We experimentally demonstrate unequal pulses delivered from an erbium-doped fiber (EDF) laser with net-normal dispersion. Two types of pulses with different durations, energies, and spectra coexist in the same ring cavity. The output spectrum exhibits a broadband base that corresponds to the main pulse and a small rectangular lump that corresponds to the additional satellite pulse. With the enhancement of pump power, the intensity of main pulse almost keeps unchanged while the satellite pulse nearly increases linearly. Based on experimental results, it is indicated that two different pulse shaping mechanisms coexist in laser cavity, where the nonlinear polarization rotation (NPR) and spectral filtering (SF) effect contribute to the formation of main pulse and satellite pulse, respectively.
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Various lasers have been proposed for their wide applications in ultrafast phenomena, optical communications, nonlinear optics, and optical sensors [1–4]. Fiber-based lasers exhibit features of broad gain spectrum, low cost, and high reliability [5–8]. Several elements including semiconductor saturable absorber , NPR technique , carbon nanotube , and atomic layer grapheme , have been widely used for ultrashort pulse generations in mode-locked fiber lasers. By enlarging the net cavity dispersion from anomalous to normal, different types of pulses such as conventional soliton , stretched pulse , self-similar pulse , and dissipative soliton (DS) [16–18] were successively achieved in fiber lasers. Generally, the DSs in large-normal or all-normal dispersion regime exhibit picoseconds durations and nanojoules pulse energies. The gain and loss play essential roles in the formation of DSs [19, 20], and various operations have been observed in such regime [21, 22].
In the high pump states, all the aforementioned lasers tend to operate at multiple-pulses emission due to the peak power clamping effect of the cavity . S. M. Kobtsev et al. have investigated pulse evolution as a function of cavity length, and found that the pulse energy increases while the stability decreases with enlarging of cavity length . The multiple pulses can scatter randomly with relatively stable (or unstable) positions in cavity. Under certain experimental settings, the multiple pulses can rearrange themselves in a regular position and form the so-called harmonic mode locking [25, 26]. Moreover, the multiple pulses can constitute the bunch-state pulses, in which each pulse vibrates randomly on a small time scale . Bound-state pulses can be generated in a special situation, where each pulse has stable location and the pulse separation is several times of pulse duration . However, the multiple pulses in a certain cavity are equal, and each pulse exhibits the same duration, pulse energy, as well as optical spectrum. It is rather a challenge to achieve mode-locked pulses with different properties in practical experiments.
In this paper, we experimentally demonstrate a single pulse and two unequal pulses delivered from an EDF laser operating in average-normal dispersion regime. Two types of pulses with different durations, energies, and spectra are emitted at fundamental cavity repetition rate from the same ring cavity. The output spectrum exhibits a broadband base corresponding to the main pulse as well as a small rectangular lump corresponding to the additional satellite pulse. With the enhancement of pump power, the intensity of main pulse nearly keeps unchanged while the satellite pulse almost increases linearly. Experimental results indicate that two different pulse shaping mechanisms coexist in the laser cavity. The NPR is responsible for main pulse generation and the SF effect contributes to satellite pulse formation. The evolution of unequal pulses in our laser is different from the conventional solitons, where each pulse shares the identical physical parameters due to the pulse competition and energy quantization effect [26, 29].
2. Experimental setup
The configuration of proposed fiber laser is schematically shown in Fig. 1 . Two 980-nm laser diodes are used to provide bidirectional pump with two 980/1550 nm wavelength-division-multiplexers (WDMs). A ~50-m EDF with dispersion parameter D of −42 ps/nm/km acts as the gain media and contributes to the large-normal dispersion. The other fibers in the cavity are the standard single mode fiber with D of 17 ps/nm/km and length of 15 m. The net dispersion and fundamental repetition of cavity are estimated as + 2.35 ps2 and 3.16 MHz, respectively. A polarization sensitive isolator (PS-ISO) and two polarization controllers (PCc) act as equivalent saturable absorber for mode-locking operation. An optical coupler (OC) with 50% output is placed after EDF to achieve as high energy as possible. An optical spectrum analyzer (OSA), an autocorrelator (AC), a radio-frequency analyzer (RFA), and a 70-GHz digital sampling oscilloscope (DSO) with a photodiode detector are employed to monitor the laser output simultaneously.
3. Experimental results and analyses
With appropriate pressure and orientation setting of PCs, single pulse emission can be easily established from continuous wave (CW) when both forward and backward pumps increase to ~120 mW, as shown in Fig. 2 . The output spectrum of the single pulse exhibits a smooth profile with 3-dB bandwidth of ~25 nm. The prolonged spectral wings extend to both sides of the spectrum, which indicates the existing of strong nonlinear effects during pulse evolution. Figure 2(b) shows the corresponding autocorrelation traces which possess smooth and clean Gaussian profiles without any spikes or other structures. The full-width at half-maximum of autocorrelation trace is ~120 ps by using Gaussian fit, and the pulse duration is estimated as 85 ps. The time bandwidth product is given as ~260, which denotes that the pulse is highly chirped. The pulse train present in Fig. 2(c) has a uniform interpulse interval of ~320 ns which is consistent with the cavity round-trip time. The radio frequency (RF) spectra in Fig. 2(d) show that signal/noise ratio is higher than 70 dB. The fundamental cavity repetition rate is 3.16 MHz, corresponding to the cavity length of 65 m. Therefore, the fiber laser operates at stable single-pulse mode locking rather than noiselike pulse emission [8, 24].
Two unequal pulses with different features can be achieved in the laser cavity by simultaneously increasing the forward and backward pumps to ~140 mW. Figures 3(a) and 3(b) show the pulse evolution with pump power in frequency and temporal domain, respectively. The output spectra of unequal pulses exhibit broadband bases with small rectangular lumps on the top. As shown in the inset of Fig. 3(a), the rectangular spectrum with central wavelength of 1569 nm almost broadens linearly from nought to 4 nm with the enhancement of pump power. The steep spectral edges indicate the existence of SF effect although no additional active spectral filter is employed here. The oscilloscope traces show that the intensity of the satellite pulse increases linearly and the main pulse almost keeps constant, which indicates that the excessive pump power beyond the capability of the main pulse induces the generation of satellite pulse. The satellite pulse always accompanies with the appearance of rectangular spectrum, and both of them exhibit the similar evolution versus pump power. Thus, we conclude that the broadband spectrum (rectangular spectrum) corresponds to the main (satellite) pulse. Figure 3(c) shows the oscilloscope trace on a large time scale when both pump powers are fixed at 200 mW. The separation between the adjacent main pulses is equal to the cavity round-trip time of 320 ns, and the separation between the main pulse and satellite pulse is about 33 ns. The results suggest that both of the main pulse and satellite pulse are emitted at fundamental cavity repetition rate. The durations of main pulse and satellite pulse in Fig. 3(d) are ~90 and 150 ps, respectively. The inset is the corresponding autocorrelation traces of the main pulse. As individual pulses are well separated, the autocorrelation traces still maintain Gaussian profile without modulated sidebands. We can confirm that the main pulse in oscilloscope is a single pulse rather than bound-state pulses or pulse bunches [27, 28]. However, this operation becomes less stable and the pulse locates randomly in cavity with the further increase of pump powers.
Moreover, other types of unequal pulses, different from the aforementioned operation states, are also observed by adjusting the PCs and pump powers. Figures 4(a) and 4(b) show the output spectra and pulse trains, respectively. Here, the forward and backward pumps are fixed at 140 and 160 mW. For case 1, the satellite pulse almost adheres to the main pulse and the duration for main pulse is estimated as ~76 ps. For case 2, the separation between the main and satellite pulses is ~300 ps. The pulse durations for the main and satellite pulses are ~90 and ~150 ps, respectively. The results suggest that the separation between the main and satellite pulses also is affected by the experimental conditions. However, once the unequal-pulses operations are initiated, the main and satellite pulses always have relatively fixed separations, which indicate that the two pulses possess the same group velocity during propagation through cavity. 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 pulses belong to vector solitons . These are easy to understand as the PS-ISO is used in cavity for mode locking.
In normal dispersion fiber lasers, there exist two pulse shaping mechanism, one is NPR technique  and the other is SF effect [31, 32]. As can be seen from Fig. 1, the NPR based on two PCs and a PS-ISO can act as the mode-locking element. The PS-ISO plays double roles of an isolator for unidirectional operation and a polarizer that forces light to be linearly polarized. The PC after the PS-ISO changes the polarization from linear to elliptical states. Then, the polarization state evolves nonlinearly during pulse propagation through cavity because of SPM- and XPM-induced phase shifts imposed on two orthogonally polarized components. As a result, the polarization state is nonuniform throughout the pulse due to the intensity-dependent nonlinear phase shift. The PC before the PS-ISO is adjusted to force the polarization to be linear in the central part of the pulse. Then the PS-ISO works as a saturable absorber that admit the central intense part of the pulse pass while blocks the weak pulse wings. We conclude that the NPR takes a critical role in the formation of main pulse with broadband spectrum as the operation state is very sensitive to the fiber birefringence. Moreover, the SF effect can be exploited to initiate the mode-locking operation in normal dispersion regime. The optical spectrum broadens strongly during pulse amplification in EDF due to the combination of normal dispersion, SPM, and other nonlinear effects. As long-wavelength components is faster than the short-wavelength components, the temporal leading of a pulse are the red-shift frequencies while the trailing are the blue-shift components. Then, the SF effect (e.g., invisible gain spectral filter) can cut off not only the spectral (temporal) but also the temporal (spectral) wings of a normal-dispersion pulse. Therefore, the SF effect acts as saturable absorber, enable the self-consistent evolution, and results in the stable mode-locked pulse with steep spectral edges. Thus, we conclude that the satellite pulse with rectangular spectrum mainly results from the SF effect. The pulse evolution may be described as follows. Under lower pump, single pulse emission can be obtained with the NPR technique. When the pump is further increased to a certain range that is too strong to sustain a single pulse while not enough to support two identical pulses, the redundant energy can form the satellite pulse due to the SF effect. Finally, two unequal pulses with different features can be obtained, and the main pulse results from the NPR technique, while the satellite pulse attributes to SF effect.
We have experimentally demonstrated single pulse and two unequal pulses delivered from an EDF laser operating in average-normal dispersion regime. The unequal pulses with different durations, energies, and spectra coexist in the same ring cavity. The output spectrum exhibits a broadband base that corresponds to the main pulse and small rectangular lump that corresponds to the satellite pulse. With the enhancement of pump power, the main pulse almost keeps unchanged while the satellite pulse almost increases linearly. Based on experimental results, it is indicated that there are two different pulse shaping mechanism coexisting in laser cavity, where NPR is responsible for the main pulse generation while the SF effect mainly contributes to the satellite pulse formation. Our results are different from that of conventional soliton lasers where each pulse is identical due to the same pulse shaping mechanism and energy quantization effect.
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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