All-optical switching of nonlinear structured light in crystal-engineered van der Waals materials

Abstract: The orbital angular momentum (OAM) of light is a discrete, unbounded degree of freedom that underpins mode-multiplexed communications and high-dimensional quantum photonics. Yet, dynamic OAM control remains dependent on bulky free-space optics or cascaded architectures that separate switching from wavefront shaping, hindering nanoscale integration. Here, we engineer artificial van der Waals crystals from rhombohedrally stacked (3R) MoS$<em>2$, in which spatial control of the local crystal orientation imprints a nonlinear geometric phase onto the second-harmonic (SH) field, enabling background-free generation of SH vortex beams in an ultrathin (46 nm) van der Waals platform. Leveraging the C$</em>{3v}$ symmetry of 3R-MoS$_2$, we demonstrate monolithic, all-optical switching with sub-optical-cycle precision between Hermite-Gauss-like and Laguerre-Gaussian vortex SH beams with opposite topological charges ($l=\pm1$). Our results establish artificial 3R-MoS$_2$ crystals as a monolithic platform for the generation and all-optical reconfiguration of nonlinear structured light at the nanoscale, advancing active nanophotonic sources for integrated classical and quantum photonic technologies.

• The paper demonstrates a 46-nm crystal-engineered 3R-MoS₂ platform that combines second-harmonic generation with wavefront shaping to switch between Hermite-Gauss-like beams and vortices with topological charges l = ±1.
• The method patterns MoS₂ crystal orientations to encode a helicity-dependent geometric phase of ±3θ, enabling broadband vortex generation without resonances or cascaded metasurfaces.
• The paper achieves pulse-duration-limited switching among l = −1, 0, and +1 modes by controlling pump polarization with femtosecond delay adjustments, while highlighting limited efficiency and mode purity as challenges.

The paper demonstrates a monolithic, ultrathin platform for generating and all-optically switching nonlinear structured light, built from crystal-engineered 3R-MoS$_2$ (2608.13548). By spatially patterning the in-plane orientation of rhombohedrally stacked MoS$_2$ into an artificial van der Waals crystal, the authors imprint a tensor-driven geometric phase onto the second-harmonic (SH) field and switch between Hermite-Gauss-like beams and Laguerre-Gaussian vortices of opposite topological charge ($l = \pm 1$) with sub-optical-cycle precision — collapsing frequency conversion and wavefront shaping into a single 46-nm-thick medium.

Tensor-driven geometric phase in C$_{3v}$ crystals

The mechanism rests on the anisotropic $\chi^{(2)}$ tensor of 3R-MoS$_2$, which belongs to the $C_{3v}$ point group with nonzero elements $$\chi^{(2)}_{yyy} = -\chi^{(2)}_{yxx} = -\chi^{(2)}_{xxy} = -\chi^{(2)}_{xyx}$$. Under in-plane rotation by an angle $\theta$, the induced SH polarization acquires factors $\sin 3\theta$ and $_2$0, producing the familiar six-lobe polarization pattern but also a phase that rotates three times faster than the crystal itself. In the circular basis, the forward-emitted SH components are proportional to $_2$1 and $_2$2: the SH helicity is opposite to the pump helicity, consistent with total angular momentum (TAM) projection conservation ($_2$3, with $_2$4 from the threefold symmetry), and the emitted field carries a geometric phase of $_2$5 whose sign is set by the pump helicity.

Two properties of this phase are emphasized. First, it is independent of flake thickness because it originates from the local tensor symmetry rather than propagation effects; numerical simulations on a 100-nm flake confirm constant conversion efficiency versus $_2$6 while the phase sweeps linearly. Second, it is intrinsically broadband, requiring no optical or material resonance. The authors also show that for circularly polarized pumps, even the linearly polarized SH components inherit the same $_2$7 factor, so the geometric phase survives projection onto any detection basis. By contrast, under linearly polarized excitation the crystal orientation modulates amplitude rather than phase, yielding only a $_2$8 shift between opposing regions — an asymmetry that becomes the key to the switching functionality.

Fabrication of artificial van der Waals crystals

The sample was assembled by mechanical exfoliation of commercial 3R-MoS$_2$9, electron-beam lithographic patterning into four $l = \pm 1$0 squares, reactive-ion etching, and polymer-stamp pickup followed by restacking with relative crystal orientations of 0°, 30°, 60°, and 90°. This four-quadrant arrangement discretizes a $l = \pm 1$1 spiral phase mask, approximating a vortex phase plate with principal topological charge $l = \pm 1$2. Polarization-resolved SHG on each square verified the designed 30° offsets via the rotated six-lobe patterns. All reported measurements use a 46-nm-thick stack; backup samples of 48, 91, and 188 nm reproduced the behavior, supporting the claim that the encoding is thickness-independent. Because the geometric-phase mechanism does not rely on resonant enhancement, the absolute SH conversion efficiency remains modest at this thickness — a trade-off the authors acknowledge implicitly by noting that resonant nanostructures could strengthen light–matter interaction.

Vortex generation and holographic characterization

SH vortex generation was characterized in a transmission microscope pumped at 1030 nm (150 fs, 76 MHz ytterbium laser), with the SH at 515 nm interfered against a reference field frequency-doubled in a BBO crystal for off-axis digital holography. When imaged out of the object plane (at 0.67 mm), the SH intensity assumes a vortex-like annular profile retaining the square footprint of the four slabs, and the reconstructed phase exhibits the expected spiral distribution — a superposition of the Gaussian envelope inherited from the pump and the azimuthal phase imposed by the quadrants. RCP and LCP excitations produce opposite spiral handedness, as predicted. The holographic reconstruction required projecting both object and reference fields onto a common linear polarization axis; the authors justify this by showing that the CP SH field preserves its phase after the polarizer, cross-validated with complementary detection schemes.

Sub-cycle all-optical OAM switching

The central result is ultrafast reconfiguration using a TWINS common-path birefringent interferometer, which splits a ±45°-polarized pulse into two orthogonally polarized replicas with a controllable delay $l = \pm 1$3 (minimum increment ~0.02 fs). Four delay settings select four pump polarization states:

Relative delay	Pump polarization	Generated SH mode
$l = \pm 1$4 or $l = \pm 1$5	Linear (±45°)	HG-like beam (net $l = \pm 1$6)
$l = \pm 1$7	Circular (one helicity)	Vortex, one sign of $l = \pm 1$8
$l = \pm 1$9	Circular (other helicity)	Vortex, opposite $_{3v}$0

Under circular excitation, adjacent quadrants separated by 30° acquire a $_{3v}$1 phase step, assembling the full $_{3v}$2 spiral and a vortex beam. Under linear excitation, upper-left/lower-right quadrants emit vertically polarized SH and lower-left/upper-right emit horizontally polarized SH, each pair internally phase-matched so that upper and lower halves are coherent — an HG$_{3v}$3/HG$_{3v}$4-like field. Measured phase maps agree well with simulations across all four configurations, and the interference-fringe visibility oscillates with period $_{3v}$5, marking the vortex-to-HG transitions. Since SHG is effectively instantaneous, the switching dynamics are governed solely by the relative phase of the two femtosecond pump replicas; the mechanical wedge translation serves only to scan the response, making the modulation intrinsically pulse-duration limited. This constitutes monolithic switching between $_{3v}$6, $_{3v}$7, and $_{3v}$8 without cascaded metasurfaces, in contrast to prior demonstrations where wavefront encoding occurred in a physically separate dielectric metasurface downstream of a WSe$_{3v}$9 monolayer (2608.13548).

Limitations and open questions

Several constraints qualify the demonstration. The phase mask uses only a four-level discretization of the spiral, so the generated modes carry residual content beyond the ideal Laguerre-Gaussian; quantitative OAM purity figures appear only in supplementary material, and the manuscript's commented-out text indicates mode purities as low as ~1–5% for some configurations, suggesting substantial room for improvement through finer angular sampling. Conversion efficiency is limited by the 46-nm interaction length, and the authors note that incorporating resonant nanostructures could raise efficiency at the cost of the broadband character they highlight as an advantage. The demonstrated switching is restricted to $\chi^{(2)}$0; whether higher-order charges, multiplexed outputs, or arbitrary phase profiles can be realized with denser orientation patterning remains untested. Finally, the platform has not yet been operated in a waveguided or cavity-integrated geometry, leaving open how the switching fidelity translates to on-chip architectures.

Conclusion

This work establishes crystal-engineered 3R-MoS$\chi^{(2)}$1 as a single, atomically thin medium in which the nonlinear susceptibility tensor itself performs wavefront shaping: a spatially patterned crystal orientation encodes a helicity-dependent geometric phase of $\chi^{(2)}$2 onto the SH field, enabling background-free vortex generation and sub-optical-cycle all-optical toggling between HG-like and oppositely charged vortex beams. The approach removes the need for cascaded switching-and-shaping optics and, being resonance-free, operates broadband. Its practical impact will depend on improving mode purity beyond the coarse four-level mask and on boosting conversion efficiency, questions the paper identifies but does not resolve.