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Abstract
Realtime spectroscopy access to ultrafast fiber lasers provides new opportunities for exploring complex soliton interaction dynamics. In this study, we employ a time-stretch technique that enables real-time access to both spectral and temporal dynamics, revealing rich nonlinear processes in asynchronous dual wavelength mode-locked pulses in an ultrafast fiber laser. Due to the different group velocities of the two wavelengths, the mode-locked solitons centered at different wavelengths periodically collide with each other. We recorded the entire process of soliton establishment, stabilization, and disappearance, shedding light on the mystery of stable transmission of dual-wavelength mode-locked pulses. These processes were observed for the first time in an ultrafast fiber laser, and the experimental evidence provides important insights into the understanding of nonlinear dynamics in fiber lasers, as well as the potential for improving laser performance for application in dual-comb spectroscopy.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Since the advent of fiber optic technology in the 1960s, ultrafast fiber lasers have emerged as highly efficient pulsed sources in numerous fields, including fiber optic sensing [1] and optical communications [2]. Mode-locked devices have enabled the production of various types of soliton pulses in fiber lasers, such as conventional solitons [3], dissipative solitons [4–6], and harmonic mode-locked pulses [7]. Dual-wavelength mode-locked fiber lasers, a member of the ultrafast fiber laser family, are increasingly gaining attention due to their utility in ultra-high-capacity optical communication systems, as well as their widespread use in spectroscopy, phased-array antennas, and microwave generation. Double soliton pulses obtained from dual wavelength mode-locked fiber lasers have found versatile applications, such as microwave/millimeter-wave signal generation [8], and phased array antennas [9].
Dual-wavelength mode-locked fiber lasers can be categorized into synchronous and asynchronous modes, depending on whether or not the output pulse sequences are synchronous. Due to the presence of dispersion in the cavity, fiber lasers exhibit slightly different repetition frequencies for different wavelength pulses, resulting in two pulse trains on the oscilloscope and two stable peaks on the spectrometer, which are known as asynchronous dual-wavelength mode-locked pulses [10–12]. Synchronous mode-locked fiber lasers are typically constructed using a shared cavity structure or a common saturable absorber in two separate fiber lasers, resulting in synchronous mode-locked pulse output. However, the synchronization produced by this method is closely linked to the cavity length of the fiber laser, causing poor stability of the output synchronized dual-wavelength pulses. On the other hand, the frequency difference between asynchronous dual-wavelength mode-locked pulses is relatively stable and consistent, making it an attractive low-complexity alternative to the stability of dual-optical frequency comb systems. As such, this has become one of the current research hotspots in the field of fiber lasers [13].
In order to understanding the soliton transient dynamic more clearly, a new technology known as the dispersive Fourier transform (DFT) has been invented [14]. With the help of this technique, soliton explosions [15], rogue waves [16], soliton pulsation [17], soliton molecule complexes [18] and deterministic chaos [19] has been researched. The purpose of exploring the soliton transient dynamics is to study the output state of the pulse and to control the output of the laser. Therefore, it is important to investigate the soliton transient dynamic.
In this study, we conducted an experiment using an Er-doped fiber (EDF) laser that was mode locked by single-wall carbon nanotubes (SWCNTs) saturable absorber (SA). Through the use of homemade adjustable attenuation, we successfully obtained asynchronous dual wavelengths at approximately 1530 nm and 1560 nm. To the best of our knowledge, this is the first time that the whole dynamics of asynchronous dual-wavelength have been experimentally investigated in detail using the DFT technique. Our investigation revealed a wealth of dynamics resulting from soliton interactions, which is worthy of further exploration.
2. Experimental setup
Figure 1 consists of two parts: Fig. 1(a), which depicts the asynchronous dual-wavelength mode-locked fiber laser, and Fig. 1(b), which illustrates the DFT measurement device. The total cavity length of the mode-locked fiber laser is ∼7.4 m and includes several components such as a SWCNT-based mode locker, a 0.35 m-long Erbium-doped fiber (EDF), a wavelength-division-multiplexed coupler (WDM), an optical coupler, a polarization-independent isolator (PI-ISO), a homemade tunable attenuator, and a polarization controller (PC). Figure 2(a) shows the curve of the transmittance vs the light intensity of the SA. The modulation depth and the saturation power of SA were estimated to 25.4% and 455 MW/cm2, respectively. To ensure unidirectional operation, the PI-ISO is utilized. The PC is used to optimize the mode-locking performance by adjusting the cavity linear birefringence. As shown in Fig. 2(b), the tunable attenuation structure is achieved using two collimators, wherein the tilt of the collimator adjusts the cavity loss.
As depicted in Fig. 1(b), the laser output was split into two ports using an optical coupler. One port, which was undispersed, was used to measure the instantaneous intensity (I(t)) and other properties of the output pulse. Measurements were taken using a real-time oscilloscope (Tektronix DPO70604C, 6 GHz) for signals and an optical spectrum analyzer (OSA, Yokogawa AQ6370C) for spectra. The other port was temporally stretched using a dispersion fiber (∼10 km in our experiments) to record its pulse spectrum in real-time via DFT analysis of the stretched temporal waveform. The dispersive fiber is normal fiber. The SMF-28 fiber was used in our experiment with a dispersion of 16.7 ps/(nm·km) at 1560 nm. An optical chopper between the LD and WDM allowed us to capture various fast laser dynamics by controlling the pump on/off continuously.
3. Experimental results
The combination of intracavity birefringence and polarization-dependent loss is well-known to generate the spectral filter effect [20]. The combination of the two acts like a tunable spectral filter. By adjusting the polarization controller and the pump power, the peak position of spectrum, free spectral range, the bandwidth and the intensity of the spectrum of the spectral filter can be changed. When the free spectral range is smaller than the spectrum range of the gain fiber, dual wavelength operates. By virtue of the saturable absorption of the SWCNT, the self-mode-locking operation could be easily achieved by adjusting intracavity loss and PC. The stable asynchronous dual-wavelength mode-locked state was summarized in Fig. 3.
Fig. 3. Characteristics of dual wavelength mode-locked pulse. (a) Spectrum; (b) The pulse trains; (c) RF spectrum; (d) Autocorrelation curve.
The spectrum of the dual-wavelength mode-locked state at a pump power of 151 mW was shown in Fig. 3(a), where the two wavelengths were estimated to be ∼1531.5 nm and ∼1556.8 nm, respectively. Figure 3(b) presented two sets of pulse trains with different intensities. Upon closer examination of the pulse trains in Fig. 3(c), it was found that the pulse train with higher intensity was at ∼1556.8 nm, while the other one was at ∼1531.5 nm. When using an oscilloscope for real-time observation, the pulse with lower intensity in two sets of pulses was constantly shifting, resulting in a brief synchronization process experienced by both pulse sequences. The measured RF spectrum of the pulse trains was shown in Fig. 3(c), wherein there were two peaks with an interval of ∼1893.4 Hz. Due to the group velocity dispersion of the fiber cavity, the repetition rates of the pulse trains at two wavelengths are slightly different. The autocorrelation trace recorded in this state showed that the pulse duration was ∼731.4 fs, as depicted in Fig. 3(d).
To analyze the evolution of asynchronous dual-wavelength pulses, we segmented the DFT record time series and redraw it as a spectra temporal picture. This allows us to analyze the whole dynamic evolution of the asynchronous dual-wavelength mode-locking. To generate an asynchronous dual-wavelength mode-locked pulse, the pump power was set to 215 mW, and the appropriate position of the polarization controllers was adjusted. The chopper was used to control the establishment and disappearance of the mode-locking, and the oscilloscope was triggered to record the transient signal. After visualizing the collected data, we obtained the spectral dynamics of the asynchronous dual-wavelength.
Figure 4(a) illustrated the spectral evolution during the establishment phase over ∼8000 round trips. The horizontal axis represented wavelength in Fig. 4(a), which mapped pulse frequency domain information to the time domain. As a result, Fig. 4(a) could represent the spectral evolution of the two solitons. Following the Wiener-Khinchin theorem, the obtained spectral data were Fourier transformed to obtain the field autocorrelation trajectory (8000 round trips in the establishment phase), as shown in Fig. 4(b). The measured DFT data in Fig. 4 revealed significant changes before a static dual-wavelength mode-locked pulse is formed. Figure 4(a) showed a period of relaxation oscillation when the cavity energy was insufficient to establish the locking mode. During the relaxation oscillation, a laser peak existed, and it was noteworthy that the position of the laser peak does not jump; all laser peaks appeared at the same time position. After the relaxation oscillation phase, a clear spectral extension was observed due to laser peak broadening at the same time position. A change in pulse shape was observed in Fig. 4(a), accompanied by the appearance of a distinct Kelley sideband, which was typical of conventional solitons. However, The Kelley sidebands were not stable, as indicated by the brightness of the spectral evolution in Fig. 4(a), and the single pulse state only lasted for 400 round trips. Modulation behavior of the spectrum became clear in the subsequent round trip.
Fig. 4. Dual-wavelength mode-locked pulse formation from noise. (a) The real-time spectra evolution measured via TS-DFT; (b) The field autocorrelation traces calculated via the Fourier transform of each single-shot spectra in (a) (black line: pulse energy); (c-d) Close-ups of the area in (a) and (b); (e–g) Repeated measurements show that the formation dynamics of dual-wavelength mode-locked pulse can be considerably different.
The modulated spectra changed in each roundtrip, indicating the existence of soliton interactions within the cavity. This method has been used to study the evolving separation between bound solitons [21] and captures the transient ordering of incoherent dissipative solitons [22]. The first-order (field) autocorrelation can reveal these interactions. It should be noted that if the number of pulses is “n,” then the corresponding field autocorrelation trace will have 2n-1 peaks. The field autocorrelation traces confirmed the intracavity status of double solitons at ∼2880th round trips, as the single peak was transformed into three peaks. Figure 4(e) and Fig. 4(f), obtained by zooming in on regions A and B, respectively, allowed us to judge the intracavity state as a double soliton at this time, in which the two generated solitons interact intensively for ∼120 round trips. At around the 3000th round trip, spectral modulation ended, indicating the end of soliton interactions, leaving only the most intense pulse for the following spectral variation. Next, the intracavity state switched back and forth between double solitons and single soliton. At around the 4600th round trip, the behavior of double solitons appeared to have a more distinct tendency to evolve, as seen in the field autocorrelation trajectory during this time, where the change from single to triple peaks was more clearly observed. By zooming in on regions C and D, we obtained Fig. 4(c) and Fig. 4(d), respectively, which represented the last double pulses of the establishment phase in the cavity. This region was the best choice for a closer look at the process, where the double solitons were present for a long time.
Figure 4(d) provided a clearer observation of the process of mutual attraction and distancing of two solitons. The solitons attracted each other (decreasing in separation) and excluded each other (increasing in separation), which lasted for ∼500 round trips. Two spectrally broadened solitons briefly appeared at around the 4870th round trip. However, since the state had not yet reached a stable level at this point, one of the solitons obliterated, and the single soliton (conventional soliton) state was restored, lasting for ∼250 round trips. At the 5500th round trip, a pulse appeared at another time position, which was not yet broadened and had unstable energy. It was not until approximately the 6800th round trip that the spectrum of the newly emerged pulse started to broaden, the Kelly sideband energy of the conventional soliton decreased, and the double pulse state in the cavity stabilizes. Similarly, we could observe the variation of the autocorrelation trace in Fig. 4(b). For a closer examination of the details in the field autocorrelation trace, refer to Fig. 4(g), which covered the 5500th round trip to the 8000th round trip. At this stage, the two pulses were separated by a significant distance, resulting in the observation of only one peak in the field correlation trace instead of three.
To study the energy evolution, we integrated the measured spectra over the complete spectra band, as shown in Fig. 4(b) (black line). As expected, the energy decreased after the cavity state was stabilized, indicating the presence of energy overshoots in the cavity. Energy overshoot refers to the occurrence of a signal exceeding its final value and is a common phenomenon in signal processing, electronics, and mathematics. In optics, energy overshoot occurs during the build-up of mode locking, where the energy increases to a maximum value before decreasing to a steady value [23]. The energy overshoot was characteristic of the mode-locking transition, which could be observed in conjunction with Fig. 4(a), where the energy increased abruptly at mode locking. Subsequently, there was also a very pronounced energy change at soliton interactions. Finally, at the end of the build-up phase, the energy was stabilized.
Soliton interactions could be altered by varying the initial conditions, resulting in diverse scenarios during the transient process. However, the generated final pulse state remained a fixed point, which was typical of many nonlinear systems. Exploring these interactions was crucial, and to achieve this, we repeated measurements several times by turning the pump power on and off to regenerate the same dual-wavelength pulse obtained in Supplement 1. Interestingly, the formation dynamics exhibited diversity because the initial conditions changed randomly for each measurement. Although the resulting processes were not identical due to the random variation in initial conditions, soliton interactions could still be observed during the establishment of the soliton, similar to the formation process presented in Fig. 4(a). We performed several repetitions of the establishment process, demonstrating that the formation of the dual-wavelength mode-locked pulse was not an accidental process but rather the ultimate result of soliton interactions.
Since different wavelengths have different group velocities, the dual-wavelength mode-locked solitons would periodically collide with each other. Figure 5 shows the pulse sequence of dual-wavelength pulses in long-range pulse train. Because dual-wavelength pulses undergo periodic collisions every 0.53 ms, the pulse intensity experiences periodic enhancement. The collision period could be calculated by $\varDelta \tau = 1/\varDelta f$, where $\varDelta f$ was the difference of the two fundamental repetition rates at two wavelengths. Then the collision period was calculated to be ∼0.528 ms, which is almost the same as 0.53 ms shown in Fig. 5. Since the resolution of the RF instrument is different from that of the oscilloscope, the calculated results have some errors.
Soliton collisions were investigated by recording pulse trains throughout the entire process using an oscilloscope and analyzing them via the DFT, as depicted in Fig. 6. Multiple representative round trips obtained via DFT were presented in Fig. 6(c) to illustrate the spectral evolution of the two solitons more effectively. Additionally, Fig. 6(a) provided a real-time representation of the complete soliton collision process by showing the dynamic evolution of ∼4000 round trips before and after the collision. Figure 6(b) displayed the field autocorrelation trace along with the corresponding variation in energy, represented by the black line. Soliton interaction would be reflected in changes to the spectral evolution and energy variation of a single round-trip pulse. However, the spectrum remained largely unchanged during the soliton collision, as indicated by Fig. 6(a). Furthermore, Fig. 6(c) presented the pulses of multiple representative round trips to provide a clearer illustration of the spectral evolution during the soliton collision process. These findings indicated that no energy exchange occurred during the soliton collision. When the solitons centered at two wavelengths transmitted in the cavity, the periodic collisions occurred because of different group velocities. The collision causes a temporary superposition of the soliton energy. Real-time spectral monitoring indicates that each wavelength has a different energy after colliding and no energy exchange occurs, as shown in Fig. 6(b). Therefore, the pulse energy produces periodic perturbations. Instead, the collision process involved the superposition of the energy of the two solitons, as shown by the black line in Fig. 6(b).
Fig. 6. Dual-wavelength mode-locking operation. (a) Stretched pulse evolution after the DFT process; (b) The field autocorrelation traces calculated via the Fourier transform of each single-shot spectrum in (a) (black line: pulse energy); (c) Several typical round-trips during the soliton collision process.
The observation and analysis of the real-time dynamic evolution of the dual-wavelength mode-locked pulse was crucial for understanding the transition from mode-locking to noise. We recorded this transition in ∼6500 round trips using DFT, as depicted in Fig. 7(a). Prior to the transition from mode-locking to noise, we observed a stable soliton collision, indicating that the collision was maintained at a stable level. However, at the 3800th round trip, the small pulse spectrum abruptly stopped broadening, resulting in a transfer of energy to the main pulse (i.e., the pulse with Kelly's sideband). This transfer caused an increasing in instability of the main pulse, as evidenced by an increase in Kelly's sideband energy. The accompanying energy change (represented by the black line in Fig. 7(b)) demonstrated a brief drop in energy followed by an upward trend. As a result of these changes, there was a significant shift in the pattern of the field autocorrelation trace, as shown in Fig. 7(b). Around the 4200th round trip, the autocorrelation curve revealed the emergence of two interacting solitons in the cavity, which could also be observed in Fig. 7(a) and Fig. 7(b). Subsequently, relaxation oscillations reappeared in the cavity due to insufficient energy. Notably, the temporal location of the energy peak in the cavity coincided with where the original small pulse should have appeared.
Fig. 7. From Dual-wavelength mode-locked pulse to noise formation. (a) The real-time spectra evolution measured via TS-DFT; (b) The field autocorrelation traces calculated via the Fourier transforms of each single-shot spectrum in (a) (black line: pulse energy).
4. Conclusions
This article presents a comprehensive record of the entire process of establishing and ultimately dissipating an asynchronous dual-wavelength mode-locked pulse. Notably, there was no significant energy change observed inside the laser following the soliton collision, prompting us to consider the underlying reasons for this phenomenon. Our hypothesis is that it is related to the formation process, during which the cavity initially shows the appearance of the soliton bound state but ultimately abandons the formation of soliton molecules due to the weak interaction between solitons. Instead, it forms an asynchronous dual-wavelength mode-locked pulse with subtle interactions between solitons. The collision of double solitons resulted in minimal energy change, and the original form of the soliton was maintained, thus highlighting the stability of the laser. Asynchronous dual-wavelength mode-locked fiber lasers are widely considered as optical sources for numerous applications, making the spectral evolution of pulses in an asynchronous dual-wavelength mode-locked fiber laser worth documenting.
Funding
Beijing Municipal Natural Science Foundation (4192015); National Natural Science Foundation of China (61975003).
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.
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