1. Introduction

Laser sources that simultaneously generate multi-wavelength pulses have attracted extensive attention due to their potential applications that single-wavelength lasers are not sufficient [1–4]. In particular, low-cost and compact erbium-doped (Er-doped) fiber lasers simultaneously producing asynchronous dual-wavelength ultrashort pulses have been extensively deployed for applications in pump-probe measurement and broadband optical and terahertz spectroscopy [5–8]. To date, several schemes have been proposed to produce dual-wavelength pulses. One effective method is to add an additional route in a laser cavity that allows dual-wavelength pulses circulating along two-branches or dual-cavity-loop separately [9–12]. By designing different physical parameters (e.g. fiber length, dispersion and nonlinearity) of the two routes, two asynchronous pulses with significantly different properties could be achieved. However, the generated pulses from the two routes have reduced mutual coherence as they propagate through different physical paths. Another effective method to obtain dual-wavelength pulses is to introduce comb filtering effect into the cavity. As the dual-wavelength pulses propagate through the same physical path, this method endows the dual-wavelength pulses with passively maintained mutual coherence due to common mode environmental noise rejection [13,14]. The spectral filtering effect can be introduced by the periodic wavelength-dependence-reflectivity of a saturable absorber (SA) [15], multimode interference effect [16,17], or birefringence-induced comb filtering effect [18–21]. These filters have a good flexibility as their filter period, center wavelength and modulation depth can be conveniently tuned by changing corresponding parameters, such as device length and fiber birefringence [16–21]. Previous demonstrations have shown that large modulation depth (generally > 3 dB) of the filter should be satisfied to isolate adjacent gain channels. However, while the filter period is fixed, large modulation depth leads to a narrower filter bandwidth and thus, narrower pulse spectral bandwidth [22]. This is especially true for Er-doped fiber lasers as erbium-doped fiber (EDF) generally has a much smaller gain bandwidth compared to that of thulium-doped fiber (TDF) and Ytterbium-doped fiber (YDF). Achieving broad bandwidth dual-wavelength pulses from Er-doped fiber lasers is therefore very challenging. Indeed, the reported full width at half maximum (FWHM) bandwidth of dual-wavelength Er-doped fiber lasers to date is limited to ∼10 nm [23]. Alternatively, EDF could exhibit saddle-like gain profile with two gain peaks under certain pump and signal conditions, providing another viable solution for dual-wavelength operation [2,24–26]. However, the potential of the two-peak gain profile of EDF for large bandwidth dual-wavelength pulses generation is yet to be investigated.

On the other hand, there has been growing interest in exploring dual-wavelength mode-locked fiber lasers producing diverse patterns [27–32]. In terms of simultaneous generation of different dispersion pattern solitons, the previous reports need either complicated cavity design [9] or specific long fibers with strong third-order dispersion (TOD) [32]. By introducing 10 m dispersion compensation fiber (DCF) with TOD of 1.67 ps³/km, Wang et al. demonstrated the coexistence of dissipative soliton (DS) and stretched pulse (SP) in a dual-wavelength mode-locked thulium-doped (Tm-doped) fiber laser [32]. The longer DCF used in their cavity could lead to unstable stationary pulse regime because of the long laser cavity and high nonlinearity coefficient of the DCF. We propose that the coexistence of these two dispersion pattern pulses can also be achieved without the use of long DCF with strong TOD.

Here, we propose a dual-wavelength mode-locked Er-doped fiber laser operating at near zero dispersion that only consists of single-mode fibers with a weak TOD (0.3 ps³/km). Both numerical and experimental results confirm its capability of delivering DS and SP simultaneously. By taking advantage of the two gain peaks of EDF without introducing any spectral filtering effects, both the DS and SP soliton achieve the widest bandwidth compared to any previously reported Er-doped dual-wavelength fiber lasers. The proposed simple, compact laser is of significant importance for diverse-pattern dual-wavelength pulses generation, and for applications requiring wide bandwidth asynchronous dual-wavelength laser sources.

2. Laser setup

The schematic of the dual-wavelength Er-doped fiber laser is shown in Fig. 1. A piece of 3.5 m EDF (YOFC-EDF1022) with a group-velocity dispersion (GVD) of 20 ps²/km at 1.55 µm is co-pumped by a 980 nm pump laser diode through a 1 m 980/1550 nm wavelength division multiplexer (WDM, where its pigtail consists of HI1060 fiber with a GVD of -7 ps²/km at 1.55 µm). In addition to the EDF and WDM, all the pigtails of the rest components in the cavity are made of single mode fiber (SMF) with a GVD of -22 ps²/km at 1.55 µm, including a 20% output coupler, an inline polarization-independent optical isolator and two polarization controllers (PCs) to balance the gain profile of the EDF by controlling the loss of the cavity. The inkjet-printed black phosphorus(BP), passivated with Parylene C for environmental stability, that has been successfully demonstrated as a broadband passive switch for ultrafast lasers [33,34], is sandwiched between two fiber connectors as SA. The total cavity length is 7.1 m. The net cavity dispersion is calculated as ∼ 0.0058 ps² at 1.55 µm, indicating the laser operates at near zero dispersion. It is important to note that no polarization maintaining fiber (PMF) is used.

 

Fig. 1. Schematic of the dual-wavelength Er-doped fiber laser.

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3. Numerical simulation

To explore the formation mechanism of the dual-wavelength pulses from the Er-doped laser setup, we perform numerical simulations based on the nonlinear Schrödinger equation (NLSE),

 

Fig. 2. Gain profile and intra-cavity comb filter transmission curves with different modulation depths. Inset shows the gain profile and transmission curves in larger Y-axis.

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Table 1. Fiber parameters of the numerical simulations

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In the simulation, an initial weak pulse could evolve to a stable dual-wavelength mode locking state when P_sat= 4.05 mW. Figures 3(a) and 3(b) shows the evolution of the spectrum and the waveform as a function of the roundtrips, respectively. The saddle-like gain spectrum provides two gain peaks, corresponding to two gain channels. The spectrum of the initial weak pulse splits into two that located on the two gain channels after several roundtrips. The isolation of the two spectra is then enhanced each time the pulses cycling through the saddle-like gain fiber. Finally, the gain competition of the two spectra (corresponding to two pulses) reaches equilibrium after ∼500 roundtrips and the stable dual-wavelength mode locking is obtained. The evolution traces of the two pulses in Fig. 3(b) have different slope, indicating that they are asynchronous dual-wavelength pulses. While the dual-wavelength spectrum centered at 1530 nm shows steep spectral edges and flat spectral top with a FWHM of 11 nm, the spectrum centered at 1556 nm has a broad spectral FWHM of 22 nm [Fig. 3(c)]. The time domain shows two pulses with different peak power and pulse width [Fig. 3(d)]. To further confirm the dispersion feature of the two pulses, the variation of the pulse duration and frequency chirp of the asynchronous pulses in one round trip are also investigated. We characterize the frequency chirp by calculating the slope of chirp at the center of the pulses. Starting from the EDF, the pulse with lower peak power breathes once in one roundtrip and is always up-chirped through the whole cavity [Fig. 3(e)]. The high peak power pulse breathes twice with alternating frequency chirp in the cavity [Fig. 3(f)]. The simulation results agree well with the typical features of a DS and an SP [32,36], respectively. Therefore, the coexistence of these two dispersion pattern pulses can be achieved in laser cavity that only consists of fibers with a weak TOD.

 

Fig. 3. Simulated results of broad bandwidth dual-wavelength pulses with saddle-like gain profile: evolution of (a) normalized spectrum in linear scale and (b) waveform as a function of roundtrips; (c) normalized spectrum and (d) waveform at roundtrip of 800 with spectral bandwidth of 11 nm and 22 nm, respectively; the variation of pulse duration and slope of chirp of (e) DS and (f) SP along the laser cavity.

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To demonstrate that the saddle-like gain profile is indeed better than a comb filter in terms of facilitating broad bandwidth dual-wavelength pulses, we substitute a comb filter in the laser cavity for the saddle-like gain profile while keeping the other parameters of the cavity unchanged. The comb filter period of 26 nm in our simulations is consistent with the separation of the two gain peaks of the saddle-like profile. The modulation depth of the comb filter is firstly set as 0.1 dB, which is comparable to the peak-dip difference of the saddle-like gain profile (labeled using the blue line in Fig. 2), leading to a single-wavelength mode-locking operation. A typical result of the simulation at the P_sat of 1.45 mW is shown by the single-wavelength spectrum [ Fig. 4(a)] and single pulse in the time domain [Fig. 4(b)]. The results are attributed to the low modulation depth of the comb filter. Unlike saddle-like gain profile of EDF, which can promote the formation of dual-wavelength along the whole length of gain fiber, the comb filtering effect only exists at one point in the cavity (e.g. polarizer) and thus the effect is weak at low modulation depth. We then change the comb filter modulation depth to 4.5 dB, as shown using the red line in Fig. 2. Under this condition, we could obtain a dual-wavelength mode-locking at the P_sat of 0.87 mW with FWHM of 8 nm and 6 nm, respectively. The spectral bandwidth increases when increasing P_sat. However, when the P_sat scales up to 1.45 mW, the spectrum of the SP shown in Fig. 4(a) exhibits obvious modulation. The corresponding waveform in the time domain splits into two sub-pulses that move together with a fixed distance, indicating a bound-soliton state [37,38]. The FWHM of the DS and bound-SP is 10 nm and 8 nm, respectively. The formation of a dual-wavelength operation opposes to a further broadening of the spectrum with the comb filtering effect. As shown in Fig. 2, the smaller modulation depth results in a broader gain channel. In order to find the widest bandwidth that could be achieved by using a comb filter, we further investigate the smallest modulation depth that required enabling a stable dual-wavelength mode-locking. It is found that the smallest modulation depth is 2.16 dB, and the corresponding widest bandwidth (11 nm for DS and 20 nm for SP) could be obtained at the P_sat of 2.32 mW [Fig. 4(g) and 4(h)]. This modulation depth is much larger than the peak-dip difference of the two-peak gain profile, leading to narrower gain channels. Thus, the two-peak gain profile of the EDF are suitable to achieve broadband dual-wavelength pulses compared to a comb filter in our cavity. However, we note that as the two peaks of saddle-like gain profile generally located around 1530 nm and 1555 nm, the comb filter will be more suitable for producing broadband dual-wavelength pulses with specific requirements such as tunable wavelength separation or switchable center wavelength.

 

Fig. 4. Simulated results with comb filter: (a) spectrum and (b) waveform with modulation depth of 0.1 dB at P_sat of 1.45 mW; (c) spectrum and (d) waveform with modulation depth of 4.5 dB at P_sat of 0.87 mW; (e) spectrum and (f) waveform with modulation depth of 4.5 dB at P_sat of 1.45 mW; (g) spectrum and (h) waveform with modulation depth of 2.16 dB at P_sat of 2.32 mW;

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4. Experimental results

In our experiment, typical dual-wavelength pulses can be generated with a fine adjustment of the intra-cavity PCs at the pump power of 43 mW. Figure 5(a) shows the dual-wavelength spectrum possessing two center wavelengths with 26 nm separation. The spectrum located at 1530 nm with a FWHM of 11.5 nm has the characteristic steep spectral edges and a flat spectral top, suggesting that it is a DS [39]. The smooth spectrum centered at 1556 nm with a FWHM of 24 nm has no sidebands, a characteristic of SP. Both the DS and SP have the widest FWHM compared to any previously reported dual-wavelength Er-doped fiber lasers. There are two set of pulse trains recorded on the oscilloscope [Fig. 5(b)]. We note that the two pulse trains have different propagation speed, indicating the existence of asynchronous pulses. The radio frequency (RF) on a span of 500 Hz shows that the dual-wavelength pulses operate at the fundamental frequency of ∼28.9036 MHz repetition rates with a difference of 58 Hz [Fig. 5(c)]. The signal to noise ratio (SNR) of the RF spectrum is 52 dB for DS and 61 dB for SP respectively, and the smaller peaks in Fig. 5(c) are beat notes. The SP and DS are then filtered out by a WDM with a passband covering from 1522.5 to 1537.5 nm external to the cavity for autocorrelation trace measurement. The average powers of the SP and DS after WDM are 1.32 mW and 0.52 mW, respectively. Figure 5(d) shows the autocorrelation trace of the DS with a pulse duration of 4.6 ps, fitted with a sech² fit. The autocorrelation trace of the SP has a pulse duration of 172 fs with a Gaussian fit [Fig. 5(e)]. We note that the measured average powers and autocorrelation traces of the two pulse trains after the WDM are not precise values as their partially overlapped spectra.

 

Fig. 5. Experimental results of dual-wavelength operation: (a) spectrum, (b) pulse train, (c) radio frequency (RF) spectrum. The autocorrelation trace of (d) amplified DS at 1530 nm and (e) SP at 1556 nm.

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5. Conclusion

In summary, we have proposed a dual-wavelength Er-doped fiber laser mode-locked at near zero dispersion using a BP SA. By exploiting the saddle-like gain profile of EDF and a weak TOD of the fiber, we numerically and experimentally achieve the generation of broad bandwidth SP and DS mode-locking simultaneously. Our proposed compact and simple design provides a new approach for diverse-pattern solitons research and for potential applications such as dual-comb metrology.