We have experimentally investigated high-energy rectangular pulses delivering from an erbium-doped fiber laser operating in ultra-large net-negative-dispersion regime. The laser oscillator emits rectangular pulses with approximately Gaussian spectral profiles, adjustable nanoseconds durations, and multi-ten nanojoule energies. The outputted pulses can be further amplified to over 2 μJ without distortion by a two-stage erbium-doped fiber amplifier. Thus, rectangular pulses with controllable durations and energies can be achieved from the compact all-fiber fiber laser system.
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Fiber laser offers several practical advantages over solid-state laser including simple design, high stability, and low alignment sensitivity [1–5]. Mode locking technique is widely used for achieving short pulse in lasers [6,7]. Different types of devices have been exploited for stable passively mode locking, such as semiconductor saturable absorber , nonlinear polarization rotation (NPR) technique [9,10], carbon nanotube , and atomic layer grapheme , etc. Conventional femtosecond pulses in net-negative dispersion regime are shaped by the interplay of positive fiber nonlinearity and negative fiber dispersion. Generally, the pulse energy is restricted to ~0.1 nJ due to the soliton area theorem [13,14], which has confined its practical applications severely.
During the past two decades, several special elements including large-mode-area fibers [15,16], double-clad gain fibers  were embodied into the passively mode-locked fiber lasers to generate high-energy pulses. However, these kinds of fiber lasers are much expensive and less stable as separate elements are indispensable for the system. Moreover, novel- structure fiber lasers operating in approximately zero-dispersion and normal-dispersion regime were proposed for high-energy pulses. Pulses with energies of 10 nJ and 20 nJ have been achieved from self-similar  and dissipative ytterbium-doped fiber lasers , respectively.
Recently, long-cavity fiber lasers have attracted significant interests for the potential of producing high-energy pulse [19–23]. M. Zhang et al. have reported an ytterbium-doped fiber laser with cavity length of 1.6 km and 75.2-nJ pulses were obtained in that all-normal-dispersion regime . Moreover, X. Wu et al. investigated the generation of 281.2-nJ rectangular pulses in a mode-locked erbium-doped fiber (EDF) laser with ultra-large normal cavity dispersion . Meanwhile, B. Nyushkov et al. obtained 1.7-µJ pulses from a self-mode-locked all-fiber EDF laser with a linear-ring cavity . The cavity consists of 1.25-km dispersion compensating fiber and 2.3-km non-zero dispersion shifted fiber, and the net cavity dispersion is estimated to be 230 ps2. As discussed above, most of the investigations for high-energy pulses are concentrated on fiber lasers with approximately zero dispersion or normal dispersion. Studies for high-energy pulse in ultra-large negative dispersion regime are relatively lacked.
In this paper, we report on the generation and amplification of rectangular high-energy pulses that were generated from an EDF laser with ultra-large negative cavity dispersion. A notable feature of the laser is that the cavity consists of a 530-m length of single-mode fiber (SMF) and a 0.8-m length of EDF. The proposed design has increased negative cavity dispersion significantly and slashed positive cavity dispersion intensively, which results in a net cavity dispersion of about −11.5 ps2. The rectangular pulses emitted by the oscillator exhibit adjustable nanoseconds durations and approximately Gaussian spectra. The energy of the initial pulse directly outputted from the laser oscillator reaches 60 nJ, after a two-stage erbium-doped fiber amplifier (EDFA), it can be boosted to ~2 μJ without distortion. Consequently, rectangular pulses with adjustable durations and energies in a wide range can be obtained from the compact all-fiber laser system.
2. Experimental setup
The experimental configurations for high-energy rectangular pulse are shown schematically in Fig. 1 . It comprises two parts: a unidirectional laser oscillator and a pulse amplifier. The ring cavity consists of a 0.8-m length of EDF with an absorption of 30 dB/m at 980 nm, two sets of polarization controllers (PCs), a polarization-sensitive isolator (PS-ISO), a fused optical coupler (OC) with 20% output, a 980-nm laser diode (LD) with pump power of 550 mW, and a 980/1550 nm wavelength-division-multiplexed (WDM) coupler. The other fibers in the cavity are the standard SMF with the length of ~530 m. The dispersions for EDF and SMF are about −12 ps/nm/km and 17 ps/nm/km at 1550 nm, respectively. The contribution of EDF to the overall group velocity dispersion of the cavity is estimated as only 0.0122 ps2, which can be almost neglected by comparing with that of SMF. The net-cavity dispersion is about −11.5 ps2. The pulse amplification system comprises a two-stage EDFA. The first-stage EDFA consists of a 0.8-m EDF backward pumped by a 550 mW LD, and the second-stage EDFA comprises a 1.2-m EDF bidirectional pumped by two LDs with each maximal output power of 550 mW. The polarization-insensitive isolators (PI-ISOs) in the EDFA are key devices that prohibit the reflected light from disturbing the signals in fiber laser. An optical spectrum analyzer, a radio-frequency analyzer, and a 70-GHz digital storage oscilloscope with a photodiode detector are employed to monitor the laser output simultaneously.
3. Experimental results and discussions
The NPR technique is exploited as artificial saturable absorber to realize the passive mode locking. With appropriate orientations and pressure settings of the PCs, self-started mode-locking operation can be achieved when the pump power P is beyond a threshold of ~80 mW. Fixing the pump power at 500 mW, the shortest stable rectangular pulse is ~8 ns while the longest reaches ~24 ns via adjusting the polarization bias, as shown in Fig. 2(a) . These pulses exhibit rectangular temporal profiles and no noise-like or other structures can be directly observed from the high resolution sampling scope. The corresponding optical spectra in Fig. 2(b) exhibit no characteristic sidebands as that of conventional femtosecond pulses  but approximately Gaussian profiles with the spectral center always near 1530 nm. The 3-dB bandwidths for 8-ns and 24-ns pulse are 4.1 and 3.5 nm, respectively. The inset of Fig. 2(b) presents the radio-frequency (RF) spectrum of the rectangular pulse. The fundamental frequency is ~395 kHz, according with ~2.53 µs pulse-pulse separation from oscilloscope trace [inset of Fig. 2(a)]. The RF spectrum and oscilloscope trace both reveal that the laser operates at stable pulse mode-locking state.
Figure 3(a) and 3(b) show the pulse evolution in temporal and spectral domain as a function of the laser pump power, respectively. We can observe that the pulse duration almost increases linearly while the pulse peak power nearly keeps invariable by increasing the pump power. Nevertheless, different from the trends in temporal domain, the spectral width nearly keeps unchanged while the spectral peak power increases linearly with the pump power. The maximum average power from the fiber laser is ~24 mW, corresponding to the pulse energy of ~60 nJ. Based on the measured result, the maximum pulse energy in the cavity is estimated as ~300 nJ and limited by the pump power launched into the cavity. A notable feature of rectangular pulses is that the pulse energy can increase to a huge level without pulse breaking or multi-pulse formation, which is distinct from that of conventional femtosecond soliton pulses . Additionally, the rectangular pulse in this ultra-large negative dispersion regime always displays resonance features , where the pulse energy and duration can increase indefinitely while the pulse peak power keeps constant by increasing the pump power. The situation here is quite similar to the fiber laser with ultra-large normal dispersion, which is described as dissipative soliton resonance .
We further investigate the amplification characteristics of rectangular pulses emitted from the ring oscillator. As shown in Fig. 1, the pulse amplification system comprises a two-stage EDFA. The ISOs in the EDFA are key devices that prohibit the reflected light from disturbing the signals in fiber laser. The EDF in the amplifier is the same type as that of fiber laser while with different lengths. These pulses exported from the laser oscillator are pre-amplified by the first-stage EDFA, which consists of a 0.8-m EDF and is forward pumped by a 550 mW single-mode LD. Then, the second-stage EDFA, which comprises a 1.2-m EDF and is bidirectional pumped by two 550 mW LDs, is exploited to achieve even higher pulse energy.
Here, the pump power of the laser oscillator is set as 500 mW and three pump powers of pulse amplifier are fixed at 550 mW. As shown in Fig. 4(a) , a good pulse profile is still maintained after the two-stage amplifier. The temporal widths of the initial and amplified pulse are 18.3 ns and 18.45 ns, respectively. It is worth noting that the amplified pulses are attenuated for measurement to protect the experimental equipment, so the red curve in Fig. 4(a) just shows the pulse profiles but not the actual relative intensity. The initial pulse spectrum exhibits a quasi-Gaussian profile with the 3-dB bandwidth of ~3.67 nm, after amplified the pulse spectrum almost maintains its shape with the 3-dB bandwidth of ~3.75 nm, as presented in Fig. 4(b). Comparing the amplified pulse with initial pulse, we can observe that the pulse duration and spectral profile almost keep unchanged after two-stage amplifications. We suggested that pulses with even higher energy could be obtained by employing more amplifiers.
Figure 5(a) shows the pulse energy and duration as a function of the amplifier pumps. By increasing three pumps simultaneously from 0 to 550 mW, the average power increases from 10 to 810 mW, corresponding to the pulse energy from 25 nJ to 2 μJ. The further increase of pulse energy is limited by the available maximal power of the amplifier LD pumps. It is worth noting that the pulse energy increases almost linearly and the pulse duration almost keep invariable with the amplifier pumps. As a consequence, pulses with controllable durations and energies in a wide range can be achieved by simply adjusting the PCs and amplifier pumps. Figure 5(b) shows the energy of initial and amplified pulses versus the pump power of laser oscillator. Here, the pump powers of pulse amplifier all are fixed at 550 mW. To make a clear comparison with amplified pulses, the energy of initial pulses have been multiplied by 40. It is obvious that rectangular pulses are amplified nearly linearly at small-signal operation in lower laser pumps. For higher laser pumps, the amplifier shows some degree of saturation features.
As mentioned above, we focus on the generation and amplification of rectangular pulses in ultra-large negative dispersion regime. The compressibility of such pulse will be further investigated in our future work. The proposed fiber laser has the compact all-fiber construction and low-cost feature for practical applications. The fiber laser can operate at the stable mode-locking state as long as external conditions such as the pump power and polarization bias are kept unchanged. Rectangular pulses with adjustable durations and energies in a vast range can be obtained from this simple design. It is no doubt that the proposed laser system can find numerous applications in the region of optical communications, biomedicine technologies, material processing, etc.
In this paper, we report the experimental results of high-energy rectangular pulses in a compact all-fiber EDF laser. The laser cavity consists of a 0.8-m EDF and a 530-m SMF, and the net-cavity dispersion is estimated as about −11.5 ps2. The rectangular pulses with approximately Gaussian spectral profiles, adjustable nanoseconds durations, and multi-ten nanojoule energies can be obtained directly from the laser oscillator. The amplification characteristics of the rectangular pulses are further studied by exploiting a two-stage EDFA. The average output power from the pulse amplifier reaches 810 mW, corresponding to the pulse energy of ~2 μJ at a 395-kHz repetition rate. The rectangular pulses with adjustable durations and energies can find important applications in many fields.
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: firstname.lastname@example.org and email@example.com.
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