Polarization-state-resolved high-harmonic spectroscopy of solids

Abstract

Attosecond metrology sensitive to sub-optical-cycle electronic and structural dynamics is opening up new avenues for ultrafast spectroscopy of condensed matter. Using intense lightwaves to precisely control the fast carrier dynamics in crystals holds great promise for next-generation petahertz electronics and devices. The carrier dynamics can produce high-order harmonics of the driving field extending up into the extreme-ultraviolet region. Here, we introduce polarization-state-resolved high-harmonic spectroscopy of solids, which provides deeper insights into both electronic and structural sub-cycle dynamics. Performing high-harmonic generation measurements from silicon and quartz, we demonstrate that the polarization states of the harmonics are not only determined by crystal symmetries, but can be dynamically controlled, as a consequence of the intertwined interband and intraband electronic dynamics. We exploit this symmetry-dynamics duality to efficiently generate coherent circularly polarized harmonics from elliptically polarized pulses. Our experimental results are supported by ab-initio simulations, providing evidence for the microscopic origin of the phenomenon.

Role of intraband dynamics in the generation of circularly polarized high harmonics from solids

“…The polarization states of the emitted harmonics driven by elliptically polarized fields, however, were shown to depend sensitively on the driving ellipticity and crystal rotation [15,16]. Moreover, they were intensity dependent and therefore directly dependent on the precise carrier dynamics [15,16]. All this is well reproduced with a time-dependent density functional theory (TDDFT) description which includes the full band and crystal structure and does not require any a-priori assumptions to match the experiments [16].…”

“…Moreover, they were intensity dependent and therefore directly dependent on the precise carrier dynamics [15,16]. All this is well reproduced with a time-dependent density functional theory (TDDFT) description which includes the full band and crystal structure and does not require any a-priori assumptions to match the experiments [16]. On the other hand, these calculations are costly and it is not always straightforward to extract an intuitive physical picture from these complex simulations.…”

“…For instance, it has been demonstrated experimentally in MgO and graphene, that the harmonic yield could be enhanced when changing from linear to elliptical driving polarization [13,14]. Subsequent works studied the polarization states of the emitted harmonics and found that circularly polarized harmonics can be generated from circularly [15][16][17] and elliptically [15,16] polarized single-color driving pulses. In the first case, the harmonics' polarization states can be understood by a group-theoretical analysis leading to selection rules for each of the crystallographic groups, which was derived already 50 years ago [18].…”

“…In the first case, the harmonics' polarization states can be understood by a group-theoretical analysis leading to selection rules for each of the crystallographic groups, which was derived already 50 years ago [18]. The polarization states of the emitted harmonics driven by elliptically polarized fields, however, were shown to depend sensitively on the driving ellipticity and crystal rotation [15,16]. Moreover, they were intensity dependent and therefore directly dependent on the precise carrier dynamics [15,16].…”

“…While both intra-and interband mechanisms are intrinsically coupled [19], it is understood that the interband mechanism only contributes for photon energies above the band gap and for a reasonably high joint density of states [20]. Because circularly polarized harmonics from elliptically polarized driving fields have also been demonstrated below the band gap and with a low joint density of states [16], we will focus our attention here on the intraband mechanism. Intraband-only calculations have been successfully utilized to reproduce the linear relationship of the cutoff energy to the driving field [9,21,22], the six-fold rotational symmetry of HHG spectra in the three-fold symmetric crystal GaSe [23], anisotropic HHG emission in ZnSe [24] as well as to reconstruct the band structure [25,26] and the Berry curvature [27] of SiO 2 .…”