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Harmonic Order-Dependent Pulsewidth Shortening of a Passively Mode-Locked Fiber Laser With a Carbon Nanotube Saturable Absorber Volume 4, Number 5, October 2012 Kuang-Nan Cheng Yung-Hsiang Lin Shinji Yamashita Gong-Ru Lin, Senior Member, IEEE

DOI: 10.1109/JPHOT.2012.2210398 1943-0655/$31.00 ©2012 IEEE

IEEE Photonics Journal

Passively Mode-Locked Fiber Laser

Harmonic Order-Dependent Pulsewidth Shortening of a Passively Mode-Locked Fiber Laser With a Carbon Nanotube Saturable Absorber Kuang-Nan Cheng, 1 Yung-Hsiang Lin, 1 Shinji Yamashita, 2 and Gong-Ru Lin,1 Senior Member, IEEE 1

Graduate Institute of Photonics and Optoelectronics, Department of Electrical Engineering, National Taiwan University, Taipei 10617, Taiwan 2 Department of Electronic Engineering, The University of Tokyo, Tokyo 113-8656, Japan DOI: 10.1109/JPHOT.2012.2210398 1943-0655/$31.00 Ó2012 IEEE

Manuscript received July 14, 2012; accepted July 21, 2012. Date of publication July 31, 2012; date of current version August 16, 2012. This work was partially supported by the National Science Council, Taiwan, under Grants NSC98-2221-E-002-023-MY3, NSC99-2622-E-002-024-CC2, and NSC1012622-E-002-009-CC2. Corresponding author: G.-R. Lin (e-mail: [email protected]).

Abstract: A pumping-power-dependent high-order harmonic mode-locking erbium-doped fiber laser (HML-EDFL) with a single-wall carbon nanotube (SWCNT)-doped polyvinyl alcohol (PVA)-based saturable absorber is investigated. The HML-EDFL systems using either all-physical-contact (PC) or all-angled-physical-contact (APC) connectors examined in this study show stably mode-locked pulse trains; however, the all-PC connector-based system requires a larger pumping power to initiate the mode-locking and generate a broader pulsewidth of 2.9–5.2 ps at same HML order. The all-APC connector-based HML-EDFL system can provide pulsewidth shortening from 3.8 to 1.9 ps associated with a spectral linewidth broadened from 0.7 to 1.36 nm by increasing the HML order from first to sixth. Either the all-PC or the all-APC connector-based EDFLs can deliver a nearly transformlimited pulse with a time–bandwidth product (TBP) of 0.32. The EDFL passively modelocked by SWCNT-doped PVA delivers a pulse train with a signal-to-noise ratio (SNR) remaining higher than 40 dB for different HML orders, whereas the side-mode suppression ratio (SMSR) lower than 32 dB inevitably introduces an unequalized peak amplitude phenomenon for adjacent pulses at higher HML operations. A modified Haus’ master equation is derived to explain the inverse proportionality of the passive HML-EDFL pulsewidth to the square root of HML order, which is correlated with the shortened carrier recombination time of the SWCNT saturable absorber at higher pumping power or circulating pulse intensity. Index Terms: Carbon nanotubes and confined systems, mode-locked lasers, erbium lasers, fiber lasers.

1. Introduction Passive mode-locking of erbium (Er)-doped fiber laser (EDFL) and ytterbium (Yb)-doped fiber lasers that generate self-started picosecond pulses by using single-wall carbon nanotube (SWCNT)-based saturable absorbers has been demonstrated in the past few years [1]–[9]. In 2004, Set et al. demonstrated an SWCNT-based saturable absorber for suppressing the intensity noise of ultrafast optical pulses in the picosecond regime [1]. By incorporating an SWCNT saturable absorber, Yamashita et al. also demonstrated the passive mode-locking of a 2-cm-long Er and Yb

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co-doped fiber Fabry–Pe´rot laser with a pulsewidth of 680 fs at a repetition rate of 5 GHz [3]. Subsequently, Martinez and Yamashita also demonstrated a linear-cavity passively mode-locked EDFL with a fundamental repetition rate of up to 19.45 GHz [4]. Recently, Chiu et al. have employed an SWCNT-doped polymer film to investigate the effects of concentration and thickness of the SWCNT-doped polymer film on starting the passive mode-locking and on shortening the EDFL pulses [8], [9]. Until recently, most works were focused on mode-locking the EDFLs at a fundamental frequency (decided by longitudinal mode spacing) using SWCNT-based saturable absorbers, whereas the harmonic mode-locking (HML) capability of the SWCNT-based saturable absorbers was seldom discussed. A 23rd-order passive HML of the EDFL with a pulsewidth of 1.3 ps was experimentally observed at a central wavelength of 1530 nm [10]. In addition, the adjustment of the repetition rate of a passively mode-locked fiber laser was proposed by using a delayed optical path scheme. The phenomenon of a passive HML-EDFL with 500-fs pulsewidth at a harmonic frequency of 2 GHz using a nonlinear amplifier loop mirror (NALM) and a multiple-quantum-well saturable absorber was demonstrated as early as 1997 [11]. Alternatively, a passive HML-EDFL based on nonlinear polarization rotation (NPR) at harmonic repetition frequency of up to 1.2 GHz has been reported [12]. In a theoretical analysis, Kutz and Sandstede characterized the nonlinear mode coupling (NLMC) behavior in a waveguide array to explain the HML mechanism [13]. An ML/HML switchable EDFL, with its pulsewidth varying at different HML orders, was also demonstrated by different pumping powers. Either the ML or the HML can be initiated with a semiconductor saturable absorber mirror (SESAM) and adjusted by controlling the intracavity polarization [14]. The HML technique has been frequently used in actively modulated EDFL systems but has been seldom observed and discussed in the passively mode-locked EDFL systems. The reason is that the HML technique is hard to control in such passively mode-locked lasers that are started with inherent saturable absorbers. Nevertheless, the passive HML of EDFL is still worthy of a detailed investigation because passive mode-locking can provide a shorter pulsewidth than active modelocking, and the higher HML order can enable a passive HML-EDFL to deliver a pulse train with repetition frequency as high as an active HML-EDFL. More specifically, the establishment of a theoretical HML model is required to understand the correlation between the pulsewidth and the HML order in a passive HML-EDFL system. In this paper, the use of intracavity polarization adjustment in the passive HML-EDFL systems with either physical-contact (PC) or angled-physicalcontact (APC) connectors is demonstrated and compared. The performances of the EDFL with variable HML from first to sixth order by using an SWCNT-doped polyvinyl alcohol (PVA) film as a fast saturable absorber are characterized. The HML performances of the EDFL systems using either all-PC or all-APC connectors are analyzed and compared. Except for the absorption and propagation losses of the EDFL cavity, all of the connectors between adjacent patchcords also contribute an additional loss in the EDFL cavity that limits the pulsewidth shortening. Using APC connectors can reduce the interfacial reflection to decrease the connection loss, thus enabling a shortened laser pulsewidth to be produced from the passively mode-locked EDFL cavity. The strong competition between the fundamental and the harmonic frequency components under highorder HML operation is observed and elucidated. In addition, the correlation between the HMLEDFL pulsewidth and the HML order is derived from the modified Haus’ master equation. The pulsewidth of the passive HML-EDFL is observed to be shortened with increasing HML order.

2. Experimental Setup The passive HML-EDFL system with an intracavity SWCNT-doped PVA film is illustrated in Fig. 1(a). The total cavity length of the EDFL is approximately 28.5 m, which consists of a 980/1550-nm wavelength-division multiplexing (WDM) coupler for launching the 980-nm pumping laser into the EDFL cavity, an isolator to control the direction of light circulating in the EDFL fiber ring, a polarization controller (PC) for adjusting the HML order, a 90/10 output coupler (OC), and the SWCNT-doped PVA-film-based saturable absorber inserted between either the FC/PC- or the FC/APC-type ferrule connectors. The remainder of the EDFL ring cavity consists of a single-mode fiber (SMF, Corning SMF-28). The group velocity delay (GVD) parameters of SMFs and Er-doped fibers (EDFs) are


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Fig. 1. (a) The configuration of the passive HML-EDFL system. Inset shows the fiber connector with the SWCNT-doped PVA film. (b) The variations of HML order of mode-locking EDFL with different pumping powers.

approximately estimated to calculate the net group delay dispersion (GDD) in the passive HMLEDFL cavity [15]. The only different parameter between the all-PC and the all-APC constructed EDFL architectures is the type of connector used in the EDFL cavity. All of the cavity parameters, including GVD, cavity length, and coupling ratio, remain unchanged for both of the passive HMLEDFL systems with all-PC and all-APC connectors. All of the fiber-based components are packaged in a cylindrical stainless steel case to ensure the robustness of the entire system. The stainless package is isolated from other circuitry and current sources to prevent the system from thermal and electromagnetic influences. Only the screw of the PC is accessible to adjust the HML order during the experiment. The intracavity polarization plays an important role to obtain stabilized HML [14]. A programmable controlled PC is inserted to record the polarization change for different HML orders quantitatively. The optimized HML varying from fundamental to the sixth order is achieved by further increasing the pumping power from 45 to 100 mW [see Fig. 1(b)]. The pulsewidth, pulse train, and spectra linewidth of the passive HML-EDFL setups with either all-PC or all-APC connectors are characterized by an autocorrelator (Femtochrome, FX103L), a sampling oscilloscope (Agilent 86100A), an optical spectrum analyzer (Ando, AQ-6317B), and an RF spectrum analyzer (Agilent 8565E).

3. Results and Discussion Fig. 2(a) and (b) shows the nonlinear transmittance and nonlinear absorption of the SWCNT-doped PVA film used as a saturable absorber. A pulsed laser with duration of 700 fs at central wavelength


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Fig. 2. (a) The nonlinear transmittance and corresponding loss and (b) the nonlinear absorption of the SWCNT-doped PVA film used for the passive HML-EDFL systems.

Fig. 3. Autocorrelation traces of the passive HML-EDFL with (a) all-PC and (b) all-APC connector systems. (c) The variations of pulsewidth with all-PC and all-APC systems versus pumping power.

of 1560 nm is employed as the pumping source. The transmittance of the SWCNT-doped PVA film increases from 0.625 to 0.7 as the pumping intensity increases from 0.3 to 300 MW/cm2 . The linear (i.e., nonsaturable) loss of the SWCNT-doped PVA film measured by using a continuous-wave laser source at same wavelength is 2.2 dB at a pumping power of 1 mW. According to the highpower pulsed laser analysis, the absorbance of the SWCNT-doped PVA film is saturated at 0.47, corresponding to a saturable loss as small as 1.5 dB. The modulation depth is up to 11%, as shown in Fig. 2(b). In the all-PC connector-based system, the higher HML order can be easily obtained by increasing the pumping power and by slightly adjusting the intracavity polarization. Fig. 3 shows the autocorrelated pulse shapes of the fundamental, second-, third-, fourth-, fifth-, and sixth-order HML under a pumping power of 45.5, 49, 52.5, 70, 85, and 100 mW, respectively. Due to the design of a completely dispersion-compensated cavity, the EDFL with an intracavity all-PC connector scheme


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Fig. 4. (a) RF spectra of the passive HML-EDFL. (b) The SNR and SMSR of the passive HML-EDFL pulse at different HML orders.

can still operate under passive HML to deliver a pulse that can be perfectly fitted by a hyperbolic secant function. However, the effective cavity gain in this all-PC connector system is not sufficient to produce a short pulse; only a modest pulsewidth shortening is provided from 5.2 to 2.9 ps by increasing the HML order, as shown in Fig. 3(a). By changing all of the intracavity patchcords from PC to APC connectors to reduce the interfacial reflection, a significantly shortened HML pulsewidth can be obtained from the all-APC connector-based EDFL system [see Fig. 3(b)]. Reducing the interfacial reflection can decrease the cavity loss, which enhances the intracavity gain and the circulating power because the pulsewidth of the passively mode-locked EDFL is inversely proportional to the square root of the intracavity power [16], as shown in 2 ¼

2Dg jAj2

(1)

where Dg is the gain dispersion, and and A are the modulation depth and the wave amplitude, respectively. Therefore, a narrower pulsewidth can be obtained by using the all-APC connector system. In comparison to the all-APC connector-based scheme, the all-PC connector-based scheme requires a higher threshold pumping power to provide the passive HML-EDFL. This result is mainly attributed to the additional loss caused by the end-face reflections of the all-PC connectors, which inevitably leads to a smaller effective cavity gain for the passive HML-EDFL. As a result, the insufficient gain leads to a broadened pulse with reduced spectral linewidth. Fig. 4(a) shows the optoelectronic-converted HML spectra involving different harmonic frequency compositions for the all-APC connector-based EDFL at different HML orders. With the same frequency ranging from 0 to 250 MHz, the dominated HML frequency component group increases


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Fig. 5. (a) The spectra of the passive HML-EDFL with all-PC connector; left: y -axis in linear scale, right: y -axis in log scale. (b) The spectra of the passive HML-EDFL with all-APC connector; left: y -axis in linear scale, right: y -axis in log scale.

its spacing from 7 to 42 MHz with increasing HML order. The side-mode suppression ratio (SMSR) in the RF power spectrum is defined as the stationary (time-averaged) RF peak power ratio of the principle mode to the second most dominant side mode, as given by SMSRdB ¼ 10logðPP =PP 0 Þ ¼ PP; dB PP 0 ; dB , where PP and PP 0 represent the RF peak powers of the desired HML frequency component and the second largest frequency component at other harmonics. The SMSR shows distinct enhancement at lower HML orders; however, a degraded SMSR of the higher HML frequency component is also observed. In addition, the signal-to-noise ratio (SNR) of the HML frequency component to the noise background mode-locked EDFL system is analyzed to characterize the mode-locking quality, which is defined as SNRdB ¼ 10logðPsignal =Pnoise Þ ¼ Psignal;dB Pnoise;dB , with Psignal and Pnoise denoting the RF peak powers of the desired harmonic signal and the noise background, respectively. The SNR remains nearly constant at 40 dB, whereas the largest SMSR at each HML condition is gradually saturated at 25–32 dB due to the competition between the harmonic and the fundamental mode-locking mechanisms [see Fig. 4(b)]. The total length of the SMF with a GVD parameter 2 of 20 ps2 =km used in the EDFL cavity is 16 m [15]. The length of the EDF with 2 of 17 ps2 =km used in the EDFL cavity is 12.5 m. After calculation, the residual GDD parameter is only 0:1 ps2 , and the EDFL cavity is in the anomalous dispersion regime. A long EDFL cavity without precise temperature and environmental control


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Fig. 6. (a) Average output power versus pumping power for both the all-PC and all-APC connector systems. (b) Output pulse energy versus pumping power for both the all-PC and all-APC connector systems.

inevitably introduces unwanted fluctuations, so the HML pulse train could become unstable for a long-cavity case. Therefore, the higher order HML is possible with a better management of the cavity dispersion, the cavity length, and the feedback control. Note that the different HML orders can also be adjusted by changing the pumping power in the all-APC EDFL system, and a pumping power lower than that required for the all-PC EDFL system (45–100 mW for first- to sixth-order HML) is observed. In comparison to the all-PC connector system, the all-APC connector system requires less pumping power to launch the HML at different orders. A comparison of the autocorrelated traces from both systems reveals that the output of the passive HML-EDFL is more stable in the all-APC connector system because the dc level and the intensity fluctuation of the autocorrelated pulse traces obtained from the passive HML-EDFL cavity is greatly suppressed [see Fig. 3(a) and (b)]. Simultaneously, the intensity fluctuation of the SWCNT-doped PVA passively mode-locked EDFL pulse train is monitored using a digital sampling oscilloscope (Agilent 86100A with 86106B plug-in module). The output of HML in the all-APC connector-based EDFL system exhibits improved stability over that in the all-PC connector-based EDFL system. The switching of HML order strongly depends on the pumping power, and the generation of a higher HML order pulse train usually requires a larger pumping power. The entire system is still operated in a self-amplitude modulation regime because the Kelly sideband spectrum is not observed [17]. Nevertheless, the pulse is significantly shortened by changing the connectors from PC to APC, thus providing pulsewidths in the range of 1.9–3.8 ps by using the all-APC connector-based EDFL system, as shown in Fig. 3(c). The all-APC connector-based EDFL delivers a shorter pulsewidth because it reduces unwanted intracavity reflection from adding to the cavity loss of the EDFL, thereby increasing the effective intracavity gain ðg 0 ¼ g LÞ to further shorten the mode-locked pulsewidth. Fig. 5(a) shows that the spectral linewidth of the HML pulse in the all-PC connector system ranges from 0.5 to 0.93 nm, whereas the spectral linewidth of the HML pulse from the all-APC connector-based EDFL is broadened from 0.7 to 1.36 nm, as shown in Fig. 5(b). Obviously, the amplified spontaneous emission (ASE) of the all-PC spectrum is larger than that of the all-APC spectrum due to the lower mode-locking strength. Due to a lower pulse-shortening force, the residual ASE component in the spectra output from the all-PC connector-based system is much broader than those from the all-APC connector-based system, as shown in Fig. 5. This result can also be treated as a direct evidence for the incomplete mode-locking of the all-PC connector-based EDFL system. Fig. 6(a) shows the average output power versus the pumping power for both the all-PC and allAPC connector systems. The pulse energy shown in Fig. 6(b) is simply calculated by Ep ¼ Ppk p ¼ cTPave , with Pave denoting the average output power, Ppk denoting the peak power, c ¼ 0:8814 for a sech2 pulse, and T and p as the pulse repetition period and the pulsewidth, respectively [18].


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Fig. 7. Relationship between pulsewidth and HML order of all-PC and all-APC connector-based EDFL systems.

Fig. 7 shows the relationship between the pulsewidth and the HML order for the EDFL with all-PC and all-APC connector-based configurations. The pulsewidth in the all-PC connector-based system is shortened from 5.2 to 2.9 ps and that in the all-APC connector system is shortened from 3.8 to 1.9 ps, with the HML order increasing from first to sixth. More specifically, the HML phenomenon observed in the passively mode-locked EDFL is quite similar to that observed in the actively mode-locked system, where the multiple-period fast saturable absorption effect of the SWCNT occurring within one period is thought to play an important role. In other words, the pumpingpower-dependent HML order indicates that the absorption of SWCNT may be saturated and recovered for several times if the pumping power is sufficiently large to support the gain of the intracavity circulated HML pulse. One piece of evidence for this saturation behavior is that the equation for the carrier recombination time can be given by ¼ h N!=I [19], where N denotes the saturable carrier density, ! represents the frequency of light, is the nonlinear saturable absorption coefficient, and h is the reduced Planck’s constant. At the same saturable carrier density, there is an inverse relationship between the carrier recombination time and the intracavity pulse intensity. However, this equation is only valid for the results obtained under continuouswave or long-pulse excitation. To clarify, Haus’ master equation for the passively mode-locked lasers is subsequently used to derive the proper relationship between the shortened pulsewidth and the HML order. Therefore, the modulation coefficient employed to describe the saturable absorption needs to be modified by a periodically changed one during such an HML process, and the modeling work using a modified Haus’ master equation is necessary to provide a proper result. The solution of such an HML pulse derived from the modified Haus’ master equation is compared with the one established for the active mode-locking case. In principle, the HML pulsewidth of an active HML laser system reveals a proportionality to the fourth root of gain and is inversely proportional to the square root of the modulating frequency and the modulation coefficient. The actively mode-locked pulsewidth shortening with increasing HML order [20] can be theoretically modeled to yield an empirical formula of p ¼ ð2ln2=2 Þ1=2 ½ð2g0 =@ 2 Þ1=4 =ðfm Þ1=2 , where p is the pulsewidth, g0 is the single-pass integrated gain, fm is the modulation frequency, is the modulation depth, and is the homogeneous linewidth. In principle, the active HML pulsewidth of the modelocking pulse is inversely proportional to the square root of the HML order M times of the fundamental frequency [21]. In the passive HML case without group-velocity dispersion and self-phase


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modulation, the pulse train exhibits a repetition time defined as one Mth of its round-trip time ðTR Þ, and the solution of the modified Haus’ master equation shown below is still a hyperbolic secant function [16], " # n 1 X TR @AðT ; t Þ @ @2 2 ¼ l þ j Dn j þgðT Þ 1 þ Dg 2 qðT ; t Þ jjAðT ; tÞj AðT ; tÞ @T @t M @t n¼2 2 @ ¼ g l þ Dg 2 q0 jAj2 AðT ; t Þ @t @2 2 ¼ g l0 þ Dg 2 þ jAj AðT ; t Þ (2) @t where AðT ; t Þ denotes the field function, l is the EDFL cavity loss, Dn is the nth-order dispersion, gðT Þ is the EDFL gain, Dg is the gain dispersion, qðT ; t Þ is the saturable absorption of the SWCNT, and @jAj2 is the self-phase modulation term. By utilizing the solution of AðT ; tÞ ¼ A0 sechðt=p Þ into the master equation, the passive HML pulsewidth can be derived from the following equation obtained under steady-state condition, Dg g0 ¼ l0 W p2 1 þ P ðT SAT

;

(3)

R =MÞ

where l0 ¼ l þ q0 denotes the total cavity loss that includes the linear absorption of the saturable absorber, W is the pulse energy, and PSAT is the saturated power of the saturable absorber. In particular, TR =M is the round-trip time of the cavity as well as the reciprocal repetition rate of the passive HML-EDFL pulse train. This equation clearly indicates the relationship between the pulsewidth and the HML order M. After the derivation under an approximation of the passive HML at near threshold (with g0 l0 ), the passive HML pulsewidth can be simplified as, vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi #1ffi u " u g0 p ¼ tDg l0 W 1 þ PSAT ðT R =MÞ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dg ½PSAT ðTR =MÞ þ W ¼ l0 ½PSAT ðTR =MÞ þ W g0 PSAT ðTR =MÞ vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i ffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uD h u g 1 þ PSAT ðTR =MÞ u l0 Dg W PSAT TR 1 t ffi ¼ 1þ : (4) l0 W M 1 ðg0 l0 Þ PSAT ðTR =MÞ l0

W

In (4), note that the passive HML pulsewidth reveals an inverse proportionality with the HML order M. The passively mode-locked EDFL exhibits a maximum pulsewidth of p ¼ ½Dg ð1þ PSAT TR =WMÞ=l0 0:5 , which can be significantly shortened to p ¼ ½Dg =l0 0:5 at an extremely high HML order. Due to the inverse square-root function and the larger gain needed to obtain a higher HML output, the pulse-shortening force [defined as the ratio of second-harmonic generation (SHG) peak intensity to the square of fundamental average power] [22] becomes smaller at higher HML orders, and the higher order operation becomes more unstable. Therefore, the optimal condition that can be obtained in this work is limited at the HML order M ¼ 6 with a pulsewidth of 1.9 ps. The experimental results almost confirm such an inverse square-root dependence except for a small deviation at lower HML orders. As the intracavity pumping power and the pulse intensity increase, the carrier recombination time reduces, and the frequency of absorption bleaching concurrently increases. When the pumping power is sufficiently large enough to provide high gain in the EDFL cavity, the saturated absorption frequency of CNT also increases to facilitate HML within one round-trip of the laser pulse. Both the experimental and simulated results indicate that the intracavity circulating intensity determines the highest HML order of the EDFL output. On the other hand, the HML order


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at a sufficiently high pumping level can be controlled by adjusting the PC prior to the SWCNT saturable absorber, which effectively adjusts the circulating intensity passing through the SWCNT saturable absorber to control the absorption bleaching frequency of the saturable absorption.

4. Conclusion An SWCNT-doped PVA film is employed as a fast saturable absorber to induce up to sixth-order passive HML-EDFL with either all-PC or all-APC connector-based EDFL cavity configurations. Both the all-PC and the all-APC connector-based passive HML-EDFL systems can deliver stable pulse trains with the robust setup of EDFL fiber-ring; however, the all-PC connector-based system requires a larger pumping power to initiate mode-locking at the same HML order. In particular, the all-APC connector-based HML-EDFL scheme can provide a shorter pulsewidth associated with a broader spectral linewidth than the all-PC connector-based system. In comparison to the pulsewidth of 2.9–5.2 ps delivered by the all-PC connector system, the all-APC connector system further shortens the pulsewidth from 3.8 to 1.9 ps as the HML order increases from first to sixth. Concurrently, the spectral linewidth is broadened from 0.7 to 1.36 nm. At the sixth-order HML condition, either the all-PC or the all-APC connector-based EDFL can deliver a nearly transformlimited pulse with time–bandwidth product of 0.32. The SNRs obtained at different HML orders remain nearly constant at 40 dB; however, the RF spectral analysis reveals a relatively strong competition between the fundamental and the harmonic frequency components especially at higher order HML conditions. This phenomenon inevitably introduces the unequalized peak amplitudes among adjacent pulses, thus leading to an SMSR saturating at 32 dB under higher HML operation. The correlation between the HML-EDFL pulsewidth and the HML order is derived from the modified Haus’ master equation. By solving the equation with a solution of hyperbolic secant function, the HML-EDFL pulsewidth shows an inverse proportionality with the square root of the HML order. In experiment, the change of HML order is preliminarily demonstrated by adjusting the pumping power of the passive HML-EDFL. The frequency of the saturated absorption in SWCNT can be increased by enhancing the pumping power in the EDFL cavity, which also facilitates HML within one roundtrip time. The experiment indicates that the intracavity circulating intensity determines the highest HML order of the passively mode-locked EDFL output.

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