Effects of substrates on the nonlinear optical responses of two-dimensional materials.

We investigated numerically and experimentally the achievement of strongly localized electric field and significantly enhanced second harmonic generation (SHG) in two-dimensional (2D) materials by using dielectric-metal hybrid substrates. Based on the theory of thin film interference, it was revealed that the strongest localization of electric field in a 2D material, which corresponds to the largest absorption in the metal film, could be achieved by minimizing the reflection of the combined structure (i.e., 2D material + hybrid substrate) because the transmission through the combined structure was negligible. By using MoS₂ as an example, it was demonstrated that a SHG enhancement factor of ~6 could be achieved in the 17-nm-thick MoS₂ layer on an Au/SiO₂ substrate as compared with the single-layer MoS₂ on the commonly used SiO₂/Si substrates with highly efficient SHG. By employing a SiO₂-SnO₂/Ag/SiO₂ substrate in which a 20-nm-thick dielectric film of SiO₂-SnO₂ was inserted in between the MoS₂ layer and the Ag film, a SHG enhancement factor as large as ~18 could be realized in the 9-nm-thick MoS₂ layer. Numerical simulations based on the finite-difference time-domain technique were employed to derive the enhancement factors for SHG and it was revealed that for thick MoS₂ layers the SHG intensity is dominated mainly by the localization of electric field induced by the dielectric-metal hybrid substrates. The dependence of the SHG enhancement factor on the thickness of the MoS₂ layer was found to be modified when the dielectric-metal hybrid substrates were adopted.