We report the generation of an optical frequency comb featuring a 28 THz bandwidth, sustained by a single 80 fs cavity soliton recirculating in a fiber Fabry–Pérot resonator. This large spectrum is comparable to frequency combs obtained with microresonators operating in the anomalous dispersion regime. Thanks to the compact design and the easy coupling of the resonator, cavity solitons can be generated in an all-fiber experimental setup with a continuous wave pumping scheme. We also observe the generation of a dispersive wave at higher frequencies, which is supported by higher-order dispersion. These observations align remarkably well with both numerical simulations and the established theory of cavity solitons.

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 equation12,13 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 microresonator15,16 is its plug-and-play feature into an all-fiber photonic device.

FIG. 1.

Description of the FFP resonator. (a) Photograph of the device with one of its deposited mirror. (b) Transmission function of the resonator in the linear regime. (c) Zoom-in view of the cavity resonance.

FIG. 1.

Description of the FFP resonator. (a) Photograph of the device with one of its deposited mirror. (b) Transmission function of the resonator in the linear regime. (c) Zoom-in view of the cavity resonance.

Close modal

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.

FIG. 2.

Experimental setup with a two-arm stabilization system. Brown line: nonlinear beam; beige line: control beam. Both beams are perpendicularly polarized to each other. TFS: tunable frequency synthesizer; PM: phase modulator; EDFA: erbium-doped fiber amplifier; PC: polarization controller; OI: optical isolator; PD: photodiode; PBS: polarization beam splitter; PDH: Pound–Drever–Hall; and SSB: single-sideband generator.

FIG. 2.

Experimental setup with a two-arm stabilization system. Brown line: nonlinear beam; beige line: control beam. Both beams are perpendicularly polarized to each other. TFS: tunable frequency synthesizer; PM: phase modulator; EDFA: erbium-doped fiber amplifier; PC: polarization controller; OI: optical isolator; PD: photodiode; PBS: polarization beam splitter; PDH: Pound–Drever–Hall; and SSB: single-sideband generator.

Close modal

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.

FIG. 3.

Experimental recordings as a function of cavity detuning. (a) Nonlinear transfer function with a fast redshift scan of the cavity (scan speed = 2 GHz/s). (b) Spectrum evolution with the cavity detuning. (c) RF beatnote evolution with the cavity detuning. (d), (e), and (f) Snapshots of each comb structure spectrum, corresponding to the black dashed lines in (b). (g), (h), and (i) Snapshots of each comb structure RF beatnote, corresponding to the white dashed lines in (c). (f) and (i) MI, δ = −0.015 rad. (e) and (h) chaos, δ = 0.06 rad. (d) and (g) soliton, δ = 0.12 rad. The video in the supplementary material provides a comprehensive overview of the comb structure variation throughout the scan. Multimedia view available online.

FIG. 3.

Experimental recordings as a function of cavity detuning. (a) Nonlinear transfer function with a fast redshift scan of the cavity (scan speed = 2 GHz/s). (b) Spectrum evolution with the cavity detuning. (c) RF beatnote evolution with the cavity detuning. (d), (e), and (f) Snapshots of each comb structure spectrum, corresponding to the black dashed lines in (b). (g), (h), and (i) Snapshots of each comb structure RF beatnote, corresponding to the white dashed lines in (c). (f) and (i) MI, δ = −0.015 rad. (e) and (h) chaos, δ = 0.06 rad. (d) and (g) soliton, δ = 0.12 rad. The video in the supplementary material provides a comprehensive overview of the comb structure variation throughout the scan. Multimedia view available online.

Close modal

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.

FIG. 4.

Comparison of different signals represented in the spectral and time domains. (a)–(d): Spectral domain measurements with an OSA. (e)–(h): Corresponding time domain measurements with a 30 GHz PD and a 70 GHz oscilloscope.

FIG. 4.

Comparison of different signals represented in the spectral and time domains. (a)–(d): Spectral domain measurements with an OSA. (e)–(h): Corresponding time domain measurements with a 30 GHz PD and a 70 GHz oscilloscope.

Close modal

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.

FIG. 5.

Phase noise spectrum measurements of different generated signals. Modulation instability: δ = −0.015 rad; multiple solitons: δ = 0.1 rad; and single soliton: δ = 0.12 rad.

FIG. 5.

Phase noise spectrum measurements of different generated signals. Modulation instability: δ = −0.015 rad; multiple solitons: δ = 0.1 rad; and single soliton: δ = 0.12 rad.

Close modal
We reproduced the experimental results by numerically solving the Lugiato–Lefever equation adapted for FFP cavities (FP-LLE),3,31,32
tRψτ=(α+iδ)ψ+θPin+2Lβ363t3iβ222t2+iγ|ψ|2+iγ2tRtR/2tR/2|ψ|2dtψ,
(1)
where ψ is the field envelope in units of W, t is the retarded time in the pulse reference frame, τ is the slow time counting the number of round trips, Pin = 0.5 W is the input power, tR = 1/FSR (=2.0056 ns) is the round trip time, θ = 0.0529 is the transmissivity of the mirror, and α=π/F accounts for the total cavity losses (valid for F1). It has recently been demonstrated that this model is well-suited within this parameter range, and its short computational time makes it highly advantageous compared to employing two-coupled nonlinear Schrödinger equations.33–35 We used the same parameters as in experiments and set the detuning to δ = 0.12. Figure 6(a) shows the measured soliton spectrum, spanning over an impressive 28 THz. The experimental spectrum is in good agreement with the numerical predictions obtained by the FP-LLE, represented in green in Fig. 6(a). As for microresonators,36 the use of a fiber with low GVD and a high nonlinear coefficient enables the generation of broader spectra, compared to those achieved with conventional telecom fibers.3,24 The simulation reveals the generation of a soliton of 80 fs duration [green line in Fig. 6(b)], which agrees with the sech2-envelope fit [yellow lines in Figs. 6(a) and 6(b)].
FIG. 6.

Cavity soliton in the highly nonlinear FFP resonator. (a) Spectral domain. (b) Time domain. Blue line: experiment; green line: simulation; yellow line: sech2 curve fit; and red line: phase matching curve. fZD indicates the frequency of the zero-dispersion wavelength, and fDW indicates the frequency of the DW.

FIG. 6.

Cavity soliton in the highly nonlinear FFP resonator. (a) Spectral domain. (b) Time domain. Blue line: experiment; green line: simulation; yellow line: sech2 curve fit; and red line: phase matching curve. fZD indicates the frequency of the zero-dispersion wavelength, and fDW indicates the frequency of the DW.

Close modal
In addition, an important spectral peak of 15 THz away from the pump is observed. This corresponds to a dispersive wave (DW), also known as Cherenkov radiation, which is emitted by the CS due to the TOD.17,37–41 Indeed, the cavity is pumped only 5 THz away from the zero-dispersion wavelength, allowing for an efficient radiation process. The frequency of the DW with respect to the soliton satisfies the phase matching condition17,37,39 reported in the following equation:
2Lβ36ω3+2Lβ22ω2Dωδ=0.
(2)

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 ΩCS/(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.

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