Twisting harmonics: Transfer of orbital angular momentum in solid-state high-harmonic generation

Abstract

Although solid-state platforms underpin modern electronics, little is known about how intense ultrashort light pulses carrying orbital angular momentum (OAM) interact with solids. This gap persists even though, for more conventional light-matter interactions, the complex underlying electron dynamics can often be confined to a single Brillouin zone and described well within the dipole approximation. Previous studies were restricted to nonlinear, perturbative regimes, largely because the generation of intense ultrashort vortex pulses, particularly in the mid-infrared spectral regime, has remained a long-standing challenge. Consequently, the role of structured light in driving nonlinear, non-perturbative processes in solids, and the associated transfer of angular momentum during these interactions, has not been systematically explored. Here, we investigate solid-state high-harmonic generation (HHG) driven by intense ultrashort structured light using a versatile experimental approach applicable to different materials and geometries. We demonstrate that the OAM of the driving field is coherently transferred to the emitted harmonics. In particular, we show that the OAM is conserved independently of the crystal symmetry, the range of electronic interactions, and the presence of strong spin-orbit coupling. These results establish OAM-resolved HHG as a robust framework for characterizing and controlling angular momentum transfer in solid-state HHG and open new avenues for structured-light-driven quantum technologies and topological materials investigations.

Figures (3)

• Figure 1: (Top) Simplified experimental setup. A fundamental Gaussian pulse first passes through a spiral phase plate (SPP) and creates a LGV beam which is focused upon different target crystals, for instance ZnO, to drive the HHG process. The harmonic vortex beams are produced either in transmission or reflection geometry, depending on the crystal angle relative to the incoming LGV beam. Here, we exemplify the reflection geometry and represent different harmonic vortices by different colors, which are separated by band-pass filters during the experimental measurements. Furthermore, the spatial characterization of both the fundamental and harmonic vortices as well as HG profiles is performed via imaging cameras. The TC of the beams is measured by performing a mode transformation with a cylindrical lens (CL), which is positioned between the target crystal and the imaging camera. In (a1), we show the fundamental Gaussian beam's spatial intensity distribution, whereas in (a2) and (a3), we display the intensity distributions of LGV beams for two different TC values. Note that the SPP does not produce LGV beams with zero radial index. In (b1) and (b2), we compare the mode-transformed intensity distributions for the Gaussian beam and LGV beam with a TC $l_0=3$.
• Figure 2: Harmonic vortices, OAM up-scaling law, and beam sizes. In (a), we show the measured intensity distributions of the harmonic vortices $q=3,4,5$ and 7 generated in the ZnO crystal with a fundamental LGV beam carrying a TC $l_{0}=1$. In (b), the resulting HG intensity distribution for the $q=4$ harmonic vortex beam, demonstrates that the TC follows: $l_q=ql_0$. In (c) and (d), the spectral characterization of the generated harmonic vortices (both, even and odd orders) in ZnO. In (e), the linear up-scaling law describing the harmonic's TC, $l_q$, as a function of the harmonic order, $q$, for GaSe, ZnO and MgO. In (f), harmonic vortices dark-core size as a function of the harmonic order, demonstrating its increment for increasing $q$ values, for the same solids. In (g), the OAM up-scaling law for silicon and WSe$_2$ (green open circles), is shown for validity for the reflection geometry. In (h), the enhancement in the size of the dark-core as a function of the harmonic's TC, $l_q$. In (i), harmonic vortices and HG intensity distributions for harmonics $q=3$ and 5 generated in silicon. For both harmonic vortices, the fundamental beam carries a TC of $l_0=3$, resulting in $l_q=9$ and 15, respectively. Note that the error assigned to all the dark-core values corresponds to 12 $\mu$m, which is the pixel pitch in the detection MIRC.
• Figure 3: Calculated far-field line intensity and phase profiles of the harmonic vortices for different materials and geometries. Results are shown for (a) ZnO, (b) MgO, and (c) GaSe, and demonstrate the enhancement in the dark-core size and reduction in the ring thickness of the harmonic vortices for increasing harmonic orders, in the transmission geometry. In (d) and (e), we present the results obtained from the reflection geometry, demonstrating the enhancement of the harmonic vortices beam size in Si and WSe$_2$, respectively. The OAM conservation law is demonstrated by counting the number of $2\pi$ phase shifts for harmonic orders $q=4$ and 5, as displayed in (f). In (a)-(e), $\beta_{x}$ denotes the far-field divergence along the $x$-axis, whereas, the horizontal, and vertical axes correspond to $\beta_{x}$, and $\beta_{y}$ in mrad unit, respectively for (f) (see Methods).