Ultrafast all-optical switching in nonlinear 3R-MoS$_2$ van der Waals metasurfaces

Abstract

Second-order nonlinear optical processes are fundamental to photonics, spectroscopy, and information technologies, with material platforms playing a pivotal role in advancing these applications. Here, we demonstrate the exceptional nonlinear optical properties of the van der Waals crystal 3R-MoS$_2$, a rhombohedral polymorph exhibiting high second-order optical susceptibility ($χ^{(2)}$) and remarkable second-harmonic generation (SHG) capabilities. By designing high quality factor resonances in 3R-MoS$_2$ metasurfaces supporting quasi-bound states in the continuum (qBIC), we first demonstrate SHG efficiency enhancement exceeding 10$^2$. Additionally, by using degenerate pump-probe spectroscopy, we harness the C$_{3v}$ system's symmetry to realize ultrafast SHG polarization switching with near-unity modulation depth. The operation speeds are limited only by the excitation pulse duration, allowing its characterization via the nonlinear autocorrelation function. These findings establish 3R-MoS$_2$ as a transformative platform for nanoscale nonlinear optics, offering large conversion efficiencies and ultrafast response times for advanced pulse measurement devices, integrated photonics, and quantum technologies.

Figures (4)

• Figure 1: Crystalline symmetry and SHG optical selection rules in 3R-MoS$_2$ metasurfaces. (a) Crystalline structure of 3R-MoS$_2$, showing the vertical stacking of three MoS$_2$ monolayers in an ABC rhombohedral arrangement. Molybdenum (Mo) atoms are depicted in blue, sulfur (S) atoms in yellow. (b) In-plane $D_{3h}$ crystal symmetry of a single MoS$_2$ layer, with the zigzag (ZZ) and armchair (AC) crystallographic directions indicated by black arrows. (c) Polar plot of the SHG intensity, $I^{2\omega}$, for a bulk 3R-MoS$_2$ crystal, measured by rotating both the excitation and collection linear polarization angle. The solid line represents a fit to a $\approx\cos^2(3\theta)$ function, confirming the six-fold symmetry of the crystal and the preferential nonlinear emission along the AC axis, oriented approximately at 0 degrees. (d) Schematic illustration of a symmetry-broken 3R-MoS$_2$ metasurface supporting quasi-bound states in the continuum for resonant SHG enhancement, along with the SHG optical selection rules for a degenerate pump-probe excitation scheme. To achieve SHG optical switching, two fundamental pulses, orthogonally polarized along the AC ($\omega_{AC}$) and ZZ ($\omega_{ZZ}$) axes, excite the sample at normal incidence. When the time delay ($\Delta t$) between the pulses exceeds their duration, SH emission is polarized along the AC axis ($2\omega_{AC}$). When both pulses overlap in time, the SH signal is instead polarized along the ZZ axis ($2\omega_{ZZ}$). For clarity, we have neglected the additional components of the SHG outputs to better illustrate the switching mechanism.
• Figure 2: 3R-MoS$_2$ metasurface design for qBIC-driven second-order nonlinear enhancement (a) Schematic illustration of the unit cell of the symmetry-broken qBIC metasurface, independent on the crystal axis orientation. The symmetry-breaking condition, introduced by a length difference ($\Delta L$), gives rise to the radiative qBIC state. (b) Simulated optical transmission spectra of a 3R-MoS$_2$ qBIC metasurface for linearly polarized excitation parallel ($E \|x$) or perpendicular ($E\|y$) to the long axis of the nanorords. (c) Spatial distribution of the simulated electric field ($E$) normalized to the incident field ($E_0$), for excitation polarized parallel to the nanorods, along the x-axis, and calculated over a plane at half-height of the resonators. (d) SHG power $W^{2\omega}$, normalized to the fundamental excitation power $W^{\omega}$, for a bulk crystal (diamond markers) and a qBIC metasurface (circular markers), excited either parallel or perpendicular to the nanorods, both with a thickness of 218 nm. The qBIC metasurface is tuned for a wavelength around 1500 nm: the black solid line depicts its optical transmission and is spectrally correlated with the SHG enhancement.
• Figure 3: Second-order nonlinear optical response of 3R-MoS$_2$ metasurfaces. (a) Bright-field optical image of a fabricated qBIC metasurface from an exfoliated 3R-MoS$_2$ crystal. (b) Tilted scanning electron microscope (SEM) image of a 3R-MoS$_2$ qBIC metasurface on a glass substrate. (c) Normalized white-light transmission spectra of 3R-MoS$_2$ qBIC metasurfaces (thickness 218 nm) for varying scaling factors ($S$) from 1.02 to 1.12, showing a redshift of the qBIC resonance with increasing unit cell size. (d) SHG intensity as a function of the fundamental excitation wavelength, scanned around the qBIC resonance for a metasurface ($S=1.12$, in purple the metasurface optical transmission spectrum). (e) Polar plot of the SHG intensity as a function of the excitation beam polarization angle, shown for a 3R-MoS$_2$ qBIC metasurface (MS, $S=1.10$ and 218 nm thickness) compared to a bulk reference sample with the same height. Left: normalized SHG signal obtained from the the nonlinear tensor model (see Methods and Supplementary Note II). Right: experimental SHG signal from a qBIC metasurface (as in Figure \ref{['fig3']}f) and a reference bulk 3R-MoS$_2$ multiplied 150 times. The signal is collected by rotating the excitation laser beam, with a fixed linear polarizer in the collection path along AC. (f,g) SHG spectra for excitation polarized parallel or perpendicular to the unit cell nanorods, for metasurfaces aligned along the AC (f) and ZZ (g) crystal directions, both showing strong SHG enhancement at the qBIC resonance centered at 1500 nm. Inset: optical transmission of each relative metasurface, showing the well-resolved qBIC resonance at approximately 1500 nm.
• Figure 4: Ultrafast all-optical SHG switching and modulation in 3R-MoS$_2$ qBIC metasurfaces. (a) Schematic of the ultrafast spectroscopy setup. The linearly polarized excitation laser is split into two arms, with one passing through a delay line and the other through a half-wave plate (HWP) to control the polarization of the second pulse. The pulses are then focused onto the sample in a confocal geometry, and the SHG signal is detected using a spectrometer (not shown) and a CCD camera after filtering (SP: shortpass filter, LP: linear polarizer). (b) In-plane structure of a 3R-MoS$_2$ monolayer crystal, indicating the armchair (AC) (horizontal arrows) or zigzag (ZZ) (vertical arrow) directions. (c) Table of optical selection rules for excitation with two linearly polarized optical pulses, $E_1(\omega)$ and $E_2(\omega)$, and the resulting polarization direction if the SHG signal, $P(2\omega)$, at zero-time delay. The SHG is directed along the ZZ direction only in case of perpendicular polarization between the excitation pulses. (d) SHG intensity from a qBIC metasurface ($S=1.10$) with linear polarization detection along the ZZ direction, $I_{ZZ}^{2\omega}$, as a function of the time delay between two excitation pulses, one polarized along AC and the other along ZZ (schematic inset). The data is compared with excitation with only one pulse along AC (black solid line). The dashed black line represents a Gaussian fit to the data. (e) SHG intensity from a qBIC metasurface, aligned along the AC direction, as a function of the time delay between two excitation pulses polarized along AC (schematic inset). The SHG signal is recorded for linearly polarized detection along AC ($I_{AC}^{2\omega}$, in yellow) and along ZZ detection ($I_{ZZ}^{2\omega}$, in blue). (f) SHG signal exhibiting a period of approximately 5 fs, originating from the interference of the two collinear beams along AC.