the nullity condition is similar to the definition of "C-lines" associated with a monochromatic electric or magnetic field, which are curves in space where the polarization ellipses degenerate to circles. However, it was noted that RS vortices of monochromatic fields generally oscillate at optical frequencies and are therefore unobservable while electric and magnetic C-lines are steady. Here I show that under the additional assumption of having definite helicity, RS vortices are not only steady but they coincide with both sets of C-lines, electric and magnetic. The two concepts therefore become one for waves of definite frequency and helicity. Since the definition of RS vortices is relativistically invariant while that of C-lines is not, it may be useful to regard the vortices as a wideband generalization of C-lines for waves of definite helicity.Comment: 5 pages, no figures. Submitted to J of Optics A, special issue on Singular Optics; minor changes from v.

Surface plasmons of metallic surfaces perforated by nanoholes

Recent works dealt with the optical transmission on arrays of subwavelength holes perforated in a thick metallic film. We have performed simulations which quantitatively agree with experimental results and which unambiguously evidence that the extraordinary transmission is due to the excitation of a surface-plasmon-polariton (SPP) mode on the metallic film interfaces. We identify this SPP mode and show that its near-field possesses a hybrid character, gathering collective and localised effects which are both essential for the transmission.Comment: 16 pages, 4 figure

Quaternion Analysis for Generalized Electromagnetic Fields of Dyons in Isotropic Medium

Quaternion analysis of time dependent Maxwell's equations in presence of electric and magnetic charges has been developed and the solutions for the classical problem of moving charges (electric and magnetic) are obtained in unique, simple and consistent manner

Effect of the human immunodeficiency virus type 1 reverse transcriptase polymorphism Leu-214 on replication capacity and drug susceptibility

A negative association between polymorphism Leu-214 and type-1 thymidine analogue mutations (TAM1) and a positive association with a clinically favorable virological response to thymidine analogue-based combination antiretroviral therapy have been described. In this study, the impact of Leu-214 on replication capacity and resistance to zidovudine (ZDV) of viruses containing TAM1 or TAM2 was determined. Leu-214 decreased the growth rate of viruses bearing Tyr-215, as well as their resistance to ZDV. This observation was confirmed by structural and molecular modeling data, suggesting a regulatory role for Leu-214 in the emergence and phenotypic resistance of TAM1

Topiramate plus nortriptyline in the preventive treatment of migraine: a controlled study for nonresponders

A sizeable proportion of migraineurs in need of preventive therapy do not significantly benefit from monotherapy. The objective of the study is to conduct a randomized controlled trial testing whether combination therapy of topiramate and nortriptyline is useful in patients who had less than 50% decrease in headache frequency with the use of the single agents. Patients with episodic migraine were enrolled if they had less than 50% reduction in headache frequency after 8 weeks of using topiramate (TPM) (100 mg/day) or nortriptyline (NTP) (30 mg/day). They were randomized (blinded fashion) to have placebo added to their regimen, or to receive the second medication (combination therapy). Primary endpoint was decrease in number of headache days at 6 weeks, relative to baseline, comparing both groups. Secondary endpoint was proportion of patients with at least 50% reduction in headache frequency at 6 weeks relative to baseline. A total of 38 patients were randomized to receive combination therapy, while 30 continued on monotherapy (with placebo) (six drop outs in the combination group and three for each single drug group). For the primary endpoint, mean and standard deviation (SD) of reduction in headache frequency were 4.6 (1.9) for those in polytherapy, relative to 3.5 (2.3) for those in monotherapy. Differences were significant (p < 0.05]. Similarly, 78.3% of patients randomized to receive polytherapy had at least 50% headache reduction, as compared to 37% in monotherapy (p < 0.04). Finally we conclude that combination therapy (of TPM and NTP) is effective in patients with incomplete benefit using these agents in monotherapy