Electrical Control of Interband Resonant Nonlinear Optics in Monolayer MoS2

Monolayer transition-metal dichalcogenides show strong optical nonlinearity with great potential for various emerging applications. Here we demonstrate the gate-tunable interband resonant four-wave mixing and sum-frequency generation in monolayer MoS2. Up to 80% modulation depth in four-wave mixing is achieved when the generated signal is resonant with the A exciton at room temperature, corresponding to an effective third-order optical nonlinearity |χ(3)eff| tuning from (∼12.0 to 5.45) × 10–18 m2/V2. The tunability of the effective second-order optical nonlinearity |χ(2)eff| at 440 nm C-exciton resonance wavelength is also demonstrated from (∼11.6 to 7.40) × 10–9 m/V with sum-frequency generation. Such a large tunability in optical nonlinearities arises from the strong excitonic charging effect in monolayer transition-metal dichalcogenides, which allows for the electrical control of the interband excitonic transitions and thus nonlinear optical responses for future on-chip nonlinear optoelectronics.


MoS2 Film Characterization
The monolayer MoS2 film is prepared by chemical vapor deposition (CVD) method. Raman spectrum shows the peaks at ~382 and 402 cm -1 (Figure S1a), 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 S1b. 1,2 The Raman and PL spectra are measured with excitation of a continuous-wave laser at 532 nm with power of ~1 mW.  A home-built femtosecond laser based microscopic system is employed to measure the nonlinear optical properties of the sample, as shown in Figure S3a. A femtosecond oscillator is used for optical excitation with an optical parametric amplifier (TOPAS), where the two incident pump laser beams (pump 1 at 1, pump2 at 2), are focused collinearly on the MoS2 device. 1 is fixed at 800 nm and 2 is tunable from visible to near-infrared (930 -1160 nm).
By controlling the delay line, the pulses of two pump beams will be temporally overlapped and then generate nonlinear optical signals in monolayer MoS2 sample. The pulse duration of both the pump1 and pump2 light is ~230 fs. The generated nonlinear optical signals are detected by a spectrometer. Figure S3b shows the typical spectra of the pump and probe beams centered at 800 nm and 940 nm. Figure S3c shows the cross-correlation spectrum of SFG signal with τFWHM ~338 fs. The pulsed duration τpump can thus be estimated as τpump= τFWHM /√2 = 230 fs. 6. Gate-Tunable SFG with C exciton resonance Figure S6 shows the SFG spectra of MoS2 with the pump at 800 nm while the probe at 980 nm and 1120 nm, corresponding to C exciton resonance and off-resonance, respectively. It is obvious that SFG is tunable at C exciton ( Figure S6a), while for off-resonance SFG, no tunability is observed at different gate voltages ( Figure S6b).
As a result, the intensities of SFG and FWM signals will be where ( ) is the average power of the pump light. This gives the law of power dependence in SFG and FWM processes.
The effective nonlinear optical coefficient will be  eff where t is the thickness of the MoS2 monolayer.
The output fields generated by the polarization (2) and ( , .  Yes Wide range Slow Plasmonic antenna 7 No Plasmonic resonances Slow

Comparison among Different Tuning Approaches
We list the comparison between different tunable approaches in TMDs ( Table 1). The gateinduced tunability of nonlinear optical signals in TMDs demonstrated here is originating from the modulation of oscillation strength of interband excitonic resonances, and thus the tuning is limited to the excitonic wavelengths. Strain tuning approach is arising from the strain-induced changing of the lattice structure and thus the optical susceptibility of the TMDs, so that the tuning is covering a wide spectral range. As for plasmon induced tuning, it is attributed to the external electric field manipulation, and the tuning wavelength is highly depending on the plasmonic resonance wavelengths. In terms of tuning speed, strain and plasmonic antenna approaches are relatively slow, while electrical gating induced dynamic tuning is fast and easy for precisely control.

Power Calibration and Measurement
To accurately measure the power of the generated nonlinear optical signals, we couple a commercial tunable femtosecond laser light into our experiment setup with the parameters (e.g., repetition rate, pulse duration) identical to the nonlinear signals generated in the experiments. By measuring the power of the commercial tunable laser with a power meter, we could correlate the incident power with the counts of our spectrometer and the system loss.