Introduction

Nonlinear frequency conversion is a highly effective approach for generating mid-infrared (MIR) emission through mechanisms such as difference-frequency generation (DFG)1, optical parametric generation (OPG)2, frequency comb generation3, supercontinuum generation4 and so on. Moreover, the intrinsic third-order nonlinear coefficients (χ(3)) in materials are typically smaller than second-order ones (χ(2)), limiting nonlinear conversion efficiency. Compared to quantum-cascade laser5, χ(2) nonlinear frequency conversion offers the advantages of ultrashort optical pulses with high pulse energies and broadband tunability. Although a single second-order parametric process (such as DFG or OPG) can efficiently generate MIR light, there are challenges in generating MIR light with tunable longer wavelengths.

Cascaded second-order nonlinear processes (χ(2): χ(2)) provide a promising pathway to generate an extended wavelength range while achieving higher conversion efficiencies than for χ(3) process. Leveraging the advantages of cascaded second-order effects, the generation of shorter wavelength signals (such as third-order harmonic wave) through cascaded second-order nonlinear parametric up-conversion has been pioneeringly demonstrated in quasi-periodic optical superlattices6. And it has also been validated in many subsequent works7,8,9,10,11. Despite these advancements, generating longer-wavelength light sources, such as MIR, through cascaded up-conversion processes remains unachievable. In contrast, the cascaded second-order parametric down-conversion process offers a promising method for producing longer-wavelength light. However, its practical implementation has yet to be demonstrated due to the narrow phase-matching bandwidth and limited optical parametric gain. The periodically poled lithium niobate (PPLN) waveguides based on quasi-phase matching (QPM) have shown high conversion efficiency and amplification gain for OPG and DFG12,13,14. However, due to the narrow phase-matching bandwidth of QPM waveguides, it is difficult to use them for cascaded second-order nonlinear parametric down conversion. The mode-phase-matched (MPM) nanophotonic thin-film lithium niobate (TFLN) waveguides have garnered attention due to their straightforward fabrication, higher conversion efficiency and broadband phase-matching bandwidth than quasi-phase matching in the near-infrared region15,16,17,18. However, the generation of MIR light based on MPM technology has not yet been experimentally validated. The reasons for choosing thin-film lithium niobate as the verification platform are detailed in Supplementary Note 1.

In this report, we demonstrate the efficient MIR generation via cascaded down-conversion OPG-DFG processes in a reverse-polarization dual-layer nanophotonic TFLN waveguide based on MPM. Optimized MPM enables highly efficient OPG with a remarkably low OPG threshold of ~1.1 pJ, two orders of magnitude lower than previously reported values19. The achieved OPG conversion efficiency of 32.1%, with an output power 12.5 μW, surpasses the performance of PPLN waveguides12. Cascaded down-conversion achieves a maximum MIR conversion efficiency of 15.3% and an output power of 9.4 μW, and enables dynamically tunable MIR output over a wavelength range of 2.06–3.12 μm—a relative bandwidth of 40%, which is unattainable through non-degenerate OPG alone. Longer-wavelength MIR emission at 3.59, 3.93, 4.31, and 4.6 μm is demonstrated using nanophotonic waveguides tailored for specific phase-matching conditions. This work establishes a robust theoretical and experimental framework for generating longer-wavelength MIR light through cascaded nonlinear frequency down-conversion, opening new avenues for integrated photonic applications.

Results

The schematic diagram of the cascaded process in a reverse-polarization dual-layer nanophotonic TFLN waveguide is shown in Fig. 1a. In this scheme, the waveguide can efficiently achieve second-order nonlinear frequency conversion without requiring additional external electric field polarization. However, the dispersion engineering and phase matching are more susceptible to variations in the waveguide geometry. This scheme can be described as: A short-wavelength NIR pump light with a frequency ω is coupled into the nanophotonic waveguide. Owing to the third-order nonlinear interactions (ω → ω′) and the degenerate OPG process (ω → ω/2) within the waveguide, the conditions are highly favorable for the generation of DFG process. Figure 1b shows the energy level diagram involved in the degenerate OPG and DFG processes. Figure 1c visually depicts the spectral frequency and wavelength variations during the cascaded process. Figure 1d illustrates the distribution of various nanophotonic waveguide modes for the cascaded process, including the pump light, the broadened pump light, the MIR light generated by degenerate OPG, and the longer-wavelength MIR light produced by the cascaded process. The modes correspond to the Ez components of the TE01, pump(ω), TE01, pump(ω′), TE00, signal (ω/2), and TE00, DFG (ω′-ω/2), respectively. Scanning electron microscopic (SEM) image in Fig. 1e displays the actual dual-layer nanophotonic waveguide structure. The upper left inset shows a top-view SEM image of the nanophotonic waveguide, while the bottom inset shows the etching depth (~650 nm) measured by a profilometer. The detailed preparation process can be found in Supplementary Note 2.

Fig. 1: Nonlinear cascaded parametric down-conversion processes.
Fig. 1: Nonlinear cascaded parametric down-conversion processes.
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a Schematic diagram of MIR light generation through the cascaded OPG-DFG process in a reverse-polarization dual-layer nanophotonic TFLN waveguide. b Energy level diagram. Left: OPG processes. Right: DFG processes. c Schematic diagram depicting the spectrum produced by the cascaded process. d Mode profiles of various frequency components in the cascaded process. The upper images depict the modes of the pump light and the newly generated pump light. The lower images illustrate the modes of the signal light generated through degenerate OPG and the MIR produced via the cascaded OPG-DFG process. e SEM image of the waveguide cross-section (Scale bar: 1 μm). The upper left inset: top view of the waveguide (Scale bar: 5 μm); Bottom inset: the waveguide height.

The theories of the cascaded process are shown in Supplementary Note 3. Based on the above theoretical analysis, the phase-matching conditions for both processes must be simultaneously satisfied for efficient cascaded OPG-DFG processes within a single structure. The reverse-polarization dual-layer nanophotonic TFLN waveguide based on MPM has garnered significant attention in nonlinear frequency conversion due to the larger mode overlap factor17,18,20,21,22. Additionally, the wide phase-matching bandwidth of DFG has been widely validated14,19,23. To further verify the feasibility of generating longer-wavelength MIR through the cascaded OPG and DFG processes, the phase-matching for both degenerate OPG and DFG is designed in the reverse-polarization dual-layer nanophotonic TFLN waveguide. Figure 2a, b show the phase-matching conditions for degenerate OPG and DFG when the waveguide ridge width is 1.7 μm and the height is 650 nm, and 1.03 μm pump can effectively generate two signal photons (2.06 μm) in the degenerate OPG process under phase-matching conditions. During the DFG process, the pump light generates new pump photons due to spectral broadening. When these pump photons are around 1.2 μm, they satisfy the phase-matching condition of DFG with the signal generated by degenerate OPG, producing longer-wavelength MIR. The high mode overlap characteristic of this waveguide leads to the efficient generation of degenerate OPG and DFG processes. Furthermore, as shown in Fig. 2c, when the pump wavelength is 1.03 μm and the signal wavelength generated by OPG is 2.06 μm, the group velocity mismatch (GVM) is zero. This means that the energy conversion between the pump and signal waves can be sustained over a longer propagation distance, significantly improving the frequency conversion efficiency. As shown in Fig. 2d, when the pump wavelength is 1.03 μm and the dispersion is in the anomalous dispersion regime, the third-order nonlinear effects are further enhanced, leading to pump spectral broadening. To further verify the relationship between the signal and light generated in the cascaded OPG-DFG process with respect to waveguide length and input pump intensity, we numerically solved coupled equations given that the damping coefficients is considered. The results are shown in Fig. 2e, f. As shown in Fig. 2e, when the input pump intensity is fixed, both the signal light generated by OPG and the new frequency light generated by the cascaded process increase with the propagation distance. In the OPG process, the signal light initially increases rapidly, then gradually slows as the cascaded process intensifies. The signal generated by the cascaded process increases exponentially due to the strong signal light. Furthermore, by gradually increasing the pump intensity, it can be observed that the total intensity generated by OPG and the cascaded process maintains a linear relationship with the increase of pump intensity, as shown in Fig. 2f. The final results indicate that a waveguide length of approximately 4 mm enables effective realization of the cascaded process.

Fig. 2: Theoretical analyses and spectral characterization of the cascaded processes.
Fig. 2: Theoretical analyses and spectral characterization of the cascaded processes.
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a Phase-matching conditions for the degenerate OPG process. The degenerate OPG process achieves perfect phase matching when the pump wavelength is 1.03 μm, and the signal wavelength is 2.06 μm, satisfying the condition \(\Delta {{{\bf{k}}}}_{1}=0\). b Phase-matching conditions for the DFG process: The DFG process achieves perfect phase-matching when the pump wavelength is 1.19 μm, the signal wavelength is 2.06 μm, and the difference-frequency wavelength is 2.82 μm, thereby satisfying the condition \(\Delta {{{\bf{k}}}}_{2}=0\). c Simulated GVM for the signal: The GVM of the signal light is simulated across the wavelength range of 1.8–3.2 μm within the reverse-polarization dual-layer nanophotonic TFLN waveguide. d Simulations of the GVD for the signal light within the wavelength range of 1.8–3.2 μm. e The calculated relative intensity of OPG (\({I}_{\omega /2}\)) and cascade (\({I}_{\omega {\prime} {\prime} }\)) versus the propagation distance. f The calculated relative intensities of OPG (\({I}_{\omega /2}\)), cascade (\({I}_{\omega {\prime} {\prime} }\)), and total (\({I}_{\omega /2}+{I}_{\omega {\prime} {\prime} }\)) versus the pump intensity. g The input pump spectrum after passing through LF. h The measured pump spectra versus the pump energy. i The measured OPG and cascaded spectra at various pump energy. The red arrow indicates the gradual increase of the input pump energy corresponding to different spectral curves, which are 37.1 pJ, 62.5 pJ, 102 pJ, 159.3 pJ, 203.3 pJ, 291.3 pJ, 355.7 pJ, 446.3 pJ, and 610.7 pJ, respectively.

According to the preceding theoretical framework, a critical precondition for the cascaded OPG-DFG processes is that the nanophotonic waveguide must initially generate both signal light and new pump light through OPG and third-order nonlinear effects (as shown in Supplementary Note 4), respectively. To verify this process, we constructed the experimental setup shown in Supplementary Note 5. Figure 2g shows the pump light spectrum output by the lensed fiber (LF). The measured output pump spectra at different pump energies are presented in Fig. 2h. As the input pump energy increases, the pump light experiences further spectral broadening with new peaks emerging due to the anomalous dispersion. Notably, a strong new peak is observed near 1.2 µm, where phase matching for DFG is achieved, providing a critical foundation for the occurrence of the DFG process. The measured cascaded spectra at different pump energies are presented in Fig. 2i. When the pulse energy is 37.1 pJ, only the OPG spectrum is detected due to the low pump energy. As the pump energy increases to 62.5 pJ, both the OPG and cascaded spectra start to appear. When the pump energy is increased to 610.7 pJ, a significant broadening of the OPG and cascaded spectra are observed due to the broadening of the parametric gain bandwidth12. This broadening can accommodate certain deviations in the MPM caused by fabrication imperfections. Notably, the generated MIR light exhibits an octave-spanning spectrum covering from 1.55 μm to 3.6 μm. Since the nanophotonic waveguide end face will be damaged by the laser when the pump energy is over 650 pJ, the maximum input pump energy used in the experiment should be less than this value. It is noted that the spectrometer employed in this study exhibits reduced sensitivity for wavelengths below 1 µm, which leads to an observed sharp decline on the left side of the broadened pump spectrum.

The generation of signal light via degenerate OPG is a critical prerequisite for realizing cascaded processes. To characterize the efficiency of the OPG process, we constructed the measurement system depicted in Fig. S6. The OPG power and efficiency from the waveguide are depicted in Fig. 3a. The OPG threshold of 1.1 pJ, is significantly reduced by over two orders of magnitude compared to state-of-the-art MIR single-pass OPGs based on ZnGeP2 waveguides19. As the pump pulse energy increases, the OPG output exhibits exponential growth. The OPG power is as high as 12.5 μW with a pump pulse energy of 388.2 pJ, corresponding to a conversion efficiency of 32.1%. This efficiency is larger than that in PPLN waveguides12. The measured saturated gain of the nonlinear waveguide is about 127.1 dB/cm, indicating that the χ(2) waveguide device provides substantial parametric gain (Fig. 3b)12,13. The high-efficiency and high-gain OPG provides a great possibility for the occurrence of cascaded OPG-DFG. Furthermore, to highlight the superior performance of our nanophotonic waveguide in terms of lower threshold pump energy, we conducted a comparative analysis with representative works on OPG in Fig. 3c. The analysis of the threshold pulse energy and peak power of the demonstrated χ(2) waveguide indicates a significant advantage over OPG devices fabricated from the other χ(2) materials, including PPLN12,24,25,26,27, OP-GaAs crystals28 and ZnGeP219.

Fig. 3: OPG efficiency, parametric gain, and pump threshold of the nanophotonic waveguide.
Fig. 3: OPG efficiency, parametric gain, and pump threshold of the nanophotonic waveguide.
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a The measured OPG efficiency and output power shown as a function of the pump energy. b The OPG output intensity versus the pump energy on a logarithm scale. c Comparison of the threshold and peak power for OPG implementations.

To provide a more comprehensive characterization of the cascaded process, Fig. 4a shows the intensities of both the OPG and the cascaded processes are measured on a linear scale. The intensity produced by the OPG process initially increases rapidly before reaching the saturable state, whereas the cascaded intensity shows a slow rise in the beginning, followed by an exponential growth. The sum intensity of these two processes increases in an approximately linear tendency. This behavior aligns well with our theoretical results, confirming the cascaded OPG-DFG process. This behavior is also consistent with previously reported cascaded SHG-SFG processes for third-harmonic generation6. We also calculate the power contributions from the cascaded process based on the spectral area fractions. Figure 4b presents the conversion efficiency and output power during the cascaded process. The maximum output power observed within the damage threshold was 9.4 μW, with a conversion efficiency of 15.3%. It is worthy to note that spectral broadening induced pump wavelength shifts with increasing pump power, which leads to the generation of dynamically tunable MIR spectra via DFG (Fig. 4c). The cascaded process produced a dynamically tunable center wavelength range of 2.06–3.12 μm—a relative bandwidth of 40%, which cannot be achieved by non-degenerate OPG. The detailed advantages of degenerate OPG over non-degenerate OPG in producing longer-wavelength MIR are discussed in Supplementary Note 6. To further confirm the feasibility and repeatability, the nanophotonic waveguides designed for phase-matching under different pump conditions are fabricated. By changing the input pump light from 1.03–1.6 μm at different nanophotonic waveguides with the same input power (fluctuations within ±3%), we still observed the occurrence of the cascaded processes. It is worth noting that the longest center wavelength generated by this method can reach 4.6 μm as demonstrated in Fig. 4d, e, which is almost close to the critical wavelength of lithium niobate. The relatively weak MIR signals (Corresponding pump wavelengths are 1.3 μm, 1.4 μm, 1.5 μm, 1.6 μm) are primarily due to differences in light coupling, absorption losses from SiO2 substrate, as well as defects in the nanophotonic waveguide fabrication. The proposed method provides new possibilities for broadening the application scope of MIR spectroscopy and metrology. From Fig. 4f, it can be found that the reverse-polarization dual-layer nanophotonic TFLN waveguide can generate the longer MIR light compared to the other works29,30,31,32,33,34,35,36,37,38,39,40,41,42,43.

Fig. 4: Representative Performance of the Cascaded OPG-DFG processes.
Fig. 4: Representative Performance of the Cascaded OPG-DFG processes.
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a The intensities of OPG and cascaded process versus the input pump energy for the reverse-polarization dual-layer nanophotonic TFLN waveguide. b The measured cascaded efficiency and output power as a function of the pump energy. c Tunable central wavelength generated by the cascaded process and tunable pump wavelength versus the pump energy. Left: cascaded OPG-DFG process. Right: spectral broadening. d Normalized MIR spectra with different pump wavelengths generated by OPG and cascaded process. e Normalized spectra generated by cascaded OPG-DFG. f Summary and comparison of PPLN, metasurface-assisted LN waveguide, and our nanophotonic waveguide in MIR.

Discussion

Our results showcase the generation of longer-wavelength MIR light output through cascaded nonlinear parametric down-conversion, and achieve tunable MIR light output by varying the input pump light energy. This study demonstrates the feasibility of the cascaded method for longer-wavelength MIR generation. This method extends beyond lithium niobate to other nonlinear materials, offering broader applicability. In future work, we plan to integrate this scheme with emerging 2D materials exhibiting strong second-order nonlinearity to achieve more efficient generation of MIR light. They promise to drive advancements in MIR integrated photonics and hold broad practical applications in spectroscopy, communication, sensing, imaging, and related areas (an application demonstration can be found in Supplementary Note 7).

Methods

Waveguide fabrication and loss characterization

The waveguides were fabricated using ultraviolet photolithography-assisted inductively coupled plasma reactive ion etching, followed by post-processing steps to form the target structure. The detailed fabrication procedure is provided in Supplementary Note 2. Subsequently, continuous-wave lasers with wavelengths of 980 nm, 1550 nm, and 2100 nm were used to characterize the waveguide losses via the Fabry-Pérot method and the cut-back method. The measurement procedures are described in Supplementary Note 2. The measured propagation loss for the pump light was 0.14 dB/cm with an insertion loss of 8.46 dB, while the signal light exhibited a propagation loss of 0.82 dB/cm and an insertion loss of approximately 9.42 dB.

The pump source

The pump source is a customized ytterbium-doped fiber laser (Yacto, YF-FL50-100-IR) that emits 1.03 µm pulses with a pulse duration of 400 fs and a repetition rate of 100 kHz. Pump light in the wavelength range of 1.3 to 1.6 µm is generated using an optical parametric amplification based on a bulk PPLN crystal (0PMIR-MA-10, HC Photonics Corp.), which is seeded by the 1.03 µm femtosecond laser. The tunability of the femtosecond pump light is achieved by adjusting the temperature of the PPLN crystal, as shown in Supplementary Fig. 13.

Coupling method

Given the difficulty of achieving a minimum spot size of 1–2 μm with spatial light lens coupling, which also increases the light energy, leading to damage at the coupling input end of the nanophotonic lithium niobate waveguide, we chose to use LF to couple the input laser to the nanophotonic waveguide. Compared to spatial light lens coupling, this method can more effectively control the coupling input end. The divergence angle of the LF is 45° to 75°, capable of achieving a minimum spot diameter of 2.0 ± 0.5 μm.

To efficiently excite the TE₀₁ mode in the waveguide, we first adjusted the fiber polarization controller to align the input polarization with the principal polarization axis of the TE₀₁ mode. While maintaining normal-incidence alignment, we further optimized mode excitation by finely tuning the vertical (Z-axis) position of the LF and adjusting the incident angle using a 6-axis translation stage on which the waveguide was mounted. This alignment strategy enabled selective coupling into the TE₀₁ mode. According to numerical simulations, a maximum coupling efficiency of 10.8% can be achieved when the LF is vertically shifted by 0.5 µm and the incident angle is set to 4°. Further details of the coupling mechanism can be found in Supplementary Note 8 of the Supplementary Information. In future work, the coupling efficiency may be further improved by employing a spatial phase plate or integrating a mode converter at the waveguide input facet.

Measurement equipment parameters

The employed MIR spectral analyzer is a grating-scanning monochromator (SR-500i-D2, ANDOR) equipped with a lock-in amplifier (SRS, SR830) and a InSb detector (631-INSB-2.0-SL12, InfraRed Associates, Inc), which are p–n junctions formed by mesa techniques using single crystal material. This process yields the highest quality photodiodes, which exhibit excellent electro-optical performance in the 1–5.5 μm wavelength region. These diodes are background-limited detectors, and their performance can be enhanced by spatial (cooled FOV stops) or spectral (cooled interference filters) reduction of the background. The average power of the generated MIR wave is detected using an InSb detector connected to a lock-in amplifier and a power meter (S148C, power range: 1 µW–1 W @ 1200–2500 nm, THORLAB). The power of NIR pump light is measured by a power meter (S120C, power range: 50 nW–50 mW @ 400–1100 nm, THORLAB). The filters used at the output end are respectively used to measure MIR power (FELH1450, THORLAB), and pump power (FELH0900, THORLAB).

To ensure measurement accuracy and precision, all experiments were conducted in an enclosed environment, with the testing apparatus mounted on an air-floating vibration isolation platform to minimize external disturbances. Additionally, a power meter was used to calibrate the photodetector, ensuring accurate readings of the MIR output power generated by the waveguide. The near-infrared spectra measured by the MIR spectral analyzer were calibrated using a Yokogawa AQ6317C optical spectrum analyzer. All data were obtained through repeated measurements to reduce experimental error and enhance the reliability of the results.