Self-consistent Maxwell–Bloch model for high-order harmonic generation in nanostructured semiconductors

Abstract

In pursuit of efficient high-order harmonic conversion in semiconductor devices, modeling insights into the complex interplay among ultrafast microscopic electron–hole dynamics, nonlinear pulse propagation, and field confinement in nanostructured materials are urgently needed. Here, a self-consistent approach coupling semiconductor Bloch and Maxwell equations is applied to compute transmission and reflection high-order harmonic spectra for finite slab and sub-wavelength nanoparticle geometries. An increase in the generated high harmonics by several orders of magnitude is predicted for gallium arsenide nanoparticles with a size maximizing the magnetic dipole resonance. Serving as a conceptual and predictive tool for ultrafast spatiotemporal nonlinear optical responses of nanostructures with arbitrary geometry, our approach is anticipated to deliver new strategies for optimal harmonic manipulation in semiconductor metadevices.

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

“…Importantly, SBE can be coupled to full-vector Maxwell equations through the nonlinear currents and polarizations in a straightforward way. 14,[45][46][47] Feasibility and robustness of a coupled Maxwell-semiconductor Bloch approach for investigating the highorder harmonic spectra for a finite slab and 3D sub-wavelength nanoparticle geometries in the non-perturbative regime of ultrashort laser pulse excitation has been recently demonstrated in Refs. 14,48 Driven either by a Fabry-Perot-like standing wave resonator or by magnetic dipole Mie resonances, inhomogeneously photo-induced carriers are localized in the semiconductor material (GaAs), producing enhanced even and odd harmonics for the resonant geometry and excitation conditions.…”

“…The numerical approaches coupling nonlinear pulse propagation with comprehensive optical response of free carriers are expected to describe the nonlinear features including enhancement and saturation in the harmonic yield, free carrier absorption losses, frequency mixing, resonance splitting and blue-shift due to laser-induced electron-hole plasma in more advanced subwavelength systems, such as Mieresonant periodic arrangements of nanostructures, 3,10,24 asymmetric metasurfaces supporting bound states in the continuum and Fano resonances. 6,9,11,16 In perspective, a microscopic approach, based on Maxwell coupled with semiconductor Bloch equations, 14 can be helpful to fully analyze time-dependent carrier dynamics and high-harmonic generation in semiconductor nanostructures, considering the electronic band structure of a specific semiconductor material, different crystal orientations and direction-dependent effects.…”

“…[8][9][10][11] In this non-perturbative regime of ultrashort laser excitation, optical properties swiftly change due to photo-ionization processes and electronic transitions between valence and conduction bands. The laser-induced inhomogeneous free carriers can serve as an additional source for optical symmetry breaking, 12,13 for enhanced high-order harmonics generation (HHG), [9][10][11]14 and participate in ultrafast self-action, all-optical switching and modulation at the nanoscale. [15][16][17] High-order odd harmonic spectra have been recently generated from a single subwavelength resonator by implementing the concept of quasi-bound states in the continuum, 18 indicating the possibility to access non-perturbative regimes and high harmonic yields in miniaturized nanoscale nonlinear optical devices.…”

Trade‐Off between Second‐ and Third‐Order Nonlinearities, Ultrafast Free Carrier Absorption and Material Damage in Silicon Nanoparticles

“…On the one hand, these effects are commonly considered as the limiting factors for the operating frequency conversion nanodevices. [1,2,[20][21][22][23] On the other hand, inhomogeneous free carriers can serve as an additional source for symmetry breaking [24,25] and for high-order harmonics generation in non-perturbative regimes, [7,8,26,27] and participate in ultrafast self-action, all-optical switching, and modulation at the nanoscale. [20,[28][29][30][31][32] While the applicability of the perturbative approaches is limited to describe weak intensity regimes, the extended hydrodynamic model for electron-hole plasma kinetics and electron-ion transfer gives a reliable estimate for the inhomogeneous absorption and heating processes inside the laser-excited nanostructures and describes the non-perturbative mechanism of harmonic generation due to direct electron transitions from valence to conduction band.…”