Broadband Plasmon-Enhanced Four-Wave Mixing in Monolayer MoS2

Two-dimensional transition-metal dichalcogenide monolayers have remarkably large optical nonlinearity. However, the nonlinear optical conversion efficiency in monolayer transition-metal dichalcogenides is typically low due to small light–matter interaction length at the atomic thickness, which significantly obstructs their applications. Here, for the first time, we report broadband (up to ∼150 nm) enhancement of optical nonlinearity in monolayer MoS2 with plasmonic structures. Substantial enhancement of four-wave mixing is demonstrated with the enhancement factor up to three orders of magnitude for broadband frequency conversion, covering the major visible spectral region. The equivalent third-order nonlinearity of the hybrid MoS2-plasmonic structure is in the order of 10–17 m2/V2, far superior (∼10–100-times larger) to the widely used conventional bulk materials (e.g., LiNbO3, BBO) and nanomaterials (e.g., gold nanofilms). Such a considerable and broadband enhancement arises from the strongly confined electric field in the plasmonic structure, promising for numerous nonlinear photonic applications of two-dimensional materials.


Device fabrication and MoS2 flake characterization
Monolayer MoS2 is grown on a SiO2/Si substrate by chemical vapor deposition (CVD) method.
Bowtie structures are patterned on the as-grown MoS2 substrate by electron beam lithography (Vistec 6000). A 50 nm Au film is evaporated by electron beam evaporation system and then lifted off after soaking in acetone for 4 h. The size of the plasmonic bowtie array is 50 × 50 Monolayer MoS2 film is prepared by chemical vapor deposition (CVD) method. By examining Raman and photoluminescence spectra ( Figure S1), the CVD MoS2 flakes are identified as monolayers. Raman spectrum shows peaks at ~382 (E2g) and 402 cm -1 (A1g), with the peak distance of ~20 cm -1 , indicating monolayer MoS2 1 . Further, photoluminescence (PL) spectrum is measured with two strong peaks at ~620 and 670 nm, corresponding to B and A excitons respectively, as shown in Figure S1(b) 1,2 . The Raman and PL spectra are measured with excitation of a continuous-wave laser at 532 nm with the power of ~1 mW.

Figure S1
Raman spectrum (a) and PL spectrum (b) of CVD MoS2 film.

Nonlinear optical measurement
A home-built femtosecond laser based microscopic system is employed for measuring the nonlinear optical signals from the fabricated samples. The schematic of this system is shown in Figure 2b. A femtosecond parametric amplifier (Spectra-Physics, TOPAS) is used for optical excitation with a repetition rate of 2 kHz. The pump and idler laser beams for optical excitation, are linearly polarized with polarization directions parallel with each other. The spectra of the pump and idler laser beams are shown in Figure S2. The polarization of the laser beam is changed via a half waveplate. The pulse duration of the incident pulses is ~230 fs. The pulses of the pump and idler beams are spatially merged through a dichroic mirror and temporally synchronized by a delay line, focused collinearly on the sample through an objective lens 3 (NA=0.75, 40×). The spot sizes of the pump and idler beams on the sample are ~2.5 µm. The FWM signal generated in the sample is detected by a detector following a monochromator (Andor 328i) in the reflection configuration.

Figure S2
Normalized spectra of the pump and idler light centered at ~800 nm and ~1020 nm.

The full spectra of different nonlinear optical processes
In the experiment (the pump wavelength 1 800nm; the idler wavelength 2 1040 nm), the SHG at ~400 nm and 520 nm, SFG at ~452 nm and FWM at ~650 nm are marked in Figure   S4. The FWM is enhanced as expected due to the pump frequency matching the longitudinal plasmonic resonance (p_L) (i.e., 1=p_L). Besides, SHG of the idler light (22) at 520 nm is also enhanced due to that the incident idler frequency is close to the plasmon resonance. SHG of the pump light (21) at ~400 nm and SFG (1+2) at ~452 nm, however, are slightly enhanced mainly because the enhanced signals are partially reabsorbed by the gold structure.
Furthermore, as the conversion efficiency of these second and third-order nonlinear optical processes in the hybrid MoS2-plasmon nanostructures is in the order of ~10 -7 , the competition among different nonlinear optical processes could be negligible, which is also confirmed by the experiments.

Numerical simulation method
Three The simulated reflectance spectra agree well with the measured data, as shown in Figure S5.
We present the experimental (solid curves) and simulated (dotted curves) relative reflectance spectra ( = MoS 2 −bowtie / sub ), where MoS 2 −bowtie is the reflection from the hybrid MoS2plasmonic structures and sub is the reflection from a bare SiO2/Si substrate. In Figure S5a, the transverse plasmonic resonances (i.e., the peak in the reflectance spectra) are shown, respectively. In Figure S5b, the plasmonic resonances show blue shift with decreasing structure sizes in both the experimental and simulated reflectance spectra. Furthermore, the small peaks at around 620 and 660 nm corresponding to the B-and A-excitonic states of MoS2 are also clearly observed both in experimental and simulated reflectance spectra.
Electric field enhancement, for the gold bowtie plasmonic nanocavities on SiO2/Si substrates is calculated via a field monitor at the resonance wavelength at the wavelent800 nm) in the simulation. The simulated electric field intensity is defined as the ratio of the simulated |E| 2 of the nanostructure to the simulated |E0| 2 on the bare SiO2/Si substrate, as show in Figure 3b in the main text.

Theoretical calculation of the enhancement factors
For theoretically quantifying the plasmonic enhancement of the FWM process, the following calculations are conducted. When the pump and idler beams are normal incident on the monolayer MoS2 with the polarizations parallel to each other, the nonlinear optical polarization (3) of the FWM process is given by 4 where FWM = 2 1 − 2 , ( 1 ) and ( 2 ) are the electric field of two incident beams.
The intensity of FWM signals will be If the electric field is not uniform over the light-matter interaction region (e.g., manipulated by the nanostructures), the average FWM intensity in the region with area A will be  Thus, the excitation enhancement factor EFth can be determined as 5 Here, we investigate the theoretical enhancement factor EFth shown in Figure 5c   (femi) enhancement factors increase when they approaches the plasmon resonance (i.e., 800 nm).

Calculation of nonlinear coefficients for FWM signals in MoS2
The third-order nonlinear optical polarization (3) induced in MoS2 monolayer from FWM processes are given by 4 where ( 1 ) and ( 2 ) are the electrical field of incident pump and idler incident light,  s is the nonlinear optical coefficients of monolayer MoS2 sheet.
The intensity of FWM signal will be  Figure 5d in the main text.