The LAC (i.e., the linear limit of the SA [44]) of the in-plane monolayer graphene is obtained through [45]αs(μm−1)=2k0neff,imag×10−6,(4)where k0 is the vacuum wavenumber, and subscript “imag” denotes the imaginary part of the ERI. The LAC is shown in Fig. 3(c) for TE and TM modes, respectively. As the two-level saturable absorber model is widely used in two-dimensional quantum wells, the absorption as a function of the light intensity can be fitted by α(I)=αs/(1+I/Is)+αns, where Is is the threshold intensity of the SA, defined as the optical intensity required in a steady state to reduce the absorption to half of the unbleached value, and αns is the non-saturable absorption coefficient mainly determined by the scattering loss of graphene [3]. When the light intensity is high enough, the absorption coefficient of graphene is close to αns. Finally, the MD is given by [44,46,47]$$\begin{gathered} ΔTTo=Tns−ToTo×100% \\ =e−αnsL−e−αLe−αL×100% \\ =(eαsL−1)×100%, \end{gathered}$$(5)where L is the length of graphene, and α is the absorption coefficient of graphene mainly resulting from the interband transition of carriers and the scattering of graphene coming from the residual aggregates, contamination, wrinkles, and cracks [3,12,15].

Moreover, we simulate the dependence of the MD on wavelengths of incident light, Fermi levels, dimensions of GSHWs, and lengths of graphene pads. Figures 3(d) and 3(e) depict the dependence of the MD on wavelengths of incident light and Fermi levels of graphene for TE and TM modes, respectively. The GSHW with a width of 500 nm, a height of 220 nm, and a 10-μm-long graphene pad is pumped by a 1550-nm input light. As shown in Fig. 3(d), the larger values of the MD are achieved with longer incident wavelengths because stronger light–matter interaction is obtained by the longer incident wavelength, in comparison to that obtained by the shorter incident wavelength shown in the inset. Also lower doping level of graphene is also preferred owing to the larger absorption of graphene. As the TM mode is shown in Fig. 3(e), the increment of the MD over 2.5 times is obtained with shorter wavelengths because of the strengthened leaky field on top of the silicon waveguides, compared to the TE mode. The dependence of the MDs on Fermi levels implies that the values of the MDs can be changed through electronic doping and optical exciters.

Fig. 4. (a), (b) Simulated MDs depending on the width and height of GSHWs with the Fermi level of 0.4 eV and 10-μm-long graphene pad for the TE and TM modes, respectively. (c) The dependence of MDs on the different lengths of graphene for the TE and TM modes with the 500-nm-wide waveguide and Fermi level of 0.4 eV.

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3. EXPERIMENTS

3.1 A. Sample Preparation

Here, we perform an experimental demonstration of the all-optical modulation based on GSHWs. The thicknesses of the top silicon layer and the buried oxide layer are 220 nm and 2 μm, respectively. The silicon waveguides supporting the TE mode consist of 500-nm-wide strip waveguides as well as input and output photonic crystal grating couplers exhibiting an insertion loss of ∼7.5dB per facet at about 1560 nm. The electron-beam lithography (EBL) is used for mask formation and inductively coupled plasma is used for etching silicon with sulfur hexafluoride gas. Then, a monolayer graphene sheet (Hefei Vigon Co., Ltd.) grown by chemical vapor deposition (CVD) is transferred onto the silicon waveguide by the wet-transferring method [37,48], which is depicted as follows. (i) The graphene film with polymer (polymethyl methacrylate, PMMA) on the top and copper foil on the bottom is floated on the etchant with 10 g of copper (II) sulfate pentahydrate (CuSO4·5H2O), 50 mL of de-ionized (DI) water, and 50 mL of concentrated hydrochloric acid (HCl). (ii) After an etching time of about an hour, the PMMA/graphene film without Cu is transferred into a clean beaker and cleaned with DI water. (iii) The chip is dipped into DI water to scoop up the floated PMMA/graphene. Then the sample bakes for 20 min to melt the PMMA resist for better contact between the graphene and waveguides. (iv) We put the chip into acetone for 10–15 min to remove the PMMA. In order to precisely control the MD of the GSHWs, the PMMA layer is coated on graphene and patterned by EBL. The redundant graphene layer is etched off through reactive ion etching (RIE) using oxygen, leaving graphene pads with tens of micrometers length on strip waveguides. The image taken by scanning electron microscopy (SEM) [inset of Fig. 5(a)] of a GSHW shows a graphene pad resting on the top of a silicon strip waveguide. Owing to the large conductivity difference between the graphene and the substrate, the shape of the graphene pad can be clearly seen.Fig. 5.

(a) Raman spectra of the GSHWs (the inset figure is the SEM picture of graphene pad, the blue circle represents the spot where graphene is etched off, the red circle represents the spot where graphene is protected). (b) The experimental transmission data and fitted curves as a function of input power for the TE mode. Here, the relative transmission is expressed as T−ToTo×100%. (c) The comparison of MDs in simulated and experimental results with 10-, 15-, 20-, and 30-μm-long graphene pads (the GSHW with 30-μm-long graphene is not saturated sufficiently with the maximum power of the femtosecond laser we use. Here, we use the fitted MD of 30.1% from the measured data).

3.2 B. SA of the GSHWs

Figure 5(a) exhibits the Raman spectra of the graphene pad which are acquired by a LabRAM HR800 with 532-nm excitation. The red curve shows a G peak (1595cm−1) with a full width at half-maximum (FWHM) of 10cm−1, a 2D peak (2683cm−1) with a 2D-to-G peak intensity ratio of about 1.6, and an inconspicuous D peak, implying the good quality of the transferred monolayer graphene with a Fermi level of about −0.4eV [49]. The blue curve shows no characteristic peaks of graphene, indicating the graphene is etched off effectively by RIE.

The LACs of the GSHWs are characterized by a cutoff method and the measured result is about 0.049 dB/μm, which is close to the simulated result (0.039 dB/μm). The error may come from the scattering loss of the graphene resulting from the process of CVD growth and transfer of graphene. A home-made femtosecond fiber laser with a center wavelength of 1560 nm (pulse width: ∼900fs, repetition rate: 92.9 MHz) is coupled into the GSHWs as a pump source. Four GSHWs with increasing lengths of graphene pads are applied for the SA measurement. The input light strongly interacts with graphene through evanescent coupling owing to the tight bonding between strip waveguides and graphene pads. As the intensity of light increases, the photogenerated carriers lead to the fulfillment of the states near the edge of the conduction and valence bands of graphene [3]. The SA or bleaching of incident light is achieved, resulting in a higher transmission of GSHWs.

As shown in the red triangles in Fig. 5(b), for the GSHW with a 10-μm-long graphene pad, the transmission increases non-linearly with rising input power. The averaged threshold power of the SA is 0.043 mW, corresponding to a threshold of 0.47 W in peak power (i.e., pulse energy of 423 fJ). For the compact silicon waveguide with an effective mode area of 1.02×10−9cm2, the peak power density arrives at 0.46GW/cm2. In addition, the MDs of 500-nm-wide waveguides with 15-, 20-, and 30-μm graphene pads are also provided in blue triangles, green circles, and black squares in Fig. 5(b), exhibiting MDs of 13.6%, 16.4%, and 22.7% with the threshold powers of 0.054, 0.065, and 0.14 mW (i.e., pulse energies of 532, 641, and 1380 fJ), respectively. It is noted that the 30-μm-long graphene pad is not saturated sufficiently with the maximum power of the femtosecond laser we have (the MD can reach 30.1% according to the fitted data). The simulated results (9.7%, 13.6%, 16.4%, and 31.9%) from Fig. 4(c) are in good agreement with the experimental results from Fig. 5(b), which is shown in Fig. 5(c).

Here, the modulation efficiency, defined as the MD per unit length of the device, is about 0.033 dB/μm, which could be further approved by the enhancement of interaction between light and graphene [16,18]. Slot waveguides with smaller effective mode areas may improve modulation efficiency and reduce energy per pulse further [25]. Although the graphene pad with longer length increases the MD, more energy consumption is brought. In order to achieve enough MD and reasonable energy consumption, we choose GSHWs with 30-μm-long graphene in the following experiments of demonstration of all-optical modulation and the response time of the devices.

3.3 C. Demonstration of All-Optical Modulation of GSHWs and Response Time of Devices

Fig. 6. (a) Schematic of the experimental system. (b) Time history of the modulated probe light with the pump light acquired by the oscilloscope (OSC). (c) Time profile of a probe pulse (the inset is the temporal profile of a pump pulse).

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To explore the ultrafast response of GSHWs, we use an asynchronous pump–probe measurement which is stable, fast, and with a longer scan range compared with the conventional pump–probe spectroscopy setups using mechanical delay lines [50,51]. Here, the pump light (about 700 fs) is filtered from 1530 to 1560 nm with an average power of 0.19 mW (2.1 pJ per pulse). The average power of the probe light (about 300 fs) is 0.021 mW with a central wavelength of 1560 nm. As shown in Fig. 7, the temporal transmission of the probe light as a function of its time delay relative to the pump light is illustrated. The rise time of temporal transmission is about 1.2 ps, which is still limited by the resolution time of the asynchronous pump–probe system. Although the time resolution of 700 fs should be achieved, dispersion elements of the system, for example, the single-mode fibers, broaden the width of the pulse in the temporal domain. The FWHM is about 1.65 ps, corresponding to the bandwidth of about 500 GHz, which is in good agreement with the previous results [6,14,16,33].Fig. 7.

Change in transmission of the probe light as a function of its time delay relative to the pump light. The FWHM is about 1.65 ps.

4. CONCLUSION

In summary, an all-optical modulator has been realized by the GSHW. The modulation depth reached 22.7% with a saturation threshold down to 1.38 pJ per pulse with a 30-μm-long graphene pad. The MD can be manipulated by the dimension of waveguides, length, and the Fermi level of graphene through electronic doping and optical exciters. An ultrashort response time of 1.65 ps was obtained by a pump–probe measurement with 2.1 pJ per pulse. The all-optical modulator based on GSHW, with the combined advantages of a compact footprint, broadband operation, the response time of few picoseconds, energy consumption of picojoule per pulse, and compatibility with CMOS, could bring us a step closer to realizing on-chip all-optical control.

5 Acknowledgment

Acknowledgment. We thank all engineers in the Center of Micro-Fabrication and Characterization (CMFC) of Wuhan National Laboratory for Optoelectronics (WNLO) for the support in fabrication.