ABSTRACT We propose a nanotube-based erbium-doped fiber laser that can deliver conventional soliton (CS) and stretched pulse (SP) based on D-shaped fiber saturable absorber (DF-SA) where evanescent-field interaction works. The novel Nanotube-based Fiber Laser can generate SP or CS by tuning pump power and polarization controller (PC) properly. The net cavity dispersion of laser is slightly negative. In our experiment, by optimizing the PC in the cavity, CS and SP can be obtained at the central wavelengths of 1530.6 nm and 1530.3 nm due to on carbon nanotubes and the spectral filtering effect induced by nonlinear polarization rotation. Although the acquired CS and SP nearly have the same central wavelengths, they show distinct optical spectra, 3-dB bandwidths. The proposed fiber laser with switchable CS and SP is attractive for ultrashort pulse generation and fast measurements in practical applications.
Due to their excellent features of generating ultra-short pulses, passively mode-locked fiber lasers have drawn a lot of attention     . Ultrafast fiber lasers with the merits of excellent heat dissipation    , freedom from alignment   and compact laser cavity design   are widely applied in the fields of biomedical diagnostics  , optical communications    and nonlinear optics   . Passively mode-locked fiber lasers can be obtained by different types of nonlinear elements, such as nonlinear polarization rotation (NPR)     , semiconductor saturable absorber mirrors    , nonlinear optical loop mirrors    , graphene   , graphite nano-particles  and single-wall carbon nanotubes (SWNTs)   . Among them, SWNTs can work as excellent saturable absorbers (SAs) due to their advantages of fast recovery time, high damage threshold, good modulation depth, broad operation bandwidth, outstand environmental stability, and affordable fabrication    . There are many investigators that pay great attention to SWNTs as SAs. A fiber laser generating a 74 fs pulse with 63 nm spectral width based on nanotube mode locker have been proposed by Popa et al.  . Recently, a distributed ultrafast laser was proposed firstly by Liu et al. by means of the linearly chirped grating technique  . Moreover, broadband operation which is the superior feature of SWNTs can be realized by mixing SWNTs with different diameters, because the diameter and chirality of nanotubes determine the absorption peak of SWNTs  .
A long interaction length for the guided light and the nanotubes is introduced by the D-shaped fiber saturable absorber, which guarantees an efficient nonlinear effect so that it facilitates laser mode locking even though the laser is under various conditions  . Higher intracavity power can be introduced for higher energy pulse formation, because only a part of the optical power of the propagating mode interacts with the SWNTs for mode locking. Lots of researchers have focused on evanescent-field interaction with SWNTs due to the outstanding performance of higher energy pulse formation and low CNT-density threshold  . The first experimental observation of four-wave mixing in SWNTs deposited on a DF has been reported by Chow et al.  . By using the evanescent-field interaction of propagating light with the nanotubes, a mode locker that is immunized to the high optical power induced damage have been demonstrated by Song et al.   .
Different types of mode-locked pulses have been obtained due to different designs of fiber laser cavity, such as CS    , SP  , self-similar pulse   , and dissipative soliton (DS)    . Because of the interaction between the fiber anomalous dispersion and nonlinear optical Kerr effect, CSs can be formed in negative dispersive regime    . When the frequencies of dispersive waves are phase-matched, discrete sidebands whose positions are determined by the cavity length, net dispersion, and pulse duration will generate and distribute on both sides of the spectrum    . When the net cavity dispersion approaches zero, SPs propagating in such a cavity are stretched and compressed periodically     . Self-similar pluses operating in normal-dispersion regime are the parabolic pulses with self-similar evolution    . Moreover, the linear-chirped self-similar pulses can avoid pulse breaking when they propagate in the routes  . The multiple interactions between fiber nonlinearity, normal dispersion, saturable absorption effect, and spectral filtering effect result in the formation of DS  . DS has higher energy and wilder pulse width than that of CS, and its characteristics change dramatically when it travels along the laser cavity  .
Although as a lot of progress has been made, fiber laser on many key physical parameters (such as pulse energy, pulse width and peak power, etc.) still lags behind that of the solid laser. Therefore, development of ultrashort pulse fiber laser has important practical significance and broad market prospect. In this paper, we propose a fiber laser that can deliver switchable CS and SP based on a SWNT mode-locker deposited on D-shaped fiber (DF). The proposed fiber laser can generate SP or CS with central wavelength of 1530 nm by tuning pump power and polarization controller (PC) properly. The spectral bandwidth and pulse duration of the CS are 4.46 nm and ~0.7 ps, and these of the SP are 9.59 nm and ~1.0 ps. A NPR-induced filter is formed by the polarization sensitive DF-SA and PC. The stretching factor plays a key role on the switchable mode-locking operation, which can be tuned by the NPR-induced filter. The saturable absorber (SA) can withstand pump power up to 550 mW and deliver stable SP or CS without damage. It is attractive for practical applications of ultrashort pulse generation and fast measurements to implement our fiber laser with switchable CS and SP.
2. Experimental Setup
Figure 1 shows the schematic diagram of our experimental setup. In the fiber laser cavity, a 980 nm laser diode (LD) is used as pump source via a 980/1550 nm wavelength-division multiplexer (WDM) coupler; an 18-m erbium-doped fiber (EDF) with the group velocity dispersion (GVD) parameter of -9 ps/nm/km and the absorption of 3 dB/m at 980 nm acts as the gain media; a PC in the cavity is used to adjust the state of polarization; the 10% port of a 90/10 coupler is adopted to extract the laser for measurement; the DF-SA integrated into the
cavity is made by using an optical-deposition technique to deposit SWNTs on the DF  ; a polarization independent isolator (PI-ISO) is adopted to realize unidirectional operation. And all the rest of fibers are single mode fibers (SMFs) whose dispersion parameter is 17 ps/nm/km. The devices of a commercial autocorrelator (AC), a radio frequency (RF) analyzer, a digital storage oscilloscope, and an optical spectrum analyzer (OSA) are employed to monitor the laser outputs simultaneously.
The employed DF is fabricated by side-polishing SMFs   . The whole procedure is monitored by a power meter to estimate the distance from polished surface to the fiber core. The DF-SA is made by using an optical-deposition technique to deposit SWNTs on the DF  and the insertion loss of the DF-SA is measured as 5 dB. As shown in Figure 1, the propagating light follows the route as WDM → EDF → PC → OC → DF-SA → PI-ISO →WDM. The dispersion parameters D of EDF and SMF are about −9 and 17 ps/(nm∙km). The net dispersion and the cavity length are −0.045 ps2 and ~29.6 m, respectively. By tuning the polarization state of propagating light through adjusting PC and providing different pump power appropriately, we can realize switchable SP and CS.
3. Results and Discussions
With the pump power of ~50 mW, the continuous wave (CW) is observed from the outputted fiber laser. When the total pump power is increased to ~70 mW, CS with its typical spectrum is shown in Figure 2(a). Figure 2(a) shows the output spectrum of CS with a bandwidth of 4.46 nm. It can be seen that obvious Kelly sidebands discretely distribute on both sides of spectrum, which reflects the soliton features of the pulses    . The sidebands originate from the constructive interference between the soliton and dispersive waves   . The
Figure 2. Conventional soliton (CS) operation of (a) Optical spectra, (b) Radio frequency spectrum (RF) spectra, (c) Autocorrelation (AC) trace, (d) Oscilloscope trace.
central wavelength of the CS locates at ~1530.6 nm, which is mainly determined by the diameter distribution of nanotubes in SWNT-SA, the intracavity loss, the transmittance peak of birefringence-induced filter, and the gain profile of EDF   . In Figure 2(b), the RF spectrum with the range of 1 KHz shows that the fundamental repetition rate of CS is ~6.95 MHz, corresponding to a round-trip time of ~144 ns. Our experimental setup of the nanotube-based Fiber Laser can realize the ultrashort pulse generation and fast measurements. The signal-to-noise ratio (SNR) is ~70.6 dB, which confirms that the CS operates at the stable mode-locking state. As shown in Figure 2(c), the full width at half maximum (FWHM) is 1.10 ps, and the pulse duration is estimated as 0.7 ps by using a Sech2 fit. The time bandwidth product (TBP) is calculated as 0.39, indicating that the output CS is slightly chirped. The oscilloscope trace plotted in Figure 2(d) demonstrates that the pulse-to-pulse separation is about 144 ns, corresponding to the cavity length of ~29.6 m.
When the output power is reduced to half of the original power, frequency bandwidth is 3-dB bandwidth. With increasing the pump power to ~90 mW and optimizing the PC, the typical spectrum of SP is shown in Figure 3(a). The SP centered at ~1530.3 nm exhibits a smooth spectral profile with a 3-dB bandwidth of ~9.59 nm. Figure 3(b) shows the RF spectrum of SP revealing that fundamental repetition rate is ~6.95 MHz, which is almost the same to that of CS due to the similar central wavelength. Meanwhile, we can get the SNR of ~52 dB, which indicates the stability of the SP. The corresponding autocorrelation trace is depicted in Figure 3(c). The FWHM of SP is ~1.42 ps, and the pulse duration is estimated as 1.0 ps if a Gaussian fits the curve. Therefore, the TBP of SP is calculated as 1.2 which is much larger than the transform limit, and is the typical characteristic of SP. Figure 3(d) illustrates the oscilloscope trace, showing that
Figure 3. Stretch pulse (SP) operation of (a) Optical spectra, (b) RF spectra, (c) AC trace, (d) Oscilloscope trace.
the round-trip time of the cavity is ~144 ns.
In our experiment, the spectral filtering effect plays an important role on the pulse formation. The polarization sensitive DF-SA and PC can be considered as a NPR-induced spectral filter and the intensity transmission of light through the filter, T, can be expressed as 
where ϕ1 is the phase delay caused by the PC and ϕ2 is the phase delay resulting from the fiber including both the linear phase delay and the nonlinear phase delay. The polarizer and analyzer have an orientation of angles θ and φ with respect to the fast axis of the fiber, respectively. From Equation (1), one knows that the bandwidth of NPR-induced filter varies with PC states. Therefore, the different PC’ settings will generate pulses with different bandwidths, which in turn lead to various stretching factors  . When the stretching factor is small enough and the interplay between anomalous cavity dispersion and positive Kerr nonlinearity of the fiber is balanced, the laser will operate in the soliton regime with spectral sidebands. As the stretching factor increases, spectral sideband generation will be reduced and there will be less dispersive radiation between pulses. Thus, stretched pulses will be generated with cleaner and broader spectra in the cavity when the stretching factor is large enough. Moreover, the solitons can be maintained as the pump power changes from the self-starting threshold to the maximum available power (550 mW), so the SA displays an ultra-high optical damage threshold.
By employing a DF-SA, we have proposed a simple and compact fiber laser system that can deliver CS and SP. With optimizing the PC properly and adjusting the pump power appropriately, we can achieve the CS and SP that have the similar central wavelengths and fundamental repetition rates. Because of the different pump powers and operations on PC, the stretching factor which is tunable due to the spectral filtering effect induced by NPR varied dramatically, they have different pulse durations, 3-dB bandwidths and optical spectra. The pulse duration and 3-dB bandwidth of CS centered at 1530.6 nm are ~0.7 ps and 4.46 nm while that of SP with central wavelength of 1530.3 nm are ~1.0 ps and 9.59 nm, respectively. Our experimental setup of the nanotube-based Fiber Laser can realize the ultrashort pulse generation and fast measurements. But the key physical parameters (such as pulse energy, pulse width and peak power) still lag behind that of the solid laser. It is attractive and convenient for practical research applications of ultrashort pulse field because of the proposed fiber laser delivering two types of pulses.
The work was supported in part by national natural science foundation of China (No. 61540012), National scholarship foundation (201609480004), Natural Science Foundation of Hunan Province (2017JJ2097, 2018JJ2132), and Education Department of Hunan Province (16A067), Hunan University of Science and Technology Research Fund (No. 908A11567), and Science research fund of Hunan Province Key Laboratory of Coal Resources Clean-Utilization and Mine Environment Protection (No. E21698).
Cite this paper
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