Layer-Dependent Nonlinear Absorption and Refraction of Re X2( X = Se

Recent studies have revealed that atomically thin two-dimensional (2D) materials exhibit outstanding nonlinear optical (NLO) properties compared with traditional NLO crystals, which provides great potential in numerous photonic devices such as integrated nonlinear photonic chips and modulators. However, the evolution of NLO response with layer number and pump intensity of various 2D materials remains unclear, but offers a basis for hunting powerful NLO materials. Herein, controllable synthesis of a series of $\mathrm{Re}$${X}_{2}$ (X = $\mathrm{Se}$, $\mathrm{S}$) films with different numbers of layers is achieved by chemical vapor deposition. Z-scan techniques are used to investigate the nonlinear absorption coefficient (\ensuremath{\beta}) and nonlinear refractive index (${n}_{2}$). Empirically, the absolute values of both \ensuremath{\beta} and ${n}_{2}$ show a downtrend as the power exponential function with the layer and pump intensity. The NLO parameters of ${\mathrm{Re}\mathrm{Se}}_{2}$ film are \ensuremath{\beta} \ensuremath{\sim} 4156 cm/GW and ${n}_{2}$ \ensuremath{\sim} 1.819 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}10}\phantom{\rule{0.2em}{0ex}}{\mathrm{cm}}^{2}/\mathrm{W}$, which are more significant than those of ${\mathrm{Re}\mathrm{S}}_{2}$ film (\ensuremath{\beta} \ensuremath{\sim} 806 cm/GW and ${n}_{2}$ \ensuremath{\sim} 2.22 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}11}\phantom{\rule{0.2em}{0ex}}{\mathrm{cm}}^{2}/\mathrm{W}$). This result is ascribed to the smaller band gap, higher carrier density, and larger ground-state absorption of ${\mathrm{Re}\mathrm{Se}}_{2}$ than that of ${\mathrm{Re}\mathrm{S}}_{2}$, which is confirmed by the theoretical analysis of the band structure and a three-energy-level system. It is worth pointing out that the \ensuremath{\beta} values for $\mathrm{Re}$${X}_{2}$ films are 10--100 times larger than those of ${\mathrm{WS}}_{2}$, ${\mathrm{Mo}\mathrm{Se}}_{2}$, and ${\mathrm{Mo}\mathrm{Te}}_{2}$. The ${n}_{2}$ values for $\mathrm{Re}$${X}_{2}$ films are 3--4 orders of magnitude larger than for traditional semiconductors such as $\mathrm{Ga}\mathrm{As}$ and $\mathrm{Si}$. Our results suggest that $\mathrm{Re}$${X}_{2}$ semiconductors are greatly anticipated in designing high-performance on-chip photonic devices.