Femtosecond-Scale Optics Part 8 pps

Lasers in Atomic Collisions, Cold Plasma and Cold Atom Physics 31 Laser wavelength range Power range External Cavity Diode Laser 800-1600 nm 1-200 mW CO laser 2.7-4, 5.1-6, μm mW-Watt CO2 laser 9-11 μm Watt Lead salt diode 4-30 μm 0.1 mW Quantum Cascade Laser 4-24 μm mW Optical parametric Oscillator 3-16 μm <1W Difference frequency generator 3-16 μm mW Table 3. Typical ranges and parameters of laser sources available for optogalvanic and spectroscopic studies. the capabilities and potential of the optogalvanic studies is more appealing today. For mid infrared application there are alternatives provided by quantum cascade lasers, as well as nonlinear optical devices, based on four wave mixing, but operating with very low powers (Markus (2003)). This very recent developments on mid infrared off the shelf optics, based on photonic band gap hollow fibers allow to forecast a very intensive use of the technique in trace detection in the mid infrared. Table 3 briefly summarizes the current situation related to the current accessible wavelengths, tuning characteristics, typical power range, and operation parameters of laser sources available for optogalvanic and spectroscopic studies in general. 4.3.2 Application of OGE spectroscopy in biology and medicine Trace gas detection is currently a very active area of applied research. With the high sensitivity provided by the optogalvanic spectroscopy, there is a great potential for this technique in the trace gas detection area. In this final part of the section devoted to the OGE some illustrative applications in the area of biology and medicine will be presented. Of particular interest for these applications is the Infrared spectral range. The applications range from the monitoring industrial processes, specially of flames and catalytic reduction of pollutants, to air quality monitoring in great cities, the quantification of CO 2 sinks and sources, to national security to the monitoring of biological processes in living organisms (including the human body). In all of these applications, the use of trace detection spectrometers coupled with laser-based spectroscopic gas are indispensable (Sigrist (2003)). The most intense absorption bands of organic molecules lie in the wavelength region between 2.5 and 20 μm, where these molecules have their fundamental rovibrational transitions. The areas of interest where the optogalvanic spectroscopy could find a future niche will involve the detection of organic molecules which absorb in this range of wavelengths. To be more specific, the detections such as ethylene, methane, CO 2 and CH 4 could open up a wealth of possibilities for the technique (Cristescu et al. (2008)). In the case of ethylene, it is a well know plant hormone that is conspicuous in many biological processes of the plant and fruits, such as death cell signaling, nitrogen fixation processes, circadian clock system of several plants, molecular alarm systems of fungi infection of fruits and tomatoes and even in the metabolic changes of human physiology induced by the light from the sun (Cristescu et al. (2008)). Acetone is a biomarker the increase of which in the human breath signals the onset of diabetes. A sensitive detector based on optogalvanic spectroscopy to quantify the presence of this molecule would have potentially a great use in hospitals and small clinics (Aman & Smith (2005)). Nitric oxide detection in the part per billion sensitivity could be of great clinical use in the early detection of lung pathologies and 199 Lasers in Atomic Collisions, Cold Plasma and Cold Atom Physics 32 Will-be-set-by-IN-TECH organ rejection monitoring, hepatopulmonary diagnostics, malaria and even gastritis, through the detection of the helicobacter pillory bacteria through its metabolic signature in the human breath. The scope and importance of these applications and several others make the area of research of new OGE detectors and techniques a very promising area of research in the future. 5. Acknowledgments We knowledge support from grants DGAPA-UNAM IN-116309 (J.J.M.), DGAPA-UNAM IN-101611-3 (R.C.T.), and DGAPA-PAPIIT IN113910 (AMJ). 6. References Aman, A. & Smith, D. (2005). Breath Analysis for clinical diagnosis and therapeutic monitoring, World Scientific Publishing Co. Pte Ltd., Singapore. Anis, F., Roudnev, V., Cabrera-Trujillo, R. & Esry, B. D. (2006). Laser assisted charge transfer in He 2+ → H collisions, Phys. Rev. A 73: 043414. Babin, F. & Gagné, J. (1992). Hollow Cathode Discharge (HCD) dark space diagnostics with laser photoionization and galvanic detection, Appl. Phys. B 54: 35. Baribieri, B., Beverini, N., & Sasso, A. (1990 ). Optogalvanic spectroscopy, Rev. Mod. Phys. 62: 603. Bergmann, K., Theuer, H. & Shore, B. W. (1998). Coherent population transfer among quantum states of atoms and molecules, Rev. Mod. Phys. 70: 1003 and references therein. Broglia, M., Catoni, F., Montone, A. & Zampetti, P. (1987). Galvanic detection of laser photoionization in hollow-cathode discharges: Experimental and theoretical study, Phys.Rev.A 36: 705. Cabrera-Trujillo, R. (2009). Laser and isotope effects in charge transfer processes in atomic collisions, Rad. Effects Defects Solids 164: 402. Carroll, C. E. & Hioe, F. T. (1988). Three-state systems driven by resonant optical pulses of different shapes, J. Opt. Soc. Am. B 5: 1335. Copeland, D. A. & Tang, C. L. (1976). Photon-assisted nonresonant charge exchange: A simple molecular model, J. Chem. Phys. 65: 3161. Cristescu, S., Persijn, S., Lintel, H. & Harrend, F. (2008). Laser-based systems for trace gas detection in life sciences, Appl. Phys. B 92: 343. Cubel, T., Teo, B., Malinovsky, V., Guest, J., Reinhard, A., Knuffman, B., Berman, P. & Raithel, G. (2005). Coherent population transfer of ground-state atoms into Rydberg states, Phys.Rev.A 72: 023405. Deiglmayr, J., Reetz-Lamour, M., Amthor, T., Westermann, S., de Oliveira, A. & Weidemüller, M. (2006). Coherent excitation of Rydberg atoms in an ultracold gas, Opt. Commun. 264: 293. Engel, A. v. (1965). Ionized Gases, second edition, Claredon, Oxford, England. Errea, L. F., Méndez, L. & Riera, A. (1983). On laser-induced charge transfer in the HeH 2+ quasimolecule, J. Chem. Phys. 79: 4221. Ferrante, G., Cascio, L. L. & Spagnolo, B. (1981). Laser-assisted symmetric charge transfer in atomic collisions, J. Phys. B 14: 3961. Gagné, J., Demers, Y., Pianarosa, P. & Dréze, C. (1983). Effet optogalvanique dans une décharge á cathode creuse: Mécanisme et dosage isotopique de l’uranium, Journal de physique (Paris) C7-44: 355. 200 Femtosecond-Scale Optics Lasers in Atomic Collisions, Cold Plasma and Cold Atom Physics 33 Gallagher, T. (1994). Rydberg Atoms, Cambridge University Press, Cambridge, UK. Gaubatz, U., Rudecki, P., Becker, M., Schiemann, S. & Bergmann, K. (1990). Population transfer between molecular vibrational levels by stimulated Raman scattering with partially overlapping laser fields. a new concept and experimental results, Chem.Phys.Lett. 92: 5363. Gearba, M., Camp, H., Trachy, M., Veshapidze, G., Shah, M., Jang, H. & DePaola, B. (2007). Measurement of population dynamics in stimulated Raman adiabatic passage, Phys. Rev. A 76: 013406. Green, R., Havrilla, G. & Trask, T. (1980). Laser-enhanced ionization spectrometry: Characterization of electrical interferences, Appl. Spectrosc. 34: 561. Gudzenko, L. I. & Yakovenko, S. I. (1972). Radiative collisions, Sov. Phys. JETP 35: 877. Havener, C. C., Rejoub, R., Krsti´c, P. S. & Smith, A. C. H. (2005). Charge transfer in low-energy collisions of He 2+ with atomic hydrogen, Phys. Rev. A 71: 042707. Hurst, G., Payne, S., Kramer, S. & Young, J. (1979). Resonance ionization spectroscopy and one-atom detection, Rev. Mod. P hys. 51: 767. Kirchner, T. (2002). Manipulating ion-atom collisions with coherent electromagnetic radiation, Phys.Rev.Lett. 89: 093203. Kirchner, T. (2004). Laser-field-induced modifications of electron-transfer processes in ion-atom collisions, Phys.Rev.A 69: 063412. Kirchner, T. (2005). Pauli blocking and laser manipulation of electron dynamics in atomic collisions, Nucl. Instr. Meth. B 233: 151. Kravis, S. & Haydon, S. (1981). Laser-induced optogalvanic effects under prebreakdown conditions in neon, J. Phys. D: Appl. Phys. 14: 151. Kuklinski, J., Gaubatz, U., Hioe, F. & Bergmann, K. (1989). Adiabatic population transfer in a three-level system driven by delayed laser pulses, Phys.Rev.A 40: 6741. Letokhov, V. & Chebotayev, V. (1977). Nonlinear Spectroscopy, Springer Verlag, Berlin. Levesque, S., Gagne, J. M. & Babin, F. (1997). Optogalvanic photoionization spectroscopy, J. Phys B: At. Mol. O pt Phys 30: 1331. Lorenzen, C J. & Niemax, K. (1983). Quantum defects of the n 2 p 1/2,3/2 levels in 39 Kand 85 Rb, Phys. Scr. 27: 300. Malinovsky, V. & Tannor, D. (1997). Simple and robust extension of the stimulated Raman adiabatic passage technique to n-level systems, Phys. Rev. A 56: 4929. Marinescu, M., H.R., S. & Dalgarno, A. (1994). Dispersion coefficients for alkali-metal dimers, Phys.Rev.A 49: 982. Marcus R.K. and Broekaert J.A.C., (2003). Glow Discharge Plasmas in Analytical Spectroscopy, John Wiley &Sons, Ltd. ISBN: 0-471-60699-5, London, England Markus, W. (2003). Trace gas monitoring by laser photoacoustic spectroscopy and related techniques, Rev. Sci. Instrum. 74: 486. Metcalf, H. & van der Straten, P. (1999). Laser Cooling and Trapping, Springer, New York. Oreg, J., Bergmann, K., Shore, B. & Rosenwaks, S. (1992). Population transfer with delayed pulses in four-state systems, Phys. Rev. A 45: 4888. Oreg, J., Hazak, G. & Eberly, J. (1985). Multilevel inversion schemes in and beyond the adiabatic limit, Phys. Rev. A 32: 2776. Oreg, J., Hioe, F. & Eberly, J. (1984). Adiabatic following in multilevel systems, Phys.Rev.A 29: 690. 201 Lasers in Atomic Collisions, Cold Plasma and Cold Atom Physics 34 Will-be-set-by-IN-TECH Pindzola, M. S., Minami, T. & Schultz, D. R. (2003). Laser-modified charge-transfer processes in proton collisions with lithium atoms, Phys. Rev. A 68: 013404. Press, W. H., Teukolsky, S. A., T.Vetterling, W. & Flannery, B. P. (1992). Numerical recipes,2nd edition, Cambridge University Press, New York, USA. Saffman, M., Walker, T. & Molmer, K. (2010). Quantum information with Rydberg atoms, Rev. Mod. Phys. 82: 2313. Sigrist, M. (2003). Trace gas monitoring by laser photoacoustic spectroscopy and related techniques, Rev. Sci. Instrum. 74: 486. Smith, A. V. (1992). Numerical studies of adiabatic population inversion in multilevel systems, J. Opt. Soc. Am. B 9: 1543. Stockhausen, G., Mende, W. & Kocj, M. (1996). Laser-induced photoionization in the dark space of a hollow cathode, J. Phys B : At. Mol. Opt Phys 29: 665. Stolterfoht, N., Cabrera-Trujillo, R., Öhrn, Y., Deumens, E., Hoekstra, R. & Sabin, J. R. (2007). Strong isotope effect on the charge transfer in slow collisions of He 2+ with atomic hydrogen, deuterium and tritium, Phys. Rev. Letters 99: 103201. Süptitz, W., Duncan, B. & Gould, P. L. (1997). Efficient 5d excitation of trapped Rb atoms using pulses of diode-laser light in the counterintuitive order, J. Opt. Soc. Am. B 14: 1001. Thoumany, P., Germann, T., Hänsch, T., Stania, G., Urbonas, L. & T., B. (2009). Spectroscopy of rubidium Rydberg states with three diode lasers, J. Mod. Opt. 56: 2055. Vitanov, N. (1998). Adiabatic population transfer by delayed laser pulses in multistate systems, Phys.Rev.A 58: 2295. Vitanov, N., Shore, B. & Bergmann, K. (1998). Adiabatic population transfer in multistate chains via dressed intermediate states, Eur.Phys.J.D 4: 15. Widiger, G., Willke, B. & Kock, M. (1994). Laser photoionization of copper atoms in the dark space of a hollow cathode discharge, J. Phys B: At. Mol. Opt Phys 27: 899. Zimmerman, M., Littman, M., Kash, M. & Klepner, D. (1979). Stark structure of the Rydberg states of alkali-metal atoms, Phys.Rev.A 20: 2251. 202 Femtosecond-Scale Optics 8 Time Resolved Spectroscopy with Femtosecond X-Ray Pulses Enikoe Seres 1,2 and Christian Spielmann 1,2 1 Institute of Optics and Quantumelectronics, Friedrich Schiller University Jena 2 Helmholtz Institute Jena Germany 1. Introduction Spectroscopy is of great interest for exploring the structure or composition of unknown matter. In 1813 Joseph von Fraunhofer discovered, independently from William Hyde Wollaston (1802), the dark lines in the spectrum of the sun, which has been later explained by the absorption of hydrogen. In 1859 Gustav Robert Kirchoff and Robert Wilhelm Bunsen discovered that the flame of gas burner changes its color, if different elements are heated up. In 1895 Wilhelm Conrad Röntgen (Röntgen, 1895) detected a new kind of radiation and named it X-ray radiation. In the first hundred years since their discovery, x-rays have played an important role in helping us understanding the structures of materials. Due to their short wavelength, x-rays are capable to resolve the structure of condensed matter but also the internal structure of atoms. The x-ray spectroscopic methods have been refined over the years. Nowadays physicists, chemists, biologists and material scientists rely on x-ray static structural analysis on a routine basis (Michette and Pfautsch, 1996). In addition to the static structural information, transient structural information is required for a deeper understanding. Such dynamic processes include the breaking and formation of chemical bonds, protein motions, charge transfer, phase transitions and so on (Sundaram 2002; La-O-Vorakiat, 2009; Woerner 2010). In Figure 1, we summarize the main applications of the time resolved spectroscopy. Many of these problems have already been tackled by means of conventional optical pump/probe spectroscopy. Unfortunately, such optical measurements cannot be directly inverted to give the position of the atoms as a function of the times expect in very favorable cases. Unlike optical spectroscopy, x-ray diffraction (XRD) and x-ray absorption (XRA) do in principle provide direct ways to reconstruct the motion of atoms during dynamic processes. Thus, time-resolved XRD and XRA may serve as a more direct way to observe the microscopic processes by which biomolecules perform their tasks or to observe ultrafast processes in solid-state materials. An ideal x-ray system for time- resolved diffraction should have sufficient temporal and spatial resolution to resolve the dynamics of fast processes. It took almost one century since the discovery of x-rays to realize x-ray sources providing a temporal resolution which is sufficient to follow the atomic and molecular motion, or to monitor the dynamics of molecules such as rotation, vibration, dissociation, or to study the dynamics of electrons on their natural time scale. Atom motion takes place on a picosecond to femtosecond time scale, whereas attosecond resolution is Femtosecond–Scale Optics 204 necessary for revealing the electron dynamics (Bressler et al., 2004, Rousse et al., 2001). Now, in the 21th century, we are in the fortunate situation to routinely generate bright femtosecond and attosecond x-ray pulses. In this chapter we review the current progress of time resolved x-ray spectroscopy and present some of our recent results about x-ray source development and x-ray absorption studies of transient states of matter. This chapter is divided into the following sections: 1. Introduction 2. X-rays and x-ray absorption spectroscopy 3. Pulsed x-ray sources 4. High harmonic generation 5. Time-resolved X-ray spectroscopy 10 -15 10 -12 10 -9 10 -6 10 -3 10 0 10 3 Time scale in seconds fourth order transfer protein folding electron-phonon scattering thermal processes shock waves re-crystallization H + transfer life time of structural transitions evaporation atomic motion 10 -12 10 -11 10 -10 10 -9 heat conduction melting Non linear absorption ablation T e-h < T L T e-h > T L phonon-phonon scattering 10 -14 10 -12 side chain effects 10 -13 electron-electron scattering 10 -15 non thermal melting third order structural changes Fig. 1. Typical time scales for structural and electronic processes in solids. 2. X-ray radiation X -ray radiation is a part of the electromagnetic radiation spectrum. The wavelength of X- rays, extends from 0.02 Å to 100 Å, and corresponds to the atomic and molecular length scales. X-ray radiation can be divided as follows: • ultra-soft <1 keV (λ > 1 nm) and XUV • soft 1 keV < E <10 keV as (0.1 nm - 1 nm), • hard 10 keV < E < 100 keV (0.1 nm - 0.01 nm) • ultra-hard E > 100 keV (λ < 0.01 nm) The use of radiation in this wavelength range provides, direct information about the structure of matter (Agarwal 1991; Rose-Petruck et al., 1999; Bressler et al., 2002). Therefore, the development and application of X-ray sources for the structure determination is of great scientific interest. The first X-ray tube was realized by W. C. Röntgen. He discovered a new type of radiation arisen from the interaction of accelerated electrons with matter. The decelerated electron beam radiates a broad continuous spectrum with sharp characteristic Time Resolved Spectroscopy with Femtosecond X-Ray Pulses 205 lines on it. The continuous part is referred to as “bremsstrahlung” and its maximum frequency depends only on the applied voltage and is independent of the anode material. The frequency of the line radiation depends on the anode material. The impacting electrons excite electrons from core levels into the continuum. The created hole is filled by an electron from a higher shell and the excess energy is emitted as a photon with an energy corresponding to the energy difference of the two involved states. For an anode material with atomic number Z, Moseley law predicts the frequency of the line: 2 22 11 f i M Rc Z mM nn ν ∞    =−   +   (1) Here m and M is the mass of the electron and the mass of the nucleus, n f and n i indicate the principal quantum number of initial and final states, R ∞ is the Rydberg constant. 2.1 X-ray spectroscopy methods Both the bremsstrahlung and the characteristic radiation are used to investigate the structure of matter. Moreover, information about the atomic structure can be also obtained from the x-ray generation itself. The sample under investigation is illuminated with an electron or x-ray beam and its properties can be obtained by measuring the absorbed, diffracted, or scattered x-rays, the emitted x-ray fluorescence, or the ejected photoelectrons. In the X-ray diffractometry (XRD) the X-ray beam interacts with the electron shells of the atoms fixed in a lattice. The diffraction pattern provides information about the atomic distances of the crystalline structure. At not too high photon energies, this scattering is elastic: there is no energy loss and then we also speak of coherent scattering (Rayleigh scattering). In this case, the wavelength of the scattered X-rays is the same as the original X- ray wavelength. When a core electron is ejected, then it may be followed by a recombination from higher occupied levels and a photon is generated. This effect is described and characterized by X-ray fluorescence (XRF). XRF is primarily only an element-specific method and allows not only qualitative but also quantitative analysis of the components contained in the sample volume. For special cases it can provide also information about the structure. X-ray spectroscopy for chemical analysis (ESCA) is based on the generation of photoelectrons. This technique is essentially limited to the surfaces. Typically, it is possibly to receive information from only two or three atomic layers, although the exciting X-rays penetrate much deeper. X-ray absorption spectroscopy (XAS) provides information about the atomic structure and also about the atomic distances and chemical bonds. Matter can be characterized by the transmitted X-ray intensity I, if the sample is illuminated by an X-ray beam with intensity of I0: 0 d IIe μ − = , (2) where d is the thickness of the material and μ is the linear attenuation coefficient. The incoming X-ray beam can excite core electrons to a higher unoccupied states or to the continuum. When the energy of the photons is increased, pronounced edges appears in the absorption spectrum, if the photon energy is high enough to excite electrons from a deeper core state (Figure 2) into the continuum. Femtosecond–Scale Optics 206 0,01 0,1 1 10 100 10 100 1000 10000 Absorption coefficience (µm -1 ) Photon energy (eV) L 2 2p 1/2 L 3 2p 3/2 L 1 2s M 2 3p 1/2 M 3 3p 3/2 M 4 3d 3/2 K1s 0.01 0.01 0.1 Fig. 2. X-ray absorption spectrum of Ti with K, L and M-edges. A closer examination shows that only the K-edge consists of a simple jump. Near the L- absorption edge well-resolved jumps can be seen. The M-edges are not so well resolved. 2.1.1 Fine structure of the XAS signal If the X-ray absorption spectrum is measured with high resolution, then a fine structure can be observed and resolved. The position and shape of the absorption edges is determined by the atom and is independent from environment of the atom, at least in a first approximation. The reason is that the x-ray absorption is related to the core levels, and only electrons from outer shell are involved in chemical bonds. However spectroscopy with sufficiently high resolution can detect an influence of the chemical bond on the energy and structure of the absorption edges. For determining the structure, i.e. getting information about the neighborhood of the atom of interest, we can rely on the following X-ray absorption methods: • XAMES (X-Ray Absorption Main Edge Spectroscopy). The position of the absorption edge contains information about the electronic structure of atoms and the structure of the material. The pre-edge contains further information about the electron configurations and the symmetry around the absorbing atom. The measurements are made in a range from -10 eV to +10 eV around the absorption edge of the atom. The shift of the edge position is often referred as “chemical shift”. • XANES (X-Ray Absorption Near Edge Spectroscopy) provides information on the valence electrons and chemical bonds. It is necessary to record the signal in a range of 10 – 40 eV above the edge. • EXAFS (Extended X-Ray Absorption Fine Structure) contains structural information, i.e. the distance to the neighboring atoms. The absorption spectrum is measured and evaluated in a range from 40 eV to 1000 eV beyond the absorption edge. Time Resolved Spectroscopy with Femtosecond X-Ray Pulses 207 XANES X-RAY NEAR ABSORPTION EDGE SPECTROSCOPY •valence electrons •chemical bonds EXAFS X-RAY ABSORPTION EXTENDED FINE STRUCTURE •atomic distances •environment of the atom XAMES X-RAY ABSORPTION MAIN EDGE STRUCTURE • coordination number • coordination geometry pre - edge post - edge Fig. 3. Structure of the absorption edge can be divided into the ranges of XAMES, XANES and EXAFS. 2.1.2 EXAFS signal at the K-edge In principle, structural information can be obtained with XANES or EXAFS. The measurement in a narrow range is easier, but XANES does not allow a simple determination of the distance to the next atoms from the experimental data. The basic principle of EXAFS is summarized in the following. The incident photons excite an electron from a core level into the continuum. The generated and outgoing photoelectron waves are elastically scattered by neighboring atoms. Quantum mechanically speaking, part of the wave function of the photoelectron is reflected by the neighboring atoms and the wave functions interfere. The modulation in the absorption spectrum depends on the path difference of the partial waves, and at a fixed atomic distance it is a function of the incident X-ray photon energy. (Stern 1974; Lytle et al., 1975; Lee et al, 1981; Rehr et al, 1992; Rehr & Albers 2000; Sipre, 2002.) The evaluation of a measured EXAFS spectrum requires the following steps. First, χ(Ε), the normalized EXAFS signal is calculated from the measured absorption spectrum: 00 00 () ( ) () () EE E E μμ χ Δμ − = , (3) where μ(E) is the measured absorption coefficient, μ 0 (E) is the smooth background function, or the absorption coefficient of the atom, and Δμ 0 (E 0 ) is the measured jump of the absorption μ(E) at the edge and the energy of the absorption edge is E 0 . Then the signal is converted into k-space: () 0 2 2 e m khE ν =−  , where hν is the incident energy of X-ray photons. The calculated signal χ(k) carries information about the distances and the type of neighboring atoms: Femtosecond–Scale Optics 208 Debye-Waller-factor () () () [] )( 2 2 2 22 2sin , 1 k r k j jj j jj j j j eekkr kr kfN k k λσ π χ − − ⋅Ψ+=  phase amplitude correction term () 0 2 2 Eh m k e −⋅= υ  wave number of the photo electrons Here, N j is the number of backscattering atoms at the same distance r j from the absorber atom. f(k) and Ψ(k) corresponds to the amplitude and phase shift of the scattered wave, and σ² is the standard deviation of atomic distance. The factor 2 2 jj k e σ − also known as Debye- Waller factor is a measure for the smearing of the interference signal. Due to the spatial dispersion of the outgoing wave only backscattering from the next neighbors must be considered. Furthermore, the photoelectron must be scattered before the generated hole was filled. If these approximations are not valid a correction term of 2() jj rk e λ is required. The size λ j (k) depicts the energy-dependent mean free path of photoelectrons. Phase shift impressed on the scattered electron wave is given () () 2 () jj l kkk δ Ψ=Φ+ (4) with Φ j (k) phase shift through the backscattering from the j th neighboring atom and δ l is the phase shift of the photoelectron in the potential of an atom in the l th shell. The amplitude of the backscattered wave is given: () 2() 1 (, ) (, ) (2 1) 1(1) 2 l iik l l fk fk e l e ik δ ππ Φ ==+−−  (5) With the help of the given formalism, the atomic distance can be precisely determined by EXAFS. Additionally it may be necessary to determine the composition of the nearest neighbors by other methods (Bzowski et al., 1993; Filiponi et al., 1989; Johnson et al.; 2003, D'Angelo et al., 1996, Bianconi et al., 1987, Farges et al., 1997; Faraci et al., 1997). 2.1.3 EXAFS signal at the L-edge Previously it was assumed that the electron is generated by an excitation from the K-shell. However, EXAFS is also possible from e.g. the L-shell. For considering absorption from the L 1 shell, the same formalism as for the K-shall can be used. However for electrons from the L 2,3 shell the evaluation is more complicated. The reason is that the electron in the initial state is a p-state instead of a s-state. Because of the selection rule, the photoelectron generated can be a s or d-like electron. The difference is not only the energy but also the phase in the scattering is different and in addition, there is a superposition of two states. For EXAFS from the L 2,3 shell the signal can be calculated according to the following formula: [...]... signature also in the fine-structure of the soft-x-ray absorption spectrum ( Nakano 1999) 185 0 184 0 K 183 0 182 0 181 0 180 0 0 100 200 300 400 500 600 Delay (fs) Position of the edge (eV) 102 L 101,5 101 100.5 100,5 100 99,5 99.5 99 0 100 200 300 400 500 600 Delay (fs) Fig 10 Measured shift of the position of the (a) K- edge (1.8k eV) and (b) L-edge (100 eV) of silicon after excitation with an ultrahsort laser... 1997), pp 180 9- 181 9 Filiponi, A., et al., (1 989 ) Structural investigations of a-Si and a-Si:H using X-ray-absorption spectroscopy at the Si K edge Phys Rev B Vol 40, No 14, (November 1 989 ), pp.9636-9643 Gibson, E A., et al (2003) Coherent Soft X-ray Generation in the Water Window with Quasi–Phase Matching Science, Vol.302 No.3 (October 2003),8may 1995), pp 95- 98 Giulietti, D., & Gizzi, L A (19 98) X-Ray... 1 781 - 181 2 Brown, F L H., et al (1999) Ultrafast extended x-ray absorption fine structure (EXAFS)theoretical considerations J Chem Phys., Vol 111, No 14, (October 1999), pp 62 386 246 Bzowski, S A., & Sham T K (1993) Pd-Ti bimetallic: A study of the electronic structure using X–ray photoelectron spectroscopy and x-ray-absorption near-edge structure Phys Rev B Vol 48, No.11, (September 1993), pp 783 6- 784 0... Vol.3, ( December 2007), pp 87 8 -88 3 Sipr, O., (2002) Spatial Distribution of photoelectrons participating in formation x-ray absorption spectra Phys Rev B Vol 65, No 20, (Mai 2002), pp 205115 Sommerer, G rottke H., & Sandner W (1999) Enhanced Efficiency in High-Order Harmonic Generation Using Sub-50-fs Laser Pulses Laser Phys Vol 9, No 1, pp 430-432 Spielmann, Ch et al, (19 98) Ultrafast near-keV coherent... 2971-2974 Kondo K et al., (1993) Wavelength dependence of nonsequential double ionization in He Phys Rev A, Vol 48, No 4, (October 1993), pp R2531-R2533 Korobkin D., (19 98) Soft X-Ray Amplification at 26.2 nm with 1-Hz Repetition Rate in a Table-Top System Phys Rev Lett Vol 81 , No 8, (August 19 98) , pp 1607-1610 Krainov, V P (1997).Ionization rates and energy-angular distributions at the barriersuppression... Generation of Coherent Ultrashort Soft-XRay Pulses Phys Rev Lett Vol 83 , No 4 (July 1999), pp 722- 725 Schnürer, M., et al., (19 98) Coherent 0.5keV x-ray emission from helium driven by a sub-10 fs laser Phys Rev Lett Vol 80 , No 15, (April 19 98) 3236 Scrinzi, A., et al (1999) Ionization above the Coulomb Barrier Phys Rev Lett Vol 83 , No.4, (July 1999), pp 706-709 Seibert, M M et al., (2010) Femtosecond... et al (2006) X-ray absorption spectroscopy in the keV range with laser generated high harmonic radiation Appl Phys Lett Vol 89 , (November 2006), pp 181 919 Seres, E et al., (2003) Sub-10-fs, terawatt-scale Ti:sapphire laser system Opt Lett Vol 28, No 19 (October 2003) Pp 183 2- 183 4 Seres, E et al., (2004) Generation of Coherent Soft-X-Ray Radiation Extending Far Beyond the Titanium L Edge Phys Rev Lett... Regime Phys Rev Lett 78, No 7, (February 1997), pp 1251-1254 Constant e., et al., (1999) Optimizing High Harmonic Generation in Absorbing Gases: Model and Experiment Phys Rev Lett Vol 82 , No 8, (February 1999), pp 16 681 671 D’Angelo, P et al., (1996) Multi electron excitations at the L edges of barium in aqueous solution Phys Rev B Vol 54, No 17, (November 1996), pp 12129-121 38 Da Silva, L B et al.,... quantum 2 28 Femtosecond–Scale Optics mechanical level (taking into account the electronic, vibration and rotation energy levels of the atoms) 3 Linear optics approximation From Maxwell’s equations we get: D   0E  P(E ) and B  0 H  0 M( H ) (1) where D - electric flux density, E - electric field vector, B - magnetic flux density, H magnetic field vector,  0 - dielectric constant of vacuum = 8. 85·10-12... al 19 98) , resulting in a single XUV/X-ray burst of attosecond duration SOURCE High Harmonic Generation Laser generated plasmas Third generation synchrotrons Slicing scheme Short pulse photon source (SPPS) PHOTONS /PULSE/ 0.1% BW PULSE WIDTH ENERGY RANGE REPETITION RATE 80 as < 4 keV kHz 102 ~300 fs ≤ 3 keV 10 Hz- 1 kHz 104-106 10-20 ps 0- 100 keV ≤ 500 MHz 101-103 ~100 fs 0-100 keV 1-10 kHz 1 08 ~ 100 . A 45: 488 8. Oreg, J., Hazak, G. & Eberly, J. (1 985 ). Multilevel inversion schemes in and beyond the adiabatic limit, Phys. Rev. A 32: 2776. Oreg, J., Hioe, F. & Eberly, J. (1 984 ). Adiabatic. Phys 27: 89 9. Zimmerman, M., Littman, M., Kash, M. & Klepner, D. (1979). Stark structure of the Rydberg states of alkali-metal atoms, Phys.Rev.A 20: 2251. 202 Femtosecond-Scale Optics 8 Time. 2055. Vitanov, N. (19 98) . Adiabatic population transfer by delayed laser pulses in multistate systems, Phys.Rev.A 58: 2295. Vitanov, N., Shore, B. & Bergmann, K. (19 98) . Adiabatic population