Optical whispering gallery mode (WGM) microresonator platforms featuring both high quality ($Q$) factors and small mode volumes can greatly enhance light–matter interaction and have attracted great attention in the field of nonlinear photonics [1–5]. In particular, the generation of optical frequency combs based on Kerr nonlinearity has sparked intense focus in both fundamental researches and technical applications in recent years [6–8]. Such Kerr microcombs rely on the balance between the cavity and nonlinear dispersion. The onset of Kerr combs is also determined by the cavity loss and nonlinear gain. These parameters are related to properties of the cavity, the pump power, and the frequency detuning between the pump laser and cavity resonance. Through monitoring the transmission spectrum of a Kerr comb device, versatile comb behaviors including modulation instability (MI), chaos, and solitons have been discovered [6,7,9–13]. Among them, the phase-locked soliton comb corresponding to a short pulse in the time domain is of particular interest. Technical achievements using such combs have also been demonstrated in areas such as high-capacity optical data transfer and processing, laser ranging, and spectroscopy [7,14].

Cavity soliton combs typically coincide with an abrupt reduced power step. Due to thermal effects, such regimes usually require specific approaches to access [7,14]. Recently, cavity solitons forming a crystal-like structure, referred to as soliton crystals, were found [10,15–20]. Avoided mode crossing (AMX) induced modulation on an intracavity continuous-wave (CW) background is found to cause the ordering of multiple Kerr solitons [10]. These soliton crystal states appear with larger conversion efficiencies and are much easier to access compared to regular soliton states. Manual tuning of the pump frequency is enough to locate a self-thermally locked position into the soliton crystal step. AMX aided Kerr frequency comb generation in the normal dispersion regime has been reported in silicon nitride (${\mathrm{Si}}_3{\mathrm{N}}_4$) microresonators [21,22]. Breathing soliton crystals with a near-octave-spanning spectral range from an aluminum nitride (AlN) microring pumped in the anomalous dispersion regime have also been demonstrated [19]. Recently, applications in the radio frequency (RF) wave field based on soliton crystal microcombs have been explored [23,24].

On the other hand, Kerr frequency comb generation also benefits from its host material platforms [25]. The property of a high refractive index leads to a better light confinement ability. Various high index materials have been exploited for Kerr comb generation. Moreover, host materials with other nonlinearities can also enrich comb performances through multi-nonlinearity [26]. For instance, Kerr and Pockel nonlinearities in a lithium niobate (${\text{LiNbO}}_3$) microring resonator have been combined to produce a stable bi-chromatic soliton comb [27]. Considering oxide material platforms, yttria-stabilized zirconia (YSZ) has a high refractive index of 2.1 at the telecommunication wavelength. Its Kerr nonlinear coefficient is about $4\times {10}^{-19}$, similar to that of the popular ${\mathrm{Si}}_3{\mathrm{N}}_4$ platform [28]. YSZ also features good mechanical and chemical stabilities, which favors its potential applications in bendable or fordable devices [29] and integrated photonics [30].

In this work, for the first time to our knowledge, we report the fabrication of YSZ optical microresonators with high-$Q$ factors up to 80 million at 1550 nm. A new absorption coefficient upper bound of about $0.001{\mathrm{cm}}^{-1}$ is obtained in this spectral window. We find that the mode coupling in a regular mode crossing is enough to cause local dispersion variation for creating soliton crystals. The pinning effect of the first comb sideband also assists in the generation of soliton crystals with multiple FSR spacing in a few-mode YSZ microresonator in the normal dispersion regime. Abrupt transmission steps are also found to be coincident with the generation of soliton crystals. A breathing comb behavior is observed. Our work shows that YSZ is a potential microplatform material for the application of Kerr microcombs. New applications could also arise considering its feature of good buffer layers for high-temperature superconducting films [31] and as host materials for rare-earth ions [32].

High-$Q$ YSZ disk microcavities were fabricated using the mechanical polishing method [33–36]. In the first step, a disk preform was cut from a commercial high-purity YSZ substrate as illustrated in Fig. 1(a). The preform was then carefully centered and attached to an aluminum post, which was later mounted on a spinning motor for further grinding and polishing with diamond slurries on the periphery of the disk rim. Figure 1(b) presents photos of a YSZ microdisk (cavity A) with a major radius of $\sim 300\mathrm{\mu m}$ measured from both top and side views. The side view photo shows the microdisk sitting on the shaped mounting tip of the 6 mm diameter cylindrical post. The magnified image on the rim of the cavity gives a minor radius of $\sim 118\mathrm{\mu m}$ with two wedge cuts to control and reduce modes as shown in Fig. 1(c). Successive total internal reflections then confine light in the rim of the disk and give rise to high-$Q$ WGMs. It should be mentioned that a further polishing with sub-micrometer diamond slurries can be used to finely shift the resonances of the microcavity.

Also shown is the field distribution of several transverse mode families of WGMs. Besides the polarization of transverse electric (TE) and transverse magnetic (TM) modes, WGMs are characterized by three mode orders determining their field distributions. The azimuthal order $\mathit{m}$ is related to longitudinal direction where the mode spacing of adjacent azimuthal modes is referred to as FSR of the cavity. The radial order $q$ gives the number of field maxima in the radial direction, while the polar order $p+1$ describes the number of field maxima in the polar direction as shown in Fig. 1(c). The polar order can be identified using the excitation mapping method [37]. The dispersion profile related to FSR values is mainly determined by the material dispersion and cavity geometry dispersion. The latter is affected by the dimension of the cavity geometry, which is usually fixed after fabrication, and by the transverse orders of the pump mode [38,39]. Although the polar mode order $p$ weakly affects the total dispersion compared to the radial mode order, they both decide where the mode crossing may occur.

As the YSZ crystal features a refractive index of 2.11 at the telecom wavelength of 1550 nm, the rutile (${\mathrm{TiO}}_2$) optical prism with a higher refractive index is used for coupling light into the microresonator. The experimental setup illustrated in Fig. 2(a) is described as follows. A CW single frequency tunable laser around 1550 nm (Toptica CTL1500) was chosen as the light source for both laser-scanned spectroscopy and pumping. A fraction of the unable laser source was sent through a fiber ring etalon as a frequency reference [40]. The etalon consisted of a $2\times 2$ ($\sim 1/99$) fiber coupler and a 2 m long single mode fiber. Two 1% fiber ports are connected with the single mode fiber into a loop. The FSR value of the etalon ${\mathrm{FSR}}_{\mathrm{e}}$ was measured to be 48 MHz using RF sideband spectroscopy with a fiber electro-optic phase modulator (EOM) [41,42]. The pump laser power was boosted by an erbium doped fiber amplifier (EDFA) to about 170 mW for Kerr comb excitation. A fiber optical circulator (FOC) collected the feedback signals from the cavity for monitoring reflected mode signals through the Rayleigh effect. The transmitted signal through the prism coupled resonator was collected and split into two parts: one was focused onto the photodetector (PD1), and the other was coupled into a multimode fiber connected to an optical spectrum analyzer (OSA, Yokogawa 6370D) for characterizing the comb spectrum. Although the multimode fiber input decreases the spectral resolution, the coupling of light from free space is much easier to align. Since leg surfaces of the right angle prism are uncoated, $p$-polarized incident beams are expected to experience lower Fresnel reflection losses in the case of an optimized incident coupling angle for a YSZ microresonator. We thereby chose to excite TM WGMs in the resonator during the experiment.

The evanescent coupling gap between the microresonator and the prism was controlled through a piezo-actuator. The photo of the coupled resonator is shown in Fig. 2(b) (top). Also presented in this figure is the laser-scanned transmission spectrum across an under-coupled WGM of the YSZ microresonator. A Lorentzian fit of the resonance peak gives a linewidth of 2.4 MHz around 1550 nm, indicating an intrinsic $Q$ factor of $8\times {10}^7$. It should be noted that the intrinsic $Q$ of a cavity is determined by $1/Q=1/Q_{\mathrm{ss}}+1/Q_{\alpha }+1/Q_r$ with subscripts ss, $\alpha$, and $r$ describing scattering, absorption, and radiation related losses, respectively [41]. Thereby, the measured $Q$ can give an upper bound of the material absorption coefficient considering that $Q_{\alpha }=2\pi n_0/(\lambda \alpha )$. As a result, we derive a material absorption upper bound of about $0.001{\mathrm{cm}}^{-1}$ for YSZ. We also fabricated millimeter-size YSZ disks and confirmed the $Q$ factor measurements.

However, it was found that the intrinsic $Q$ factor degraded during repeated resonator cleaning, dispersion, and comb measurements. We placed another high-$Q$ YSZ resonator in the setup to monitor the $Q$ factor of $7.4\times {10}^7$ for a selected mode over 24 h. It was found that the $Q$ factor did not degrade. Thereby, we infer that the $Q$ factor in this level is not sensitive to humidity. Moreover, we repeatedly cleaned the degraded resonator, but the intrinsic $Q$ factor remained unchanged. We suspect that the degraded $Q$ factor could result from surface degradation due to mis-positioning of the prism coupler or failed attempts to further increase the $Q$ factor with nanodiamond slurries.

It has been shown that the generation of soliton crystal combs is linked to mode crossing phenomena in microcavities [10]. Here, we carried out laser-scanned spectroscopy on cavity A featuring a few modes within one FSR to reveal mode crossing effects. Figure 3(a) shows the spectroscopy result over a 17 nm spectral window. The bottom curve is the simultaneously recorded fiber etalon signals as frequency markers. It is found that the free spectral range of the cavity around 1550 nm is about 0.6 nm through both optical spectrum and transmission spectrum analysis. One clearly sees that only two mode families feature the best mode contrast over 20% within one FSR. Zoomed-in spectra as shown in the inset of Fig. 3(a) give two examples of the mode spacing between these two transverse modes (A and B). We plot the absolute values of mode spacing between modes A and B families as a function of the center wavelengths between them in Fig. 3(b). The mode crossing phenomenon is clearly visible around 1553.4 nm where the mode spacing reaches its minimum. Examples of Kerr frequency comb spectra when pumping mode A families are presented as insets. We observe the pinning phenomenon of the first comb line around the crossing regime. Abrupt transmission steps appear to be coincident with the comb generation, in agreement with reported soliton crystal generation [15]. For the pump mode in the mode crossing regime where the spacing between modes A and B reaches the minimum, we find the generation of a symmetric Kerr comb.

Through observing the spacing distribution of each mode family in Fig. 3, it is still difficult to determine the mode coupling conditions. We thereby further derive the FSR values of modes A and B families. For clarity, we first plot relative frequency positions of both modes A and B families in Fig. 4(a). A constant increment of one FSR value $D_1/2\pi$ of 74.5 GHz is used for both subtractions in each plot, such that the mode crossing effect can be clearly seen. Here, weak coupling of modes instead of AMX is observed. The mode coupling occurs in a single resonator when two longitudinal mode families overlap in space. As their resonant center frequencies approach each other, the resulting mode interaction leads to a frequency shift and thereby changes the local dispersion. Both regular mode crossing and AMX have been reported in other microcomb platforms [21,43]. By plotting FSR values of modes A and B families as a function of resonant wavelengths as shown in Fig. 4(b), we find that the mode coupling has induced a repelling effect on FSR variations of both modes, where FSR shifts away from each family. In contrast, it has been previously reported that AMX can lead to an appealing effect on FSR values between two mode families [21]. The disruption of FSR values can thereby lead to local variations of dispersion conditions and assist in the generation of Kerr frequency combs.

To theoretically investigate the total dispersion profile of this cavity, we calculated the eigenfrequencies by using the analytical approximation of WGMs in a toroid [44,45]. We use a major radius of 300.24 μm and a minor radius of 118.18 μm for the calculation. The Sellmeier equation of YSZ is utilized to take into account the material dispersion. By solving the formulation, we find that the estimated eigenfrequencies of $q=1,p=0$ and $q=2,p=2$ modes are coincident with modes A and B families as shown in both Figs. 4(a) and 4(b) as solid lines. Although such analytical estimates of WGM positions still lack precision compared to numerical results using the finite element method—often used in Kerr microcomb designs [7]—the analytical solution does provide quick insight into tailoring WGM dispersion [38].

In general, anomalous dispersion refers to decreased FSR values as wavelengths increase and vice versa [39]. When second order dispersion $D_2/2\pi$ is dominant, this parameter then equals the difference between adjacent FSR values $\mathrm{\Delta }\mathrm{}\mathrm{FSR}$. In the case of a fiber ring etalon, we can theoretically derive a $D_{2e}/2\pi$ of about 49.1 mHz at 1550 nm. Considering the FSR of the whispering gallery mode resonator (WGMR) of 74.5 GHz and the etalon ${\mathrm{FSR}}_{\mathrm{e}}$, the dispersion of the fiber etalon contributes $\sim 60\mathrm{kHz}$ deviation from the equidistant grid of the etalon FSR. For an adjacent FSR of the whispering gallery mode resonator (WGMR), the difference of such deviation is of the order of $\sim 1\mathrm{kHz}$, which is much smaller than the large normal dispersion with $D_2/2\pi$ of $\sim -340\mathrm{kHz}$ for the fundamental WGM family of the YSZ microresonator. To minimize the jitter of etalon signals, we took average values from 10 ${\mathrm{FSR}}_{\mathrm{e}}$ values around the WGM peaks of interest and neglected the dispersion of the etalon. It should be noted that the dispersion of the etalon should be taken into account for other resonators with similar orders of dispersion.

YSZ cavity A was fabricated such that only the sharp rim of the disk was selectively fine polished. As a result, many high-order transverse WGMs encounter higher scattering losses when their mode fields reach the rough surface. Furthermore, the prism coupling setup can be used to excite mainly low-order modes with an optimized incident angle of the input beam. Therefore, we were able to observe the few-mode spectrum in such a cavity as shown in Fig. 3. We refer to this cavity as the few-mode cavity.

The generation of Kerr frequency combs relies strongly on many parameters including pump power, detuning frequency of the pump laser from the mode, and the dispersion profile. Versatile comb regimes can be excited depending on parameters such as an MI comb, chaotic comb, breathing solitons, single solitons, and soliton crystals [10]. The pump power should not be too much above threshold for accessing phase-locked solitons. The threshold of a Kerr frequency comb can be estimated by [46] $$P_{\mathrm{th}}\approx 1.54\frac{\pi }{2}\frac{1}{\eta }\frac{n}{n_2}\frac{\omega }{D_1}\frac{A}{Q_{\mathit{L}}^2},$$(1)where $\eta$ is the coupling factor, $n$ is the refractive index of the cavity, $n_2$ is the effective Kerr coefficient, $\omega /2\pi$ is the resonant frequency, $D_1/2\pi$ is the FSR value, $A$ is the mode area, and $Q_L$ is the loaded $Q$ factor. Considering the case of the YSZ microcavity in this experiment, the estimated mode area $A$ for $q=1$, $p=0$, and $\mathit{m}=2542$ is about $18{\mathrm{\mu m}}^2$ using the analytical approximation in Ref. [44].

We then use $n_2$ of $4\times {10}^{-19}\mathrm{}{\mathrm{m}}^2·{\mathrm{W}}^{-1}$ [28], FSR of 74.5 GHz, $n$ of 2.1, and $\eta$ of 1 for the in-coupled threshold. The estimated in-coupled threshold is about 1.5 mW. In our experiment, we have observed the onset of Kerr combs at the threshold of absorbed pump power of about 2.1 mW. If we take into account the expected Fresnel reflection loss of 11%, this value would be about 1.9 mW. To generate soliton crystal combs, we use an incident pump power around 170 mW at the prism. The maximum coupling contrast of WGMs is about 20% in our setup. For Kerr comb generation, the under-coupled condition is used. Therefore, the actual in-coupled pump power is usually less than 30 mW.

Due to the presence of Rayleigh scattering in the high-$Q$ resonator, we are able to monitor the comb line power in the backward direction of the signal. Note that the comb signal can be easily distinguished from the reflected coupled pump power since soliton or soliton crystal microcombs occur with the concurrent appearance of an abrupt transmission step or an increased comb power step [10]. Such steps are also coincident with the phase-locking transition steps in either pure Kerr combs or Raman–Kerr combs [47]. Unlike integrated comb platforms, the coupling gap in our experiment can be conveniently altered through a piezo controller. Therefore, it is possible to find a specific coupling gap under which condition the soliton step becomes very unstable and can quickly switch its appearance (see Visualization 1).

Figure 5 shows the observation of a single soliton frequency comb transition in YSZ cavity A when pumping mode A at 1554.7 nm. The coupling condition was under-coupled. The appearance of the soliton step in the transmission spectrum is highlighted with a green background in Fig. 5(a). We find that this step accompanies the observation of Kerr combs in the normal dispersion regime, similar to that of the reported mode crossing induced soliton crystals [15]. The self-thermal locking regime can be easily accessed when pump mode A is on the blue side of mode B. In this experiment, we stopped laser scanning and manually located the thermal locking of the pump frequency into mode A. We observed a comb spectrum clearly disrupted by the mode crossing as shown in Fig. 5(b) (left). The first comb line appears to be pinned at the mode around 1554.1 nm, while the comb line power encountered a sudden drop at the mode around 1553.5 nm. It is consistent with the reported pinning effect and the envelope disruption of the mode crossing in the Kerr comb spectrum [21,43]. However, when we further redshifted the wavelength of the pump laser in regime II, a stable single FSR spaced soliton comb was then formed as shown in Fig. 5(b) (right). The envelope of the comb fits well with a ${\mathrm{sech}}^2$ shape. It should be emphasized that the generation of such a single soliton comb is repeatedly manually accessed due to the pinning effect of the first sideband. Moreover, the appearance of the transmission step is similar to those of soliton crystals [10]. It is therefore easy to access and is more efficient than traditional single Kerr solitons.

We further chose to pump other adjacent mode A families and observed similar transmission steps in the forward direction, while an abrupt increased signal power step appeared in the backward direction. Using self-thermal locking [48], we obtained the generation of soliton crystal combs with different comb line spacings. Figure 5(c) shows examples of such spectra with 2-FSR, 3-FSR, 9-FSR, and 10-FSR spacings when the pump modes are around 1555.3 nm, 1555.9 nm, 1559.5 nm, and 1560.1 nm, respectively. It is found that the pinned first comb lines all appear around 1554.1 nm. The power of this comb line is found to be stronger than others. In particular, we observed wider comb spectra with line spacing from 3-FSR to 6-FSR with dispersive-wave-like tails as shown in Fig. 5(d), which could result from the dispersive wave induced by other mode interactions [43].

Furthermore, we studied the evolution of the soliton crystal combs in such a cavity as shown in Fig. 6. The pump laser frequency was first scanned across mode A around 1555.8 nm, and the coupling gap was optimized for comb generation. We then stopped the laser ramping, manually tuned the laser wavelength into the resonance, and recorded the corresponding comb spectra. Figures 6(a)–6(c) present comb spectra in three different detuning regimes marked in the transmission spectrum in the inset of Fig. 6(d). As the wavelength was redshifted and self-thermally locked to the resonance, the primary comb with 3-FSR spacing, the breathing comb with 1-FSR spacing, and the soliton crystal comb with 3-FSR spacing were observed, respectively. We used the fast Fourier transform (FFT) function of the oscilloscope ($\mathrm{R}\&\mathrm{S}$ RTB2004, bandwidth 200 MHz) to obtain the corresponding RF power spectrum from PD1 (Thorlabs PDA05CF2, bandwidth 150 MHz). Visible breathing behavior at the frequency of about 7.3 MHz was found in detuning regime ii, which is consistent with the oscillatory trace in the time domain as shown in the inset of Fig. 6(e). Our observation is similar to those breathing combs in either anomalous or normal dispersion cavities [11,19,49]. In particular, we find that regime ii can be fully suppressed by optimizing the coupling gap. It should be mentioned that the breathing behavior was also observed before visible 1-FSR comb lines were filled in.

In addition, we also investigate the comb generation with another YSZ microresonator (cavity B) with a major radius of about 456 μm. This resonator supports rich transverse high-$Q$ modes within one FSR and is referred to as an over-mode microresonator [50]. In comparison with the engineered few-mode cavity A, mode crossing phenomena are apparently more common. As a result, we find that abrupt steps together with the comb generation became much easier to find. Within one FSR spectral range, several mode families featuring abrupt transmission steps were found. Figure 7(a) shows an example of the transmission spectrum covering about a 12 GHz range. Two modes appear with the transmission steps as highlighted in green. These steps were verified by adjusting the coupling gap such that they became unstable and vanished time after time (see Visualization 2). The inset presents the photo of cavity B coupled with the rutile prism.

When the pump laser was thermally locked to the transmission step of mode A in cavity B, we found that Kerr combs with very different frequency spacings could be generated depending on the detuning of the pump. For instance, the Kerr comb with 4-FSR or 0.2 THz frequency spacing transited into the comb with 30-FSR or 1.48 THz frequency spacing when the pump wavelength was redshifted. Further redshifting the pump wavelength, a very asymmetric comb with 3-FSR spacing was obtained as shown in Fig. 7(b). For pump mode B, we observed a relatively weaker feedback signal. However, it should be mentioned that the feedback strength of a Kerr comb in the cavity does not rely merely on comb power, since it is also determined by Rayleigh scattering strength. When pumping into this mode, we found less complicated comb transitions. A comb with 1.24 THz spacing or 25-FSR’ was observed as shown in Fig. 7(c).

To the best of our knowledge, we have demonstrated the fabrication of the first high-$Q$ YSZ WGM optical microresonators. We obtained a new upper bound absorption coefficient of YSZ at the telecom wavelength. We further report the generation of soliton crystal Kerr combs in a few-mode YSZ microresonator assisted by mode interactions. Table 1 presents the performances of reported low threshold Kerr microcomb platforms made from different optical materials with high refractive indices larger than 2.0. Although the comb spanning is quite limited due to the large normal dispersion, our work paves the way for further design of on-chip YSZ wideband microcombs in abnormal dispersion. New opportunities with high-$Q$ YSZ optical microresonators could arise when considering its high chemical and thermal stability and mechanical flexibility, ideal for bendable devices for light sources and sensors.Table 1.

Performances of Various Kerr Microcombs on High Refractive Index ($n>2$) Platforms