VUV Spectroscopy of Atoms, Molecules and Surfaces

More documents

Recommendations

Info

8 VUV light generation: possibilities and limitations Figure 1.2: A schematic of the tunneling picture, or two-step model, used to describe the mechanism of high-harmonic generation for a single atom. From [34]. multi-photon ionization with the absorption of more photons than required for ionization, giving rise to peaks in the photoelectron kinetic-energy spectrum separated by one photon energy [35]. In the two-step model the electric light field is assumed to vary sufficiently slowly that it makes sence to consider an electron tunneling through the barrier created in the atomic Coulomb potential by the field. Since the Coulomb potential is most strongly bent at the field extrema, the ionization probability is strongly peaked in time. The possibility exists that an electron released this way is pushed back towards the residual ion, following the sign change of the electric field vector, as shown in figure 1.2. Upon re-scattering the electron may acquire additional kinetic energy, recognized as a plateau in the ATI spectrum extending from ∼3Up to ∼10Up [36, 37, 38] where Up is the average quiver energy of the free electron oscillating in the field. The electron may also recombine with the ion, thereby releasing a photon with a frequency which is an odd multiple of the laser frequency (HHG). The maximum instantaneous kinetic energy of a returning electron turns out to be equal to 3.2Up, and adding the ionization potential Ip—the energy released upon recombinement to the ground state—yields the cut-off energy, Ecut=Ip +3.2Up, observed in high-harmonic radiation spectra [32]. The average quiver energy of a free electron with charge −e and mass m depends on the frequency ω and peak intensity I of the light field through the relation Up = e 2 I/4mω 2 =9.33 × 10 −14 I[W/cm 2 ]λ[µm] 2 and is often called the ponderomotive energy. This originates from the fact that the timeaverage of the Lorentz force, also called the ponderomotive force, in the case of a light field with slowly varying electric- and magnetic field amplitudes,
1.3 High-harmonic generation 9 can be expressed as the negative gradient of a term equal to Up [39, 40]. Although a wiggle energy, Up in this case acts as a potential energy because it is converted to translational kinetic energy of an electron leaving the optical field [41]. In a real experiment utilizing laser pulses the intensity will always be time-dependent but Up can be considered a potential energy in the longpulse limit (ns range), where the electron escapes the interaction region before the intensity changes significantly. In this regime the kinetic energy of an ATI electron leaving the laser focus is given by Ekin = N�ω − Ip, whereIp is the field-free ionization potential and N the number of absorbed photons [42, 43]. The ponderomotive energy manifests itself in the ATI spectrum as a suppression of peaks corresponding to kinetic energies less than Up. Inthe short-pulse limit (picosecond–femtosecond range), where the electron does not accelerate significantly before the pulse is gone, Up is not converted to translational kinetic energy and a kinetic energy Ekin = N�ω − Ip − Up is detected [42]. Since Up is proportional to I, this effect becomes more pronounced the higher the intensity and for an intensity of 10 15 W/cm 2 , typical for HHG, Up is equal to 60 eV for 800 nm light [44]. Such an intensity implicitly assumes a pulse duration in the femtosecond regime since the rise time of the pulse must be sufficiently short that the gas is not fully ionized before HHG can occur. According to the cut-off formula, the highest possible harmonic order is generated by using the highest possible intensity and wavelength in addition to a medium with a high ionization potential, favouring the lighter noble gases (He and Ne). Attempts have been made to enhance the cut-off frequency by using the rare-gas like ions Na + and K + but with limited success due to defocusing effects arising from the presence of free electrons [45]. Focusing instead on the generation efficiency, this may be enhanced orders of magnitude by using a shorter wavelength [46] or by choosing a medium with a lower ionization potential, e.g. Ar or Xe, corresponding to a higher polarizability [47]. Since the time spent by the electron in the continuum is proportional to the wavelength, the spread in the associated wavepacket will, upon its return to the nucleus, be larger the longer the wavelength. As a consequence, the recombination probability is reduced and the harmonic yield lowered [34]. With the two-step model in mind it is also easily realized why harmonics are generated much more efficiently with linearly than with elliptically polarized light: in the latter case the emitted electron misses the nucleus upon returning from its excursion to the continuum [48]. One usually distinguishes between two regimes of ATI or HHG, depending on the value of the Keldysh parameter γ = ω/ωt, which is the ratio between the optical field frequency ω and the frequency ωt for tunneling of an electron through the barrier induced to the Coulomb potential by the electric field [49].
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-
Page 10 and 11: viii
Page 12 and 13: 2 VUV light generation: possibiliti
Page 20 and 21: 10 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
Page 68 and 69:
58 High-resolution VUV spectroscopy
Page 70 and 71:
60 REFERENCES [19] J. S. Nielsen an
Page 72 and 73:
62 Lifetimes of molecular negative
Page 74 and 75:
Page 76 and 77:
Page 78 and 79:
Page 80 and 81:
Page 82 and 83:
Page 84 and 85:
Page 86 and 87:
76 REFERENCES [19] V. V. Petrunin e
Page 88 and 89:
78 REFERENCES [66] F. Robicheaux, P
Page 90 and 91:
80 Chapter 5. Femtosecond VUV core-
Page 92 and 93:
Page 94 and 95:
Page 96 and 97:
Page 98 and 99:
Page 100 and 101:
Page 102 and 103:
Page 104 and 105:
Page 106 and 107:
Page 108 and 109:
Page 110 and 111:
100 Chapter 5. Femtosecond VUV core
Page 112 and 113:
Page 114 and 115:
Page 116 and 117:
Page 118 and 119:
Page 120 and 121:
Page 122 and 123:
Page 124 and 125:
Page 126 and 127:
Page 128 and 129:
Page 130 and 131:
120 REFERENCES [17] A. Cavalleri et
Page 132 and 133:
122 REFERENCES [61] R. J. Finlay et
Page 134 and 135:
124 REFERENCES [104]R.W.Joyner,inTh
Page 136 and 137:
126 REFERENCES [152] T.-C. Chiang,
Page 138 and 139:
128 Chapter 6. Two-colour pump-prob
Page 140 and 141:
Page 142 and 143:
Page 144 and 145:
Page 146 and 147:
Page 148 and 149:
Page 150 and 151:
Page 152 and 153:
Page 154 and 155:
144 REFERENCES [16] Information ava
Page 156 and 157:
146 REFERENCES [62] S. Baier et al.
Page 158 and 159:
148 The following three chapters ar
show all

VUV Spectroscopy of Atoms, Molecules and Surfaces

Create successful ePaper yourself

Delete template?

Save as template?