Supercontinuum generation (SCG) is a phenomenon in which an ultrashort and intense pulse experiences significant spectral broadening when propagating in a nonlinear optical material/structure. Recent work has extensively explored SCGs with various optical waveguides based on silicon,1Si3N4,2^–7 silica,8 lithium niobate,9^–17 and chalcogenide fibers.18^,19 Among them, silicon photonic waveguides offer the advantages of broad transparent windows and complementary metal oxide semiconductor (CMOS) compatibility.20^,21 In 2014, Leo et al.1 reported SCG ranging from 1.1 to 1.7μm on a silicon-on-insulator (SOI) platform with a 150-fs pulsed pump source with the wavelength centered at 1.55μm. The first octave-spanning SCG in silicon waveguides with a 2.5-μm pump was also demonstrated in the same year.22 In 2018, Nader et al.23 reported that the mid infrared (MIR) SCG using a silicon-on-sapphire optical waveguide pumped by a 100-fs pulsed source with the wavelength centered at 3.06μm. Kou et al.24 also reported the MIR SCG ranging from 2 to 5μm with a suspended silicon photonic waveguide by utilizing a 300-fs pulsed pump source around 4μm. In 2024, Boukar et al.25 reported the numerical study of the supercontinuum phenomenon raised from Airy pulses.

To broaden the SCG bandwidth, dispersion engineering was extensively employed. However, for the most popular standard silicon photonic waveguide, which usually has a thickness of 220 nm, the dispersion property is not as satisfactory as what is desired for SCG, resulting in low spectral energy, especially in the wavelength range beyond 2μm. Previously, there were some works that attempted to address this issue by increasing the core layer thickness to be more than 220 nm26^–28 or by introducing some special cladding.28 These approaches, however, make the structure/processes of the SCG chip incompatible with the standardized silicon photonics.

In addition to dispersion engineering, several alternative physical mechanisms have also been explored to improve SCG spectra. Among them, varying the dispersion profile of a waveguide has significant promise. Some works were reported with simple tapered waveguides to vary the dispersion. In 2019, Singh et al.29 presented width-varying waveguides on silicon, enabling 16-dB signal enhancement and wavelength extension of 100 nm in the 1550-nm window when compared with a fixed-dispersion waveguide. In 2023, Torre et al.30 reported mid-infrared SCG in a tapered Si–Ge waveguide. Moreover, complex waveguide profiles in the propagation direction were used and usually designed by the optimization method or algorithm. In 2020, Wei et al.31 reported SCG assisted by wave trapping in dispersion-managed silicon photonic waveguides. In 2023, Zia et al.32 reported SCG from sign-alternating-dispersion waveguides on Si3N4. More recently, Lee et al.33 reported the SCG realized using inverse-designed freeform Si3N4 waveguides.

Moreover, the periodic-structure-assisted broadband phase-matching method holds significant promise. In 2017, Hickstein et al.34 experimentally demonstrated a quasi-phase-matched SCG with the TE20 and TE00 modes in Si3N4 optical waveguides. However, the generated spectra are mixed with different optical transverse modes, which is not easy to couple and becomes challenging in real applications such as optical coherence tomography (OCT) or optical communications. In addition, the grating also causes frequency conversion among different modes, which further lowers the energy carried by the fundamental mode.

The grating structure also has a much higher loss than the uniform optical waveguide (without grating). In 2021, Singh et al.35 introduced a silicon Bragg grating through periodic deposition of charge carriers.20 Although they tried to weaken the Bragg reflection using a weak grating, the reflection remained more than 90% at quasi-phase-matched wavelengths. Consequently, a significant portion of the SCG light was reflected. Moreover, the spectrum of SCG is almost the same as that generated with an undoped waveguide, except that a single narrow peak is generated around 1220 nm. Such a weak grating also has less transfer efficiency, and the carrier doping also introduces some additional losses. Because the index changing is small, the grating-induced dispersive wave is not yet strong.

In this work, we propose and demonstrate long-period-grating (LPG) waveguides for SCG on silicon with a C-band pump. Unlike previous works using waveguides without gratings,1^,28 we introduce LPG waveguides for quasi-phase matching to improve the SCG. Here, the entire spectrum is generated with the fundamental mode (TE00), eliminating the need for additional mode manipulating or mode purification, which thus greatly simplifies the device fabrication and reduces the loss as well. Compared with previous silicon SCGs based on gratings,34^,35 the present work achieves improved spectral characteristics with broader, stronger, and more concentrated dispersive waves beyond 2μm. Notably, the present LPG waveguide shows an ultrabroad extent from 1150 to 2300 nm, which is much wider by 200 nm than that achieved by conventional dispersion-engineered silicon photonic waveguides on the same chip. This spectral broadening is enhanced, even without requiring any special materials, so that it is compatible with the standard structure/processes of silicon photonics. In addition, the long grating period facilitates the structure to be adiabatic, resulting in minimal linear loss comparable with the regular uniform waveguides without gratings. Furthermore, the Bragg reflection in the present waveguide structure is very weak, which helps to improve overall efficiency. These key features make the present approach highly attractive and potentially valuable for applications in spectroscopy and imaging systems.

Here, an SOI wafer with a 220-nm-thick silicon core layer and a 3μm-thick buried-oxide layer is used. Figure 1(a) schematically illustrates the proposed LPG waveguide based on triangular corrugations with a period of Λ and a corrugation depth of δ. As the period Λ of the LPG is >100μm, the grating becomes almost adiabatic, and the linear propagation loss is nearly the same as the uniform waveguides (δ=0). Figure 1(b) schematically illustrates the theory of the grating-induced phase matching. Unlike traditional Bragg gratings, which are designed to realize the phase matching between the optical transverse modes with different orders or directions, here, the present LPG is designed to realize the phase matching between the soliton and quasi-plane wave of the same TE00 mode. When the phase mismatch intersects with the grating-induced phase mismatch, the matching condition is satisfied, and a grating-induced dispersive wave is generated at this frequency accordingly. The frequency of grating-induced dispersive waves is calculated by36βs(ω)−β(ω)=2πΛm,(1)where m=0,±1,±2,…,ω is the angular frequency of the grating-induced dispersive wave, and βs(ω) is the soliton wave vector given as βs(ω)=β(ωs)+(ω−ωs)β1(ωs)+γP/2,(2)in which P is the peak power of the first ejected soliton, ωs is the frequency of the soliton frequency, γ is the nonlinear coefficient, and β1(ωs) is the first-order dispersion coefficient at ωs.

As the core width is changing for the present LPG waveguides, the effective index is a function of the propagation distance. Hence, we use the effective dispersion Deff and the effective phase mismatch β1,eff, which are given as Deff=1Λ∫0ΛD(l)dl,(3)β1,eff=1Λ∫0Λβ1(l)dl,(4)where D is the dispersion of the waveguide and l is the propagation length in a single period. As the core width of the LPG waveguide varies with the propagation distance, D and β1 also depend on the propagation distance.

Previous grating-based SCG on silicon35 was designed for the +1-order phase-matching wavelength in the reflection region, as shown in Fig. 1(c), which results in a Bragg-grating forbidden band overlapping with the generated SCG spectrum.35 Even though this issue can be alleviated by employing a weak Bragg-grating waveguide with depositing charge carriers, the reflection remains significant (even exceeding 90%).35 In contrast, our LPG design generates dispersive waves, relying on quasi-phase matching within the slowly varying region, which offers three key advantages. First, the matching order of the TE00 reflection modes is even more than 1000, and the total periods are fewer than 20. Consequently, Bragg reflection becomes negligible across the entire spectrum in our case. Second, the increased Bragg period from micrometers to submillimeters ensures an adiabatic structural design, mitigating Bragg-grating-induced propagation losses (as verified in experiments below). As shown in Fig. S1 in the Supplementary Material, the simulated Bragg reflection is close to 100% in the Bragg forbidden band for conventional Bragg grating waveguides. For the present LPG waveguide, the transmission is higher than 99.99% according to the simulation. Another challenge in the grating waveguide for SCG is grating-induced mode conversion among different modes in the propagation direction, which makes the modes complex and difficult to convert to the fundamental mode. The mode converting is almost impossible to avoid in the TE00-pumped and TE20-supported SCG waveguides, which are the conditions in previous works.28^,34 In Fig. S2 in the Supplementary Material, we simulate the TE00 and TE20 mode coupling in the grating structure, showing a complex spectrum mixed with a different order of modes. It should be noted that as the generated spectrum is so broadband, it is almost impossible to avoid mode converting for all the wavelengths. As a result, we choose 220-nm-thick strip silicon photonic waveguides and make the single-mode condition satisfied for the pump wavelengths, whereas for the shortest wavelengths, not only the TE00/TM00 mode but also the TE10 and TM10 modes are supported, as shown in Fig. S2(c) in the Supplementary Material. As a result, with the present symmetric LPG waveguide, all the generated SC light is in the TE00 mode.

Figures 2(a) and 2(b) show the results of the dispersion and phase mismatch of the uniform waveguides (i.e., δ=0) with a core width of W=525, 550, 575, 600, and 625 nm. As can be seen, the waveguide has anomalous dispersion when the width is chosen within the range of 525 to 600 nm when the pump wavelength is 1550 nm. Figures 2(c) and 2(d) show the calculated results of the dispersion and phase mismatch for the waveguides designed with W=550nm and δ=100, 200, 300, and 400 nm. As can be seen, D becomes smaller as δ increases, whereas D becomes less than 0 when δ comes to 400 nm. Although the waveguide with larger δ has a stronger interaction between the pump and the grating-induced dispersive waves, the soliton fission length becomes larger when D becomes smaller, and thus, δ should be chosen appropriately to enhance the grating-induced dispersive waves.

In our experiment, we first used a 1550-nm 230-fs pulse pump with a pulse energy of 200 pJ on the chip. The experimental setup is shown in Fig. 3, where a mode-locked Er-fiber laser oscillator produces optical pulses with a center wavelength of 1550 nm at a repetition rate of 100 MHz. The optical pulses are then delivered through a length-designed polarization-maintaining fiber (PM 1550), and the polarization is set to the TE mode with the help of a rotary fiber holder. On the output side, the spectrum is collected by a small-mode-size fiber and then sent to an optical spectrum analyzer (OSA). Figure 4(a) shows the output spectra measured for the cases with W=525, 550, 575, 600, and 625 nm. It can be seen that the 550-nm-wide silicon photonic waveguide enables the SCG with a bandwidth from ∼1330 to 1990 nm. The waveguide loss is measured to be ∼5dB/cm using the cut-back methods. It should be noted that with a shorter pulse duration and higher pulse power, the bandwidth could be extended further. When comparing the SCGs in different waveguides, the pulse energy and the pulse duration should be the same. Figure 4(b) shows the output spectra of the present LPG waveguides designed with Λ=0.5mm, W=550nm, and δ=100, 200, and 300 nm. It can be seen that the LPG-induced dispersive waves have different wavelengths when varying δ, mainly because larger δ has a larger phase mismatch, as shown in Fig. 2(d). When δ=100nm, the quasi-phase matching grating-induced dispersive waves are not obvious, mainly because the grating is weak and the efficiency is low. Figure 4(c) plots the output spectrum of the LPG waveguides designed with W=550nm, δ=200nm, and Λ=1, 0.5, 0.3, and 0.1 mm. It can be seen that the grating-induced dispersive waves are too weak to be seen when Λ=0.1mm. On the other hand, when Λ=1mm, the peaks of the grating-induced dispersive waves are too close to be distinguished. For the case with Λ=0.5mm (0.3 mm), the +1 and +2-order grating-induced dispersive waves are located at wavelengths 1982 nm (2033 nm) and 2051 nm (2100 nm), respectively.

Figure 5(a) shows the generated spectra in the LPG waveguides with W=550nm, δ=200nm, and Λ=0.3mm when the pulse energy increases from 2 to 10 dBm. To give a comparison, the measured results for the 550-nm-wide uniform silicon photonic waveguide are also given, as shown in Fig. 5(b). In this experiment, the input coupling loss is excluded. Generally speaking, the bandwidth increases with the average pump power. It can be seen that the +1 grating-induced dispersive wave can still be detected when the average power is only 7 dBm. Moreover, these spectra shown in Fig. 5(a) are obviously wider than those generated in the uniform waveguide shown in Fig. 5(b), particularly when the pump power is relatively low (e.g., 2 and 5 dBm). The main reason is that the LPG waveguide has near-zero β1,eff in these wavelengths, which is not achievable for the 550-nm-wide uniform waveguide.

To demonstrate the ultrabroad bandwidth, we use a 75-fs 1550-nm pump with 100 pJ pulse energy, and the LPG waveguide with the parameters of W=550nm, δ=300nm, and Λ=1mm. The parameters δ and W are chosen according to the principle that the tooth depths should be larger to get stronger dispersive waves while ensuring anomalous dispersion. Figures 6(a) and 6(b) show the simulated temporal and spectral evolution along a 7-mm-long silicon LPG waveguide. Unlike those previous simulation works, which include only the SCG waveguides,1^,28 the pulse-broadening happening in the butt-coupler is considered in our simulation to be more accurate. The butt coupler is a 200-μm-long inverse taper with a core width that varies linearly from 180 to 250 nm. As shown in Fig. 6(a), the temporal simulation results show that the pulse is intensively broadened in the 200-μm-long region at the input end (i.e., 0<z<200μm), where the waveguide is narrower than 300 nm and thus has a huge normal dispersion. In contrast, when propagating in the grating region, the pulse is first compressed in the first period of the grating, whereas the spectrum is broadened to cover the range of 1300 to 1900 nm at the end of the first period (i.e., z=1000μm). Then, the soliton fission is observed at the location of z∼1.2mm, where the pulse is intensively broadened both in the time and frequency domains. When 2mm<z<7mm, the spectrum width is almost unchanged, whereas the pulse width in the time domain continues to be broadened. The ripples in the time domain shown in Fig. 6(a) are mainly due to the periodic modulation of the group velocity in the LPG waveguide. The simulated output spectrum is as wide as 1.1 to 2.3μm. Figure 6(c) shows the measured final output spectra from the present LPG waveguide and the 550-nm-wide uniform waveguide (δ=0). The simulation results are also shown in the figures (see the dashed lines). In the experiments, the continuing spectrum covering from 1150 to 2300 nm is obtained for the LPG waveguide, which is ∼200nm wider than that (1200 to 2150 nm) obtained from the uniform (δ=0) waveguide. As the LPG used here has a period as large as 1 mm, the grating-induced dispersive waves are so close to each other, and thus, we can achieve continued and flattened spectrum broadening rather than several separate peaks.

Table 1 gives a comparison of the reported works about SCG based on silicon, indicating that the present work features the most broadband spectrum among all with standard 220-nm SOI photonic waveguides pumped at the C band. Specifically, the spectra obtained by our LPG waveguide are >300nm wider than that from the Bragg-grating SCG developed on silicon.35 Note that the LPG waveguides SCG could be further improved when combined with other methods, such as introducing a thick-silicon photonic waveguide26 for optimal dispersion, special cladding material/design28 for dispersion/coupling improvement, or longer pump wavelength for smaller nonlinear loss.27

We have proposed and demonstrated on-chip SCG covering the range from 1.15 to 2.3μm with a C-band pump laser by introducing LPG waveguides. We have introduced an LPG waveguide for quasi-phase matching to broaden the output spectrum. The wavelength location of these grating-induced dispersive waves can be designed according to the calculated effective dispersion. We have also obtained continuing and ultrabroad SCG covering the wavelength range of 1150 to 2300 nm (more than one octave) using 1550-nm 75-fs pulses with a pulse energy of 200 pJ. The obtained SCG bandwidth is 200 nm broader than that achieved with conventional dispersion-engineered silicon photonic waveguides on the same chip. Note that the SCG could be further broadened by shortening the butt coupler and lowering its dispersion. Moreover, instead of directly choosing the triangular corrugations, the inverse-designed corrugations may have further improved performances in obtaining high peak power and low pulse duration. Unlike previous works exhibiting high-order transverse modes,34 the present SCG on silicon is with the TE00 mode so that the SCG spectrum can be collected by a single-mode fiber without additional mode conversion. The present LPG waveguide designed with a slowly varying grating corrugation can effectively suppress the spectrum reflection and mode conversion,34^,35 greatly reducing the reflection losses to near zero, which is even at the same level as the width-fixed waveguides or extremely slow varying but aperiodic waveguides.32^,33 Furthermore, the present on-chip SCG waveguides can be fabricated easily with standard foundry processes for passive silicon photonics. In summary, the proposed LPG waveguide structure provides an attractive option for realizing on-chip SCG sources.

See the Supplementary Material for details of the simulated Bragg reflection of traditional Bragg grating SCG waveguides in Fig. S1 in the Supplementary Material, the simulated TE00 and TE20 mode coupling in the TE20 supported grating waveguide in Fig. S1(a) in the Supplementary Material, and the effective index of different modes as a function of wavelengths in a typical TE20 supported waveguide and our LPG waveguide in Figs. S2(b) and S2(c) in the Supplementary Material, respectively.

Hongzhi Xiong is pursuing a PhD at the College of Optical Science and Engineering, Zhejiang University, Hangzhou, China. His current research interests include nonlinear optics and silicon photonics.

Xinmin Yao is pursuing a PhD at the College of Optical Science and Engineering, Zhejiang University, Hangzhou, China. His research interests include nonlinear optics.

Qingrui Yao is pursuing a PhD at the College of Optical Science and Engineering, Zhejiang University, Hangzhou, China. Her current research interests include silicon photonics.

Qingbo Wu is pursuing a PhD at the College of Optical Science and Engineering, Zhejiang University, Hangzhou, China. His current research interests include silicon photonics.

Hongyuan Cao is pursuing a PhD at the College of Optical Science and Engineering, Zhejiang University, Hangzhou, China. His research interests include silicon photonics and nonlinear optics materials.

Yaoxin Bao is pursuing a PhD at the College of Optical Science and Engineering, Zhejiang University, Hangzhou, China. Her research interests include silicon photonics and Raman amplifiers.

Fei Huang is pursuing a PhD at the College of Optical Science and Engineering, Zhejiang University, Hangzhou, China. His current research interests include optical frequency combs.

Zejie Yu is an associate professor at Zhejiang University, Hangzhou, China, and mainly works on integrated photonics.

Ming Zhang is an associate professor at Zhejiang University, Ningbo Research Institute, Ningbo, China, and mainly works on integrated photonics.

Daoxin Dai is a QIUSHI Distinguished Professor at Zhejiang University, Hangzhou, China, and mainly works on silicon photonics. He has published several refereed papers in international journals. He was one of the most cited Chinese researchers from 2015 to 2021 (Elsevier).