Spatial coherence in the transition radiation spectrum

The formal expression of the spectral distribution of the transition radiation intensity will be here derived in the case of a relativistic three-dimensional charged beam. Charged beams with a particle density such as is typically encountered in a particle accelerator will be considered. In particular, a sufficiently high particle density will be supposed so that a continuous spatial distribution function can be reliably attributed to the charged bunch. The formula of the spectral distribution of the transition radiation intensity originated by a relativistic three-dimensional charged beam - already presented in a previous work - will be here submitted to a formal check and interpreted in the physical consequences. The present work contains an additional mathematical derivation of the radiation energy spectrum consisting in a different method to implement the continuous limit in the distribution function of the particle coordinates. In the former derivation of the formula, the average operation with respect to the continuous distribution function of the particle coordinates was applied to the radiation intensity of a N electron bunch. In the present one, it is applied to the radiation electric field of a N electron bunch. The comparison of the two alternative but in any case equivalent formal routes to the spectral distribution of the transition radiation intensity will offer the possibility to directly cross-check the mathematical self-consistency of the presented results within the limits of applicability of the continuous limit approximation. According to such results, both the flux and the angular distribution of the photons emitted at a given wavelength - even shorter than the longitudinal length of the bunch - are expected to undergo a modification as the beam transverse size is varied with respect to the observed wavelength. As a function of the beam transverse size the spatial coherence degree of the transition radiation source is thus expected to change. The physical consistency of such an effect occurring in the transition radiation emission by a charged beam can be argued on the basis of a compatibility criterion with other similar relativistic electromagnetic radiative phenomena and interpreted in the framework of the temporal causality and the Huygens-Fresnel principles. Finally, the aspect of the applicability of the continuous limit approximation to the case of a charged beam in a particle accelerator is treated in terms of a practical quantitative criterion.     

Multiferroics: Different ways to combine magnetism and ferroelectricity

Multiferroics — materials which are simultaneously (ferro)magnetic and ferroelectric, and often also ferroelastic — attract now considerable attention, both because of the interesting physics involved and as they promise important practical applications. In this paper, I give a survey of microscopic factors determining the coexistence of these properties, and discuss different possible routes to combine them in one material. In particular, the role of the occupation of d-states in transition metal perovskites is discussed, possible role of spiral magnetic structures is stressed, and the novel mechanism of ferroelectricity in magnetic systems due to combination of site-centred and bond-centred charge ordering is presented. Microscopic nature of multiferroic behaviour in several particular materials, including magnetite Fe₃O₄, is discussed.     

Spatial coherence of an optical turbulent beam in a biased photorefractive crystal due to the spatiotemporal modulation instability

We report the experimental observation of the dynamic pattern formation of a broad coherent light beam in a biased photorefractive crystal due to the spatiotemporal modulation instability. When the nonlinearity exceeds a specific threshold, the coherent light beam not only breaks up into light spots due to the modulation instability but also fast fluctuates both spatially and temporally, forming an optical turbulent beam, which behaves as a quasi-homogeneous speckled beam or a partially incoherent beam. We investigate the spatial coherence property of an optical turbulent beam from the visibility of the averaged double-slit interference fringe. We also numerically demonstrate the visibility variation of the instantaneous interference fringe of an optical turbulent beam.     

Growth of Co-Silicides from single crystal and evaporated Si

We have investigated the reaction of a thin Co film with a (100) Si (Si ^c ) or an evaporated Si (Si ^e , which is amorphous) substrate during thermal annealing. On either substrate, Co₂Si and CoSi form simultaneously and the growth of each phase has a square root of time dependence. Both silicides grow faster on Si ^c than on Si ^e . A model is proposed to calculate the effective diffusion constant in each silicide from the growth data of the silicides. The activation energies of the effective diffusion constants in Co₂Si and CoSi grown on Si ^c are 1.7±0.1 eV and 1.8±0.1 eV, respectively; while those on Si ^e are 1.85±0.1 eV and 1.9 ±0.1 eV, respectively. The differences observed for the two substrates are tentatively attributed to the presence of impurities in Si^e and to the microstructural differences of the silicides formed on either substrate.     

Spin density wave dislocation in chromium probed by coherent X-ray diffraction

We report on the study of a magnetic dislocation in pure chromium. Coherent X-ray diffraction profiles obtained on the incommensurate Spin Density Wave (SDW) reflection are consistent with the presence of a dislocation of the magnetic order, embedded at a few micrometers from the surface of the sample. Beyond the specific case of magnetic dislocations in chromium, this work may open up a new method for the study of magnetic defects embedded in the bulk.     

Propagation of partially polarized, partially coherent beams in uniaxial crystals orthogonal to the optical axis

The propagation of partially polarized and partially coherent beams in uniaxial crystals orthogonal to the optical axis is investigated. The analytical formulae for the elements of the cross-spectral density matrix of partially polarized and partially coherent beams propagating through uniaxial crystals orthogonal to the optical are derived. The numerical results show that the degree of polarization decreases with the increase of the ratio of extraordinary to ordinary refractive indices at a certain propagation distance, and the influence of uniaxial crystals on the degree of coherent is not so evident. And the beams spread more rapidly in the direction parallel to the optical axis than orthogonal to the optical axis in positive crystal with the propagation distance increasing.     

Coherent Beam Combination of Three Fiber Amplifiers with Multi-dithering Technique

Coherent beam combination of three W-level fiber amplifiers with multi-dithering technique is demonstrated. The multi-dithering technique is used for phase control in two channels. In the experiment, two channels are modulated by sine wave with 70 kHz and 100 kHz respectively, and two regular commercial DSP lock-in amplifiers and an industrial computer are used for electric signal processing in the feedback loop. The fringe contrast is advanced from 12% to 81%, and 78% coherent combination efficiency is obtained when the feedback loop is closed.     

Multi-color XUV interferometry using high-order harmonics

We present a novel interferometric setup operating in the XUV spectral range. The interferometer consists of a combination of a double pinhole (similar to Young’s double slit) and a transmission grating. In the case of a light source consisting of discrete spectral lines, it allows recording interferograms for multi-colors simultaneously. We present two experiments in which high-order harmonics generated by a titanium sapphire laser were used as the light source for the interferometer. First, the temporal coherence lengths of the single harmonics were determined, and second, the index of refraction and the absorption of a thin beryllium foil were measured simultaneously in the range of 17–25 nm.     

Propagation of a stochastic electromagnetic Gaussian Schell-model beam through an optical system in turbulent atmosphere

A generalized diffraction integral formula for stochastic electromagnetic beams propagating through an optical system in turbulent atmosphere is derived with the help of tensor method. Some analyses are illustrated by a numerical example relating to changes in the average intensity and the degree of polarization of an electromagnetic Gaussian Schell-model beam propagating through a double-lenses system. It is shown that the optical system has strong influence on the propagation properties of the beam. The method used in this paper can be widely applied to the propagation of astigmatic beams through an optical system in turbulent atmosphere.