High-harmonic generation

A typical high-harmonic spectrum is shown in Fig. 4.4 for the helium atom. The squares represent experimental data taken from [66], and the solid line was obtained from a calculation using the EXX/EXX functional [67]. The spectrum consists of a series of peaks, first decreasing in amplitude and then reaching a plateau that extends to very high frequency. The peaks are placed at the odd multiples of the external laser frequency (the even multiples are dipole forbidden by symmetry). We note that any approach based on perturbation theory would yield a harmonic spectrum that decays exponentially, i.e. such a theory could never reproduce the measured peak intensities. TDDFT, on the other hand, gives a quite satisfactory agreement with experiment. 

As mentioned above, high-harmonics can be used as a source of soft X-ray lasers. For such purpose, one tries to optimize the laser parameters, the frequency, intensity, etc., in order to increase the intensity of the emitted harmonics, and to extend the plateau the farthest possible. By performing virtual experiments , TDDFT can be once more used to tackle such an important problem. As an illustration, we show in Fig. 4.5 the result of irradiating a hydrogen atom with lasers of the same frequency but with different intensities. For clarity, we only show the position of the peaks, and the points were connected by straight lines. As we increase the intensity of the laser. 

An example of HHG in He, obtained using the laser system of fig. 9.5 is shown in fig. 9.9 the driving laser has a photon energy of 1 eV, and so the harmonics extend up to over 100 eV in energy. 

The laser field which is responsible for HHG acts similarly in some respects to the oscillating fields experienced by an electron in a synchrotron high harmonics are emitted under semiclassical conditions at many times the fundamental frequency, which in this case is the frequency of the laser. For reasons of symmetry, only the odd harmonics are observed. Also (for reasons mentioned below) the dominant contribution comes from initially bound electrons. 

This rule is only approximate because it misses out many important physical considerations. For example, e/ is taken as the field-free ionisation limit for a one-electron system, and the rule contains nothing explicit about pulse duration. Nevertheless, it has been found to work reasonably well. From this rule, we can see that a well-developed spectrum of high harmonics is only expected in species with a high ionisation threshold. 

Even the existence of a plateau turns out to be a very general feature calculations with a square well potential containing only one bound state of suitable binding energy reproduce a plateau, so that, in this case, a minimal atomic physics description (option (i) of section 9.18) proves adequate to interpret most HHG experiments. 

Experimental studies of the time dependence of harmonic generation [506] also show that harmonic generation becomes very weak once ionisation occurs, so that shorter pulses are preferable to generate harmonics in elements of lower ionisation potential. 

In order to develop high harmonics into an attractive general purpose source of spectroscopic radiation it is necessary to optimize the generation 

The harmonics are particularly attractive in terms of the radiation peak power, which can be 10 times higher than for synchrotron undulators. Thus, it should open the way for nonlinear laser spectroscopy in the short-wavelength (10 nm) regime. A competing technology requiring much larger installations is Self Amplified Spontaneous Emission used for Free-Electron-Laser action (SASE-FEL) [9.262]. 

Harmonics arc tunable when the primary laser radiation is obtained from a tunable laser, such as a titanimn-doped sapphire laser. However, the need for wavelength-dependent adjustments in the CPA chain can make the tuning 

The tiinability of such a system could also be utilized for measurmg autoionisation widths of Rydberg states of molecules [9.267]. More fmidamentally, similar techniques, emphasizing a maximal resolution, have been used for studies of the He atom, yielding accurate Lamb-shift data [9.268]. 

Photoionization experiments are conveniently performed with monochro-matized synchrotron radiation. However, if a high temporal resolution is required, harmonics provide unique possibihties, as recently demonstrated [9.269]. 

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While excitation processes in strong laser fields have not received as much attention as ionization rates and high-harmonic generation, the study of excitation is an important aspect of our overall understanding of the behavior of molecules in strong laser fields. 

These advances have opened new fields of relativity-related research in two complementary directions. One is related to the advent of laser-based sources of coherent radiation in the X-UV domain, either from high harmonic generation [6], [7] or from X-ray-laser devices, [8], The imple-... 

The generation of attosecond laser pulses in high-harmonic generation is a natural consequence of the physics discussed in Sects. 3.2 and 3.3. As discussed in Sect. 3.3, the ionization that launches the electron into the continuum is a highly non-linear phenomenon that will favor field maxima in the femtosecond driver laser. Following this ionization step, and in the spirit of the results presented in Sect. 3.2, the electrons will be accelerated by the oscillatory field of the laser and move along relatively well-defined trajectories that carry the electron back to the parent ion at well-defined times. Consequently, we expect the electron-parent ion recombination and the XUV production to occur only during a small portion of the optical cycle. 

Control of High Harmonic Generation Processes Using Chirped and Self-Guided Femtosecond Laser Pulses... 

High Harmonic Generation in an Ionizing Gaseous Medium... 

Basic spectral features of high harmonics can be obtained from the HHG calculation of a single atom. Calculations of the time-dependent Schrodinger equation (TDSE) for a single atom may reveal the characteristic features of high harmonic generation, such as the plateau and cutoff in the high harmonic... 

The shortest directly produced optical pulses, produced by Kerr-lens mode-locked Ti-sapphire lasers, last around 3.4fs = 3.4 x 10 15s. However, the minimum pulse duration is limited by the period of the carrier frequency (which is about 2.7 fs for Ti S systems). Some advanced techniques (involving high harmonic generation with amplified fs laser pulses) can be used to produce pulses as short as 10 16s for X < 30 nm. 

Fig. 1. Schematic diagram showing above threshold ionization (ATI) and high harmonic generation (HHG)...

The irradiation of atoms and molecules with two lasers of different frequency and known relative phase has been shown not only to throw light on the ATI process in atoms [46] but has produced a dramatic enhancement in the conversion efficiency in high harmonic generation [47]. In addition, there is theoretical evidence that molecular dynamics may be controlled using two-colour excitation [48]. 

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