Degree Of Transverse Coherence Research Articles

Transfer of orbital angular momentum superposition from asymmetric Laguerre–Gaussian beam to Bose–Einstein Condensate

In this paper, we have formulated a theory for the microscopic interaction of the asymmetric Laguerre–Gaussian (aLG) beam with the atomic Bose–Einstein condensate (BEC) in a harmonic trap. Here the asymmetry is introduced to an LG beam considering a complex-valued shift in the Cartesian plane keeping the axis of the beam and its vortex states co-axial to the trap axis of the BEC. Due to the inclusion of the asymmetric nature, multiple quantized circulations are generated in the beam. We show how these quantized circulations are transferred to the BEC, resulting in a superposition of matter vortex states. The calculated Rabi frequencies for the dipole as well as quadrupole transitions during the transfer process show distinct variability with the shift parameters of the beam. A significant enhancement of the quadrupole Rabi frequency for higher vorticity states is observed compared to the symmetric single orbital angular momentum (OAM) mode beam at a particular range of the shift parameters. We also demonstrate the variation of superposition of matter vortex states and observe its distinct feature compared to the superposition of the LG modes for different shift parameters. The first order spatial correlation of the superposed states supports this feature and highlights asymmetry in the degree of transverse coherence along orthogonal directions on the surface.

Statistical properties of the radiation from SASE FEL operating in a post-saturation regime with and without undulator tapering

We describe statistical and coherence properties of the radiation from X-ray free-electron lasers (XFEL) operating in the post-saturation regime. We consider the practical case of the SASE3 FEL at the European XFEL. We perform comparison of the main characteristics of the X-ray FEL operating in the post-saturation regime with and without undulator tapering: efficiency, coherence time, and degree of transverse coherence.

Coherence properties of the European XFEL

The European x-ray free-electron laser (XFEL) provides x-ray self-amplified spontaneous emission (SASE) FEL radiation in the wavelength range from 0.1 to 3 nm using three undulator systems. The SASE mode of operation at the European XFEL defines specific behavior of longitudinal and transverse coherence properties. In this paper, we describe the evolution of the temporal and transverse correlation functions along the undulator length, and we extract the corresponding evolution of coherence time and degree of transverse coherence as typical figures of merit. Generation of coherent radiation inside the FEL undulators is followed by beam transport to the experiments. During transport, the total number of coherent modes is preserved, but the wavefront can be disturbed, and we analyze the conditions under which this occurs. It is emphasized that the development of experimental observables for the degree of coherence and wavefront properties will be important for experiments using coherent x-ray radiation.

Statistical and coherence properties of radiation from x-ray free-electron lasers

We describe the statistical and coherence properties of radiation from x-ray free-electron lasers (XFEL). It is shown that the XFEL radiation before saturation is described with Gaussian statistics. Particularly important is the case of the optimized XFEL studied in detail. Applying similarity techniques to the results of numerical simulations allowed us to find universal scaling relations for the main characteristics of an XFEL operating in the saturation regime: efficiency, coherence time and degree of transverse coherence. We find that with an appropriate normalization of these quantities, they are functions of only the ratio of the geometrical emittance of the electron beam to the radiation wavelength. Statistical and coherence properties of the higher harmonics of the radiation are highlighted as well.

Output power and degree of transverse coherence of X-ray free electron lasers

The explicit solution of the initial value problem is obtained for a SASE FEL (self-amplified spontaneous emission free electron laser) operating with a large ratio of electron beam emittance to the reduced wavelength, ϵ ˆ = 2 π ϵ / λ ≫ 1 . The output power and the degree of transverse coherence are explicitly calculated for a high-gain linear regime. The degree of coherence is shown to be dependent on the ratio of the number of FEL gain lengths to the parameter ϵ ˆ . In particular, in the multi-mode limit the radiation from a SASE FEL has by the squared number of gain lengths higher degree of transverse coherence than a synchrotron radiation generated by a beam with the same emittance. An estimate for the degree of coherence of the radiation from X-ray SASE FEL at saturation is presented.

X-ray speckles from an optical grating

We report a study of speckles produced by x rays of partial transverse coherence scattered from the surface of an optical reflection grating. This study reveals the presence of surface inhomogeneity that is undetectable with either laser (visible) light or transversely incoherent x rays. Qualitative analysis of the speckle patterns provides us with information on the surface morphology of the optical grating. The underlying order due to the periodicity of the grating enhances the detection of the x-ray speckles. The speckle patterns are obtained using a well-characterized partially transverse-coherent source (a secondary source) produced with an arrangement of slits and a focusing mirror in a synchrotron x-ray beamline. The degree of transverse coherence is measured and compared quantitatively with statistical optics predictions for the complex-coherence factor. {copyright} {ital 1998} {ital The American Physical Society}