VUV Spectroscopy of Atoms, Molecules and Surfaces

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10 VUV light generation: possibilities and limitations The situation covered by the two-step model is called the tunneling regime and is characterized by a value γ1, is called the ”ordinary ATI” regime, for which the proces of ATI dominates that of HHG [35]. In this regime the fast oscillations of the electric field prevent an atomic electron from escaping by tunneling. It sees on the average a zero field, resulting in an ionization probability that is uniform in time [50]. In the tunneling regime the periodicity of maximum ionization, i.e. harmonic generation, equal to half an electric field cycle, explains the periodicity in the frequency spectrum of the emitted harmonic radiation, being equal to twice the frequency of the fundamental laser light [50]. The two ways of ionization may be compared with emptying a bowl of water by shaking it at a high frequency or by tilting it at a low frequency, respectively [51]. Tunneling may be recognized as a smearing of the ATI peak structure, but the boundary between the two regimes, on which most studies have been performed, is not well defined [35]. In practice, the high-harmonic photon-energy cut-off is often limited by the saturation intensity at which the medium is fully ionized rather than by the intensity that is physically provided by the laser. This means that in order to obtain the highest possible harmonic orders, the rise time (in most cases equivalent to the duration) of the laser pulses must be shortest possible. As a consequence of the Fourier transform limit, imposing a minimum value to the product of the laser bandwidth and pulse duration [52], and the fact that the harmonic generation process introduces additional bandwidth broadening [53], there is an upper (lower) limit to the pulse duration (bandwidth) of the harmonics that can be generated at a desired minimum photon energy. Or stated the other way around: there is an upper limit to the photon energy that can be reached with a desired maximum bandwidth. The saturation intensity may be determined experimentally from a measurement of the yield of high-order harmonics of a given order as a function of laser intensity, resulting in an increase which levels off when ionization becomes dominant [44]. Such measurements have only been performed for a few different combinations of pulse durations and wavelengths and only a very limited effort has been directed towards establishing eventual scaling relations [54]. Theoretically, saturation intensities can be calculated in the perturbative regime from a knowledge of the N-photon generalized photoionization cross sections, which, however, are not easily calculated [55]. An attempt to estimate the generalized cross sections of heavier atoms by scaling from those known for the neutral hydrogen atom resulted in an order of magnitude disagreement with experimental data [56]. As a consequence, a relation for the photon energy that can be obtained as a function pulse duration and wavelength is at present not readily available.
1.3 High-harmonic generation 11 To the single-atom picture, outlined in its simplest form above, must be added the phase-matching effects arising from the propagation of the generated harmonic radiation through the gas medium. The medium most often has the shape of a gas jet generated by supersonic expansion through a ∼1 mm diameter cylindrical nozzle. In the strong-field regime the phase shift from the dispersion of the gas medium is entirely dominated by the Gouy phase shift (Nπ radians along the focus for the Nth harmonic) and a strong intensity-dependent variation of the phase of the non-linear polarization along the laser focus (∼100 radians) [57]. Combining these two effects it can be shown that optimum phase-matching may be obtained by focusing either a few millimeters in front of or behind the gas jet. By focusing in front of the gas jet harmonics will be generated with regular Gaussian spatial profiles while focusing at or behind the jet results in distorted annular profiles [58, 59]. Another consequence of the phase-matching conditions is a modification of the cut-off formula to Ecut=Ip +2Up [60]. The interest in generation and applications of high-order harmonics has grown tremendously since the initial indications in the 80’s that very short wavelengths could be obtained by focusing of intense laser light into noble-gas jets without the need for resonant enhancement [61, 62, 63]. The fundamental properties of the radiation have been thoroughly characterized [64] and advanced optimization procedures utilizing gas-filled hollow waveguides [65] and pulse-shaping of the driving field [66] are now being explored. Harmonics have been generated with many different laser sources and almost any kind of medium that one can think of: in molecular gases [67], atom clusters [68], carbon nanotubes [69] and at solid surfaces [70]. In the latter case both evenand odd orders are obtained because the inversion symmetry is broken at the surface. At present the shortest wavelengths generated are 7.8 nm with 1 ps, 1053 nm Nd:Glass pulses [47], 7.5 nm with 100 fs, 800 nm Ti:Sapphire pulses [71], 6.7 nm with 380 fs, 249 nm KrF pulses [72], and
Page 1: VUV Spectroscopy of Atoms, Molecule
Page 4 and 5: ii CONTENTS 4 .6 Conclusion . . . .
Page 6 and 7: iv Experimental and theoretical stu
Page 8 and 9: vi me to the principle of negative-
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Page 12 and 13: 2 VUV light generation: possibiliti
Page 22 and 23: 12 VUV light generation: possibilit
Page 28 and 29: 18 REFERENCES [14 ] C. R. Vidal, in
Page 30 and 31: 20 REFERENCES [55] C. J. G. Uiterwa
Page 32 and 33: 22 REFERENCES [98] Parameters from
Page 34 and 35: 24 Negative ions ing the binding en
Page 36 and 37: 26 Negative ions located energetica
Page 38 and 39: 28 Negative ions available has been
Page 40 and 41: 30 Negative ions assignment will th
Page 42 and 43: 32 Negative ions feel the repulsion
Page 44 and 45: 34 Negative ions Figure 2.1: Adiaba
Page 46 and 47: 36 Negative ions
Page 48 and 49: 38 REFERENCES [16] E. Kopp, Adv. Sp
Page 50 and 51: 40 REFERENCES [63] P. Balling et al
Page 52 and 53: 42 REFERENCES
Page 54 and 55: 44 High-resolution VUV spectroscopy
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60 REFERENCES [19] J. S. Nielsen an
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62 Lifetimes of molecular negative
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76 REFERENCES [19] V. V. Petrunin e
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78 REFERENCES [66] F. Robicheaux, P
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80 Chapter 5. Femtosecond VUV core-
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100 Chapter 5. Femtosecond VUV core
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120 REFERENCES [17] A. Cavalleri et
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122 REFERENCES [61] R. J. Finlay et
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124 REFERENCES [104]R.W.Joyner,inTh
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126 REFERENCES [152] T.-C. Chiang,
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128 Chapter 6. Two-colour pump-prob
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144 REFERENCES [16] Information ava
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146 REFERENCES [62] S. Baier et al.
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148 The following three chapters ar
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VUV Spectroscopy of Atoms, Molecules and Surfaces

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