28 THz soliton frequency comb in a continuous-wave pumped fiber Fabry–Pérot resonator

Nonlinear Kerr cavities have enabled the generation of cavity solitons (CSs),^1–5 which offer precise femtosecond sources and wide-ranging optical frequency combs (OFCs) with repetition rates spanning from MHz to THz, impacting a wide range of cross-disciplinary applications: data transmission⁶ and processing,⁷ ranging,⁸ microwave photonics,⁹ dual-comb spectroscopy,¹⁰ and astronomical spectrograph calibration.¹¹ These solitons arise as localized solutions of the Lugiato–Lefever equation^12,13 and can be observed in resonators with high-quality factors. The emergence of CSs relies on the double balance between anomalous group velocity dispersion (GVD) and Kerr nonlinearity on one side and between losses and energy injection [typically achieved through continuous-wave (CW) laser pumping] on the other side. Owing to their high-quality factor and compact design (cavity length of hundreds of microns), microresonators have attracted significant attention over the past decade.^4,5,14 Despite these impressive performances, launching and collecting light in these resonators can be challenging, requiring advanced fiber coupling devices, such as a prism fiber taper,¹⁵ or advanced coupling methods for chip microresonators,¹⁶ and while progress on packaging is ongoing, it is still an obstacle for fiber applications. Another way to generate OFCs in resonators consists in using all-fiber ring cavities of tens of meters in length,^1,17 whose effective quality factor can reach several millions by including an amplifier within the cavity.¹⁸ The spectra obtained using these resonators’ architecture extend over several THz, almost like microresonators, but they have two major drawbacks. First, the line spacing is in the MHz range, which limits the field of application (mostly in the GHz range¹⁴), and second, they are not compact. An interesting alternative consists in taking benefit of fiber Fabry–Pérot (FFP) resonators of several centimeters in length. They are a good compromise between fiber ring cavities and microresonators, offering several tens of millions of Q-factors, as well as easy connection to photonic devices with a standard physical-contact fiber connector (FC/PC) and small size.^3,19–23 CS generation has already been demonstrated with these devices using either a pulsed pumping scheme³ or stabilization management through the Brillouin effect.^19,24 These recent studies have paved the way for this novel method of OFC generation. However, the generated CSs via CW pumping still have durations exceeding 200 fs,^19,24 which falls short of the performance achieved by microresonators.

This study demonstrates that manufacturing a FFP resonator using a highly nonlinear fiber with low GVD at the pump wavelength enables the generation of sub-100 fs CSs. Moreover, we implemented an advanced triggering experimental setup enabling an accurate and easy control of the detuning to explore the different regimes of the cavity before reaching the soliton states together with an efficient stabilization feature. In addition, the inherent low GVD characteristics, combined with the large spanning of the generated CS, lead to the emergence of dispersive radiation due to higher-order dispersion, which permits us to observe a broad spectrum spanning over 28 THz.

The FFP cavity used for this study is depicted in Fig. 1. It is made from an optical highly nonlinear fiber (HNLF Thorlabs-HN1550P) of length L = 20.63 cm, a group velocity dispersion (GVD) of β₂ = −0.8 ps² km⁻¹, a third-order dispersion (TOD) of β₃ = 0.03 ps³ km⁻¹ at the pump wavelength (1550 nm), and a nonlinear coefficient of γ = 10.8 W⁻¹ km⁻¹. Both fiber ends are mounted in FCs/PC, and Bragg mirrors are deposited at each extremity with a physical vapor deposition technique, to achieve 99.86% reflectance over a 100 nm bandwidth.²⁵  Figure 1(a) shows a connector with its deposited mirror. The linear transfer function is shown in Figs. 1(b) and 1(c). This architecture leads to a resonator with a linewidth resonance of 0.8 MHz at full width half maximum, a linear coupling efficiency of 25%, and a peak resonance transmission of 5%. The free spectral range (FSR) is measured at 498.6 MHz, resulting in a finesse $F=620$⁠, and a quality factor Q = 230 × 10⁶. One of the great advantages of this FFP cavity with respect to a microresonator^15,16 is its plug-and-play feature into an all-fiber photonic device.

The FFP resonator is exploited in the experimental setup shown in Fig. 2. The generation of CSs requires a bistable operation and specific excitation protocols.^5,14 One of the most popular and efficient solutions consists in performing a scan of the resonance from blue to red and to stop at a precise laser frequency, which fixes a specific cavity detuning. To achieve precise control over the cavity detuning, a two-arm stabilization scheme is implemented.^22,26 The CW laser is split into two beams: one beam serves as the control beam for stabilizing the laser on a cavity resonance (control beam), while the other beam acts as the pump beam for the cavity (nonlinear beam). To allow for independent handling of the beams and prevent their interaction within the cavity, we take advantage of the natural birefringent of optical fibers. The polarization states of the control and nonlinear beams are crossed polarized, along the two main polarization axes of the fiber cavity by means of polarization controllers. They are separated at the output using a polarization beam splitter [see the PBS in Fig. 2]. The stabilization process [lower beige arm in Fig. 2] is achieved through a Pound–Drever–Hall (PDH) system, enabling laser locking at the top of cavity resonance, and with the main interest to be insensitive to amplitude variations.^27,28 Meanwhile, the detuning of the nonlinear beam [upper brown arm in Fig. 2] is controlled using a homemade tunable single-sideband generator [see the SSB in Fig. 2]. The nearest sideband of a modulated beam, obtained with a phase modulator driven by a 30 GHz tunable frequency synthesizer (TFS), is isolated to obtain a pump signal with a tunable frequency shift. This approach allows the nonlinear beam frequency to experience similar variations to those of the control beam. It also makes possible to adjust the frequency shift between the two and, consequently, to control the detuning value of the nonlinear beam, by simply modifying the value of the TFS frequency. Thanks to the TFS frequency ramp function, it is possible to scan cavity resonances or manually change the TFS frequency and, therefore, the detuning value. The nonlinear beam is further amplified by an erbium-doped fiber amplifier to reach a power of 1 W before being launched into the cavity. However, the SMF-HNLF transitions, at the cavity input and output, induce important losses due to the difference in the effective area overlap, which is estimated to be 3 dB. Thus, the effective pump power at the cavity input is estimated to be 0.5 W.

Thanks to this setup, we can easily observe the distinct nonlinear regimes of the cavity, varying with the detuning, through the use of a basic CW pump. It is worth noting that the use of a PDH system for stabilization makes the experimental setup very robust compared to the use of a simple Proportional–Integral–Derivative (PID) system. It allows us to compensate environmental vibrations and the thermal variation. First, a classic fast redshift scan is applied. The TFS frequency is swept from 30 GHz to 30.5 GHz with a speed of 2 GHz/s. The evolution of the output power through the scan is recorded, thanks to a photodiode and an oscilloscope, and is represented in Fig. 3(a). As expected, we observe three different regions [(1), (2), and (3) in Fig. 3(a)], corresponding to the different well-known comb structures in Kerr resonators, in sequence: modulation instability (MI), chaos, and CSs.^2,4,5,29,30 Second, in a way to observe the evolution of these three nonlinear regimes, we manually change the detuning value (i.e., TFS frequency value), recording the optical spectrum and radio frequency (RF) beatnote centered at the first beatnote (498.6 MHz), of the generated signal, with an optical spectrum analyzer (OSA) and an electrical spectrum analyzer (ESA), respectively. Figures 3(b) and 3(c) illustrate the evolution of the experimentally generated signals as a function of detuning, which can be obtained by the relation $Δδ=−4πnLcΔν$⁠, where Δδ and Δν are the detuning variation and TFS frequency variation, respectively (c and n are the speed of light in vacuum and the effective refractive index of the fiber mode, respectively). In these figures, the three nonlinear regimes can easily be identified with a clear separation between each. Figures 3(d)–3(i) show several characteristic examples of the spectrum and RF beatnote of the three comb structures to get a clearer insight. (1) MI comb formation, characterized by its symmetric sidelobes around the pump in the spectral domain [Figs. 3(b) and 3(f)], resulting in a stable oscillation as the RF spectrum shows [Figs. 3(c) and 3(i)]. (2) MI lobe mixing leads to a chaotic transmission variation and produces a chaotic comb [Figs. 3(b) and 3(e)]. The chaotic regime is well illustrated by a huge broadening of the beatnote as shown in Figs. 3(c) and 3(h). The spectrum broadens, and a spectral component appears at 1430 nm due to the TOD as we will discuss below [Figs. 3(b) and 3(e)]. (3) CSs are generated, resulting in a broad coherent OFC over 200 nm (i.e., 28 THz) [Figs. 3(d) and 3(g)]. Interestingly, Fig. 3(b) shows the existence of different CSs’ regime, indicating the circulation of multiple solitons within the cavity. However, the sensitivity of the detection system in Fig. 3(a) does not allow us to clearly highlight the different soliton regimes, from several CSs to a single one. The low sensitivity of the used photodiode might be the reason behind this discrepancy, as multiple steps may be present but not detectable.

Furthermore, establishing the presence of a single soliton within the resonator is not straightforward, and a seemingly smooth spectrum at the cavity output is not sufficient for confirmation. This is exemplified in Fig. 4, where both time domain and spectral domain measurements, conducted using an OSA and a 30 GHz PD combined to a 70 GHz oscilloscope, respectively, are depicted. In Figs. 4(a) and 4(e), the presence of multiple solitons circulating in the cavity results in a scrambled spectrum and a continuous sequence of oscillations in the time domain due to the limitations of the PD in resolving all circulating solitons. When a cluster of solitons propagates, the time trace reveals a single pulse every round trip time (=1/FSR = 2.0056 ns) [Fig. 4(f)], potentially suggesting a single soliton generation process. However, the periodic modulation of 1.5 THz in the spectrum [Fig. 4(b)] indicates that several solitons spaced by 600 fs (=1/1.5 THz) are generated at each round trip.³ They cannot be resolved through the time domain measurements due to the limited bandpass of the detection system (30 GHz). Conversely, Figs. 4(c) and 4(g) illustrate a different scenario where multiple solitons propagate far apart, resulting in modulations within the spectrum that are too narrow to be resolved in the spectral domain with a common OSA. However, these instances are discernible in the time domain measurement, where several pulses appear each cavity round trip time. The only case demonstrating the generation of a single soliton is depicted in Figs. 4(d) and 4(h), characterized by a smooth recorded spectrum and a time domain measurement exhibiting a single pulse every round trip time at the same time. This comprehensive analysis underscores the system’s capability to generate a single soliton within the FFP resonator employing CW pumping.

In order to get a complete characterization of the dynamics of the system, we record the phase noise spectra corresponding to each regime in Fig. 5: MI comb, multiple soliton comb, and single soliton comb. These measurements confirm that CSs present the most stable regimes. As expected, the phase noise of the MI comb is significantly higher (40 dB) compared to CSs. An interesting observation is that the phase noise of the multiple soliton comb closely resembles that of the single soliton comb in the low frequencies. However, in the high frequencies, the multiple soliton comb demonstrates considerably higher phase noise compared to the single soliton comb, 30 dB higher, with a comparative level to the MI comb.

Here, ω is the normalized angular frequency shift of the driving field and D represents the group-delay accumulated by the temporal CS with respect to the driving field over one round trip (in units of time). Indeed, the TOD makes the CS group-velocity slightly different from that of the driving field, leading to a spectral recoil.^17,39 This phenomenon is observable in both the experimental and simulated spectra presented in Fig. 6(a). Thus, the soliton propagates together with the extended radiation tail attached to it [green line in Figs. 6(b) and 6(c)]. The measured DW frequency position (15.77 THz) is almost identical to the one derived from the phase matching condition (15.69 THz) [red line in Fig. 6(a)], which, in turn, is identical to the frequency position of the simulated DW [green line in Fig. 6(a)]. The drift delay is calculated as $D=β2ΩCS2L+β3ΩCS2L$⁠, where the recoil frequency shift Ω_CS/(2π) = 1105 GHz is determined through the numerical simulation¹⁷ [green line in Fig. 6(a)]. It is worth noting that the nonlinear contribution, which depends on the cavity length and CS background power, is not incorporated in the phase matching condition, due to its negligible impact. Nevertheless, it becomes relevant in specific studies.¹⁷ In the context of FFP cavities, accounting for this would entail considering the specific characteristics of the two-way light circulation and the additional phase arising from the cross-phase modulation.^31,34,35 However, this aspect falls outside the scope of this study but presents a potential avenue for exploration in subsequent investigations involving adapted cavities.

In this study, we have reported the generation of an OFC spanning over 28 THz (i.e., 200 nm), corresponding to a 80 fs cavity soliton duration emitting a dispersive wave, by using a FFP resonator pumped by a CW laser. The highly reflective mirrors and the use of highly nonlinear fiber contribute to achieving a high-quality factor cavity, enhancing nonlinear performance and proving advantageous for Kerr comb generation. The use of this kind of cavity benefits from the ease of implementation into photonic systems by means of its FC/PC connectors. Moreover, our advanced setup with an independent control of the cavity detuning enabled a smooth tuning of the cavity detuning to observe the dynamics of the system, as well as an excellent stabilization of the cavity with a PDH system to reach −115 dBc/Hz in the best case. The overlap of the CS with the normal dispersion leads to the generation of a DW at 15 THz from the pump. These experimental results are in excellent agreement with numerical simulations. This work contributes to the development of new platforms to generate OFCs, with a view of new applications for fiber systems.

The authors thank Nicolas Englebert and François Leo for fruitful discussions.

The present research was supported by the Agence Nationale de la Recherche (Programme Investissements d’Avenir, I-SITE VERIFICO, FARCO); Ministry of Higher Education and Research; European Regional Development Fund (Photonics for Society P4S), the CNRS (IRP LAFONI); Hauts de France Council (GPEG project); A.N.R. ASTRID ROLLMOPS; and the University of Lille (LAI HOLISTIC).

The authors have no conflicts to disclose.

T. Bunel: Investigation (equal); Writing – original draft (equal). M. Conforti: Conceptualization (equal); Investigation (equal); Software (equal); Supervision (equal); Writing – review & editing (equal). Z. Ziani: Investigation (equal); Software (equal). J. Lumeau: Investigation (equal); Resources (equal). A. Moreau: Investigation (equal); Resources (equal). A. Fernandez: Conceptualization (equal); Investigation (equal); Validation (equal). O. Llopis: Investigation (equal); Validation (equal). G. Bourcier: Investigation (equal); Validation (equal); Writing – review & editing (equal). A. Mussot: Conceptualization (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.