1. INTRODUCTION

Temporal cavity solitons are ultrashort pulses of light that propagate indefinitely and do not change their shape in a driven Kerr-nonlinear optical cavity [1–4]. The formation of temporal cavity solitons, as the most fundamental example of self-organization phenomena in nonlinear optics [5], requires the double balance between Kerr nonlinearity and anomalous dispersion [6], along with a driving light compensating for the cavity loss [7]. Only recently were temporal cavity solitons observed experimentally in three types of optical cavities, including fiber cavities, microresonators, and free-space enhancement cavities [1,8–13]. The first experimental observation of temporal cavity solitons was demonstrated in a fiber cavity in which a continuous-wave (CW) laser was used as the driving light and addressing optical pulses wrote temporal solitons in the cavity [1]. Such temporal solitons could be used as bits in an all-optical buffer for optical signal processing applications. Subsequently, temporal cavity solitons were observed in optical microresonators [8], which provides a way of not only generating low-noise optical frequency comb spectra with smooth spectral envelopes in the frequency domain but also optical ultrashort pulses at tens of gigahertz (GHz) repetition rates in the time domain. Recently, microresonator-based soliton frequency combs have achieved great breakthroughs, such as microresonator soliton dual-comb spectroscopy [14–17], massively parallel coherent optical communications [18], soliton microcomb range measurement [19,20], self-referenced chip-scale soliton frequency combs [21], integrated-photonics optical-frequency synthesizers [22], the observation of dispersive waves [23], Stokes solitons [24], and soliton crystals [25].

At present, there are several major challenges in the generation of temporal cavity solitons in driven Kerr-nonlinear optical cavities. First, to drive the cavity coherently for generating temporal solitons, the operating frequency of the pump laser must be red detuned finely from the cavity resonance for a microresonator or a fiber resonator [1,8], which is still a big challenge for such experiments, although temporal cavity solitons were already demonstrated experimentally. Second, since the cavity resonance can be easily affected by thermal effects and other environmental perturbations, precise and rapid control of the relative pump laser-to-resonator detuning is required for achieving long-term operation of solitons [1,8,26]. Third, since the repetition rate of the generated temporal cavity soliton is decided by the cavity length, it is a challenge to obtain microresonator-based soliton frequency combs with large tunable mode spacing [25], which are required for many applications such as optical communications [18,27], optical sensing, optical spectroscopy [14,17,28], tunable microwave or terahertz (THz) wave generation [29,30], and so on.

 

Fig. 1. Generation of temporal soliton and optical frequency comb using the Kerr nonlinear cavity by intra-cavity pumping. (a) Schematic diagram of the experimental setup. (b) The schematic diagram of intra-cavity lasers generation at the situation of the normal (dotted line) and red-detuned operation (active line) in the Brillouin cavity. (c) Generation of optical frequency comb in Brillouin laser cavity by stimulated Brillouin scattering and four-wave mixing.

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Here, instead of using external pump light to drive the cavity coherently, intra-cavity pumping is proposed to drive a Kerr-nonlinear optical cavity for generating temporal solitons and soliton frequency combs. The detail of intra-cavity pumping is explained as follows (Fig. 1). First, single-longitudinal-mode Brillouin lasers are generated inside the Kerr-nonlinear optical cavity by introducing Brillouin gain into it [Fig. 1(a)] [31]. The generated intra-cavity Brillouin lasers have a spectral bandwidth of less than that of the cavity, and their frequencies are located at the cavity resonances naturally, which make them become a promising pump light to drive the cavity coherently for generating temporal solitons. Furthermore, the resonance frequency is shifted towards lower frequencies by the Kerr nonlinearity when the power of the generated intra-cavity lasers increases, causing the red-detuned operation of the generated intra-cavity lasers from the cavity resonance [Fig. 1(b)]. Therefore, by controlling the power of the intra-cavity lasers, the frequencies of the intra-cavity lasers can be red detuned finely from the cavity resonance, which is required for the generation of temporal cavity solitons. Second, even if the cavity resonance is affected by thermal effects and other environmental perturbations, the frequencies of the generated intra-cavity lasers are always located at the cavity resonances, enabling to achieve long-term operation of stable temporal solitons. Third, when the generated multiple wavelength intra-cavity lasers with an equal frequency separation $f$ (corresponding to an integral multiple of the cavity’s free spectral range) propagate inside the cavity with anomalous dispersion at the intra-cavity laser frequencies, as chromatic dispersion is balanced by nonlinearity and loss is balanced by gain, temporal cavity solitons can emerge from the modulated intra-cavity waveform by controlling the power of the intra-cavity lasers (or the red-detuned operation of the generated intra-cavity lasers from the cavity resonance), accompanying the generation of soliton frequency comb via cascaded four-wave mixing (FWM) between multiple wavelength intra-cavity lasers [Fig. 1(c)]. Furthermore, by varying the frequency separation $f$, soliton frequency combs with step tunable mode spacing from GHz to THz can be achieved by using the above approach.

In this paper, we demonstrate for the first time, both theoretically and experimentally, temporal cavity soliton and optical frequency comb generation in a Brillouin laser cavity via intra-cavity pumping. In contrast to temporal cavity soliton generation via external pump light, the soliton pulses form spontaneously via intra-cavity pumping without the need for fine-tuning of the external pump light (to match the cavity resonance). Furthermore, by varying the frequency separation $f$ of multiple wavelength intra-cavity lasers, the soliton pulses with a pulse width of hundreds of femtoseconds and a repetition rate of GHz–THz are achieved via intra-cavity pumping, corresponding to the generation of soliton frequency combs with step tunable mode spacing from GHz to THz. To the best of our knowledge, this is the first time soliton frequency combs with step tunable mode spacing from GHz to THz have been reported.

2. EXPERIMENTS AND RESULTS

Stimulated Brillouin scattering has always been prohibited in all the previous works on temporal cavity solitons since Brillouin scattering depletes the external pump light [1,11,12]. In our approach, Brillouin gain is used to achieve intra-cavity pumping for the generation of temporal cavity solitons owing to its narrow gain bandwidth ($\sim{\rm megahertz}$, MHz) and the unique Brillouin frequency shift [32]. Once multiple-wavelength narrow-linewidth CW lasers with an equal frequency separation $f$ are launched into the Brillouin laser cavity, multiple-wavelength Brillouin lasers with an integral multiple of the cavity free spectral range, a spectral linewidth of few kilohertz (kHz) and improved optical signal-to-noise ratios (OSNRs) are generated inside the cavity (in the direction opposite to the pump laser), and all the intra-cavity laser frequencies are always located exactly at the cavity resonances. Such intra-cavity lasers are promising driving light for temporal cavity soliton and optical frequency comb generation.

Our experimental setup is depicted in Fig. 2. Two CW single-frequency laser beams at the C band (line widths $\sim{150}\;{\rm kHz}$, two external cavity semiconductor lasers) with a frequency separation $f$ were amplified with a two-stage ${{\rm Er}^{3 + }}$-doped fiber amplifier (EDFA) and launched into a 500 m highly nonlinear fiber for achieving multiple-wavelength narrow-linewidth CW lasers with an equal frequency separation $f$ via cascaded FWM. The generated multiple-wavelength narrow-linewidth CW lasers were launched into the ring cavity by terminal 1 of an optical circulator for generating multiple-wavelength Brillouin lasers inside the cavity, which were used as the driving light for temporal cavity soliton and optical frequency comb generation. An all-fiber multiple-wavelength Brillouin ring cavity laser was constructed by connecting terminals 2 and 3 of the optical circulator through a 300 m highly nonlinear fiber (HNLF), an optical isolator, and a 10 dB wavelength-division multiplexing (WDM) coupler. The HNLF used in our experiments had a nonlinear coefficient of $\sim {10}\;{{\rm W}^{ - 1}}\;{{\rm km}^{ - 1}}$, a zero-dispersion wavelength of $\sim {1535}\;{\rm nm}$, and a dispersion slope of $\sim {0.022}\;{{\rm ps/nm}^2}/{\rm km}$ (see Supplement 1). Multiple-wavelength Brillouin lasers, temporal cavity solitons, and optical frequency combs (OFCs) were output from one port (10%) of the 10 dB WDM coupler. The output light was analyzed by using an optical spectrum analyzer, a radio frequency spectrum analyzer equipped with a high-speed photodetector, an autocorrelator, and a power meter.

 

Fig. 2. Schematic diagram of the experimental setup: multi-wavelength CW laser; EDFA, erbium-doped fiber amplifier; optical circulator; HNLF, highly nonlinear fiber; an optical isolator; a 10 dB wavelength division multiplexing (WDM) coupler; OSA, optical spectrum analyzer; ESA, electrical spectrum analyzer; PD, photodiode; frequency-resolved optical gating (FROG) scan.

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In the first experiment, a multiple-wavelength narrow-linewidth CW laser with $\sim {14}$ lines, a central wavelength of $\sim {1550}\;{\rm nm}$, and a frequency separation $f$ of $\sim{80}\;{\rm GHz}$ was used as the pump source for achieving multiple-wavelength Brillouin lasers inside the cavity (see Supplement 1). By introducing the optical circulator and the optical isolator into the laser cavity, the pump laser performs only a single turn, and there is no resonant condition for the pump laser and no need for servo locking it. Furthermore, higher-order ($ \ge 2$) Brillouin lasers can be efficiently suppressed even at high power [32–34]. For a pump power of $\sim {200}\;{\rm mW}$, first order multiple-wavelength Brillouin lasers with 10 lines and a linewidth of $\sim{4.8}\;{\rm kHz}$ (see Supplement 1) were obtained. Not only that, high OSNR was also achieved for multiple-wavelength Brillouin lasers since the Brillouin laser acted as an efficient low-pass filter, rejecting both the pump relative intensity noise (RIN) and its phase information [35]. Therefore, first-order multiple-wavelength Brillouin lasers with narrow linewidth and high OSNR could be generated in the above laser cavity. The generated intra-cavity lasers had a spectral bandwidth of less than that of the cavity (see Supplement 1), the frequencies of the generated intra-cavity multiple-wavelength Brillouin lasers were located at the cavity resonances naturally and also at the anomalous dispersion region of the cavity, and the frequency separation $f$ of the intra-cavity multiple-wavelength Brillouin lasers was a multiple of the cavity free spectral range (FSR $\sim{622}\;{\rm kHz}$), which made the intra-cavity multiple-wavelength Brillouin lasers become a promising pump light to drive the cavity coherently for generating temporal solitons.

Note that, as mentioned before (shown in Fig. 2), an intra-cavity circulator and an optical isolator were used to suppress the cavity resonances in the forward direction, which further suppresses the Stokes shifts of the Brillouin lasers. This allows the weaker FWM nonlinearity to take over. By controlling the power of intra-cavity multiple-wavelength Brillouin lasers, their frequencies can be red detuned finely from the cavity resonance, which is required for achieving temporal cavity solitons. Furthermore, as chromatic dispersion is balanced by nonlinearity and loss is balanced by gain, temporal cavity solitons can emerge from the modulated intra-cavity waveform, accompanying with the generation of soliton frequency combs via cascaded FWM between intra-cavity multiple-wavelength Brillouin lasers.

To verify the above idea, we performed the following experiments. With gradually increasing the pump power, we monitored the output signals from the 10% port of the 10 dB WDM coupler by using the autocorrelator. The measured results showed that we could achieve regular pulses when the pump power was larger than 600 mW. Figure 3(a) shows the measured pulse profile for a pump power of $\sim {650}\;{\rm mW}$. The time interval between two adjacent pulses is about 12.5 ps, which corresponds to a frequency separation of 80 GHz in frequency domain. By fitting one of the pulses with a hyperbolic secant function, the calculated pulse width is about 920 fs, and the pulse has a sech profile. The pulses sit on a CW background, and the dips in the CW background exist on both sides of the pulses, which are well-known features of temporal cavity solitons [1,11,12,36–38]. This confirms that the measured pulses are temporal cavity solitons. Figure 3(b) shows the corresponding spectrum of output signals for a pump power of $\sim{650}\;{\rm mW}$. Temporal cavity solitons in a Brillouin laser cavity have a spectrum with a comb structure including more than 150 individual spectral lines, whose envelope near the pump follows closely the ${{\rm sech}^2}$-shape characteristic for temporal cavity solitons. The 3 dB bandwidth of 1.68 THz corresponds to 188 fs optical pulses, which is smaller than the measured pulse width ($\sim{920}\;{\rm fs}$) since the obtained pulses are dissipative solitons. Since both the pulse profile and the spectrum of the temporal solitons have the ${{\rm sech}^2}$-shape characteristic, the generated temporal solitons are in a single-soliton state. The generation of a single Kerr-cavity soliton state is desirable for many applications. The emission near 1504.5 nm corresponds to the soliton Cherenkov radiation (dispersive wave), which is generated due to the presence of higher-order dispersion [39]. The conversion efficiency, defined as the output power of the soliton pulse versus input multi-wavelength pump laser power into the cavity, is about 3%.

 

Fig. 3. (a) Output temporal properties of the cavity pulse in repetition rate of 80 GHz when the pump power is 650 mW. (b) Output spectrum of the frequency comb in frequency separation of 80 GHz when the pump power is 650 mW. The red curves indicate the ${{\rm sech}^2}$ fitting for the envelope of the spectrum and pulse profile.

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In order to confirm the long-term operation stability of the temporal cavity solitons, we measured the pulse profiles of the temporal cavity solitons every 10 min for half an hour. The measured pulse profiles are shown in Fig. S4. It can be seen that the temporal cavity solitons are stable for more than half an hour (see Supplement 1).

To interpret the above experimental results, we performed numerical simulations by solving the nonlinear coupled-mode equations [8,40–42]. These equations describe the nonlinear interactions of multiple-wavelength Brillouin lasers with a frequency separation $f$ of $\sim {80}\;{\rm GHz}$ inside the resonator through external driving (the multiple-wavelength narrow-linewidth CW laser with $\sim{14}$ lines, a central wavelength of $\sim{1550}\;{\rm nm}$, and a frequency separation $f$ of $\sim{80}\;{\rm GHz}$) and nonlinear optical frequency conversion (e.g., cascaded FWM). The intra-cavity pumping or driving is described by in-phase multiple-wavelength Brillouin lasers with a frequency separation $f$ of $\sim{80}\;{\rm GHz}$ and the same optical power for each laser. The parameters of the Kerr-nonlinear optical cavity are same as that of the above Brillouin laser cavity. The intra-cavity pump laser contains 10 comb lines with the same power of $\sim{20}\;{\rm mW}$ (corresponding to the total power of $\sim{200}\;{\rm mW}$). Figures 4(a) and 4(b) show the simulated output pulse profiles and spectrum, respectively. Both the pulse profile and the spectrum of the simulated temporal solitons have the ${{\rm sech}^2}$-shape characteristic. The simulated pulse width is about 410 fs. The Cherenkov radiation near 1504.5 nm is also observed in the simulated spectrum of the temporal soliton. The simulated results agree with the experimental results.

 

Fig. 4. Numerical results of (a) output temporal pulse in repetition of 80 GHz and (b) output spectrum of soliton frequency comb in frequency separation of 80 GHz. The red curves indicate the ${{\rm sech}^2}$ fitting for the envelope of the spectrum and pulse profile.

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In previous works on temporal cavity solitons and soliton frequency combs, since the repetition rate of the generated temporal cavity soliton is decided by the cavity length, it is a challenge to obtain microresonator-based soliton frequency combs with large tunable mode spacing, which are desirable for many applications such as optical communications, optical sensing, optical spectroscopy, tunable microwave or THz wave generation, and so on. For soliton frequency comb generation via intra-cavity pumping in Brillouin laser cavity, by varying the frequency separation $f$ of the multiple-wavelength narrow-linewidth CW laser, multiple-wavelength Brillouin lasers with the same frequency separation $f$ can be obtained, and furthermore soliton frequency combs with step tunable mode spacing can be generated in Brillouin laser cavity with an increase of the pump power. To clarify tunablity of the mode spacing of soliton frequency combs generated in a Brillouin laser cavity, we measured the dependence of the spectra and pulse profiles of the generated soliton frequency combs on the frequency separation $f$ of the multiple-wavelength narrow-linewidth CW laser, and the measured results are shown in Fig. 5. Both the pulse profiles and the output spectra have the ${{\rm sech}^2}$-shape characteristic, all the pulses sit on a CW background, and the dips in the CW background exist on both sides of the pulses, which indicate the generation of temporal cavity solitons. The measured pulse widths are 2.9, 1.16, 0.92, 0.78, 0.58, and 0.54 ps; the 3 dB bandwidths of the spectra are 1.3, 1.5, 1.68, 1.52, 1.85 and 1.85 THz; and the corresponding time-bandwidth products are 3.77, 1.74, 1.54, 1.18, 1.07 and 0.99 for soliton frequency combs with mode spacings of 37.5, 55, 80, 110, 200, and 300 GHz, respectively. The generated pulses are dissipative solitons. The above results show that soliton frequency combs with step tunable mode spacing from GHz to THz can be achieved by using the proposed approach. To the best of our knowledge, this is the first time soliton frequency combs with step tunable mode spacing from GHz to THz have been reported, which may find significant applications in many fields.

 

Fig. 5. Output soliton frequency comb and temporal pulse in frequency separation of (a1), (a2) 37.5 GHz; (b1), (b2) 55 GHz; (c1),(c2) 80 GHz; (d1),(d2) 110 GHz; (e1),(e2) 200 GHz; (f1),(f2) 300 GHz for a cavity length of $\sim{322.6}\;{\rm m}$. The red curves indicate the ${{\rm sech}^2}$ fitting for the envelope of the spectrum and pulse profile. The inset in (a1) shows the measured RF beat note in the frequency separation of 37.5 GHz for a cavity length of $\sim{322.6}\;{\rm m}$, which is resolution bandwidth limited to 200 kHz width.

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A key signature of stable soliton formation is a low-noise narrow radio frequency (RF) signal that results from the repetitive output coupling of a soliton pulse [8,14,23]. To clarify the formation of stable soliton pulses, we reduced the repetition rate of the comb to 37.5 GHz and measured the RF beat note of the comb excluding the pump light (the intra-cavity Brillouin lasers) as shown in the inset of Fig. 5(a1). It is evidently that a main peak around 37.5 GHz was observed [shown in Fig. 5(a1)], accompanying the generation of several side peaks. The frequency separation between the main peak and the side peak is about 622 kHz, which corresponds to the FSR of the Brillouin laser cavity. It shows that multiple longitudinal modes are excited for a cavity length of $\sim{322.6}\;{\rm m}$, since many longitudinal modes exist within the Brillouin gain bandwidth (several tens of MHz). In order to realize single-longitudinal-mode operation for the comb line, we reduced the cavity length to 34.5 m, and the corresponding FSR is $\sim{6}\;{\rm MHz}$. Then we investigated temporal soliton and optical frequency comb generation for a cavity length of 34.5 m. Figure 6(a) shows the measured pulse profile for a pump power of $\sim{1300}\;{\rm mW}$. The time interval between two adjacent pulses is about 26.7 ps, which corresponds to a frequency separation of 37.5 GHz in the frequency domain. By fitting one of the pulses with a hyperbolic secant function, the calculated pulse width is about 3.0 ps, and the pulse has a sech profile. Figure 6(b) shows the corresponding spectrum of output signals for a pump power of $\sim{1300}\;{\rm mW}$. The envelope near the pump closely follows the ${{\rm sech}^2}$-shape characteristic for temporal cavity solitons. The 3 dB bandwidth of 0.207 THz corresponds to 1.52 ps optical pulses, which is smaller than the measured pulse width ($\sim{3.0}\;{\rm ps}$), since the obtained pulses are dissipative solitons. The inset of Fig. 6(b) shows the measured RF beat note of the comb excluding the pump light (the intra-cavity Brillouin lasers). A single low-noise RF beat note was observed, which indicated the formation of stable soliton pulses in Brillouin laser cavity via intra-cavity pumping and single-longitudinal-operation for the comb line.

 

Fig. 6. Output soliton frequency comb and temporal pulse in frequency separation of 37.5 GHz for a cavity length of $\sim{34.5}\;{\rm m}$. The red curves indicate the ${{\rm sech}^2}$ fitting for the envelope of the spectrum and pulse profile. The inset in (a) shows the measured RF beat note in the frequency separation of 37.5 GHz for a cavity length of $\sim{34.5}\;{\rm m}$, which is resolution bandwidth limited to 200 kHz width.

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Since stimulated Brillouin scattering (SBS) frequency shift is a function of pump wavelength [6], the multi-wavelength SBS lasers generated from equally spaced multi-frequency pump lasers injected out of the fiber ring cavity may not have equal space. Furthermore, the generated soliton frequency combs may not have equal space. Even so, as the FSR of the Brillouin laser cavity is a little bit smaller (or larger) than the Brillouin gain bandwidth, and the frequency separation of multi-frequency pump lasers is not as large (several tens of GHz), the variation of the Brillouin frequency shift is less than the FSR of the Brillouin laser cavity in the wavelength range of multi-frequency pump lasers, and the multi-wavelength SBS lasers generated from equally spaced multi-frequency pump lasers injected out of the fiber ring cavity may have equal space. Furthermore, the generated soliton frequency combs may have equal space [shown in the inset of Fig. 6(b)], as with the case of Fig. 6 (the FSR is $\sim{6}\;{\rm MHz}$). In addition, by reducing the number of multi-frequency pump lasers to two, the generated dual-wavelength Brillouin lasers have a fixed frequency separation, and furthermore the generated soliton frequency comb has equal space.

In addition, by introducing an optical isolator into the racetrack resonator cavity and modifying the chromatic dispersion of the suspended waveguides [43,44], soliton frequency combs with tunable mode spacing might be generated in the chip-scale Brillouin laser cavity via intra-cavity pumping.

3. CONCLUSIONS

In summary, we have investigated, both theoretically and experimentally, temporal cavity soliton and optical frequency comb generation via intra-cavity pumping in a Brillouin laser cavity. This approach is different from previous works on temporal cavity soliton and soliton frequency comb generation via external pump light. In contrast to previous works, the soliton pulses form spontaneously via intra-cavity pumping without the need for fine-tuning of the external pump light (to match the cavity resonance). Very interestingly, by varying the frequency separation $f$ of multiple wavelength intra-cavity Brillouin lasers, the soliton pulses with a pulse width of hundreds of femtoseconds and a repetition rate of GHz–THz are achieved via intra-cavity pumping, corresponding to the generation of soliton frequency combs with step tunable mode spacing from GHz to THz, which was inaccessible in previously reported soliton frequency combs.