Multielectron interference of intraband harmonics in solids

Abstract

High harmonic generation in solids provides us compact and coherent UV sources. Our simulations illustrate abnormal harmonic yield dependence on the intensity of driving or pre-excitation pulses. A multielectron interference model is proposed to reveal the mechanism of the extreme nonlinear optical phenomena. We find that the k-resolved intraband harmonic demonstrates different symmetry, phase, and amplitude, which can be observed by using a resonant pre-excitation pulse. The position of the interference minimum obtained by solving the semiconductor Bloch equations agrees well with that obtained by our k-resolved semiclassical model. This interference model can help us probe the k-resloved band structure and optimize the ultrafast electron-hole dynamics for solid harmonic processes.

Crystal-momentum-resolved contributions to multiple plateaus of high-order harmonic generation from band-gap materials

“…5-7, a correct description of the intraband harmonics in the below-band-gap regime still requires the contributions from all the occupied orbitals to be coherently taken into account, as also found in Ref. [43].…”

“…Two main theoretical approaches to study HHG in solids include (i) the time-dependent Schrödinger equation (TDSE) for individual Bloch electrons with specific k values [25][26][27][28][29][30][31][32][33][34][35], and (ii) many-electron approaches such as the semiconductor Bloch equations (SBEs) [36][37][38][39][40][41][42][43][44][45][46] and the time-dependent density-functional theory (TDDFT) [23,[47][48][49][50][51][52][53][54][55][56]. In Ref.…”

“…[57], limitations of considering the response from a single electron with the TDSE in the studies of HHG in solids were discussed via comparisons with the SBEs, where the contributions from different Bloch electrons are coherently taken into account. Although focusing on the response of a single Bloch electron (e.g., at the point) has provided useful insights into the HHG mechanisms [26,27], the contributions from multiple k points and their quantum interference have turned out to be important for both intraband and interband harmonics, attracting more and more attention (see, e.g., recent works [43,45,46]). In addition to the methods mentioned above, the strong-field approximation (SFA) method was used to investigate HHG in solids [58].…”

High-harmonic Generation in Metallic Titanium Nitride

“…Here e is the elementary charge and a is the lattice constant. Similarly, expanding the fielddependent energy of a 1D single-band conductor in a power series of the crystal momentum k, it can be shown that the mth spectral component of the induced current has a leading term proportional to E m 0 , where E 0 is the laser electric field amplitude 25 . The intensity of the m-th harmonic would therefore scale as I m , where I is the driving laser intensity, for low enough I.…”

High-harmonic generation in metallic titanium nitride

“…Here e is the elementary charge and a is the lattice constant. Similarly, expanding the field-dependent energy of a 1D single-band conductor in a power series of the crystal momentum k , it can be shown that the m th spectral component of the induced current has a leading term proportional to , where E 0 is the laser electric field amplitude 25 . The intensity of the m -th harmonic would therefore scale as I m , where I is the driving laser intensity, for low enough I .…”