We report on experimental observation of dual-wavelength step-like pulses delivered from an erbium-doped fiber laser operating in ultra-large negative-dispersion regime. The step-like pulses consist of two rectangular pulses with different energies, durations as well as optical spectra, and are distinct from the conventional multi-solitons or bound-state solitons in that each pulse holds the same property. We find the weaker (or stronger) rectangular pulse in step-like pulses is more sensitive to the backward (or forward) pump while is less sensitive to the forward (or backward) pump. Our results demonstrate that the dual-wavelength operation results from the combination of fiber dispersion, fiber birefringence, as well as cavity filtering effect, and the intensity difference between rectangular pulses can be attributed to different gain characteristics of the forward and backward pump.
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Fiber lasers have attracted a great deal of research interests for their promising applications in optical communications, ultrafast optics, and fiber sensors [1–5]. The broad-gain spectrum of gain medium has resulted in extensive development of broadband wavelength  and multiple wavelength fiber lasers. By exploiting Fabry-Perot filter, a 90-wavelength pulse emission has been obtained in a Q-switched fiber laser . Several approaches for achieving dual-wavelength mode locking have been proposed in actively mode-locked fiber lasers [8,9]. Although dual-wavelength actively mode-locked fiber lasers exhibit the advantages including high repetition rates, narrow line width, they also have the drawbacks of low peak power and high cost as a modulator is needed in the cavity. In passively mode-locked lasers, dual-wavelength soliton has been obtained in Yb:YAG ceramic laser . In their experiment, mode locking was achieved at 1033 and 1047 nm simultaneously and each soliton exhibits almost the same pulse duration and energy. Furthermore, dual-wavelength mode-locked operation was obtained in a fiber ring laser by exploiting nonlinear polarization rotation (NPR) technique . However, the formation mechanism of the dual-wavelength mode locking was not further discussed. Moreover, multi-wavelength dissipative soliton operation was realized in an all-normal-dispersion fiber laser passively mode-locked with a semiconductor saturable absorber mirror . Two dissipative solitons with different wavelength exhibit orthogonal polarization states, which can be regarded as a novel kind of vector soliton.
In addition, rectangular pulses were also extensively investigated in the fields of fiber gratings , optical communications , and ultrafast optics . In the past two decades, optical pulses with steep leading and trailing edges have been mainly achieved in directly modulated semiconductor lasers . Several special elements, including fiber grating, spectrum filter, were exploited to produce rectangular pulse by using pulse shaping technique [17,18]. As particular components are indispensable for systems mentioned above, the fiber lasers thus became more expensive and less convenient for practical applications. Recently, picoseconds [19–21] and nanoseconds  rectangular pulses have been achieved in passively mode-locked erbium doped fiber (EDF) lasers, respectively. A common feature of rectangular pulses in these fiber lasers is that the pulse duration and energy can increase infinitely while the pulse peak power almost keeps constant with the increase of pump power, which is described as dissipative soliton resonance [23,24].
In this paper, we reported on the dual-wavelength step-like pulse operation of an ultra-large negative-cavity-dispersion fiber laser. The step-like pulses are constituted of two rectangular pulses with different energies, durations and spectra, and are distinct from the conventional multi-solitons  and bound-state solitons  in that each pulse holds the same property. Moreover, the output spectra of the step-like pulses exhibit two spectral humps corresponding to independent rectangular pulses. Experimental results also show that the weaker (or stronger) rectangular pulse in the step-like pulses is more sensitive to the backward (or forward) pump, but is less sensitive to the forward (or backward) pump. Based on experimental results, it is indicated that the dual-wavelength step-like pulse operation derives from the combination of fiber dispersion, fiber birefringence, as well as cavity filtering effect, and the intensity difference between the two rectangular pulses can be attributed to different gain characteristics of the forward and backward pumps. To the best of our knowledge, it is the first time that the dual-wavelength step-like pulses have been experimentally investigated in a passively mode-locked fiber laser.
2. Experimental setup
The current experimental setup is schematically shown in Fig. 1. The ring cavity is constituted of an 11-m-long EDF with an absorption of 6 dB/m at 980 nm, two sets of polarization controllers (PCs), a polarization-sensitive isolator (PS-ISO),a fused optical coupler (OC), two identical 980-nm laser diodes providing bidirectional pumps with the total power up to 1 W, and two 980/1550 nm wavelength-division-multiplexed (WDM) couplers. The other fibers in the cavity are the standard single mode fiber (SMF) with the length of ~730 m. The dispersion parameter D for EDF and SMF are about -9 ps/nm/km and 17 ps/nm/km at 1550 nm, respectively. The net cavity dispersion and fundamental cavity repetition rate of the ring laser are estimated as -15.5 ps2 and 278 KHz, respectively. The PS-ISO plays double roles of an isolator and a polarizer in the laser oscillator. The dual-wavelength pulse is further studied by exploiting a bandpass spectrum filter. An optical spectrum analyzer, a radio-frequency (RF) analyzer, and a high-resolution digital storage oscilloscope with a 50-GHz photodiode detector (PD) are employed to monitor the laser output simultaneously.
3. Experimental results and discussions
The NPR technique based on the PS-ISO and two PCs is used to realize self-started passive mode locking. By appropriately adjusting PC states and pump powers, various types of laser operations are observed, including the single-wavelength rectangular pulse with quasi-Gaussian spectral profiles and conventional femtosecond soliton with spectral sidebands. In particular, a dual-wavelength step-like pulse has also been achieved when both the forward and backward pumps beyond a threshold of ~50 mW. Figure 2(a) shows a typical spectrum of the step-like pulse directly observed from the fiber laser. It exhibits two spectral humps centered at 1559 and 1568 nm, respectively. The intensity difference between the spectral peak and valley is about 6 dB. By exploiting a bandpass spectrum filter, the initial dual-wavelength spectrum (i.e., the black curve) can be resolved as two independent spectra (i.e., the red and blue curves). Figure 2(b) shows the corresponding pulse profiles. The pulse directly outputted from the laser oscillator exhibits step-like profiles. After being resolved by the spectrum filter, the output pulse can be separated into two independent pulses, both of which exhibit a quasi-rectangular shape with durations of 50 and 120 ns, respectively. The spiky peak appearing on the pulse leading may be attributed to the imperfect response characteristic of the PD. No fine structure can be directly observed by exploiting a 70-GHz high-resolution sampling oscilloscope. However, we can not simply conclude that the rectangular pulse is single pulse. As shown in the oscilloscope trace, two rectangular pulses with different energies and durations coexist in the laser cavity. Here, the step-like pulses are distinct from conventional multi-solitons  and bound-state solitons  in that each pulse exhibits the same property. Figure 2(c) shows the pulse train on a large scale. The pulse-pulse separation between the step-like pulses is about 3.6 µs. The ratio frequency spectrum presented in Fig. 2(d) reveals a fundamental cavity repetition rate of ~278 KHz, which is in good agreement with the pulse-pulse separation in oscilloscope traces. Based on experimental results, we conclude that the fiber laser operates at stable dual-wavelength mode-locked state and the wider (or narrower) spectrum corresponds to the stronger (or weaker) pulse.
The duration of rectangular pulses in step-like pulses can be precisely controlled by slightly adjusting the polarization bias. Figure 3 shows some typical states of step-like pulses directly observed from the fiber laser. We can observe that the rectangular pulse with higher intensity can locate either left or right depending on the PC states and pump powers. In our experiment, once the dual-wavelength mode-locking operation is initiated, two rectangular pulses with different wavelength always adhere to each other. The results may be explained as the balance between anomalous dispersion and positive nonlinearity. In anomalous dispersion regime, the high-frequency stronger pulse travels faster than the low-frequency weaker pulse. However, as the stronger pulse induces higher nonlinearity, it will experience larger intensity-dependent refractive index and smaller propagating velocity. As a result, two rectangular pulses with different wavelength move as a unity in cavity and form the step-like pulse.
We further investigated the pulse evolution as a function of forward and backward pumps. As shown in Figs. 4(a) and (b) , the pulse duration of the weaker rectangular pulse in step-like pulses increases almost linearly while, for the stronger pulse, the duration changes slightly with the increase of the backward pump power. The evolution of step-like pulses in temporal domain is in good agreement with that in spectral domain, which confirms again that each mode-locked spectrum corresponds to an independent rectangular pulse. Figures 4(c) and (d) show the pulse evolution for fixed backward pump power. Contrarily, we find that the stronger pulse broadens linearly while the weaker pulse almost keeps invariable with increase of the forward pump. The experimental results show that the rectangular pulse with lower (or higher) intensity is more sensitive to the backward (or forward) pump, but is less sensitive to the forward (or backward) pump. Moreover, it is apparent that the pulse peak power always keeps constant by increasing both pumps, which is described as dissipative soliton resonance [23,24].
From experimental results, we conclude that the dual-wavelength mode locking results from the combination of fiber birefringence as well as cavity filtering effect. Based on the linear transmission model, fiber lasers can generate a cavity filtering effect  determined by the net phase delay. By adjusting fiber birefringence induced by the PCs, the shorter and longer wavelengths of the spectrum can experience either the same or different cavity loss due to the cavity filtering effect. In a particular case, both the shorter and longer wavelengths experience quite lower loss, while the mid-wavelength band undergoes much higher loss. As a result, the longer and shorter wavelengths will be amplified simultaneously, while the mid-wavelength band will be suppressed. Then, within the effective gain bandwidth, the two spectral components will be sufficiently separated and the dual-wavelength emission is obtained. With appropriate adjustment of pump powers, the laser will finally operate at dual-wavelength mode-locking state, and each mode-locked spectrum corresponds to an independent rectangular pulse. Moreover, the formation of single rectangular pulse in step-like pulse may be attributed to strong dispersion and saturation of the nonlinear transmission in the long-cavity oscillator. Dispersion tends to broaden short pulses, and peak power of the pulse is limited by saturation characteristics of the mode-locking device. Thus, output pulse exhibits nanosecond duration and rectangular profile with a flat top.
The step-like pulse mode-locked operation is quite different from other dual-wavelength mode locking [10,11], where each soliton exhibits almost the same property. By employing a PC and polarization beam splitter external to the cavity, we find that the two spectral components nearly exhibit the same polarization features. Thus, we also exclude the possibility that the output pulse belongs to vector soliton . Moreover, experimental results show that the forward and backward pumps have different influence on pulse profiles, as can be seen in Figs. 4(b) and (d). The different intensity of rectangular pulses in step-like pulses can be understood by noting that the fiber laser is bidirectional pumped. As each pump is responsible for an independent mode-locked rectangular pulse, different gain characteristics of the forward and backward pumps will cause the distinct properties of rectangular pulses in step-like pulses such as pulse energy and duration.
In this paper, we have experimentally reported dual-wavelength step-like pulses in an EDF fiber laser operating in ultra-large negative dispersion regime. The optical spectra of step-like pulses exhibit a particular shape with two mode-locked spectral humps. After being resolved by a bandpass spectrum filter, we find that each spectrum corresponds to an independent rectangular pulse. The step-like pulses consisted of two rectangular pulses with different energies are distinct from the conventional multi-solitons or bound-state solitons in that each pulse holds the same property. It is indicated that the dual-wavelength mode-locking derives from the combination of the fiber birefringence and cavity filtering effect. Moreover, the experimental results show that the rectangular pulse with lower (or higher) intensity is more sensitive to the backward (or forward) pump, but is less sensitive to the forward (or backward) pump. The intensity difference between the two rectangular pulses in step-like pulses can be attributed to the different gain characteristics of the forward and backward pumps.
This work was supported by the “Hundreds of Talents Programs” of the Chinese Academy of Sciences and by the National Natural Science Foundation of China under Grants 10874239 and 10604066. Corresponding author (X. Liu). Tel.: +862988881560; fax: +862988887603; electronic mail: email@example.com and firstname.lastname@example.org.
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