The mid-infrared (MIR) spectral range (2–20 μm) is attracting increasing interest due to its enormous potential in sensing, biomedicine, free-space communication, and spectroscopy applications [1–3]. Photonic integrated circuits (PICs) are playing a crucial role in miniaturizing optical laboratory experiments and transitioning them into portable commercial technologies. While active and passive PICs in the near-infrared (IR) and visible spectrum are well established, the MIR range has not fully tapped into the advantages of integrated photonics solutions, though the low-loss propagation ability of MIR light up to 3.39 μm through SOI waveguides has been demonstrated [4]. Indeed, light sources operating above 1.8 μm, including optical parametric oscillators and thulium-doped fiber lasers (TDFLs), are not as mature as their counterpart at near-IR and visible wavelengths. Integrated on-chip laser sources operating in the 2 μm waveband have been recently demonstrated based on III-V materials like InP and GaSb. For instance, significant breakthroughs have been made in heterogeneously hybrid [5,6] or monolithically [7] integrated wavelength-tunable lasers. The availability of these light sources sparked efforts towards photonic integration in the 2 μm waveband with numerous demonstrations of integrated devices, including active modulators [8,9], photodetectors [10,11], and passive components [12–15].

The 2 μm spectral range presents a promising opportunity for leveraging nonlinear effects within silicon-based PICs because a decrease in two-photon absorption (TPA) occurs when the combined photon energy is lower than the bandgap energy of silicon [16], reducing the impact of free-carrier absorption (FCA). This highlights the potential of silicon as a suitable platform for parametric nonlinear optics, especially in scenarios where a tunable MIR source is crucial. Furthermore, previous studies have demonstrated efficient wavelength conversion using straight silicon waveguides, indicating that SOI is the preferred integrated platform for nonlinear applications for the 2 μm waveband [17–22]. However, these studies rely on high-power pulsed pump sources or use centimeter-long waveguides with custom-designed silicon layer thickness, introducing complexity and limiting practical usability. Meanwhile, microring resonators serve as critical components in PICs, essential for various optical functions like filters [23], modulators [9], nonlinear frequency converters [24], and frequency comb generators [25] due to their adaptability and versatility. However, in the 2 μm waveband, achieving efficient nonlinear processes using microring resonators is typically hindered by the relatively low $Q$-factor [26–28].

In this work, we demonstrate high-efficiency and broadband MIR wavelength conversion in a high-$Q$ silicon microring resonator under low CW pump power. Based on the standard 340 nm SOI platform, the waveguide dimension is carefully designed for dispersion engineering. At 1999.3 nm, the measured loaded $Q_l$ of the fabricated microring resonator is $1.11\times {10}^5$, corresponding to a low propagation loss of 1.68 dB/cm. With only 4.42 dBm of input pump power, a maximum conversion efficiency (CE) of $-15.57\mathrm{dB}$ is achieved. Experimental results show frequency mixing processes in a 140.4 nm wavelength range with a CE of $-19.32\mathrm{dB}$, while simulations suggest a conversion bandwidth exceeding 400 nm.

The diagram illustrates the structure of the silicon microring resonator incorporating a cavity length denoted as $\mathit{L}$, as shown in Fig. 1. The pump and signal powers are coupled into the resonator through a directional coupler (DC) with the coupling coefficient ${\mathit{\kappa }}_{\mathit{m}}$ ($\mathit{m}=\mathit{p},\mathit{s},\mathit{i}$ corresponds to pump, signal, and idler, respectively). These coefficients represent the fraction of the field cross-coupled at the DC, with ${\mathit{\kappa }}_{\mathit{m}}^2$ as the power coupling ratio. When both phase and frequency matchings are satisfied, the microring resonator can facilitate stimulated degenerate four-wave mixing (FWM). The inset in Fig. 1 illustrates the interaction of two pump photons and one signal photon generating an idler photon at a new optical frequency, following the principle of energy conservation. The presence of a high intracavity circulating power enables the enhancement of the FWM process.

To analyze the FWM process in a silicon microring resonator and determine the waveguide cross-sectional dimensions and cavity parameters, the theoretical undepleted pump model can be used to calculate the CE [29]: $$\mathrm{C}\mathrm{E}={\gamma }^2{P}_p^2{L}_{\mathrm{eff}}^2\mathrm{F}{\mathrm{E}}_p^4\mathrm{F}{\mathrm{E}}_s^2\mathrm{F}{\mathrm{E}}_i^2,$$(1)$$L_{\mathrm{eff}}^2=L^2{e}^{-\alpha L}{\left|\frac{1-e^{-\alpha L+i\mathrm{\Delta }kL}}{\alpha L-i\mathrm{\Delta }kL}\right|}^2,$$(2)$$\mathrm{F}{\mathrm{E}}_m=\left|\frac{\kappa }{1-t{e}^{-\alpha L/2+i{k}_{m}L}}\right|,$$(3)where $\gamma =(2\pi {\mathit{n}}_2)/({\lambda }_{\mathit{p}}{\mathit{A}}_{\mathrm{eff}})$ is the nonlinear coefficient, ${\mathit{n}}_2$ is the nonlinear refractive index, ${\lambda }_{\mathit{p}}$ is the pump wavelength, ${\mathit{A}}_{\mathrm{e}\mathrm{f}\mathrm{f}}$ is the effective mode area, ${\mathit{P}}_{\mathit{p}}$ is the pump power, ${\mathit{L}}_{\mathrm{eff}}$ is the effective length, and $\mathit{L}$ is the cavity length of the microring resonator. The term $\mathit{\alpha }$ represents the loss mechanisms, taking into account linear propagation loss and nonlinear losses due to the TPA and TPA-induced FCA effects [30]. The mismatch between the wavenumbers is given by $\mathrm{\Delta }\mathit{k}=2{\mathit{k}}_{\mathit{p}}-{\mathit{k}}_{\mathit{s}}-{\mathit{k}}_{\mathit{i}}$. $\mathrm{F}{\mathrm{E}}_{\mathit{m}}$ is the field enhancement factor in the microring resonator. $\mathit{\kappa }$ and $\mathit{t}$ are the coupling and transmission coefficients of the microring resonator, respectively, and their relationship is ${|\mathit{\kappa }|}^2+{|\mathit{t}|}^2=1$.

The optimized group velocity dispersion (GVD) and high $Q$-factor readily ensure an efficient and broadband FWM process within the microring resonator by using the three resonant modes as pump, signal, and idler [31]. A small and anomalous GVD is often required for broadband phase-matching, which enables a broad FWM conversion bandwidth [32]. The refractive indices of silicon and silica can be calculated by the Sellmeier equation [33], as shown in Fig. 2(a). Figure 2(a) also illustrates the effective indices of the fundamental transverse-electric (${\mathrm{TE}}_0$) mode as a function of wavelength for different widths of 1050, 1150, and 1250 nm. Figure 2(b) plots the calculated GVD ${\beta }_2$ of the different silicon waveguides. The dispersion curve can be flexibly engineered by adjusting the silicon waveguide cross-sectional dimensions. The dimension of the waveguide is set to $1150\mathrm{nm}\times 340\mathrm{nm}$, resulting in a GVD of $-0.05{\mathrm{ps}}^2/\mathrm{m}$ at the pump wavelength. The inset in Fig. 2(b) shows the distribution of the ${\mathrm{TE}}_0$ mode in the silicon strip waveguide, which is well confined in the silicon core.

The FWM CE of the cavity, defined as $\mathrm{10}{\log }_{\mathrm{10}}({\mathit{P}}_{\mathit{i}}^{\mathrm{out}}/{\mathit{P}}_{\mathit{s}}^{\mathrm{in}})$, is calculated by solving Eqs. (1)–(3), where ${\mathit{P}}_{\mathit{i}}^{\mathrm{out}}$ is the idler power coupled out of the microring resonator to the bus waveguide and ${\mathit{P}}_{\mathit{s}}^{\mathrm{in}}$ is the input signal power in the bus waveguide. For the degenerate FWM process, the contributions from weak signal and converted wave powers are negligible due to the predominant influence of the strong pump power throughout this process. Therefore, the following calculations use the nonlinear parameters of a silicon waveguide at the designed pump wavelength of 2 μm, including the TPA coefficient ${\mathit{\beta }}_{\mathrm{TPA}}\sim 2\times {10}^{-12}\mathrm{m}/\mathrm{W}$ [16], the nonlinear refractive index ${\mathit{n}}_2\sim 10.8\times {10}^{-18}{\mathrm{m}}^3/\mathrm{W}$ [17], and the effective free-carrier lifetime of $\sim 8\mathrm{ns}$ [34]. The linear loss coefficient is $\alpha =1.68\text{dB/}\mathrm{cm}$.

The simulated CEs, as a function of cavity length $\mathit{L}$ and ${\mathit{\kappa }}_{\mathit{m}}^{\mathrm{2}}$, are depicted in Fig. 3(a). Optimal CE is achieved with a shorter cavity length. To mitigate excessive bending losses, a relatively large radius of 50 μm is used. Therefore, the resonator cavity, consisting of two sections of 60-μm-long waveguides connected by two 180° bends, has a minimum length of 434 μm. Figure 3(b) illustrates the power coupling ratio ${\mathit{\kappa }}_{\mathit{m}}^{\mathrm{2}}$ with variations in the DC width across different wavelengths, with inset profiles showing calculated light propagation. $A\pm 10\mathrm{nm}$ change in waveguide width shifts ${\mathit{\kappa }}_{\mathit{m}}^{\mathrm{2}}$ from 0.023 to 0.028 at 2 μm wavelength. As depicted in Fig. 3(a), CE peaks under critical coupling and declines rapidly in under-coupled conditions, with a slower decline in over-coupled scenarios. Therefore, taking the fabrication variations into account, our microring resonator is designed to have a gap of 300 nm, operating slightly over-coupled near critical coupling, resulting in a negligible change ($<0.5\mathrm{dB}$) in the CE. Figure 3(c) displays discrete wavelength conversion in microring resonators due to resonant effects.

As the waveguide exhibits a very small negative GVD of $-0.05{\mathrm{ps}}^2/\mathrm{m}$ at the pump wavelength, the waveguide theoretically supports broadband wavelength conversion. Figure 4(a) illustrates the calculated resonance wavelengths of the designed resonator. Since energy conservation is always satisfied in the FWM process, the generated idler wavelength does not precisely match a resonance wavelength [35]. The CE decreases as the signal wavelength deviates from the pump wavelength because slightly different dispersions could lead to a mismatch between the idler wavelength and the resonance wavelength [29]. As depicted in Fig. 4(b), wavelength conversion can span over 400 nm of signal-idler separation. Utilizing a pump wavelength near 2 μm, a substantial 3 dB conversion bandwidth of 150 nm is achieved.

The silicon microring resonator is fabricated using standard processes provided by our in-house Micro&Nano Fabrication and Characterizing Facility, including electron beam lithography and inductively coupled plasma techniques. A 1-μm-thick silica cladding is deposited through plasma-enhanced chemical vapor deposition. The scanning electron microscope (SEM) image of the fabricated device and a magnified view of the coupling region are displayed in Fig. 5(a). A tunable laser (OETLS-300) with a minimum scan step of 4 pm is employed, and the polarization is adjusted to TE mode using a polarization controller (PC). The optical power at the output port is monitored with a power meter (Thorlabs PM100D). The measured transmission spectrum is illustrated in Fig. 5(b). From the transmission spectrum, the free spectral range (FSR) of the 434-μm-long microring resonator can be measured to be approximately 2.42 nm.

Due to the limited wavelength resolution of the 2 μm tunable laser, the microwave method is employed to characterize the $Q$-factor of the microring resonator using an electrical spectrum response [36]. The experimental setup is shown in Fig. 6(a). A 2 μm laser diode (EP2000-DM-HAA) is used as the input light source (inset i), and then the light is modulated by a Mach–Zehnder modulator (MZM, MX2000-LN-10), with the signal format of optical double sideband (ODSB) modulation (inset ii). The blue dashed rectangles represent the ODSB modulation. The upper sideband of the ODSB signal is filtered by the microring resonator (see insets iii and iv). Then, the signal is collected by a photodetector (EOT ET-5000F), and converted to a radio frequency (RF) signal (inset v). A vector network analyzer (Anritsu MS2028C) generates sweeping RF signals (amplified by an RF amplifier, AT-BB-0022-2730A) for the MZM (inset vi) and subsequently monitors the output RF signal.

The microwave approach utilizes the RF signal to accurately reflect the resonator’s response, enabling precise $Q$-factor measurement. Additionally, this optical-to-electrical conversion facilitates the realization of a microwave photonics notch filter [37]. Figure 6(b) shows the normalized resonance peak of the fabricated microring resonator when its central frequency is 8.73 GHz at the corresponding resonance wavelength of 1999.3 nm, and the data can fit well with Lorentz transmission. The measured extinction ratio is 11 dB, and the 3 dB bandwidth is calculated to be 1.35 GHz, indicating a $Q$-factor of the microring resonator at a very high value of $1.11\times {10}^5$. By analyzing the measured spectral response at the through port of the microring resonator, the waveguide propagation loss can be extracted to be 1.68 dB/cm, corresponding to a high intrinsic $Q_i$ up to $3.09\times {10}^5$. To achieve a high $Q$ value, the resonator loss should be minimized, and the gap between the bus waveguide and the resonator requires precise control. In this work, 1.15-μm-wide waveguides are used, reducing the optical field intensity at the sidewalls and thereby lowering scattering from the rough sidewalls. A relatively large radius of 50 μm is employed to avoid excess bending losses. Using the aforementioned standard fabrication processes, a low-loss microring resonator can be readily fabricated.

The silicon microring resonator’s resonance wavelength is highly sensitive to temperature fluctuations, attributed to its elevated thermo-optical coefficient ($\mathrm{TOC}=1.8\times {10}^{-4}{\mathrm{K}}^{-1}$) [38]. The microring resonator was affixed to a thermoelectric cooler (TEC) to ensure precise control over the resonance wavelength. In Fig. 6(c), the relationship between the measured resonance frequency of the microring resonator and varying temperature is depicted. By adjusting the temperature from 31.2°C to 31.7°C in increments of 0.1°C, the central frequency of the microring resonator could be tuned from 6.71 to 10.18 GHz. The green circles represent the experimental data, while the blue line represents the linear fitting. The frequency-temperature efficiency is $\mathrm{d}\nu /\mathrm{d}\mathit{T}=6.89\text{GHz/}°\mathrm{C}$, demonstrating the flexible tunability of the microring resonator’s central frequency.

The FWM process is subsequently investigated in the fabricated silicon microring resonator, with the experimental setup illustrated in Fig. 7(a). Two homemade tunable CW TDFLs are used as pump and signal light sources. The pump and signal light wavelengths are carefully aligned to the resonance wavelengths. A TDFA then amplifies the pump light. Two PCs are used to adjust the pump and signal light to the TE mode. Then, the two TE mode lights are combined by a 90/10 coupler and coupled into the bus waveguide. A TEC is used to maintain the temperature of the device. The FWM spectrum of the microring resonator is measured by an optical spectrum analyzer (Yokogawa AQ6375B). Figure 7(b) shows the FWM spectrum at the through port of the microring resonator, which is normalized to the transmission of the grating couplers on the same chip. The two resonance wavelengths for the pump and signal light are 1999.3 and 1931.7 nm, respectively; as can be seen from the figure, the converted idler wavelength is 2072.1 nm.

For the microring resonator, the FWM CE is calculated by the ratio between the off-resonance signal power collected by the output coupling fiber ($P_{s,\text{off}}^{\text{output}}$) and the on-resonance idler power collected by the output coupling fiber ($P_{i,\mathrm{on}}^{\text{output}}$), defined as $10{\log }_{10}(P_{i,\mathrm{on}}^{\text{output}}/P_{s,\mathrm{off}}^{\text{output}})$ [39]. The measured CE achieved in the microring resonator is $-19.32\mathrm{dB}$ over a wide conversion bandwidth of $\sim 140.4\mathrm{nm}$. As the simulated conversion bandwidth is $\sim 400\mathrm{nm}$, the bandwidth measurement is limited by the tunable range of the laser source and the operation bandwidth of the grating couplers. This experimental result still represents the broadest FWM conversion bandwidth reported in a silicon microring resonator to date, owning the optimized GVD characteristics. As shown in the inset in Fig. 7(b), the microring resonator achieves a maximum CE of $-15.57\mathrm{dB}$, marking the highest CE observed for CW FWM for the 2 μm waveband based on the SOI platform.

As shown in Fig. 7(c), the FWM CE is measured in the microring resonator as a function of the input pump power when the signal wavelength is fixed to 1985 nm. Due to the resonance enhancement of the high-$Q$ microring resonator, a peak CE of $-15.57\mathrm{dB}$ can be obtained and the required CW pump power is only 4.42 dBm, showing a substantial decrease compared to the 22 dBm pump power used in a straight SOI waveguide [40]. With a low input pump power of $-8.38\mathrm{dBm}$, one could still obtain a moderate CE of $-35.31\mathrm{dB}$. It can be seen that the CE varies as the square of the pump power. When the input pump power is increased beyond 4.42 dBm, a saturation of the CE can be observed due to the TPA and the resulting FCA effects. Further increasing the pump power to 8.88 dBm leads to a decrease in CE to $-16.5\mathrm{dB}$. To enhance CE, one approach is to implement the free carrier sweep-out scheme or to use longer wavelengths beyond the TPA edge, albeit with increased complexity [41,42]. Alternatively, emerging integrated platforms utilizing materials with larger bandgaps such as AlGaAs, ${\mathrm{Si}}_3{\mathrm{N}}_4$, SiC, and ${\mathrm{Ta}}_2{\mathrm{O}}_5$ can also be considered. FWM experiments are also performed in an 18-mm-long silicon waveguide with the exact cross-sectional dimensions to verify the enhancement of resonance effects. The results are plotted as blue dots in Fig. 7(c). The maximum CE is only $-26.37\mathrm{dB}$, with an input pump power of 19.74 dBm.

Additional FWM characterization was also conducted by changing the input signal power and wavelength. Figure 7(d) shows the CEs of 1985 nm signal wavelength under different signal powers, where the pump power is kept at 4.42 dBm. The measured CE remained constant at around $-15.84\mathrm{dB}$, consistent with the fitting result shown in the dashed line. Figure 7(e) shows the measured CE as a function of signal-idler wavelength separation. The signal light is tuned into the resonant peaks of the microring resonator at intervals of one FSR of 2.42 nm, ranging from 1931.7 to 1996.9 nm, as we can see that the CE varies from $-15.57$ to $-19.32\mathrm{dB}$ over a broad bandwidth of 140.4 nm.

Demonstrations of wavelength conversion based on the FWM effect in microring resonators have been reported on various integrated platforms. Figure 8 summarizes the performances of FWM in microring resonators using pump sources in the near-IR and 2 μm waveband. The inset color bar indicates the pump power used in the experiments. As shown in Fig. 8, microring resonators with high $Q$-factors ($\sim {10}^5$) are typically utilized to achieve high CEs. The maximum achievable CE depends on the material nonlinearity. For low-index-contrast Hydex microring resonators [43–45], despite a $Q$-factor as high as $1.2\times {10}^6$ [43], achieving a CE of $<-25\mathrm{dB}$ requires a high pump power of 158 mW [44]. AlGaAs microring resonators are particularly suitable for nonlinear frequency conversion due to their significant nonlinear refractive index and minimal TPA effects in the telecom band [24,46,47]. Currently, the highest CE of AlGaAs microring resonators is up to $-12\mathrm{dB}$ with only 7 mW pump power [24]. Recent advancements have demonstrated AlGaAs microring resonators achieving a broad FWM bandwidth of 130 nm with a maximum CE of $-16\mathrm{dB}$ [46]. Emerging SiC microring resonators can achieve a CE of $-21\mathrm{dB}$ with a pump power of 15 mW [39].

Reference [48] reported a silicon multimode microring resonator with an ultrahigh $Q$ of $1.1\times {10}^6$, achieving a CE of $-15.5\mathrm{dB}$. However, this high CE was observed only within a 1 nm bandwidth due to the lack of dispersion engineering. Tunable $Q$-factor silicon microring resonators have demonstrated the achievement of a conversion bandwidth of over 100 nm with a maximum CE of $-16.3\mathrm{dB}$ at a low power level of 0.7 mW [49]. For silicon microring resonators, most previous work has focused on the near-IR waveband [35,50–52], where TPA-induced FCA remains the primary limiting factor for nonlinear performance [35]. In this work, a high-$Q$ resonator operating in the 2 μm waveband, benefiting from reduced TPA effects, achieved a CE of $-15.57\mathrm{dB}$, which we believe is among the highest reported values. Notably, thanks to careful dispersion engineering, the measured conversion bandwidth of 140.4 nm is the broadest ever demonstrated in silicon microring resonators.

Additionally, materials with larger bandgaps, such as AlGaAs, ${\mathrm{Si}}_3{\mathrm{N}}_4$, SiC, and ${\mathrm{Ta}}_2{\mathrm{O}}_5$, hold promise for nonlinear applications at the 2 μm band. However, apart from the ultrabroadband spectral translators using AlGaAsOI nanowaveguides [53], there have been very few experimental demonstrations of efficient wavelength conversion in this wavelength range. To achieve parametric oscillation, it is imperative to continue reducing both linear and nonlinear losses in silicon waveguides operating at the 2 μm wavelength. Promising approaches include employing techniques such as etchless fabrication processes and implementing free carrier sweep-out schemes, similar to those utilized in generating silicon mid-IR combs [25].

In conclusion, combining optimized GVD and resonance effects enables a high-efficiency and broadband CW FWM process in a high-$Q$ silicon microring resonator for the 2 μm waveband. The loaded $Q_l$ of the fabricated microring resonator is measured to be $1.11\times {10}^5$, corresponding to a low propagation loss of 1.68 dB/cm. By using a low pump power of 4.42 dBm, a maximum CE of $-15.57\mathrm{dB}$ can be achieved. A high CE of $-19.32\mathrm{dB}$ can still be obtained under a broad conversion bandwidth of 140.4 nm. Furthermore, the simulation results suggest the conversion bandwidth is $\sim 400\mathrm{nm}$. We anticipate this high-$Q$ silicon microring resonator will pave the way for high-efficiency and broadband wavelength conversion for future communication and sensor applications from the near-IR to the 2 μm waveband.

Acknowledgment. The authors thank the Center of Optoelectronic Micro&Nano Fabrication and Characterizing Facility, Wuhan National Laboratory for Optoelectronics of Huazhong University of Science and Technology for the support in device fabrication.