High harmonic generation

High harmonic generation (HHG) is a non-linear process during which a target (gas, plasma or solid sample) is illuminated by an intense laser pulse. Under such conditions, the sample will emit the high harmonics of the generation beam (above the fifth harmonics). Due to the coherent nature of the process, high harmonics generation is a prerequisite of attophysics. High harmonic generation (HHG) is a non-linear process during which a target (gas, plasma or solid sample) is illuminated by an intense laser pulse. Under such conditions, the sample will emit the high harmonics of the generation beam (above the fifth harmonics). Due to the coherent nature of the process, high harmonics generation is a prerequisite of attophysics. Perturbative harmonic generation is a process whereby laser light of frequency ω and photon energy ħω can be used to generate new frequencies of light. The newly generated frequencies are integer multiples nω of the original light's frequency. This process was first discovered in 1961 by Franken et al., using a ruby laser, with crystalline quartz as the nonlinear medium. Harmonic generation in dielectric solids is well understood and extensively used in modern laser physics (see second harmonic generation). In 1967 New et al. observed the first third harmonic generation in a gas. In monatomic gases it is only possible to produce odd numbered harmonics for reasons of symmetry. Harmonic generation in the perturbative (weak field) regime is characterised by rapidly decreasing efficiency with increasing harmonic order. This behaviour can be understood by considering an atom absorbing n photons then emitting a single high energy photon. The probability of absorbing n photons decreases as n increases, explaining the rapiddecrease in the initial harmonic intensities. The first high harmonic generation was observed in 1977 in interaction of intense CO2 laser pulses with plasma generated from solid targets. HHG in gases, far more widespread in application today, was first observed by McPherson and colleagues in 1987, and later by Ferray et al. in 1988, with surprising results: the highharmonics 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.Plateau harmonics spanning hundreds of eV have been measured which extend into the soft x-ray regime. This plateau ends abruptly at a position called the high harmonic cut-off. High harmonics have a number of interesting properties. They are a tunable table-top source of XUV/Soft X-rays, synchronised with the driving laser and produced with the same repetition rate. The harmonic cut-off varies linearly with increasing laser intensity up until the saturation intensity Isat where harmonic generation stops. 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. High harmonic generation strongly depends on the driving laser field and as a result the harmonics have similar temporal and spatial coherence properties. High harmonics are often generated with pulse durations shorter than that of the driving laser. Thisis due to the nonlinearity of the generation process, phase matching and ionization. Often harmonics are only produced in a very small temporal window when the phase matching condition is met. Depletion of the generating media due to ionization also means that harmonic generation is mainly confined to the leading edge of the driving pulse. 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. The maximum photon energy producible with high harmonic generation is given by the cut-off of the harmonic plateau. This can be calculated classically by examining the maximum energy the ionized electron can gain in the electric field of the laser. The cut-off energy is given by, E m a x = I p + 3.17 U p {displaystyle E_{max}=I_{p}+3.17U_{p}}