(b) Write out the equations for the time dependence of ρ11, ρ22, ρ12 and ρ21 assuming that a light field interaction V = -μ12Ee iωt + c.c. couples only levels |1> and |2>, and that the excited levels exhibit spontaneous decay. (8 marks) (c) Under steady-state conditions, find the ratio of populations in states |2> and |3>. (3 marks) (d) Find the slowly varying amplitude ̃ ρ 12 of the polarization ρ12 = ̃ ρ 12e iωt . (6 marks) (e) In the limiting case that no decay is possible from intermediate level |3>, what is the ground state population ρ11(∞)? (2 marks) 2. (15 marks total) In a 2-level atom system subjected to a strong field, dressed states are created in the form |D1(n)> = sin θ |1,n> + cos θ |2,n-1> |D2(n)> = cos θ |1,n> sin θ |2,n-1>

The Quantum Theory of Light

Advanced materials and processing techniques are based largely on the generation and control of non-homogeneous microstructures, such as precipitates and grain boundaries. X-ray tomography can provide three-dimensional density and chemical distributions of such structures with submicrometre resolution; structural methods exist that give submicrometre resolution in two dimensions; and techniques are available for obtaining grain-centroid positions and grain-average strains in three dimensions. But non-destructive point-to-point three-dimensional structural probes have not hitherto been available for investigations at the critical mesoscopic length scales (tenths to hundreds of micrometres). As a result, investigations of three-dimensional mesoscale phenomena--such as grain growth, deformation, crumpling and strain-gradient effects--rely increasingly on computation and modelling without direct experimental input. Here we describe a three-dimensional X-ray microscopy technique that uses polychromatic synchrotron X-ray microbeams to probe local crystal structure, orientation and strain tensors with submicrometre spatial resolution. We demonstrate the utility of this approach with micrometre-resolution three-dimensional measurements of grain orientations and sizes in polycrystalline aluminium, and with micrometre depth-resolved measurements of elastic strain tensors in cylindrically bent silicon. This technique is applicable to single-crystal, polycrystalline, composite and functionally graded materials.

Three-dimensional X-ray structural microscopy with submicrometre resolution

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Reactivity of Surface Species in Heterogeneous Catalysts Probed by In Situ X-ray Absorption Techniques

This review highlights recent advances in X-ray microcomputed tomography (microCT) as applied to materials, specifically advances made since the first materials microCT review appeared in Internati...

Recent advances in X-ray microtomography applied to materials

The following topics are dealt with: TTF/FLASH in the XFEL context, general layout of the XFEL facility, the XFEL accelerator, undulators for SAES and spontaneous emission, photon beamlines and scientific instruments, infrastructure and auxiliary systems, commissioning and operation, project management and organization, cost and time schedule. (HSI)

XFEL: The European X-Ray Free-Electron Laser - Technical Design Report

The manufacture and properties of compound refractive lenses (CRLs) for hard X-rays with parabolic profile are described. These novel lenses can be used up to ∼60 keV. A typical focal length is 1 m. They have a geometrical aperture of 1 mm and are best adapted to undulator beams at synchrotron radiation sources. The transmission ranges from a few % in aluminium CRLs up to about 30% expected in beryllium CRLs. The gain (ratio of the intensity in the focal spot relative to the intensity behind a pinhole of equal size) is larger than 100 for aluminium and larger than 1000 for beryllium CRLs. Due to their parabolic profile they are free of spherical aberration and are genuine imaging devices. The theory for imaging an X-ray source and an object illuminated by it has been developed, including the effects of attenuation (photoabsorption and Compton scattering) and of the roughness at the lens surface. Excellent agreement between theory and experiment has been found. With aluminium CRLs a lateral resolution in imaging of 0.3 µm has been achieved and a resolution below 0.1 µm can be expected for beryllium CRLs. The main fields of application of the refractive X-ray lenses are (i) microanalysis with a beam in the micrometre range for diffraction, fluorescence, absorption, scattering; (ii) imaging in absorption and phase contrast of opaque objects which cannot tolerate sample preparation; (iii) coherent X-ray scattering.

/pdf/imaging-by-parabolic-refractive-lenses-in-the-hard-x-ray-335k2lxryz.pdf

Imaging by parabolic refractive lenses in the hard X-ray range

We describe refractive x-ray lenses with a parabolic profile that are genuine imaging devices, similar to glass lenses for visible light. They open considerable possibilities in x-ray microscopy, tomography, microanalysis, and coherent scattering. Based on these lenses a microscope for hard x rays is described, that can operate in the range from 2 to 50 keV, allowing for magnifications up to 50. At present, it is possible to image an area of about 300 μm in diameter with a resolving power of 0.3 μm that can be increased to 0.1 μm. This microscope is especially suited for opaque samples, up to 1 cm in thickness, which do not tolerate sample preparation, like many biological and soil specimens.

A microscope for hard x rays based on parabolic compound refractive lenses

Hard x-ray absorption spectroscopy is combined with scanning microtomography to reconstruct full near-edge spectra of an elemental species at each location on an arbitrary virtual section through a sample. These spectra reveal the local concentrations of different chemical compounds of the absorbing element inside the sample and give insight into the oxidation state, the local atomic structure, and the local projected free density of states. The method is implemented by combining a quick scanning monochromator and data acquisition system with a scanning microprobe setup based on refractive x-ray lenses.

Mapping the chemical states of an element inside a sample using tomographic x-ray absorption spectroscopy

The time-resolved x-ray absorption spectroscopy (QEXAFS) yields structural information about e.g. fast chemical decomposition reactions, thin film deposition, solid-state reactions, and phase transformations. Here we describe a new experimental set-up for QEXAFS experiments enabling the acquisition of full EXAFS spectra with a scan range of up to about 3 keV and a repetition rate of typically 10 Hz. Depending on photon flux and sample quality, repetition rates of up to 40 Hz can be used. The new monochromator design employs a fixed-exit channel cut crystal and a cam driven tilt table for rapid angular oscillations. The detection of fluorescence radiation or surface sensitive techniques can be applied. The new monochromator in combination with refractive x-ray lenses for beam focusing also allows XANES-microtomography in a reasonable time frame.

Recent Advances and New Applications of TimeResolved Xray Absorption Spectroscopy

The Piezo-QEXAFS technique is a novel tool for time-resolved X-ray absorption spectroscopy in the hard X-ray range. Monochromator components consisting of specialized tilt stages to perform fast energy scans, lightweight crystal holders, bending mechanics, and control electronics are being installed and commissioned. It is planned to perform fast EXAFS scans with time resolution in the millisecond range. With Piezo-QEXAFS all typical X-ray absorption experiments will be possible as it retains the standard linear geometry. The achieved time resolution opens interesting insights into the dynamics of phase transitions and chemical reactions.

M. Richwin

Papers

Imaging by parabolic refractive lenses in the hard X-ray range

A microscope for hard x rays based on parabolic compound refractive lenses

Mapping the chemical states of an element inside a sample using tomographic x-ray absorption spectroscopy

Recent Advances and New Applications of TimeResolved Xray Absorption Spectroscopy

Piezo-QEXAFS: advances in time-resolved X-ray absorption spectroscopy.