Gain-assisted chiral soliton microcombs

Despite these enormous advances, the existing strategies for the dynamical control of soliton microcomb are restricted to passive microresonators, while the optical gain provides a potential way to enable all-optical control of the microcomb, an exotic degree of freedom that is exclusive to active microresonators villegas2014all ; zhu2018all ; chen2017exceptional . In this work, we report the soliton slingshot effect and the chiral modulation of the counter-propagating soliton in an erbium-doped active microcavity. The soliton slingshot effect arises from the extra energy accumulation induced by the modal coupling in the over-moded resonator. The operation window of the slingshot single soliton can be actively regulated by tuning the erbium gain, with a maximum of 18 GHz. Furthermore, the chirality of the counter-propagating soliton is demonstrated and dynamically controlled through the erbium gain, realizing a rapid on-off switch of soliton with a modulated bandwidth of 7 MHz.

In the experiment, a silica microsphere with a diameter $\approx$ 600 $\upmu$m and 99.7 GHz free spectral range (FSR) is prepared (Fig. 1a), which contains rich mode families, for example 241 transverse modes per FSR (see Supplementary Information). The erbium particles are then doped on the cavity surface via the arc plasticity annealing technique kotz2017three (details see Methods and Supplementary Information), which is characterized by the green light emission under the pump of a 980 nm control laser (Fig. 1b). The device coupled with a fiber taper is mounted into an all-fiber-connected centimeter-size package (Fig. 1b), for facilitating measurements and enabling portability. By tuning the 1550 nm pump laser frequency into the cavity resonance, soliton combs are obtained, exhibiting a smooth sech² spectral envelope, as shown in Fig. 1c.

Different from the conventional generation process, the solitons directly burst in an extremely short time, behaving as a slingshot, in which extra optical energy is accumulated in the pump mode and then transfered to the side modes. Moreover, the soliton combs are generated in both counterclockwise (c.c.w.) and clockwise (c.w.) direction due to the backscattering of the pump laser induced by the cavity-fiber coupling spot (see Supplementary Information). Here the backscattering excites different transverse modes in c.w. direction, enabling the backward soliton formation in another mode family. The dynamics of multimode co-existence in the microresonator is demonstrated by real-time video recording (see Supplementary Movie 1). The counter-propagating solitons can be also formed in the same mode family (Extended Data Fig. 1). The counter-propagating solitons share the same pump wavelength, but are different in both the spectral shape and bandwidth (Fig. 1c). Besides, by injecting both the c.c.w. and c.w. soliton combs into a photodetector, the radio-frequency (RF) beat note signal is obtained through a electrical spectrum analyzer, indicating a 48.6 MHz repetition rate difference of the counter-propagating solitons (Fig. 1d). Such dual-comb in opposite directions can also turn into chiral regime with the unbalanced intensity output by adjusting the intracavity erbium-based gain, as shown in Fig. 1a.

The aforementioned soliton slingshot phenomenon is attributed to the modal-coupling-induced energy accumulation. In a microsphere resonator with a few hundreds of microns in diameter, numerous transverse modal couplings emerge (see Supplementary Information), forming hybrid modes $h_{0+}$ and $h_{0-}$ with a considerable frequency shift $\pm\gamma_{0}$ (Inset of Fig. 2a). When the frequency shift $\gamma_{0}$ is large enough, the parametric oscillation threshold of the red-shifted mode $h_{0-}$ increases along the oscillation stability curve (Fig. 2b), giving rise to the extra accumulation of intracavity pump power (see Supplementary Information for details). Once the intracavity power reaches the elevated threshold, a rapid energy transition from the pump mode to the side modes takes place as well as the subsequent burst of soliton microcombs. As for the blue-shifted mode $h_{0+}$, the oscillation threshold remains unchanged, so that no extra energy accumulation of the pump mode is provided in this resonance. The soliton slingshot processes are recorded by an optical spectrum analyzer in Supplementary Movie 2.

Experimentally, as the pump laser frequency scans over the two modes from the blue to the red side with a speed of 10 pm/s, the output comb power evolution trace is monitored in real time. It is found that the high-frequency mode $h_{0+}$ experiences a regular comb generation, while in the $h_{0-}$ resonance the soliton slingshot effect is observed, featuring an abrupt rising step at 44s (Fig. 2a, detail evolution process in spectral and time domain see Extended Data Fig. 2). The optical spectrum of the rapidly generated soliton at $h_{0-}$ mode spans from 1500 nm to 1600 nm, meeting the sech² function fitting of the soliton spectral envelope (orange dash line in Fig. 2c) and a repetition rate of $\approx$ 99.7 GHz. The corresponding low-frequency spectrum at 0 to 1 GHz in Fig. 2d reveals the phase-locked property of the microcombs. The temporal profile is also measured by frequency-resolved optical gating (FROG), indicating the narrow pulsewidth of the slingshot soliton being $\approx$ 350 fs, and pulse-to-pulse distance of 10.3 ps. Moreover, due to the rich modal couplings in the cavity, such single soliton slingshots are generated with a high possibility. By repeating 100 times scan for each of the 40 microsphere samples, we obtain 3,640 cases of soliton slingshot ($>$90% in possibility)in which 2,575 cases generates the single soliton state ($>$60% in possibility, details in Section 2 in Supplementary Information). We would note that the similar spontaneous formation process of the soliton pulse is also reported recently yu2020spontaneous ; zhou2019soliton .

The demonstrated soliton microcomb slingshot can be regulated actively by tuning the optical gain from the doped erbium particles. By launching a 980 nm control laser into the cavity via the same tapered fiber, the erbium particles are excited, characterized by the down-conversion fluorescence (see the inset of Fig. 3a). With increasing the control laser power, the erbium gain rises considerably, compensating significantly the photon losses. This energy enhancement further leads to the extension of soliton existence range as well as greater possibilities of multi-soliton and soliton crystal slingshots.

By repeating the pump laser frequency scan from blue to red detuned region under control laser power of 0 mW, 50 mW and 100 mW, we record the comb power evolution traces, as shown in Fig. 3a. The extension of slingshot soliton existence range and the generation of multi-soliton state with higher optical power are obtained, as increasing the erbium gain. Details of obtained multi-soliton and soliton crystal are presented in Extended Data Figure 3. The slingshot single soliton existence ranges are 6.2 GHz, 12.5 GHz and 18 GHz under control laser power of 0 mW, 50 mW and 100 mW, respectively. Such an extended single soliton existence range also increases the maximum spectral span of the soliton microcomb, corresponding to 66 nm, 93 nm and 115 nm span under control laser power of 0 mW (i), 50 mW (ii) and 100 mW (iii) (Fig. 3b). We summarize such gain based enhancements as increasing the power of control laser in Fig. 3c.

To exploit the controllability of this slingshot soliton in the active system, we demonstrate the fast on-off switch of soliton microcombs. As aforementioned, the 1550 nm pump light is partially backscattered to c.w. direction at the cavity-fiber coupling point and excites different transverse mode families in c.w. and c.c.w. directions. Thus, the counter-propagating solitons are generated in the two disparate mode families, while sharing the same pump frequency. The refractive index of c.c.w. and c.w. mode families reacts differently to the erbium excitation, thus resulting in the resonance shift with different velocities in opposite directions. The c.w. resonance frequency, with higher sensitivity to the erbium-based modulation, is tuned out of soliton existence range when increasing the control laser power. By decreasing the control laser power, the c.w. resonance is tuned back towards shorter wavelengths, resulting in the slingshot recovery of c.w. soliton microcomb. The less sensitive c.c.w. soliton remains almost unaffected in the entire modulation process, enabling the on-off chirality control of counter-propagating soliton (More details are shown in the Extended Data Fig. 4 and Supplementary Section 2). Since the slingshot effect requires energy accumulation in the pump mode, the c.w. comb power exhibits hysteresis behavior, because the iterated-slingshot of soliton needs higher optical energy accumulation than the original soliton build-up. Meanwhile, the c.c.w. comb power remains almost unchanged, as shown in Fig. 4b. The fact that the counter-propagating solitons belong to different mode families is also proven by the beat note signal between the output c.c.w. and c.w. microcombs, forming a set of dual-comb with different repetition rate. Moreover, the asymmetrical regulation of counter-propagating soliton provides a novel method to tune the repetition rates of the dual comb actively. By tuning the control laser power from 0 to 80 mW, the repetition rate difference of the dual comb changes from 48.6 MHz to 51.2 MHz (Fig. 4d). It is noted that when the control laser power reaches 100 mW, the c.w. soliton vanish gradually, and no dual-comb beating is observed. Due to the instantaneous response of all-optical control, the fast on-off switch is realized. By turning a 100 mW control laser on and off periodically, the output intensity of the c.w. soliton microcombs is well modulated in a square wave, with modulation extinction ratio (ER) almost 100%. The ramp-up and ramp-down dynamics are quite sharp, with a typical measured temporal delay $\approx 0.14\upmu$s, corresponding to 3-dB ER bandwidth of 7 MHz (Fig. 4c, also see details in Supplementary Movie 3). The modulation bandwidth is mainly limited by the on-off speed of the control laser, but it is still over 2 orders of magnitude faster than the state-of-the-art turnkey solitons shen2020integrated .

In summary, we experimentally demonstrated the soliton slingshot effect and the dynamical control of counter-propagating solitons by using erbium-doped active microsphere resonators. Besides the fundamental significance in physics, the optical gain implementation in the soliton system also offers unprecedented capabilities to actively regulate the multi-soliton states, the soliton access range, the spectral spans, and the propagation chirality of the solitons, all in one device. Such realizations also pave the way for the ultrafast switch of the soliton microcombs and the tunable dual comb spectroscopy. Finally, due to its physical generality, this scheme also could be applied in other microresonator platforms, to attain soliton microcombs with broader span and richer diversity, further expanding the potential of microcomb tools for wide applications such as optical communication and sensing.