1. INTRODUCTION

Dissipative Kerr solitons (DKSs) can be self-organized in high-Q Kerr nonlinear cavities based on a double balance of group velocity dispersion (GVD) and Kerr effects, and coherent pumping as well as intra-cavity dissipation [1]. In the frequency domain, the DKS corresponds to a Kerr optical frequency comb with equal frequency spacing. Due to its compactness, high repetition frequency, and good comb coherence, it has been widely used in recent years for applications such as optical communications [2], low-noise microwave generation [3], ranging lidar [4,5], dual-comb spectroscopy [6], etc. DKS was first discovered and applied in fiber rings as an optical buffer [7] and then emerged in various integrated platforms including ${{\rm MgF}_2}$ [8], ${{\rm Si}_3}{{\rm N}_4}$ [9–11], silica [12–15], ${{\rm LiNbO}_3}$ [16,17], AlN [18], etc. These fiber rings, whispering gallery mode (WGM) cavities, or micro-rings usually require anomalous GVD to satisfy the spontaneous four-wave mixing phase matching condition. The DKSs are, to some extent, limited by thermal instability, low conversion efficiency, and low comb energy due to their presence in the red detuned regime of the bistable curve [19]. The material dispersion of most materials is usually normal GVD in the NIR, so additional waveguide dispersion designs are required to meet the anomalous GVD requirements. In the normal dispersion regime, self-organized structures called dark pulses [20,21] exist. These dark pulses follow the upper branch of the bistable curve and have a high duty cycle with high conversion efficiency, which can be seen arising from the interlocking of the bottom oscillations of the up-switching wave (SW) and the down-SW [22]. The bifurcation structure shows that the stable regime of dark pulses decreases with their different orders, which is known as the collapsed snake structure [23]. The platicon with flat-top pulse profiles [24–26], usually regarded as higher-order dark pulses, is accessible at the stable Maxwell point. Due to the absence of modulation instability at low detuning in the normal dispersion regime [27], the excitation of dark pulses needs to be realized by employing avoided mode crossing [28–30], amplitude-modulated optical pumping [31–33], spectral filtering [34], self-injection locking [35], pulsed pumping [36], double-cavity coupled photonic molecules [37,38], or a photonic crystal microcavity [39] in the experiment.

 

Fig. 1. Simulation of SRS-LS formation. (a) Conceptual diagram for the SRS-LS generation in a fiber Fabry–Perot resonator with normal GVD and pulse pumping. (b) Energy level diagram for the SRS. (c) Temporal and (d) spectral evolution of the intra-cavity fields with respect to the detuning $\delta \omega$. The arrows (red, blue, and yellow) correspond to $\delta \omega = {13}\kappa$, ${17.4}\kappa$, and ${18.9}\kappa$, respectively. The up-switching wave (SW) and down-SW are also denoted by black arrows in (c). The red and blue circles in (d) represent the theoretical estimated positions of the dispersive waves. (e) Enlarged view of the SRS-LS region of (c). The white arrows indicate the propagation direction of the bottom oscillation of up-SW. (f) Corresponding temporal waveforms and (g) spectra marked by the arrows in (c) and (d). Purple line in (f): normalized profile of pump pulse. Arrows in (g): red, DWs of platicon; black and blue, primary Stokes and anti-Stokes lights; purple and green, secondary Stokes and anti-Stokes lights.

Download Full Size | PDF

In addition to the Kerr effect in the microcavity, the nonlinear scattering, stimulated Raman scattering (SRS), caused by the delayed response of the molecular vibrations also changes the dynamical properties and spatiotemporal stability of the field. When driven in an anomalous GVD regime, the effect of SRS mainly manifests itself in three ways. First, SRS causes the soliton self-frequency shift [40], i.e., the center of the spectral envelope is shifted away from the pump. Second, SRS can introduce additional Hopf bifurcations, thereby changing the stability of the solitons and leading to breather solitons [41,42]. Third, the cavity with SRS can support the generation of Stokes solitons [43,44]. In contrast, when driven in a normal GVD regime, SRS affects the spatiotemporal stability of the platicon, leading to additional branching in the time domain [45], and the generation of the breather solitons [46] and the Raman solitons [47] (Raman gain region has anomalous GVD). Meanwhile, the SRS can cause the locking of SWs, resulting in the formation of localized structure (LS). Third order dispersion (TOD) can play a similar role, but there are clear differences: the role of TOD is expressed as the modulation of the spectrum, while SRS can introduce additional spectral components; the top oscillation of TOD enabled LS is initiated from the up-SW, while that of SRS enabled LS (SRS-LS) is initiated from the down-SW [48,49]. The effect of TOD has been confirmed in $\rm Si_{3}\rm N_{4}$ microrings [50], FP resonators [51], and fiber rings [52]. However, to the best of our knowledge, the SRS enabled LS is not yet reported and investigated experimentally, due to the lack of suitable experimental parameters designed to effectively enhance the interaction between SRS and Kerr effects in the normal GVD regime.

In this work, we report for the first time the dynamical evolution of the fields under the influence of SRS driven in the normal GVD regime, based on a flexible fiber-based Fabry–Perot (FP) resonator platform. The effect of SRS on the stability of platicons is experimentally investigated, showing clear evidence for the formation of SRS-LS based on the binding of SWs. It is found that the dispersion plays a key role in the generation of SRS-LS—the value of GVD should be in a proper region to simultaneously enable the interaction between the Raman gain and conventional Kerr platicon spectrum. The SRS-LS state features a temporal oscillation and a broadband spectrum benefited from the interplay among four-wave mixing (FWM) and primary and secondary SRS effects. We obtain an SRS-LS comb with a ${-}{30}\;{\rm dB}$ bandwidth of 255 nm covering S $+$ C $+$ L telecommunication bands, and a comb tooth spacing of 3.6787 GHz. The corresponding comb tooth number is greater than 8500, which is much larger than that reported in normal GVD microcavities. The SRS-LS state also exhibits low-noise operation, good long-term stability, and spectral tunability by desynchronization. Our work reveals a novel localized structure of mode-locked combs and is essential to facilitate the fundamental studies of SRS participated Kerr combs.

2. THEORY

Figure 1(a) shows a schematic diagram for the study of SRS-LS in a normal dispersion FP resonator. The SRS-LS can be excited by pulsed pumping at a repetition rate that is an integer multiple of the cavity free spectral range (FSR) [53]. Two nonlinear processes take place in the cavity. One is the SRS [see Fig. 1(b)], where a pump photon is red shifted to produce a Stokes photon with energy $\hbar{\omega _s}$ and release a phonon with energy $\hbar{\Omega _R}$. A wide range of SRS components can be generated due to the broad Raman gain spectrum of silica. The other is the four-wave mixing (FWM) dependent on the Kerr effect. The mutual interaction between FWM and SRS allows the generation of a broadband frequency comb. To simulate the evolution of the internal optical field of the system under the combined effect of SRS, Kerr effect, and normal GVD, we start from the well-known Lugiato–Lefever equation (LLE) with a Raman scattering term and solve the equation using the Runge–Kutta method. The LLE in the FP resonator can be expressed as follows [50,54]:

The SRS term is described by the corresponding time function ${h_R}(\tau)$, given by [55]

The values of these parameters are listed in Appendix A, Table 1.

The intra-cavity field in the simulation is excited by a Gaussian driving pulse ${f_p}(\tau)$, which is defined as exp (${-}{\tau^2}/\tau_p^2$). We set the pulse width 2.5 ps and the peak power 20 W (see Supplement 1, Section 1 for the choice of pump parameters). A desynchronization frequency $\delta {f_{{\rm eo}}} = {2} \times {\rm FSR -}\;{f_{{\rm eo}}} = - {15}\;{\rm kHz}$ is introduced to tune the emission position of dispersive waves (DWs) to reach the Raman gain spectrum. The detuning $\delta \omega$ is scanned linearly from red to blue detuning, i.e., from ${-}{5}\kappa$ to ${25}\kappa$, to drive the cavity through all possible states.

The evolution of the intra-cavity field in the time and frequency domains is shown in Figs. 1(c) and 1(d). Three typical optical states are identified during scanning: the platicon state, intermediate state (IS), and SRS-LS state, and their regions are marked by the dashed lines. When scanning from ${5}\kappa$ to ${17.4}\kappa$, the intra-cavity field experiences a conventional platicon evolution. That is, the up-SW and the down-SW [marked by black arrows in Fig. 1(c)] can stabilize at the corresponding Maxwell points (specific pumping power for each detuning), e.g., the certain positions for $\delta \omega = {13}\kappa$ [marked by the blue dot in the time-domain envelope of the pump pulse; see Fig. 1(f) purple line], where the speed of the SWs can be regarded as almost zero relative to the pump pulse, thereby forming a stable platicon structure. If the SWs are pumped with a pumping power greater (or less) than the Maxwell point, the platicon temporal profile would expand (shrink) until the SWs stabilize at the Maxwell point. As the detuning $\delta \omega$ is gradually increased, the pumping power required at the Maxwell point for each detuning gradually increases, so the platicon temporal profile would become narrow and the corresponding spectrum would gradually broaden [see the platicon region of Figs. 1(c) and 1(d)]. The platicon temporal profile at $\delta \omega = {13}\kappa$ is plotted in Fig. 1(f) (red line), with the trailing tails [marked by red arrows in Fig. 1(f)] at the bottom of the pulse corresponding to the DWs in the two wings (marked by red arrows) of the spectrum in Fig. 1(g) (red line).

As the detuning $\delta \omega$ is increased to ${17.4}\kappa$, a transition of the intra-cavity fields occurs from the platicon state to the intermediate state (IS) as shown in Fig. 1(e). In the time domain, the SRS effect generates an oscillatory feature on the flat-top of the platicon pulse, as shown in Fig. 1(f) (blue line). This oscillatory feature initiates from the down-SW [48] (see Supplement 1, Section 3). As the detuning further increases, the oscillation moves towards the up-SW. The existence of IS is similar to the intermediate process observed in the transition from the platicon to the bright LS induced by TOD (or called zero dispersion solitons) [50,52]. However, in the case of TOD enabled LS, the oscillation is initiated by the up-SW [20] and moves towards the down-SW. In the frequency domain, the primary Stokes (indicated by black arrow) and anti-Stokes (indicated by blue arrow) lights begin to appear and grow in the spectrum, as shown in Fig. 1(g) (blue line).

 

Fig. 2. Experiment of the SRS-LS formation. (a) Photograph of the FP resonator. (b) Image of the reflective film at a facet of ceramic ferrule. (c) Reflection of the cold cavity near 1550 nm. (d) Experimental setup. IM, intensity modulator; PM, phase modulators; $\Phi$, phase shifter; DCF, dispersion compensating fiber; SMF, single mode fiber; EDFA, erbium-doped fiber amplifier; OSO, optical sampling oscilloscope; PD, photodetector; BPF, band-pass filter; OSC, oscilloscope; ESA, electronic spectrum analyzer; OSA, optical spectrum analyzer; PDH, Pound–Drever–Hall. (e) Resonance reflection at a pump tuning speed of 58 GHz/s. Green region: platicon state; gray region: intermediate state (IS); orange region: SRS-LS state. (f) Temporal waveform and (g) spectrum of the initial pump pulse. (h) Temporal waveform and (i) spectrum of the nonlinearly compressed pulse.

Download Full Size | PDF

As the detuning $\delta \omega$ is increased to ${18.9}\kappa$, the intra-cavity fields undergo a transition from the IS to the SRS-LS state, as shown in Fig. 1(e). In the time domain, it can be seen that the DW induced oscillatory feature on the left wing (i.e., the bottom oscillation of the up-SW) is captured by the SRS induced oscillatory feature (i.e., the top oscillation of the down-SW) and changes its propagation direction [denoted by arrows in Fig. 1(e)]. It has been confirmed that such an SRS-LS state cannot be obtained without SRS (see Supplement 1, Section 4). Figure 1(f) exhibits the typical temporal profile of the SRS-LS state (yellow line). In the frequency domain, four-wave mixing (FWM) and high-order Stokes/anti-Stokes processes all interplay with each other, leading to a significant spectral broadening within a very short pump detuning range [45]. The theoretical estimation of DW positions is shown in the red and blue circles in Fig. 1(e) (also see Supplement 1, Section 5). The appearance of secondary Stokes/anti-Stokes peaks, as illustrated in Fig. 1(g) (yellow line, $\delta \omega = {18.9}\kappa$), can be a clear indication on entering the SRS-LS state.

As the detuning value $\delta \omega$ is further increased to ${20.2}\kappa$, the SRS-LS disappears as shown in Fig. 1(e). The corresponding spectral feature is an obvious power drop at the pumping wavelength as shown in Fig. 1(d).

3. EXPERIMENTAL SETUP

The experimental demonstration of the SRS-LS state is performed in a fiber FP resonator with a cavity length of ${\sim}{5}\;{\rm cm}$, as shown in Fig. 2(a). The corresponding FSR is measured to be ${\sim}{1.8393}\;{\rm GHz}$ by using a dual-cavity method [51] (see Supplement 1, Section 6). The cavity is made of a highly nonlinear fiber (Thorlabs HN1550). Two facets of the fiber are fixed in ceramic ferrules, then polished to achieve a surface roughness of 0.5 nm (see Supplement 1, Section 7), and coated with a highly reflective film of 25 pairs of ${{\rm SiO}_2}$ and ${{\rm Ta}_2}{{\rm O}_5}$ [see Fig. 2(b)]. The films can form a Bragg mirror with reflectivity up to 99.6%. The films have a thickness of ${\sim}{7}\;\unicode{x00B5}{\rm m}$ with uniform layers, and the dispersion introduced by the films is negligible compared to the dispersion of the fiber cavity. Additionally, the entire FP resonator is fixed in a homemade copper fixture to control the temperature. Due to the low film absorption and fiber transmission loss (0.9 dB/km), the resonator linewidth is measured to be 19 MHz [see Fig. 2(c)], corresponding to a loaded ${\rm Q}$ factor of ${1} \times {{10}^7}$.

The experimental setup is shown in Fig. 2(d). An electro-optical comb (EO comb) source is used to pump the FP resonator at a repetition rate of 3.6787 GHz (${\sim}{2} \times {\rm FSR}$). The light from the EO comb is first compressed by a dispersion compensation fiber (DCF) to 3.1 ps, measured by a 500 GHz optical sampling oscilloscope (OSO, Alnair Labs EYE-2000C) as shown in Fig. 2(f), and the EO comb spectrum is shown in Fig. 2(g). Then a second nonlinear compression stage is adopted. The light is amplified to 28 dBm by an erbium-doped fiber amplifier (EDFA) and fed to 100 m single mode fiber (SMF) for nonlinear spectral broadening and pulse compression. As shown in Figs. 3(h) and 3(i), the pulse duration is compressed to 2.58 ps with a wider spectrum of 10 nm (10 dB). This stage is important for SRS-LS generation. See Supplement 1, Section 1 for more discussion on the choice of pump pulse parameters. The repetition rate of the pulse ${f_{{\rm eo}}}$ is set to 3.6787 GHz (${\sim}{2} \times {\rm FSR}$) with a desynchronization frequency $\delta {f_{{\rm eo}}} = {2} \times {\rm FSR} - {f_{{\rm eo}}} = - {13}\;{\rm kHz}$. The rate of the generated SRS-LS combs will follow the pump pulse [53]. The average optical power coupled to the FP microcavity is estimated to 23 dBm due to fiber optic connection loss.

 

Fig. 3. Spectrum evolution for the formation of the SRS-LS: (a) Experimental evolution of the spectrum and (b) reflected power versus forward tuning. (c) Experimental evolution of spectrum and (d) reflected power versus backward tuning. (e) Curve of ${D_{{\rm int}}} + \mu {\rm \cdot 2}\pi \;{\cdot}\;\delta {f_{{\rm eo}}}$ profile to calculate the position of DWs. (f) Comb spectra corresponding to the arrows in (c) (red, blue, dark green, light brown, indigo, dark brown, and deep blue lines, correspond to ${-}{836.0}$, ${-}{608.0}$, ${-}{564.2}$, ${-}{555.38}$, ${-}{546.6}$, ${-}{476.4}$, and ${-}{447.2}\;{\rm MHz}$ from top to bottom), and the simulation spectra (yellow and light green), (40 dB vertical offsets). Blue shaded areas show the bandwidth with 10 dB threshold. (g) Simulated temporal profile of an SRS-LS state corresponding to red line in (f). (h) Enlarged individual comb lines near 1660 nm. (i) Beatnote of the SRS-LS comb detected by a 20 GHz PD.

Download Full Size | PDF

The dispersion parameters of the fiber are crucial for observing the SRS-LS. First, the GVD and TOD should be small enough so that DWs can overlap with the Raman gain spectrum and stimulate the interaction of FWM and SRS (see Supplement 1, Section 2 and Visualization 1. Second, it is necessary to ensure that the normal GVD requirement is met both in the pump region and the entire Raman gain region for the generation of SRS-LS. Only a conventional soliton is experimentally observed in a recent work [36], because the anomalous GVD in the Raman gain region could hinder the formation of SRS-LS.

A Mach–Zehnder interferometer is used to characterize the dispersion profile ${D_{\rm int}} = {D_2}\;{\cdot}\;{\mu ^2} + {D_3}\;{\cdot}\;{\mu ^3}$ of the FP resonator by sweeping the position of the resonance mode of the FP resonator. The details can be found in Supplement 1, Section 8. The ${D_2}$ and ${D_3}$ are estimated as ${2}\pi \;{\cdot}\;-\! {28.2}\;{\rm Hz}$ and ${2}\pi \;{\cdot}\;{5.2}\;{\rm mHz}$, respectively.

4. EXPERIMENTAL OBSERVATION OF SRS-LS

To explore the comb evolution of the cavity, the laser frequency is first swept across a resonance mode from the blue-detuned side to the red-detuned side at a high speed of 58 GHz/s. The light power reflected from the FP resonator detected by PD2 is plotted in Fig. 2(e). A step feature can be clearly observed. The intracavity field initially enters a platicon state (green region), characterized by an increase (decrease) in intracavity power (reflected power) with detuning. Subsequently, the intracavity field undergoes a gradual transition (gray region, intermediate state or IS) and finally reaches the SRS-LS state (orange region). In the SRS-LS state, the intracavity power (reflected power) decreases (increases) with the further increase of detuning.

As the platicon and SRS-LS states are generated in the effectively blue-tuned region in a normal GVD microcavity, a pulsed pumping scheme (with a weaker thermal effect) allows us to scan the pump frequency at a very low speed [15]. To effectively record the spectral evolution of the platicon state, IS, and the SRS-LS state, we then adopt a slow detuning speed of 1.7 MHz/s by programmatically varying the laser’s internal PZT voltage and simultaneously use an optical spectrum analyzer (OSA, AQ6370D) to record the spectra and a photodetector (PD2) to record the reflected light power.

The recorded spectrum is shown in Fig. 3(a), where the horizontal axis represents the wavelength, and the vertical axis represents the frequency offset relative to the initial laser frequency calculated from the PZT voltage change. Note that the offset is the absolute offset of the laser frequency, not the offset relative to the resonance mode due to the red shift of the resonance mode with tuning. The initial tuning position is defined as the start position (0 MHz), and forward tuning is performed by decreasing the laser frequency at a tuning rate of 1.7 MHz/s. The output spectra [Fig. 3(a)] are gradually broadened during forward tuning, while the reflected light power [Fig. 3(b)] is gradually reduced, i.e., more pump power is coupled into the cavity. When the detuning exceeds $-650\,\,\rm MHz$, a step feature occurs with a length of 185 MHz, as shown in Fig. 3(b). As mentioned in the Section 2, the presence of secondary anti-Stokes at 1360 nm is treated as a sign of entering the SRS-LS state. According to the analysis in Fig. 1(c), the intracavity state first enters the platicon state but it stops at the SRS-LS state. This is because the response speed of the thermal effect is much faster than the tuning speed; when we visit the spectral state on the step, the resonance mode will move towards the blue side due to the sudden power reduction in the cavity, resulting in only the back edge of the step, i.e., SRS-LS state, being addressed.

To explore the field state of the entire step, a similar backward tuning method [56] is used. First, the laser frequency is tuned to ensure that the cavity outputs the widest SRS-LS comb state [Fig. 3(c)], where the detuning is defined as the same value with the same state in Fig. 3(a). Then, backward tuning is performed, i.e., the laser frequency is increased. Benefiting from the weaker thermal influence during backward tuning [56], the step width increases to 382 MHz as shown in Fig. 3(d). The regions of the SRS-LS state, IS, and platicon state are marked in Fig. 3(c). Three spectra [red, blue, and dark green lines correspond to the arrows in Fig. 3(c)] of the SRS-LS state with different detunings (${-}{836.0}\;{\rm MHz}$, ${-}{608.0}\;{\rm MHz}$, ${-}{564.2}\;{\rm MHz}$) are plotted in the top three lines of Fig. 3(f). The 30 dB bandwidth is 255 nm (1441–1696 nm). We also provide the 10 dB bandwidth to evaluate the spectrum flatness, which is 77.3 nm/95 nm for the two flat wings of red-line spectrum and 67.8 nm/118 nm for the blue-line spectrum, as denoted in blue shaded areas in Fig. 3(f). These spectra cover the range from 1350 nm to 1700 nm with a comb spacing of 3.6787 GHz. The enlarged comb spectrum near 1660 nm is shown in Fig. 3(h).

In the widest SRS-LS comb spectrum [red line in Fig. 3(f)], five peaks (marked by different colored arrows) are identified. These peaks are not caused by the reflectance variations of the mirror coating (see Supplement 1, Section 7). From left to right, these peaks are the secondary anti-Stokes light, the primary anti-Stokes light, dispersive wave 1 (DW1), DW2, and the primary Stokes light. The high power of the secondary anti-Stokes light indicates the power transfer by FWM from the pump and the primary anti-Stokes light. The detection of the secondary Stokes light is limited by the detection range of the OSA (600–1700 nm). The shift of DW1 and DW2 with detuning is marked by dashed lines. Note that the positions of DW2 and the primary Stokes light overlap, which would be separated with backward detuning. The position of DW1 and DW2 can be derived from the formula ${D_{{\rm int}}} + \mu \;{\cdot}\;{2}\pi \;{\cdot}\;\delta {f_{{\rm eo}}} = \;{2}\;{\cdot}\;\gamma \;{\cdot}\;P\;{\cdot}\;{\rm L}\;{\cdot}\;{\rm FSR} - \;\delta \omega$. The predicted position of DWs is marked by green dots in Fig. 3(e) when ${2}\;{\cdot}\;\gamma \;{\cdot}\;P\;{\cdot}\;{\rm L}\;{\cdot}\;{\rm FSR} - \delta \omega = - {6.2}\kappa$, which is consistent with the measured position of DWs in the dark green line in Fig. 3(f). The desynchronization frequency $\delta {f_{{\rm eo}}}$ can provide additional degrees of freedom to tune the spectra, which will be demonstrated in subsequent experiments. The simulation results (yellow and light green lines) show good agreement with the experimental spectra (red and indigo lines) at desynchronization frequency $\delta {f_{{\rm eo}}} = - {15}\;{\rm kHz}$. Furthermore, the maximum conversion efficiency of the SRS-LS state can reach 19% based our simulation. (see Supplement 1, Section 9).

The simulated temporal profile of the widest SRS-LS state [red line in Fig. 3(f)] is shown in Fig. 3(g). The SRS induced strong oscillation can be clearly observed on the top of a flat-top pulse. The locked oscillation period is 74.6 fs corresponding to the Raman gain peak frequency of ${\sim}{13}\;{\rm THz}$. The small ringing tails before and after the pulse are caused by DW2 and DW1. Note that the SRS-LS state is self-stable and can be trapped at a position on the trailing edge of the pump pulse similar to the zero dispersion soliton [50], which distinguishes it from the platicon state in which the SWs depend on the Maxwell point.

The beatnote of this widest SRS-LS comb (red line) is measured directly with a 20 GHz PD, as shown in Fig. 3(i). It can be observed that there only exist a repetition frequency of 3.6787 GHz and its harmonics, indicating that all the comb lines in the SRS-LS spectrum belong to the same mode family, which is different from the Stokes soliton [44]. This result supports our analysis that the DWs of the platicon act as seeds and are amplified by the gain of SRS, and finally the broadband SRS-LS comb is generated by the mutual interaction of FWM and SRS. Note that ps pulse pumping suppresses stimulated Brillouin scattering without generating any additional signals near the third harmonic of ${\sim}{11.0}\;{\rm GHz}$, distinct from Brillouin combs [57,58].

The spectrum of the IS shown in the light brown line (${-}{555.8}\;{\rm MHz}$) exhibits weak primary Stokes and anti-Stokes light. The spectra of the platicon state at different detuning values (${-}{546.6}\;{\rm MHz}$, ${-}{476.4}\;{\rm MHz}$, ${-}{447.2}\;{\rm MHz}$) are also plotted in the bottom three lines (indigo, dark brown, and deep blue) in Fig. 3(f). With the backward detuning, the spectral width (span between two DWs) of platicon combs varies from 170 nm to 100 nm experimentally.

5. CHARACTERISTICS OF PLATICON AND SRS-LS COMBS

To confirm the low-noise operation of platicon and SRS-LS states, we measure their noise performance. The combs are first amplified by an EDFA, and then a portion of the combs near 1520 nm is filtered out by a band-pass filter (40 nm bandwidth). The beatnotes of the filtered combs are measured by a high-speed PD (FINISAR 40 GHz). The RF spectra of the beating signals of SRS-LS (red line) and platicon (indigo) are shown in Fig. 4(a). A noise increase within 10 MHz offset can be observed in the SRS-LS beatnote. This reduces the signal-to-noise ratio (SNR) to 35.5 dB, while the SNR of the platicon is 43.7 dB. The phase noise spectra are shown in Fig. 4(b). At 2.5 MHz offset, the SRS-LS exhibits a ${\sim}{8}\;{\rm dB}$ higher noise bump (denoted by a red arrow) compared to the platicon, which is consistent with the SNR difference observed in Fig. 4(a). For the offset frequency below 20 kHz, the noise levels of SRS-LS are ${-}{86}\;{{\rm dBc \cdot Hz}^{- 1}}$ at 1 kHz and ${-}{105}\;{{\rm dBc\cdot Hz}^{- 1}}$ at 10 kHz, degraded by ${\sim}{4}\;{\rm dB}$ compared to the platicon. However, the noise level of SRS-LS is still comparable to our recent work on the solitons in a near zero dispersion FP cavity [51] as well as other platicon works in silicon nitride microresonators [33]. The low-frequency noise of different SRS-LS and platicon states are also measured by an APD (bandwidth 200 MHz) and electrical spectrum analyzer, as shown in Fig. 4(c). The colored lines correspond to the comb states with the same color (top three and bottom three) in Fig. 3(f). It can be seen that the noise slightly increases in the SRS-LS states; the noise is attributed to the noise introduced by the Raman amplification [59].

 

Fig. 4. Characteristics of the optical frequency combs. (a) Beatnote signals ($f - {3.6787}\;{\rm GHz}$) of platicon (indigo) and SRS-LS (red) near 1520 nm (resolution bandwidth 100 kHz). (b) Phase noise spectra of platicon (indigo), SRS-LS (red), and pump light (yellow); local oscillator (LO) (green). (c) Low-frequency noise of different spectra (Lines 1–6 correspond to the same color spectra in Fig. 3(f) (top three and bottom three lines)). Inset: a zoomed view of the spectra below 15 MHz. (d) Spectral tunability versus different $\delta {f_{{\rm eo}}}$. (e) Experimental (red) and simulated (blue) spectra at $\delta {f_{{\rm eo}}} = {180}\;{\rm kHz}$. (f) Measured long-term spectral stability with PDH locking.

Download Full Size | PDF

The platicon spectrum can be tuned experimentally by the desynchronization frequency $\delta {f_{{\rm eo}}}$. In the experiments, the pump repetition frequency is fixed, and the cavity FSR is finely tuned by changing the cavity temperature. The changing spectra at different $\delta {f_{{\rm eo}}}$ are plotted in Fig. 4(d). The frequency combs exist in the range of $\delta {f_{{\rm eo}}}$ from ${-}{270}$ to 270 kHz. When $\delta {f_{{\rm eo}}}$ is positive, the spectra are shifted towards the short wavelength (e.g., span: 1400 nm ${\sim}\;{1600}\;{\rm nm}$ at $\delta {f_{\rm eo}} = \;{180}\;{\rm kHz}$). When $\delta {f_{{\rm eo}}}$ is negative, the spectra are shifted towards the long wavelength (e.g., span: ${1500}\;{\rm nm}\;\sim\;{1700}\;{\rm nm}$ at $\delta {f_{{\rm eo}}}\; = -{180}\;{\rm kHz}$), and the maximum wavelength tuning range is up to 100 nm. The simulated spectrum shows a good agreement with the experimental result at $\delta {f_{{\rm eo}}} = {180}\;{\rm kHz}$, as shown in Fig. 4(e).

The long-term stability of the SRS-LS combs is crucial for practical application scenarios. Switching between the platicon state and SRS-LS state causes a dip (i.e., IS) in the soliton step of reflected light power [marked by the gray region in Fig. 2(e)], which allows the Pound–Drever–Hall (PDH) technique to be used to stabilize the frequency at a fixed detuning relative to the resonant mode. A digital laser locking module (TOPTICA DigiLock110) is used to modulate the laser current to generate sidebands, and the reflected light is sent to the module to generate an error signal to lock the detuning. When unlocked, the comb typically loses its state after a few minutes due to the environmental perturbation even though it is thermally stable. Once locked, the comb can be stable for more than 6 h, as shown in Fig. 4(f).

6. CONCLUSION

In summary, we report the first direct experimental observation of an SRS-LS state based on a fiber FP resonator platform made of low normal GVD fiber. This SRS-LS state has a featured oscillation locked to the down-SW in the time domain and a broadband SRS enabled comb spectrum in the frequency domain. Experimentally, we have obtained a SRS-LS comb with a repetition rate of ${\sim}{3.68}\;{\rm GHz}$, a spectral width of 255 nm, and a comb line number ${\gt}{8500}$. Compared with the conventional platicon, the SRS-LS combs show excellent performance in terms of bandwidth and comb line number (see Supplement 1, Section 10). The rich dynamics of field evolution under the mutual interaction of FWM, SRS, and dispersion is revealed both in simulation and in experiment. The low-noise property, spectral tunability, and long-term operation are also demonstrated. Our work facilitates the fundamental studies of SRS participated Kerr comb evolution as well as paves a way for a novel stable and tunable optical frequency comb source for wide applications.

APPENDIX A: PARAMETER VALUES

In the Table 1, we provide all the parameters that are measured in the experiment and used in simulation. These parameters include the GVD coefficient ${D_2}$, TOD coefficient ${D_3}$, nonlinear coefficient $\gamma$, cavity linewidth $\kappa /{2}\pi$, peak power of the pump pulse ${P_0}$, pump pulse width ${\tau_p}$, desynchronization frequency $\delta {f_{{\rm eo}}}$, vibration damping times ${\tau_1}$, ${\tau_2}$, and the contribution coefficient of Raman response ${f_R}$. 

Table 1. Values of Parameters Measured in the Experiment and Used in the Simulation

View Table

Funding

National Natural Science Foundation of China (61922056).

Acknowledgment

Author contributions: K.W. led this work. Under the supervision of K.W., T.L. performed the fabrication of the high Q normal dispersion FP resonator, conducted the simulations, experiments, and analyzed the data. X.Z. and M.C. conducted the characterization of the resonator. K.W., T.L., and J.C. contributed to the preparation and revision of the manuscript.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Supplemental document

See Supplement 1 for supporting content.

REFERENCES

1. T. J. Kippenberg, A. L. Gaeta, M. Lipson, et al., “Dissipative Kerr solitons in optical microresonators,” Science 361, eaan8083 (2018). [CrossRef]  

2. P. Marin-Palomo, J. N. Kemal, M. Karpov, et al., “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017). [CrossRef]  

3. W. Liang, D. Eliyahu, V. S. Ilchenko, et al., “High spectral purity Kerr frequency comb radio frequency photonic oscillator,” Nat. Commun. 6, 7957 (2015). [CrossRef]  

4. P. Trocha, M. Karpov, D. Ganin, et al., “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359, 887–891 (2018). [CrossRef]  

5. J. Wang, Z. Lu, W. Wang, et al., “Long-distance ranging with high precision using a soliton microcomb,” Photon. Res. 8, 1964–1972 (2020). [CrossRef]  

6. A. Dutt, C. Joshi, X. Ji, et al., “On-chip dual-comb source for spectroscopy,” Sci. Adv. 4, e1701858 (2018). [CrossRef]  

7. F. Leo, S. Coen, P. Kockaert, et al., “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4, 471–476 (2010). [CrossRef]  

8. T. Herr, V. Brasch, J. D. Jost, et al., “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2013). [CrossRef]  

9. M. H. Anderson, R. Bouchand, J. Liu, et al., “Photonic chip-based resonant supercontinuum via pulse-driven Kerr microresonator solitons,” Optica 8, 771–779 (2021). [CrossRef]  

10. X. Wang, P. Xie, W. Wang, et al., “Program-controlled single soliton microcomb source,” Photon. Res. 9, 66–72 (2021). [CrossRef]  

11. S. Wan, R. Niu, Z.-Y. Wang, et al., “Frequency stabilization and tuning of breathing solitons in Si₃N₄ microresonators,” Photon. Res. 8, 1342–1349 (2020). [CrossRef]  

12. C. Qin, K. Jia, Q. Li, et al., “Electrically controllable laser frequency combs in graphene-fibre microresonators,” Light Sci. Appl. 9, 185 (2020). [CrossRef]  

13. X. Yi, Q.-F. Yang, K. Y. Yang, et al., “Soliton frequency comb at microwave rates in a high-Q silica microresonator,” Optica 2, 1078–1085 (2015). [CrossRef]  

14. L. Yao, P. Liu, H.-J. Chen, et al., “Soliton microwave oscillators using oversized billion Q optical microresonators,” Optica 9, 561–564 (2022). [CrossRef]  

15. E. Obrzud, S. Lecomte, and T. Herr, “Temporal solitons in microresonators driven by optical pulses,” Nat. Photonics 11, 600–607 (2017). [CrossRef]  

16. Z. Gong, X. Liu, Y. Xu, et al., “Near-octave lithium niobate soliton microcomb,” Optica 7, 1275–1278 (2020). [CrossRef]  

17. Y. He, Q.-F. Yang, J. Ling, et al., “Self-starting bi-chromatic LiNbO₃ soliton microcomb,” Optica 6, 1138–1144 (2019). [CrossRef]  

18. H. Weng, J. Liu, A. A. Afridi, et al., “Directly accessing octave-spanning dissipative Kerr soliton frequency combs in an AlN microresonator,” Photon. Res. 9, 1351–1357 (2021). [CrossRef]  

19. J. Li, C. Bao, Q.-X. Ji, et al., “Efficiency of pulse pumped soliton microcombs,” Optica 9, 231–239 (2022). [CrossRef]  

20. P. Parra-Rivas, D. Gomila, and L. Gelens, “Coexistence of stable dark- and bright-soliton Kerr combs in normal-dispersion resonators,” Phys. Rev. A 95, 053863 (2017). [CrossRef]  

21. P. Parra-Rivas, E. Knobloch, D. Gomila, et al., “Dark solitons in the Lugiato-Lefever equation with normal dispersion,” Phys. Rev. A 93, 063839 (2016). [CrossRef]  

22. J. Lottes, G. Biondini, and S. Trillo, “Excitation of switching waves in normally dispersive Kerr cavities,” Opt. Lett. 46, 2481–2484 (2021). [CrossRef]  

23. P. Parra-Rivas, D. Gomila, E. Knobloch, et al., “Origin and stability of dark pulse Kerr combs in normal dispersion resonators,” Opt. Lett. 41, 2402–2405 (2016). [CrossRef]  

24. V. E. Lobanov, A. V. Cherenkov, A. E. Shitikov, et al., “Dynamics of platicons due to third-order dispersion,” Eur. Phys. J. D 71, 185 (2017). [CrossRef]  

25. V. E. Lobanov, G. Lihachev, T. J. Kippenberg, et al., “Frequency combs and platicons in optical microresonators with normal GVD,” Opt. Express 23, 7713–7721 (2015). [CrossRef]  

26. V. E. Lobanov, G. Lihachev, and M. L. Gorodetsky, “Generation of platicons and frequency combs in optical microresonators with normal GVD by modulated pump,” Europhys. Lett. 112, 54008 (2015). [CrossRef]  

27. C. Godey, I. V. Balakireva, A. Coillet, et al., “Stability analysis of the spatiotemporal Lugiato-Lefever model for Kerr optical frequency combs in the anomalous and normal dispersion regimes,” Phys. Rev. A 89, 063814 (2014). [CrossRef]  

28. Y. Liu, Y. Xuan, X. Xue, et al., “Investigation of mode coupling in normal-dispersion silicon nitride microresonators for Kerr frequency comb generation,” Optica 1, 137–144 (2014). [CrossRef]  

29. S. W. Huang, H. Zhou, J. Yang, et al., “Mode-locked ultrashort pulse generation from on-chip normal dispersion microresonators,” Phys. Rev. Lett. 114, 053901 (2015). [CrossRef]  

30. C. Bao, Y. Xuan, C. Wang, et al., “Observation of breathing dark pulses in normal dispersion optical microresonators,” Phys. Rev. Lett. 121, 257401 (2018). [CrossRef]  

31. V. E. Lobanov, N. M. Kondratiev, A. E. Shitikov, et al., “Generation and dynamics of solitonic pulses due to pump amplitude modulation at normal group-velocity dispersion,” Phys. Rev. A 100, 013807 (2019). [CrossRef]  

32. V. E. Lobanov, A. E. Shitikov, R. R. Galiev, et al., “Generation of vector flat-top solitons and hybrid bright--flat-top soliton complexes in optical microresonators via modulated pump,” Phys. Rev. A 104, 063511 (2021). [CrossRef]  

33. H. Liu, S.-W. Huang, W. Wang, et al., “Stimulated generation of deterministic platicon frequency microcombs,” Photon. Res. 10, 1877–1885 (2022). [CrossRef]  

34. C. Spiess, Q. Yang, X. Dong, et al., “Chirped dissipative solitons in driven optical resonators,” Optica 8, 861–869 (2021). [CrossRef]  

35. G. Lihachev, W. Weng, J. Liu, et al., “Platicon microcomb generation using laser self-injection locking,” Nat. Commun. 13, 1771 (2022). [CrossRef]  

36. Y. Xu, A. Sharples, J. Fatome, et al., “Frequency comb generation in a pulse-pumped normal dispersion Kerr mini-resonator,” Opt. Lett. 46, 512–515 (2021). [CrossRef]  

37. Ó. B. Helgason, F. R. Arteaga-Sierra, Z. Ye, et al., “Dissipative solitons in photonic molecules,” Nat. Photonics 15, 305–310 (2021). [CrossRef]  

38. B. Y. Kim, Y. Okawachi, J. K. Jang, et al., “Turn-key, high-efficiency Kerr comb source,” Opt. Lett. 44, 4475–4478 (2019). [CrossRef]  

39. S.-P. Yu, E. Lucas, J. Zang, et al., “A continuum of bright and dark-pulse states in a photonic-crystal resonator,” Nat. Commun. 13, 3134 (2022). [CrossRef]  

40. X. Yi, Q.-F. Yang, K. Y. Yang, et al., “Theory and measurement of the soliton self-frequency shift and efficiency in optical microcavities,” Opt. Lett. 41, 3419–3422 (2016). [CrossRef]  

41. Y. Wang, M. Anderson, S. Coen, et al., “Stimulated Raman scattering imposes fundamental limits to the duration and bandwidth of temporal cavity solitons,” Phys. Rev. Lett. 120, 053902 (2018). [CrossRef]  

42. W. Chen, B. Garbin, A. U. Nielsen, et al., “Experimental observations of breathing Kerr temporal cavity solitons at large detunings,” Opt. Lett. 43, 3674–3677 (2018). [CrossRef]  

43. T. Tan, Z. Yuan, H. Zhang, et al., “Multispecies and individual gas molecule detection using Stokes solitons in a graphene over-modal microresonator,” Nat. Commun. 12, 6716 (2021). [CrossRef]  

44. Q.-F. Yang, X. Yi, K. Y. Yang, et al., “Stokes solitons in optical microcavities,” Nat. Phys. 13, 53–57 (2016). [CrossRef]  

45. A. V. Cherenkov, N. M. Kondratiev, V. E. Lobanov, et al., “Raman-Kerr frequency combs in microresonators with normal dispersion,” Opt. Express 25, 31148–31158 (2017). [CrossRef]  

46. S. Yao, C. Bao, P. Wang, et al., “Generation of stable and breathing flat-top solitons via Raman assisted four wave mixing in microresonators,” Phys. Rev. A 101, 023833 (2020). [CrossRef]  

47. Z. Li, Y. Xu, S. Shamailov, et al., “Ultrashort dissipative Raman solitons in Kerr resonators driven with phase-coherent optical pulses,” arXiv, arXiv:2212.08223 (2022). [CrossRef]  

48. P. Parra-Rivas, S. Coulibaly, M. G. Clerc, et al., “Influence of stimulated Raman scattering on Kerr domain walls and localized structures,” Phys. Rev. A 103, 013507 (2021). [CrossRef]  

49. M. G. Clerc, S. Coulibaly, and M. Tlidi, “Time-delayed nonlocal response inducing traveling temporal localized structures,” Phys. Rev. Res. 2, 013024 (2020). [CrossRef]  

50. M. H. Anderson, W. Weng, G. Lihachev, et al., “Zero dispersion Kerr solitons in optical microresonators,” Nat. Commun. 13, 4764 (2022). [CrossRef]  

51. Z. Xiao, T. Li, M. Cai, et al., “Near-zero-dispersion soliton and broadband modulational instability Kerr microcombs in anomalous dispersion,” Light Sci. Appl. 12, 33 (2023). [CrossRef]  

52. Z. Li, Y. Xu, S. Coen, et al., “Experimental observations of bright dissipative cavity solitons and their collapsed snaking in a Kerr resonator with normal dispersion driving,” Optica 7, 1195–1203 (2020). [CrossRef]  

53. Y. Xu, Y. Lin, A. Nielsen, et al., “Harmonic and rational harmonic driving of microresonator soliton frequency combs,” Optica 7, 940–946 (2020). [CrossRef]  

54. D. C. Cole, A. Gatti, S. B. Papp, et al., “Theory of Kerr frequency combs in Fabry-Perot resonators,” Phys. Rev. A 98, 013831 (2018). [CrossRef]  

55. Q. Lin and G. P. Agrawal, “Raman response function for silica fibers,” Opt. Lett. 31, 3086–3088 (2006). [CrossRef]  

56. H. Guo, M. Karpov, E. Lucas, et al., “Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators,” Nat. Phys. 13, 94–102 (2016). [CrossRef]  

57. C. Qin, J. Du, T. Tan, et al., “Co-generation of orthogonal soliton pair in a monolithic fiber resonator with mechanical tunability,” Laser Photon. Rev. 17, 2200662 (2023). [CrossRef]  

58. H. Zhang, T. Tan, H.-J. Chen, et al., “Soliton microcombs multiplexing using intracavity-stimulated Brillouin lasers,” Phys. Rev. Lett. 130, 153802 (2023). [CrossRef]  

59. M. Yu, Y. Okawachi, R. Cheng, et al., “Raman lasing and soliton mode-locking in lithium niobate microresonators,” Light Sci. Appl. 9, 9 (2020). [CrossRef]