Modulating nonlinear optical responses in 3R-MoS$_2$ Fabry-Pérot microcavities

Abstract

Rhombohedrally stacked transition metal dichalcogenides such as 3R-MoS$_2$ offer an exceptional platform for nonlinear optics, naturally forming Fabry-Pérot (FP) microcavities due to their giant dielectric contrast with the surrounding media. However, rigorously tracking the evolution of multiple harmonic fields within these unpatterned monolithic crystals remains a fundamental challenge. Here, we establish a self-consistent framework, spanning from linear broadband reflectance to second- and third-harmonic generation (SHG and THG), to systematically decode these nonlinear behaviors. Moving beyond conventional models, we demonstrate that the nonlinear emission is dictated by a delicate interplay among the intrinsic material absorption, the FP effects at the fundamental frequency, as well as those at the harmonic frequencies. When harmonic photons lie below the bandgap, weak absorption allows the nonlinear spectra to exhibit a complex modulation driven by the synergistic contribution of FP effects from both fundamental and harmonic waves. In stark contrast, severe intrinsic absorption of higher-energy photons heavily damps the FP effects of the harmonic fields, reducing the nonlinear response to an absorption-limited regime modulated almost exclusively by the FP effects at the fundamental frequency. By successfully decoupling these geometric and material contributions across different harmonic orders, our findings provide a precise design paradigm for engineering next-generation van der Waals photonic architectures.

Figures (4)

• Figure 1: Concept and linear optical responses of 3R-MoS$_2$ microcavities.a Schematic of the physical mechanisms in a 3R-MoS$_2$ microcavity. The strong refractive index contrast among air, the 3R-MoS$_2$ flake, and the silica substrate naturally forms a FP cavity. Multiple interfacial reflections induce strong interference, fundamentally modulating both the linear reflectance and the higher-order harmonic generation (SHG, $2\omega$; THG, $3\omega$) driven by a fundamental pump field ($\omega$). b, c Linear relative reflectance spectra of a representative thin ($\sim$ 100 nm) flake (b) and a thick ($\sim$ 2000 nm) flake (c). The pronounced periodic oscillations in the thick flake are a direct manifestation of the linear FP interference effect. d 2D contour map depicting the global evolution of the linear reflectance spectra as a function of incident wavelength spanning from 600 to 1570 nm and flake thickness up to $\sim$3210 nm.
• Figure 2: Broadband reflectance spectra and thickness calibration for 3R-MoS$_2$.a Experimental two-dimensional mapping of the broadband reflectance spectra (measured continuously from 600 to 1570 nm under halogen lamp illumination) as a function of wavelength and sample thickness. The trajectory of the interference fringes clearly exhibits the FP cavity mode evolution. b Corresponding theoretically calculated two-dimensional reflection intensity distribution based on the TMM, accurately capturing the fringe compression and mode dispersion bending behavior. c--h Detailed spectrum-by-spectrum comparisons between the experimental measurements (orange curves) and theoretical calculations (solid blue lines) for six representative thicknesses ranging from the hundred-nanometer to the micrometer scale (126.4 nm (c), 344.2 nm (d), 617.0 nm (e), 1089.8 nm (f), 1422.3 nm (g), and 1821.4 nm (h)). The data gap between 965 nm and 985 nm arises from the low-sensitivity crossover region between the visible and infrared detectors.
• Figure 3: Giant cavity-induced modulation and complex spectral reshaping of SHG.a SHG spectra recorded at different excitation powers under a fundamental wavelength of 1550 nm. The inset presents the power-dependent SHG intensity on a double-logarithmic scale, giving a fitted slope of 2.01 $\pm$ 0.01. b--g Experimental (scatter points) versus theoretical (solid lines) SHG excitation spectra for representative flakes. Their calibrated thicknesses are 126.4 nm (b), 139.4 nm (c), 617.0 nm (d), 1089.8 nm (e), 1650.0 nm (f), and 1821.4 nm (g). Measurements were performed from 1400 to 1600 nm in 10-nm steps. h SHG intensity ratio (maximum divided by minimum intensity across the measured excitation wavelengths) as a function of sample thickness. A constant incident excitation power was maintained for all recorded data in panels (b--h). i Theoretical 2D contour map of the calculated SHG intensity as a function of excitation wavelength (1400 to 1600 nm) and flake thickness (up to 3210 nm), illustrating the complex topology of intertwined resonance branches.
• Figure 4: Absorption-limited cavity modulation of THG.a THG spectra recorded at different excitation powers under a fundamental wavelength of 1550 nm. The inset presents the power-dependent THG intensity on a double-logarithmic scale, yielding a fitted slope of 2.98 $\pm$ 0.01. b--e Comparison of measured THG excitation spectra (scatter points) and theoretical predictions (solid lines) for the four representative flakes from the preceding SHG study. Their calibrated thicknesses are 126.4 nm (b), 617.0 nm (c), 1089.8 nm (d), and 1821.4 nm (e). Left and right axes denote experimental and theoretical values, respectively. Measurements were performed at 1400, 1420, and 1440 nm, and across 1500--1600 nm (10-nm steps) using a constant excitation power. The 1450--1490 nm range is excluded as the laser's maximum output in this band falls below the required excitation power target. f 2D contour map of the theoretically calculated THG intensity as a function of excitation wavelength and continuous flake thickness, illustrating the absorption-limited modulation governed almost entirely by the fundamental resonance.