Modeling of low- and high-order harmonic generation in ultrashort laser-excited resonant semiconductor nanostructures

Ultrashort laser-excited semiconductor nanostructures, supporting individual Mie or collective resonances, can serve as efficient miniaturized sources for low- and high-order harmonic generation. Upon laser excitation, multiple nonlinearities come into interplay on subwavelength spatial and ultrafast temporal scales, including surface and bulk effects, contributions from bound electrons and photo-excited carriers. In turn, transient optical properties affect the structure and the amplitude of the transmitted laser pulse. Computational approaches, coupling ultrashort pulse propagation with semiconductor nonlinear optical response, compatible with the considered spatial and temporal scales, are urgently needed to provide new strategies for efficient light modulation and manipulation, for instance, in order to enhance the nonlinear conversion efficiency. Nonlinear dynamics in ultrashort laser-excited nanostructures will be discussed from the perspective of classical perturbative, semi-classical, and microscopic non-perturbative models based on semiconductor Bloch equations, considering electronic multi-band structure of the material and involved intra- and inter-band transitions. As an example, an enhanced harmonic generation will be shown from a single nanoparticle or periodic array of nanoparticles, supporting Mie and collective lattice resonances, and a subwavelength resonator supporting quasi-bound states in the continuum. Ultrafast processes involved in nonlinear pulse propagation such as spectrum broadening and plasma blue-shift, frequency mixing and saturation in the harmonic yield, as well as the restrictions due to carrier absorption and heating of the sample, will be discussed within the framework of a classical model. Perspectives of applying self-consistent nonlinear Maxwell-based approaches to large-scale problems in nonlinear meta-photonics as well as their current limitations will be finally outlined.