Making electromagnetic wavelets

Electromagnetic wavelets are constructed using scalar wavelets as superpotentials, together with an appropriate polarization. It is shown that oblate spheroidal antennas, which are ideal for their production and reception, can be made by deforming and merging two branch cuts. This determines a unique field on the interior of the spheroid which gives the boundary conditions for the surface charge-current density necessary to radiate the wavelets. These sources are computed, including the impulse response of the antenna.Comment: 29 pages, 4 figures; minor corrections and addition

Searching atomic spin contrast on nickel oxide (001) by force microscopy

The (001) surface of NiO, an antiferromagnet at room temperature, was investigated under ultra-high vacuum conditions with frequency modulation atomic force microscopy (FM-AFM). The antiferromagnetic coupling between ions leads to a spin superstructure on (001) surfaces. Exchange interaction between the probe of a force microscope and the NiO (001) surface should allow to image spin superstructures in real space. The surface was imaged with three different probing tips: nonmagnetic W tips, ferromagnetic Co tips and antiferromagnetic NiO tips - and atomic resolution was achieved with all three of them in various distance regimes and in several channels. Evidence for spin contrast was obtained in experiments that utilize NiO tips and oscillation amplitudes in the \AA-regime, where optimal signal-to-noise ratio is expected. The spin contrast is weaker than expected and only visible in Fourier space images.Comment: 7 pages, 6 figures, submitted to Physical Review

Raman spectroscopy with ultrashort coherent excitation. Narrowing of spectral lines beyond the dephasing linewidth

Spectroscopists are constantly faced with the task of improved spectral resolution. Two points are of major interest: (i) The precise frequency of the quantized transition and (ii) the detection of new neighboring transitions. Besides experimental factors the ultimate spectral resolution is determined by the inherent linewidth of the transition. Optical spectroscopists have to deal with different line-broadening processes; for instance with the Doppler effect or with collision broadening in gases, with dephasing processes in condensed systems and with the population relaxation which results in the natural linewidth. In recent years, different novel techniques have been devised which provide spectral resolution beyond the transition linewidth. For instance, Doppler broadening can be eliminated by saturation spectroscopy or by two counter-propagating beams for two-photon transitions/I/. Even measurements beyond the natural linewidth have been performed taking biased signals from the fluorescent decay /2-5/. Techniques have been proposed where the difference between the decay rates of the two states rather than their sum determines the linewidth /6,7/, and narrowing of the natural linewidth by decaying-pulse excitation has been discussed /8/. Very recently, we have demonstrated substantial line narrowing of Raman type transitions in condensed phases /9-11/. The lines were broadened by vibrational dephasing. New information was obtained in congestedspectral regions

The partially averaged field approach to cosmic ray diffusion

The kinetic equation for particles interacting with turbulent fluctuations is derived by a new nonlinear technique which successfully corrects the difficulties associated with quasilinear theory. In this new method the effects of the fluctuations are evaluated along particle orbits which themselves include the effects of a statistically averaged subset of the possible configurations of the turbulence. The new method is illustrated by calculating the pitch angle diffusion coefficient D sub Mu Mu for particles interacting with slab model magnetic turbulence, i.e., magnetic fluctuations linearly polarized transverse to a mean magnetic field. Results are compared with those of quasilinear theory and also with those of Monte Carlo calculations. The major effect of the nonlinear treatment in this illustration is the determination of D sub Mu Mu in the vicinity of 90 deg pitch angles where quasilinear theory breaks down. The spatial diffusion coefficient parallel to a mean magnetic field is evaluated using D sub Mu Mu as calculated by this technique. It is argued that the partially averaged field method is not limited to small amplitude fluctuating fields and is hence not a perturbation theory

A new approach to cosmic ray diffusion theory

An approach is presented for deriving a diffusion equation for charged particles in a static, random magnetic field. The approach differs from the usual, quasi-linear one, in that particle orbits in the average field are replaced by particle orbits in a partially averaged field. In this way the fluctuating component of the field significantly modifies the particle orbits in those cases where the orbits in the average field are unrealistic. The method permits the calculation of a finite value for the pitch angle diffusion coefficient for particles with a pitch angle of 90 rather than the divergent or ambiguous results obtained by quasi-linear theories. Results of the approach are compared with results of computer simulations using Monte Carlo techniques

Wide Angle Redshift Distortions Revisited

We explore linear redshift distortions in wide angle surveys from the point of view of symmetries. We show that the redshift space two-point correlation function can be expanded into tripolar spherical harmonics of zero total angular momentum $S_{l_1 l_2 l_3}(\hat x_1, \hat x_2, \hat x)$. The coefficients of the expansion $B_{l_1 l_2 l_3}$ are analogous to the $C_l$'s of the angular power spectrum, and express the anisotropy of the redshift space correlation function. Moreover, only a handful of $B_{l_1 l_2 l_3}$ are non-zero: the resulting formulae reveal a hidden simplicity comparable to distant observer limit. The $B_{l_1 l_2 l_3}$ depend on spherical Bessel moments of the power spectrum and $f = \Omega^{0.6}/b$. In the plane parallel limit, the results of \cite{Kaiser1987} and \cite{Hamilton1993} are recovered. The general formalism is used to derive useful new expressions. We present a particularly simple trigonometric polynomial expansion, which is arguably the most compact expression of wide angle redshift distortions. These formulae are suitable to inversion due to the orthogonality of the basis functions. An alternative Legendre polynomial expansion was obtained as well. This can be shown to be equivalent to the results of \cite{SzalayEtal1998}. The simplicity of the underlying theory will admit similar calculations for higher order statistics as well.Comment: 6 pages, 1 figure, ApJL submitte