Recently, with the development of high-$Q$ optical microresonators and nonlinear photonics, Kerr soliton microcombs1^–4 have been widely studied and demonstrated in many microresonator platforms of different materials and structures1^–11 and can be even produced with turn-key operations.12^,13 These soliton microcombs have been applied for coherent optical communications,14 ultrafast optical ranging,15^,16 optical atomic clocks,17 optical frequency synthesis,18 dual-comb spectroscopy,19 spectrometers,20^,21 microwave photonics,22^–24 and astronomical spectrograph calibration.25^,26 One of the important applications is the atomic clock as many high-performance clock transitions lie within the visible spectrum, such as the 729 nm transition in calcium ion, 698 nm in strontium atom, 674 nm in strontium ion, 657 nm in calcium atom, and 578 nm in ytterbium atom.27 It would be ideal for the bandwidth of a microcomb to cover these transitions, which are critical for achieving optical atomic clocks with ultrahigh performance. Yet, to date, most of the soliton microcombs are generated at the near-infrared wavelengths as the generation of the visible soliton microcombs remained challenging due to the reasons we will detail in what follows.

Optical frequency combs at visible wavelengths play important roles in essential technologies, including optical atomic clocks, astronomical spectrograph calibration, and biological medical imaging.2 At visible wavelengths, the available materials exhibit strong normal group velocity dispersion (GVD), but a prerequisite for the bright soliton generation in an optical microresonator is an anomalous dispersion instead. A possible way to overcome such natural material dispersion and achieve a total anomalous dispersion is to engineer the geometry of a microresonator. For this purpose, it is usually necessary to fabricate the optical microresonators with a relatively small thickness28^–30 and a high index difference at the same time. Then, the unavoidable surface roughness will induce a significantly increased scattering loss at the shorter wavelengths, especially in the microresonators with a small mode volume. On the other hand, self-referencing31 of visible Kerr soliton microcombs is required in the applications of optical atomic clocks and optical frequency synthesizers. For the realization of the self-referenced Kerr soliton microcomb,17^,18 the spectral bandwidth of the microcombs should cover at least two-thirds of an octave (2f to 3f referencing)32^,33 or a full octave (f to 2f referencing),8^,34^–41 which usually demands the formation of dispersion waves (DWs) induced by higher order dispersion to extend the spectral bandwidth of the soliton microcomb (the repetition rate of which is typical close to 1 THz) and increase the comb powers at the ends of the spectrum. Moreover, the exact control of the positions of the DWs requires an exact fabrication of the dimensions of microresonators. All these factors contribute to the high difficulty in generating broadband visible DKS microcombs for self-reference based on a high-$Q$ optical microresonator of appropriate GVD at the visible wavelength. Previous studies have demonstrated the generation of nonsoliton state microcombs at visible wavelengths on different platforms.30^,42^–48 However, to date, only near-visible soliton microcombs have been achieved by employing spatial mode interaction,29^,49 geometrical dispersion engineering,37^,50^,51 and second-harmonic generation.52 Moreover, with a pump laser of $\sim 780\mathrm{nm}$, the obtained shortest visible wavelengths are only 755 nm for a single-soliton microcomb29 and 710 nm for a multisoliton microcomb,51 respectively.

In this study, we overcome the above-mentioned challenge by fabricating a dispersion-engineered, ultrahigh-$Q$ silica microdisk resonator through an optimized dry-etching process.53^,54 With that platform, we realize a chip-based visible single-soliton microcomb spanning two-thirds of an octave, which has already covered several clock transitions of atoms or ions and can be used for microcomb self-referencing. Owing to the high $Q$-factor and small mode volume of the silica microdisk resonator, the soliton microcombs can be even generated with a low pump power of 1.1 mW. To improve the power of comb teeth at the end of the spectrum, we especially develop an engineering of dual DWs, combining both geometric dispersion and mode interactions. Moreover, by making use of the soliton self-frequency shift effect, we implement a precise tuning of the position of the DW at the short wavelength of the spectrum.

In this work, we use the dry-etched silica microdisk resonators53^,54 for visible soliton microcomb generation. As compared with other materials, silica inherently possesses a lower material dispersion at the visible wavelength,28 which makes it easier to achieve an anomalous dispersion by engineering the geometry of a microresonator. In other words, the GVD of the microdisks can be engineered by carefully designing the three parameters: the diameter ($D$), the silica thickness ($t$), and the wedge angle ($\alpha$), as shown in the right inset of Fig. 1(a).

To achieve an anomalous total dispersion of the microresonator ($\mathrm{GVD}>0$) at the visible wavelength, a straightforward way is to reduce the thickness of the microdisk (change the geometric dispersion) so that the field modes can be well compressed. Based on the finite element method, Fig. 1(a) shows the simulated GVD–wavelength curves of the fundamental transverse magnetic (${\mathrm{TM}}_{10}$) mode for different microdisk thicknesses but with a fixed diameter ($86\mu \mathrm{m}$) and wedge angle (37 deg). It indicates an overall increase in GVD and a blue-shifted zero-dispersion point of the GVD with the decreased thickness. When the thickness is decreased and approaches $1\mu \mathrm{m}$, the ${\mathrm{TM}}_{10}$ mode family achieves anomalous dispersion at a wavelength of 780 nm. Moreover, by further reducing the thickness of the silica microdisk resonator, it is feasible to achieve anomalous dispersion as well as generate soliton microcomb at a shorter wavelength (see more details in Section I of the Supplementary Material).

To extend the comb spectrum to a normal GVD regime, it is generally required to achieve the emission of DW.55^,56 The spectral positions of DWs can be conveniently predicted by applying the integrated dispersion ($D_{\mathrm{int}}$). The $D_{\mathrm{int}}$ takes the approximate form $D_{\mathrm{int}}(\mu )={\omega }_{\mu }-{\omega }_0-D_1\mu =D_2{\mu }^2/2+D_3{\mu }^3/6$, where $\mu$ is the relative mode number, ${\omega }_{\mu }$ is the angular frequencies of the cavity resonances, and ${\omega }_0$ is the pumped mode frequency. Moreover, $D_1/2\pi$ is the free spectral range (FSR), $D_2/2\pi$ is the variation of adjacent FSR, and $D_3/2\pi$ denotes the third-order dispersion. For a microdisk resonator with a thickness of $1\mu \mathrm{m}$, the $D_{\mathrm{int}}$ relative to the pump mode at 780 nm is depicted in the left inset of Fig. 1(a). In the presence of third-order dispersion ($D_3/2\pi <0$), a zero-crossing point of $D_{\mathrm{int}}$ occurs in the short-wavelength region, after passing through the zero-dispersion point. Only when the spectrum is extended to the point where $D_{\mathrm{int}}=0$ for the generated soliton, the DWs will be excited near the corresponding zero-crossing points. However, due to the coexistence of a significant anomalous geometric dispersion and a decreased normal material dispersion with the wavelength increased, the $D_{\mathrm{int}}$ rapidly increases with the involved wavelength, resulting in a considerable wavelength separation between the zero-crossing point in the long-wavelength region [the wavelength of the zero-crossing point is greater than the second zero-dispersion point ($\sim 1400\mathrm{nm}$)] and the pump wavelength. As a result, it is difficult to excite the DW on the side of long wavelength by means of only employing the third-order dispersion.

Figure 1(b) shows a typical scanning electron microscopy (SEM) image of the fabricated silica microdisk resonator using inductively coupled plasma (ICP) dry-etching.53^,54 As compared with the wet-etching process,57 the wedge angle of the dry-etched microdisks can be easily controlled by changing the ICP power during the etching process. By optimizing the fabrication process, we have obtained a high $Q$-factor silica microdisk resonator with $1\mu \mathrm{m}$ thickness and a small diameter ($\sim 82\mu \mathrm{m}$) at the wavelength of $\sim 775.9\mathrm{nm}$. Figure 1(c) presents the detailed transmission spectrum of the ${\mathrm{TM}}_{10}$ mode with a doublet feature,58 which indicates an intrinsic quality factor of $6.7\times {10}^7$ (the high $Q$-factor originates from the low sidewall roughness $\sim 0.52\mathrm{nm}$, as shown in Fig. S2 of the Supplementary Material). By using this cavity mode with a loaded $Q$-factor of $2.4\times {10}^7$, achieved by adjusting the coupling between the microresonator and the tapered fiber,59 we demonstrate an optical parametric oscillation with a threshold as low as $138.4\mu \mathrm{W}$. To the best of our knowledge, this is the lowest threshold power for the chip-based optical parametric oscillation at the wavelength around 780 nm29^,30^,60 (see more details in Section V of the Supplementary Material).

Experimentally, we employ the auxiliary laser heating approach to access the soliton states of the visible Kerr microcomb;61^–63 see more details in Section III of the Supplementary Material. Due to the high $Q$-factor and the small volume of the fabricated microdisk resonator, we experimentally achieve a broadband (718.7 to 816.9 nm) visible single-soliton Kerr microcomb with a pump power of only 1.1 mW [Figs. 2(a)–2(c)] using a microdisk resonator with a thickness of $1\mu \mathrm{m}$, a diameter of $82.3\mu \mathrm{m}$, and a wedge angle of 34.4 deg [the same device with Fig. 1(c) and the top panel of Fig. 2(e)]. This optical spectrum exhibits a clear high-order dispersion-induced DW at 721.6 nm. A significant soliton self-frequency shift (around 1.9 THz) arises from the broad spectral range associated with a shorter pulse duration.64^,65 The soliton spectrum is confirmed by a good agreement of the measured results with the Lugiato–Lefever equation (LLE) simulation65^,66 (compare the spectrum profile with the simulated gray curve). If we further increase the pump power to 2.5 mW, the generated spectral range can be expanded to 713.2 to 831.5 nm [the top panel of Fig. 2(e)].

Though the modal confinement is primarily set by the thickness, the dispersion can also be slightly impacted by modifying the wedge angle for a fixed thickness and a fixed diameter. It can be seen from the simulated $D_{\mathrm{int}}$ curves in Fig. 2(d). Due to the increase of the anomalous dispersion, the third-order dispersion-induced $D_{\mathrm{int}}$ zero-crossing point on the side of short wavelengths keeps shifting to an even shorter wavelength after the wedge angle is increased. The measured dispersion of the microresonator around 780 nm is shown by hollow dots in Fig. 2(d). By using a silica microdisk resonator with a wedge angle of 39.2 deg, we observe a soliton microcomb with a broader bandwidth of 674.8 to 852.5 nm and a blue shift of the DW to 679.7 nm under a pump power of 8.2 mW [the middle panel of Fig. 2(e)]. This observation is consistent with our numerical simulation. Further increasing the wedge angle to 43.1 deg, we achieve visible soliton microcombs with a short-wave DW at 657.2 nm under a pump power of 32.6 mW, as shown in the bottom panel of Fig. 2(e). The spectrum spans the visible light wavelengths of 650.9 to 759.1 nm, equivalent to a range of 65.6 THz, with a repetition rate of 791 GHz. Due to the generation of the DW at the short wavelength, a red light [Fig. 1(d)] can be clearly seen during the generation of the Kerr single-soliton microcomb.

In some applications such as optical clocks and optical frequency synthesis, it is necessary to have sufficient power at the two ends of the soliton microcomb spectrum for the self-reference of the microcomb.17^,18 An efficient way to overcome the rapid increases of $D_{\mathrm{int}}$ and excite DW at long-wavelength regions is to make use of the spatial mode interactions in whispering gallery mode optical microresonators.67 After a modification of the dimensions of the microdisk resonator, we see the emergence of an obvious DW near 860.8 nm [Fig. 3(a)]. To explain the existence of this DW, we simulate the relative mode frequency curves of the ${\mathrm{TM}}_{10}$ and ${\mathrm{TM}}_{20}$ mode families with respect to the unperturbed ${\mathrm{TM}}_{10}$ mode at $\mu =0$ [Fig. 3(d)]. The intersection point of these curves indicates a proximity of the resonant frequencies of these two different mode families. By increasing the diameter of a microdisk resonator, as seen from Figs. 3(a)–3(c), we can shift the DW in the long (short) wavelength range to an even longer (shorter) wavelength. These results are consistent with the tendency of the simulated intersection points [Figs. 3(d)–3(f)], indicating an excellent predictability of our dispersion engineering. Finally, with a microdisk resonator of the diameter $91.3\mu \mathrm{m}$, we achieve a visible single-soliton microcomb spanning over two-thirds of an octave (632.5 to 950.1 nm) with a repetition of 720 GHz, as shown in Fig. 3(c). To effectively extract the broadband microcomb, both the diameter of the fiber taper and the coupling distance between the microresonator and the straight taper are optimized (see more details in Section IV of the Supplementary Material). Due to the higher frequency of the visible microcomb, the span of the obtained soliton microcomb has been already similar to those of the octave soliton microcombs at the near-infrared wavelength.8^,34^–36^,38^–41 It should be noted that this is the first chip-based visible soliton microcomb that covers the transition lines of both ${}^{87}\mathrm{Sr}$ (698 nm) and ${}^{88}{\mathrm{Sr}}^{+}$ (674 nm).27 Also, the measured peak powers of the short-wave DWs are 143.3 nW in Fig. 3(a), 331.8 nW in Fig. 3(b), and 25.9 nW in Fig. 3(c), respectively, after calibrating the loss in the optical path during the measurements. The relatively lower optical power of the short-wave DWs can be attributed to the lower coupling efficiency between the microresonator and the fiber taper at shorter wavelengths (see more details in Section IV of the Supplementary Material), which can be mitigated by adding an additional fiber taper to extract the short-wavelength comb lines.68

For optical atomic clock application, one of the comb teeth with enough optical power should match an atomic transition. However, the positions of DWs are highly susceptible to the geometric dimensions of the fabricated microresonator. Consequently, the generated frequency of the highest power comb line (the one that best phase-matches55^,67 with the pump laser) within the DW commonly exhibits deviations from the desired atomic transition frequency. Here, we introduce a method of precisely tuning the relative mode number associated with the highest power comb line within the short-wavelength DW, simply by altering the detuning of the pump laser. It is based on the Raman-induced soliton self-frequency shift and DW-induced recoil existing in the silica microdisk resonator to change the phase match condition.67^,69 As shown in Fig. 4(b) from top to bottom panels, when the red-detuning of the pump increases (the frequency is decreased), the total shift of the soliton spectral center will be over a range from $-2.7$ to $-5.7\mathrm{THz}$, which is primarily attributed to the prominent Raman-induced soliton self-frequency shift (see more details in Sections VI and VII of the Supplementary Material). As the pump is more tuned to the side of red-detuning, which leads to an overall red-shift of the comb power, we will gain control over the power of the long-wavelength DW (marked by arrows around 855 nm). Meanwhile, on the short-wavelength side of the comb spectrum, we observe a gradual movement of the DW toward the shorter wavelengths, which arises from the increasing of the relative frequencies between the individual comb teeth and the optical resonances.67

In Fig. 4(a), we provide a further clarification of our system’s ability to precisely tune the relative mode number of the highest power tooth within the short-wavelength DW, which indicates that a high-power comb line within the DW has already overlapped with the clock transition of ${{}^{88}\mathrm{Sr}}^{+}$. It also shows that the relative mode number of the comb tooth with the highest power can be adjusted from $\mu =71$ to $\mu =80$. The large DW tuning range is mainly attributed to the significant variation of the soliton self-frequency shift with pump detuning, which results from the ultranarrow soliton pulse width, as well as the relatively wide detuning range enabled by the high $Q$-factor and small mode volume. To further elucidate the precision of this tuning mechanism of controlling the position of the DWs, which realizes the adjustment of the highest power tooth within the DW precisely from one relative mode number to the next, we perform the simulations of the soliton microcombs based on the LLE.65^,66 As shown in Fig. S6(b) of the Supplementary Material, we demonstrate that the power of the comb tooth in the DW alternates as the pump red-detuning increases and the relative mode number of the highest power comb tooth grows from 71 to 80. These simulations are well consistent with our experimental observations in Figs. 4(a) and 4(b).

In summary, we have demonstrated broadband visible Kerr soliton microcombs using dry-etched silica microdisk resonators on the chip. The widest comb spectrum ranges from 632.5 to 950.1 nm (a frequency spacing of 158.5 THz). Broadband visible soliton microcombs with two DWs at their ends of spectra are achieved by delicately engineering the dispersion of microresonators. Even though the diameter and thickness are considerably reduced, we have still managed to obtain an ultrahigh quality factor of the silica microdisk resonator with an appropriate dispersion so that a visible soliton microcomb can be generated under a pump power as low as 1.1 mW. The dispersive wave at the short-wavelength end of the spectrum can be precisely tuned by the detuning of the pump laser through a soliton self-frequency shift effect. The obtained visible soliton microcomb spanning two-thirds of an octave can be self-referenced based on the 2f to 3f scheme.32 Like some recently explored octave-spanning Kerr soliton microcombs (with repetition rates of $\sim 1\mathrm{THz}$),34^–41 our single-soliton microcomb has a high repetition rate of $\sim 720\mathrm{GHz}$. By employing the techniques, such as interlocking the broadband visible microcomb to a narrowband microcomb with an electronically detectable repetition rate17 or through a Vernier dual-microcomb scheme,70 this broadband visible soliton microcomb with a high repetition rate can be used for an application in miniature optical lattice clocks and visible-wavelength frequency synthesizers. By further optimizing the dispersion of the silica microdisk resonator and integrating a ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguide and the silica microresonator on the same chip,71 together with an integrated pump laser, we expect to achieve a fully integrated octave-spanning visible soliton microcomb for practical applications. Beyond the generation of Kerr soliton microcombs, our demonstrated high-$Q$ microresonator with small mode volume at the visible wavelength will find wide applications such as in cavity quantum electrodynamics,72 visible narrow-linewidth laser,73^,74 as well as in sensing.75

Acknowledgment. This research was supported by the Guangdong Major Project of Basic and Applied Basic Research (Grant No. 2020B0301030009), National Natural Science Foundation of China (NSFC) (Grant Nos. 12293054, 12341403, and 92463304), National Key R&D Program of China (Grant Nos. 2021YFA1400803 and 2023YFB3906401), and Fundamental Research Funds for the Central Universities (Grant Nos. 021314380260 and 021314380283).

Xuan Li received his MS degree from Hebei University of Technology in 2020. He is currently pursuing a PhD at the College of Engineering and Applied Sciences, Nanjing University. His research focuses on the fabrication of on-chip high-Q optical microresonators and the generation of optical frequency combs.

Kai Qi received his bachelor’s degree in physics from East China Normal University. He is currently a PhD candidate at the College of Engineering and Applied Science, Nanjing University. His research interest includes on-chip high-Q optical microresonators and their applications for nonlinear photonics.

Bing He is an associate professor at Multidisciplinary Center for Physics, Universidad Mayor, Chile. He received his PhD from Graduate Center, City University of New York in 2009. His current research interests cover quantum nonlinear optics, nonlinear dynamical systems, and quantum information processing.

Xiaoshun Jiang is a professor at the College of Engineering and Applied Sciences at Nanjing University. He received his PhD from Zhejiang University in 2010. His research interests include the fabrication of on-chip high-Q optical microresonators and their applications in Kerr soliton microcombs, narrow-linewidth microlasers, and cavity optomechanics.

Biographies of the other authors are not available.