The integration of two-dimensional (2D) materials, such as graphene and transition metal dichalcogenides (TMDCs) with photonic integrated circuits, has been emerging for applications in optical modulation^[1], detection^[2,3], and nonlinear signal processing^[4,5], owing to the unique optical and electronic properties^[6,7] of 2D materials, the giant interaction between 2D materials and light in waveguide devices^[8,9], as well as the CMOS-compatible device fabrication processes. PtSe2 is a newly discovered group-ten TMDC with a tunable bandgap, the carrier mobility of more than 16,300cm2V−1s−1^[10], and stable physical and chemical properties^[11,12], which makes PtSe2 promising for various optoelectronic applications^[7,12]. To date, waveguide-integrated PtSe2 devices have been explored for optoelectronic applications of light modulation^[13] and photodetection^[14,15].

On the other hand, optical bistability can be used to construct all-optical switches, optical memories, and all-optical logic gates, which are believed to break through the bottleneck of information exchange in future communication and computing systems, playing a crucial role as the core of the next-generation communication and signal processing systems^[16]. Optical bistability was realized in silicon waveguide devices at the beginning of this century^[17]. To further enhance the on-chip optical bistability, graphene-on-waveguide structures have been applied for developing bistable devices. For example, by integrating graphene on the waveguide-integrated Fabry–Perot resonator^[18] and microring resonator (MRR)^[19], the photo-induced joule heating in graphene can lead to enhanced effective thermal nonlinear index compared with the bare silicon waveguides. Besides, optical bistability with low input power requirement induced by the Kerr effect in graphene has been theoretically studied in the graphene-on-silicon slot MRR^[20]. However, the optical bistability has seldom been reported based on waveguide-integrated PtSe2 devices.

In this paper, we studied an integrated nonlinear optical device based on 2D few-layer PtSe2-on-silicon nitride MRR. We measured the transmission spectra of the silicon nitride MRRs before and after covering the PtSe2 film and calculated the absorption coefficients of the fabricated devices. We selected a representative device to measure its transmission curve while gradually increasing the optical power. The resonance shifts to longer wavelengths linearly with the input power, and a clear optical bistability effect was observed. In addition, we used the time-domain coupled mode theory (CMT) to simulate the thermo-optic effect in the device, which agrees well with the experimental results. The subsequent finite-element method (FEM) simulation also shows that the integration of PtSe2 greatly enhances the photo-thermal conversion in the waveguide device. This study is expected to provide a useful reference for developing subsequent nonlinear devices for all-optical signal processing applications.

We designed and fabricated the PtSe2-on-silicon nitride MRR based on the standard nanofabrication technology and home-developed wet-transfer method. We first fabricated silicon nitride MRRs using electron beam lithography and inductively coupled plasma-deep reactive ion etching (ICP-DRIE). The low-pressure chemical vapor deposited (CVD) top silicon nitride layer is 720 nm thick (H1), the buried oxide (BOX) is 4 µm thick (H3), and the etching depth of the silicon nitride layer is 400 nm (H2), as shown in Fig. 1. The gap between the bus waveguide and the microring is 390 nm (g). The width of the waveguide (W) and the diameter (D) of the MRR are 1.2 and 200 µm, respectively. A pair of focusing one-dimensional grating couplers is used for the fiber-to-waveguide optical coupling. Next, we covered the MRR with commercial CVD-grown five-layer PtSe2 film on the sapphire substrate (Six Carbon Technology Shenzhen). To transfer the material, a layer of polymethyl methacrylate (PMMA) was spin-coated on the surface of the PtSe2 sample, and the PMMA layer was heated and cured to form a solid protection layer. Then the sample was immersed in the KOH solution to separate the PMMA-on-PtSe2 layer from the sapphire substrate. After cleaning in the deionized water, the PMMA-on-PtSe2 layer was transferred onto the silicon nitride chip. Then the chip was dried in the air. Finally, the PMMA was removed with an acetone solution. The flowchart for the fabrication process is shown in Fig. S1 in the Supplementary Material.

Next, we characterized the five-layer PtSe2 film on the surface of the silicon nitride chip. The thickness of the PtSe2 film was measured to be ∼2.5nm using atomic force microscopy (AFM), as shown in Fig. 2(a). Figure 2(b) shows the Raman spectrum of the PtSe2 film on the surface of the silicon nitride chip. Three major Raman peaks appeared at 177, 206, and 225cm−1, related to the Eg, A1g, and LO vibration modes of Se atoms, respectively, and the locations of Raman peaks were consistent with the previous report^[21]. X-ray photoelectron spectroscopy (XPS) analysis was also performed to characterize the PtSe2 film further. As shown in Fig. 2(c), C, O, Pt, and Se peaks mainly existed in the film. The peaks of C1s and O1s come from the air absorbed by the surface of the PtSe2 film. Two peaks of 72.72 and 76.02 eV corresponding to Pt 4f7/2 and Pt 4f5/2 were obtained by Gaussian fitting of the Pt 4f peak, as shown in Fig. 2(d). The fitting of the Se 3d peak in Fig. 2(e) also results in two main peaks located at 54.02 and 54.88 eV, corresponding to Se 3d5/2 and Se 3d3/2. The atomic numbers of Pt and Se were calculated based on the measured spectra, as shown in the inset table of Fig. 2(c), which was consistent with the theoretical values^[21].

Next, we characterized the optical absorption of the PtSe2-on-silicon nitride MRRs. The scanning electron microscopy (SEM) images of the devices are shown in Figs. 3(a) and 3(d). The wet-transfer process resulted in PtSe2 film breakages on the MRRs. The material-covered lengths on the MRRs were estimated at 125 µm [Fig. 3(a)] and 471 µm [Fig. 3(d)] from the contrast of the images. For the MRR in Fig. 3(a), from the Lorentz fittings of the full width at half-maximum (FWHM) of the measured resonance (λres) spectra in Figs. 3(b) and 3(c), the Q factor is obtained as Q=λres/FWHM, with 12,300 and 5800 before and after the PtSe2 film coverage. The transmission spectra of the MRR in Fig. 3(d) before and after the PtSe2 film integration are shown in Figs. 3(e) and 3(f). The quality (Q) factor decreases from 16,000 to 2500 after the PtSe2 film integration. Combined with the estimated PtSe2 film covered length, and the measured transmission spectra before and after the PtSe2 film integration, the optical absorption coefficients of the PtSe2-on-silicon nitride waveguide were calculated^[22] as 172 dB/cm [Fig. 3(a)] and 171 dB/cm [Fig. 3(d)]. The resonances have redshifts after the PtSe2 film integration due to the effective refractive index change induced by the PtSe2 film. We also simulated the optical absorption coefficient of the PtSe2-on-silicon nitride waveguide to be ∼179dB/cm, using the FEM simulator (COMSOL Multiphysics) with the complex dielectric constant of the five-layer PtSe2 in the previous study^[21], which was measured using the spectroscopic ellipsometry method. The simulation result agrees well with the experimental estimation.

To measure the nonlinear property of the fabricated device, we set up an experimental system, as shown in Fig. 4(a). We used a variable optical attenuator (VOA) to vary the input optical power, and the 1% output of the 1:99 optical coupler to monitor the input power with a power meter (PM1). The coupling efficiency of the grating coupler at 1550 nm wavelengths is ∼−5.5dB. The input power in the following experiment refers to the optical power coupled into the bus waveguide from the grating coupler. We chose the device shown in Fig. 4(a) for the optical-bistability exploration. We started by setting the output power of the erbium-doped fiber amplifier (EDFA) to a high value that the device can withstand, while the VOA attenuation was set to the maximum attenuation. In this way, we can start the measurement at a low input power, ensuring a stable and continuous tuning of the input power. The measured transmission spectra for different input powers are shown in Fig. 4(b). As the input power increases, the resonance shifts to longer wavelengths, with a linearly fitted slope of ∼6.8pm/mW, as shown in Fig. 4(c). In addition, as the optical power increases, the resonance curve is no longer symmetrical, and eventually, there is a significant power jump on the longer wavelength side, which indicates the emergence of the bistable state.

To further evaluate the nonlinear effect in the PtSe2-on-silicon nitride MRR, we used the time-domain CMT^[23,24] method to calculate the energy distribution (|a|2) in the microring cavity with the input power in the bus waveguide (Pin) and the transmission spectrum of the MRR (Ttrans). We established the CMT model as follows^[25,26]: 1Q0=1Qinst+1Qext,(1)2τext(inst)=ω0′Qext(inst),(2)ω0′=2πcλ0+Δλtherm+ΔλKerr,(3)Δλtherm=2|a|2τlinear−1λ0Rn0∂n∂T,(4)ΔλKerr=|a|2n2λ0cn0ngV,(5)|a|2=2τext−1Pin(ω−ω0′)2+(τext−1+τinst−1+τlinear−1)2,(6)Ttrans=(ω−ω0′)2+(τext−1+τlinear−1−τinst−1)2(ω−ω0′)2+(τext−1+τinst−1+τlinear−1)2,(7)where Q0 is the loaded Q factor of the MRR, τext and Qext are related to the intracavity mode reduction rate caused by the light coupling output, τinst and Qinst are related to the dissipation rate caused by the intrinsic loss in the microring cavity, and τinst can be regarded as the time that the mode amplitude attenuates to 1/e of the initial amplitude under the effect of the intrinsic loss in the microring cavity. ω0′ is the resonant frequency, considering the thermo-optic effect (Δλtherm) and Kerr effect (ΔλKerr). λ0 is the resonance without nonlinear effect (i.e., at low input powers), τlinear is the amplitude loss rate caused by the linear optical loss, R is the thermal resistance of the MRR, n0 is the refractive index of the waveguide, ∂n/∂T is the thermo-optic coefficient, n2 is the Kerr coefficient of silicon nitride, c is the speed of vacuum light, and ω is the angular frequency of the input light. ng and V are the group index and the mode volume in the MRR cavity, respectively, which are calculated by the frequency-difference time-domain (FDTD) method (Lumerical FDTD). The values of the parameters are shown in Table 1. Specifically, parameters of Qext, Qinst, τlinear, and R were obtained by fitting the measurement of the transmission spectrum of the PtSe2-on-silicon nitride MRR at the low input power of −15.5dBm. The simulation results are shown in Fig. 4(d). The transmission spectrum becomes unsymmetrical at high input powers, with a resonance increasing slope of 6.85 pm/mW [shown in the linear fit in Fig. 4(e)], which is consistent with the measurement result, indicating that our model can well describe the nonlinear effects in the device. In addition, it can be known from Eqs. (4) and (5) that the resonance shift due to the thermo-optic effect dominates, while the Kerr effect is almost negligible. We also calculated the power transmission of the device for different input wavelengths based on the time-domain CMT model. As shown in Fig. 4(f), with an input wavelength of 1541.55 nm, there is always only one solution to the equations with the change of the input power, which means that the MRR has only one steady state, which is the same as the shorter wavelengths. At the longer input wavelength of 1541.56 nm, a hysteresis loop appears and represents the appearance of bistability [Fig. 4(g)]. By further increasing the input wavelength to 1541.57 nm, the hysteresis loop is extended, and the gap between the two steady states increases [Fig. 4(h)]. In addition, the stronger thermal-optic effect can lead to the redshift of the bistable threshold wavelength and a decrease of the bistable threshold power and a reduction in the width and area of the hysteresis loop. The device itself works like an optical static random-access memory. Decreasing or increasing the input optical power can be regarded as writing data, after which the device can hold the written data by setting the input power between the two edges of the hysteresis loop, and the data can be read by detecting the output of the device. We also measured the switching time of the bistable state to be ∼30μs by synchronously recording the input and output powers with the two power-sensor ports of the optical power meter (N7744A) while tuning the input power.

Finally, we performed a simulation of the photothermal effect in the waveguide using the FEM simulator (COMSOL Multiphysics) with the electromagnetic heating module. We modeled the waveguide cross section and simulated the cases with and without the PtSe2 film integration. In the simulation, the electromagnetic loss was used as the heat source for heat transfer calculations, and then the temperature distribution can be obtained. We gave the model an initial input light source of about 30 mW and set the ambient temperature to 293.15 K. The thermal conductivities of air, silicon nitride, PtSe2, and BOX were chosen as 0.026, 29, 51^[32], and 1.4m·K, respectively. The conductivity of PtSe2 film was set to 1×10−5S/m^[33]. The simulation results are shown in Fig. 5. The average temperature of the waveguide region is about 366.2 K, which is a significant improvement compared with the case of bare silicon nitride waveguide with an average temperature of 297.9 K. This result also indicates that the application of PtSe2 film can enhance the photothermal conversion in the waveguide. The results demonstrate the application and potential of PtSe2-based bistable devices in all-optical signal processing.

In summary, we have studied the optical bistability in the five-layer PtSe2-on-silicon nitride MRR. The absorption coefficient of the PtSe2-on-silicon nitride waveguide was obtained from the transmission spectra of the MRR with/without PtSe2 film coverage at the low input optical power. By increasing the input power, the resonance of the PtSe2-on-silicon nitride MRR has redshifts, and the transmission spectrum becomes unsymmetrical, showing the optical bistability. We have also theoretically studied the nonlinear effects in the device by developing the time-domain CMT method; the results were consistent with the measurement results. In addition, the FEM simulation also shows that the addition of the five-layer PtSe2 film significantly enhances the photothermal conversion in the waveguide device. The results obtained in this study provide some references to the combination of PtSe2 with waveguide devices and its mechanism of action, which will help us to advance the application of TMDC thin-film materials in integrated photonics, as well as provide a new direction of exploration for integrated optoelectronic devices.