No abstract

Tabletop coherent x-ray sources extending to multi-keV or higher photon energies have versatile applications, including in 4D imaging and semiconductor detectors. However, these sources can be realized only via high-order harmonic generation (HHG) with an ∼ 10 µ m laser interacting with neutral atoms. As shown in previous work by Popmintchev et al. [Science 350, 1225 (2015)10.1126/science.aac9755SCIEAS0036-8075], multiply ionized plasmas can efficiently produce hundred-eV harmonics with an ultraviolet laser. Here, we experimentally investigate multi-keV x-ray sources up to ∼ 5.2 k e V , the highest photon energy generated via HHG to date, to our knowledge, using a 1.45-µm driving laser that interacts with multivalent ions. Both the angular distribution and the ellipticity dependence of the signal are strong evidence of the HHG mechanism.

The quantum evolution of particles under strong fields can be essentially captured by a small number of quantum trajectories that satisfy the stationary phase condition of the Dirac-Feynmann path integral. The quantum trajectories are a key concept in understanding extreme nonlinear optical phenomena, such as high-order harmonic generation (HHG) and highorder terahertz sideband generation (HSG). In contrast to HHG in atoms and molecules, HSG in semiconductors can have interesting effects due to nontrivial 'vacuum' states of band materials. We find that, in a semiconductor with nonvanishing Berry curvature in its energy bands, the cyclic quantum trajectories of an electron-hole pair under a strong elliptically polarized terahertz field can accumulate a Berry phase. Taking monolayer MoS 2 as a model system, we show that the Berry phase appears as a Faraday rotation angle in the pulse emission from the material under short-pulse excitation. This finding reveals an interesting transport effect in the extreme nonlinear optics regime.

High-order terahertz (THz) sideband generation in semiconductors is a phenomenon with physics similar to that of high-order harmonic generation but in a regime of much lower frequency. Our previous paper [1] found that the electron-hole pair excited by a weak optical laser can accumulate a Berry phase along a cyclic trajectory under the driving of a strong elliptically polarized THz field. Furthermore, the Berry phase appears as the Faraday rotation angle of the emission signal under short-pulse excitation in monolayer MoS 2 . In this paper, the theory of the Berry phase in THz extreme nonlinear optics is applied to biased bilayer graphene with Bernal stacking, which has similar Bloch band features and optical properties to monolayer MoS 2 , such as the time-reversal related valleys and the valley contrasting optical selection rule. However, the biased bilayer graphene has much larger Berry curvature than monolayer MoS 2 , which leads to a large Berry phase of the quantum trajectory and in turn a giant Faraday rotation of the optical emission (∼1 rad for a THz field with frequency 1 THz and strength 8 kV cm −1 ). This surprisingly big angle shows that the Faraday rotation can be induced more efficiently by the Berry curvature in momentum space than by the magnetic field in real space. It provides opportunities to use bilayer graphene and THz lasers for ultrafast electro-optical devices.