High-harmonic generation in zinc oxide subjected to intense mid-infrared femtosecond laser pulse

Abstract

We theoretically investigate photo-excitation of electron–hole pairs and high harmonic generation in the bulk of zinc oxide (ZnO) subjected to intense femto-second laser pulses with mid-infrared wavelength. The main microscopic mechanism of solid-state HHG is identified by separating resonant from non-resonant non-linear optical responses in the photo-excited solid. We obtain an effective light-matter interaction in which electrons are subject to weak atto-second pulse train with the second harmonic of the drive laser frequency being the repetition frequency in the train. Under a condition of constructive interference of electronic transitions between consecutive half-cycles of the drive laser pulse, resonant-like excitation of electron–hole pairs occurs which contribute to the multi-cycle accumulation of photo-current. The inter-band motion of charge carriers creates rapidly oscillating electric dipole moment, which emits continuum bremsstrahlung-like radiation during each half-cycle of the drive laser pulse. If the laser-cycles of the drive pulse are identical, the emissions from consecutive half-cycles are phase-coherent, and their mutual interference produces a frequency comb in the spectral domain, which is composed of the odd-integer harmonics of the drive laser frequency. The spectral intensity of each harmonic scales with the fourth power of the total number of cycles in the drive pulse. In contrast, if consecutive cycles in the pulse are non-identical, the interference pattern in the frequency domain is less well defined and blurred. The importance of the pulse envelope for producing clean frequency combs as observed in the experiments is discussed. Good semi-quantitative agreement with the experimental data is found: clean and well defined odd-order harmonic peaks extending well beyond the band edge of ZnO are exhibited for laser linearly polarized at right angles to the optical axis of the crystal.