Microscopic theory of the extremely nonlinear terahertz response of semiconductors

Abstract

The extreme nonlinear terahertz response of initially unexcited intrinsic semiconductor nanostructures is studied theoretically by solving extended semiconductor Bloch equations numerically. The coupled dynamics of intraband acceleration and multiphoton interband transitions leads to high-harmonic generation up to several tens of the exciting terahertz frequency. It is shown that the actual cut-off frequency is determined by the band structure and not by the excitation strength. 1 Introduction Terahertz (THz) spectroscopy provides a powerful method to experimentally identify different quasi-particle states in optically excited semiconductors [1,2]. When the intra-excitonic 1s-to-2p transition is excited with a strong THz pulse, several different nonlinear and extreme nonlinear effects are observed [3,4] including Rabi flopping, generation of high THz harmonics, and the excitonic dynamical Franz-Keldysh effect.In this paper, we present calculations showing that very strong THz fields can even induce interband transitions via multi-photon processes. This establishes a new regime of THz physics that connects conventional THz excitations of semiconductors with the field of extreme nonlinear optics [5][6][7].We use our microscopic theory to compute the coherent light emission of an unexcited intrinsic semiconductor nanostructure in the presence of an extremely intense THz field. For strong enough excitation, we obtain high-harmonic generation (HHG) with frequency components within the far ultraviolet range. This HHG results from the coupled dynamics of the interband transitions and the classical intraband acceleration of the charge carriers. Since the THz field is highly off-resonant with respect to the interband transitions, peak field strengths of few MV/cm are required in order to excite a sufficient amount of carriers across the bandgap. Such strong fields have recently become available experimentally in the THz range [8,9].

High-order harmonic generation in solids: A unifying approach

“…Field-driven electronic dynamics in solids is a wellestablished aspect [17][18][19], and HHG from solids has been investigated and predicted [20][21][22][23][24][25][26] up to the visible range of the spectrum. Several classes of techniques have been used to investigate this interesting topic.…”

Impact of the Electronic Band Structure in High-Harmonic Generation Spectra of Solids

“…In the case of solids, electrons are promoted to discrete conduction bands, where they do not evolve freely. This leads, for instance, to a different linear field dependence for the cutoff energy [6], different time-frequency characteristics of the harmonic emission between atoms and solids [8,11,16], and a different ellipticity dependence [6,17].Historically, HHG in solids was first discussed in terms of Bloch oscillations (i.e., pure intraband dynamics) [18][19][20], and more recently mainly analyzed using simplified models based on numerical solutions of the semiconductor Bloch equations [21][22][23] treating the complex, coupled interband and intraband dynamics, with the exception of the ab initio simulations of Ref. [24].…”

“…Historically, HHG in solids was first discussed in terms of Bloch oscillations (i.e., pure intraband dynamics) [18][19][20], and more recently mainly analyzed using simplified models based on numerical solutions of the semiconductor Bloch equations [21][22][23] treating the complex, coupled interband and intraband dynamics, with the exception of the ab initio simulations of Ref. [24].…”

Ab initio multiscale simulation of high-order harmonic generation in solids

“…The processes underlying solid-state HHG have remained a matter of debate. Several simplifying models have been proposed accounting for Bloch oscillations within a single band ("intraband harmonics") [22,23] and non-linear interband polarization ("interband harmonics") [15,24,25] as sources of HHG. Most descriptions involve the semiconductor Bloch equations (SBE, [26]) using input parameters on various levels of sophistication and a varying number of energy bands [27,28].…”