High harmonic generation

High-harmonic generation (HHG) is a non-linear process during which a target (gas, plasma, solid or liquid sample) is illuminated by an intense laser pulse.

Due to the coherent nature of the process, high-harmonics generation is a prerequisite of attosecond physics.

This process was first discovered in 1961 by Franken et al.,[1] using a ruby laser, with crystalline quartz as the nonlinear medium.

[4] HHG in gases, far more widespread in application today, was first observed by McPherson and colleagues in 1987,[5] and later by Ferray et al. in 1988,[6] with surprising results: the high harmonics were found to decrease in intensity at low orders, as expected, but then were observed to form a plateau, with the intensity of the harmonics remaining approximately constant over many orders.

[7] Plateau harmonics spanning hundreds of eV have been measured which extend into the soft X-ray regime.

They are a tunable table-top source of XUV/soft X-rays, synchronised with the driving laser and produced with the same repetition rate.

[9] The saturation intensity can be increased by changing the atomic species to lighter noble gases but these have a lower conversion efficiency so there is a balance to be found depending on the photon energies required.

Often harmonics are only produced in a very small temporal window when the phase matching condition is met.

[12] High harmonics are emitted co-linearly with the driving laser and can have a very tight angular confinement, sometimes with less divergence than that of the fundamental field and near Gaussian beam profiles.

This can be calculated classically by examining the maximum energy the ionized electron can gain in the electric field of the laser.

The electron is assumed to be born into the vacuum with zero initial velocity, and to be subsequently accelerated by the laser beam's electric field.

Half an optical cycle after ionization, the electron will reverse direction as the electric field changes sign, and will accelerate back towards the parent nucleus.

In the semiclassical picture, HHG will only occur if the driving laser field is linearly polarised.

Ellipticity on the laser beam causes the returning electron to miss the parent nucleus.

At intensities above 1016 W·cm−2 the magnetic component of the laser pulse, which is ignored in weak field optics, can become strong enough to deflect the returning electron.

[20] Furthermore, the implementation of loose focusing geometry for the driving field enables a higher number of emitters and photons to contribute to the generation process and thus, enhance the harmonic yield.

[21] When using a gas jet geometry, focusing the laser into the Mach disk can increase the efficiency of harmonic generation.

, we need to find such parameters in the high dimensional space that will effectively make the combined refractive index at the driving laser wavelength nearly 1.

In order to achieve intensity levels that can distort an atom's binding potential, it is necessary to focus the driving laser beam.

This introduces dispersion terms affecting the phase mismatch, depending on the specific geometry (such as plane wave propagation, free focusing, hollow core waveguide, etc.).

Additionally, during the high harmonic generation process, electrons are accelerated, and some of them return to their parent ion, resulting in X-ray bursts.

The returning electrons carry phase due to processes like ionization, recombination, and propagation.

Furthermore, the ionized atoms can influence the refractive index of the medium, providing another source of dispersion.

To phase-match the process of HHG, very high pressures and low ionization levels are required, thus giving a large number of emitters.

This gives HHG photon energy scalability with the intensity of the driving UV laser.

[25] Such geometries benefit, especially X-ray spectra generated by IR beams, where long interaction volumes are needed for optimal power extraction.

[24] For UV-VIS driven high harmonics, the waveguide term is small, and the phase-matching picture resembles the plane-wave geometry.

In such geometries, narrow bandwidth harmonics extending to the carbon edge (300 eV) have been generated.