The dependence of thickness and concentration product (TCP) of single-wall carbon nanotubes saturable absorber (SWCNTs SA) on stabilizing and shortening pulsewidth in mode-locked fiber lasers (MLFLs) was investigated. We found that an optimized TCP for pulse energy and nonlinear self-phase modulation (SPM) enabled to determine the shorter pulsewidth and broader 3-dB spectral linewidth of the MLFLs. The shortest MLFL pulsewidth of 418 fs and broad spectral linewidth of 6 nm were obtained as the optimized TCP was 70.93 (μm•wt%), which was in good agreement with the area theorem prediction. This significant effect of TCP on pulse energy, SPM, pulsewidth, and spectral linewidth of MLFLs suggests that the TCP represents the total amount of SWCNTs in SA, which can be used as one of important and key parameters for characterizing the passive MLFL pulsewidth.
© 2011 OSA
Passively mode-locked erbium-doped fiber laser (MLEDFL) generating optical pulses in picosecond and femtosecond regimes [1,2] is often initiated from noise filtering by nonlinear optical elements with nonlinearly intensity-dependent response to facilitate optical pulsation from continuous–wave (CW) emission . The single-wall carbon nanotubes saturable absorber (SWCNTs SA) has been developed by a simple spin or spray coating process to function as a nonlinear optical element for mode-locking lasers [4–8]. The stabilization and shortening of MLEDFL pulse based on the parametric tuning of SWCNTs SA has been presented [9,10]. It was found that the compromise between thickness and concentration of SWCNTs SA is critical to optimize pulse shortening of the MLEDFL.
Despite numerous studies on shortening the pulsewidth of MLEDFL [9,10], limited information is available for quantitatively analyzing the optimized concentration and thickness of the SWCNTs SA for the MLEDFL. Our early study focused on the individual effect of thickness and concentration on MLEDFL pulsewidth . In this work, we extend our study to emphasize the effect of thickness and concentration product (TCP) on optimizing the pulse duration. The TCP represents the total amount of SWCNTs, which the optical beam encountered when passing through the SWCNTs SA in three spatial dimensions. The total amount of SWCNTs in SA is one of important characteristics to determine the shorter pulsewidth and broader 3-dB spectral linewidth of the MLFLs. We further survey the influence of the nonlinear SPM on shortening the MLEDFL pulse under the presence of SWCNTs SA.
When operating at quasi-soliton mode with enhanced SPM, the pulsewidth was characterized based on the area theorem. From the measured pulse energy and estimated SPM, the area theorem is employed to evaluate the behavior of pulsewidth. The optimized TCP of SWCTNs SA is determined by the existence of shortest pulsewidth. The analysis via area theorem thus provides an efficient method to design and fabricate the SWCNTs SA for obtaining shortest pulsewidth of the MLEDFLs initiated by SWCNTs SA. In comparison with the previous work using the same system, we discuss the parametric optimization by detuning the TCP and investigate the SPM effects in EDFL fiber ring and SWCNT based SA to shorten the mode-locked EDFL puslewidth from ps to fs regime. In particular, the EDFL cavity length is shortened to make the repetition rate enlarged from 11.1 MHz to 26.32 MHz, such that the intra-cavity GVD is also optimized to compensate the SPM for a chirp-free soliton pulse generation in this work.
The SWCNT material was purchased from Golden Innovation Business Company. The diameter distribution of the SWCNTs was chosen from 1 to 1.5 nm to match the EDFL ring operating at 1550 nm. The water-soluble polyvinyl alcohol (PVA) of high molecular weight was used as the substrate for films. A detailed fabrication of the SWCNTs SA was described in the reference 9. Figure 1 illustrates the setup of the MLEDFL with an intra-cavity SWCNTs SA. The total length of the ring cavity was 7.6 m with average GVD of −0.02 ps2/m. A 980 nm diode laser was used to pump the erbium-doped fiber (EDF) based gain medium. The SWCNTs SA inserted between two FC/APC fiber connectors was integrated into the MLEDFL to generate ML pulses. An isolator was employed to prevent back reflection and to ensure the unidirectional propagation. The emission light passes through the SWCNTs SA and feedbacks into the MLEDFL through a 40% output coupler. The 60% output port was connected to the autocorrelator, the oscilloscope, and the optical spectrum analyzer for monitoring the pulsewidth, the pulse-train, and the spectral linewidth, respectively. For single pulse soliton ML regime, the pumping level is detuned from 35 to 55 mW according to the SWCNTs SA that we used. The output energy ranged from 35 to 60 pJ. The repetition rate of the MLEDFL was 26.32 MHz under single-pulse ML operation.
First of all, the pulse shaping ability under quasi-soliton ML operation is investigated to be sustained by increasing the TCP of the SWCNTs SA. In order to avoid the aggregation of SWCNTs and remain the uniformity of the dispersed SWCNTs in thin film, the SWCNT concentration cannot be infinitely increased [9,11]. In this work, the density of PVA is set to be equivalent with that of the SWCNT, such that the SWCNT concentration could be simply calculated as the total amount of SWCNTs within the beam cross section per unit length. Therefore, the TCP exactly represents the total amount of SWCNTs that the optical beam encountered when passing the SWCNTs SA.
Based on area theorem , the SPM can be estimated from the measured pulsewidth, the intra-cavity energy, and the linear GVD according to the following relationship12]Eq. (2) clearly elucidates that the SPM is proportional to the thickness of the medium (in consistence with the estimated SPM).
3. Results and discussions
First of all, the effects of the TCP on the absorption and modulation depth are characterized. The measurements of Figs. 2(a) and 2(b) were performed by a single pass optical transmission in external cavity. Figure 2(a) shows the modulation depth as a function of the TCP of SWCNT based SA. The modulation depth is sensitive to the TCP, which significantly reduce from 5% to 2% as the TCP enlarges 40 μm-wt% or higher. The decreased modulation depth is mainly due to the coupling loss from the connector of saturable absorber.
As expected, the Fig. 2(b) depicts the nonsaturable loss induced by inserting the SWCNT based SA into the EDFL cavity as function of TCP. The nonsaturable loss linearly increased as TCP increases from 20 to 50 μm-wt%, which eventually saturates at 7% as the TCP increases up to 80 μm-wt% or higher. It indicates that the lower intra-cavity pulse energy remains in the EDFL as the non-saturable loss increases.
To examine the performance of the quasi-soliton MLEDFL pulses initiated by different SWCNTs SAs used in the ring cavity, the whole laser parameters were hold except the TCP of the SWCNTs SA. Figure 3 shows that the threshold pumping powers required for the EDFL working in continuous-wave lasing, mode-locking and harmonic mode-locking regimes are plotted as a function of the TCP of SWCNTs SAs. When the pumping power was lower than the threshold condition set for CW lasing, the Er fluorescence based spontaneous-emission spectra can be measured. As the pumping power becomes larger than the threshold value of CW emission at around 1560 nm, the laser output transfers from CW lasing to single-pulse ML operation (through an unstable and temporary Q-switch operation). When the pumping power is increased above threshold value at single-pulse ML operation regime, the spectrum broadens and the pulsewidth shortens with increasing pumping power. With the pumping power exceeding the threshold pumping power of harmonic mode locking (HML) regime, the MLEDFL starts to deliver multiple pulse-train. As obtained from Fig. 2, it is necessary to employ a higher threshold pumping power for achieving CW lasing, ML, and HML operation of the EDFL as the TCP increases.
Figure 4(a) shows the optical spectrum of the MLEDFL output with TCP of 10.66 and 93.83. Both the two optical spectra reveal the Kelly sideband. In addition, the central wavelength blue-shifts from 1560.92 to 1557.32 nm as the TCP increased. The Fig. 4(b) plots the spectral linewidth as a function of TCP. By increasing the TCP from 10.66 to 93.83, the spectral linewidth slightly broadens from 5.04 to 6.00 nm.
Figure 5(a) depicts the measured autocorrelation traces of the MLEDFL with TCP of 10.66 and 93.83. The autocorrelation traces can be well fitted by the hyperbolic-secant-square pulse profile. The MLEDFL pulsewidth versus TCP is shown in Fig. 5(b). With the TCP increasing from 10.66 to 70.93, the pulsewidth is decreased from 493 to 418 fs. However, an oppositely increasing pulsewidth is observed as the TCP further detunes to exceed 70.93. The spectral linewidth and pulsewidth of the MLEDFL reach a limit at about 6.00 nm and 418 fs, respectively. The time-bandwidth product (TBP) ranged between 0.315 and 0.33 which is relatively close to the theoretical value of 0.315 (the minimum TBP of a hyperbolic-secant-square pulse under transform limit). From the results shown in Figs. 4 and 5, the total effective amount of SWCNTs is critical to the pulsation characteristics of the MLEDFL.
It is important to discuss the variation of the individual parameters in the TCP, i.e. the concentration and thickness of the SWCNT based SA, and their effects on the MLEDFL pulsewidth and linewidth. The pulsewidth and spectral bandwidth of the mode-locked EDFL versus the thickness and concentration of the SWCNT based SA are illustrated as below (see Fig. 6 ). With a constant SWCNT concentration at 0.375 wt%, the spectral linewidth is broadened from 1.5 to 6.0 nm by increasing the SWCNT SA thickness from 10 to 200 μm. The MLEDFL pulsewidth is decreased from 1.8 ps to <500 fs as the thickness is increased to 136 μm. In the mean time, the spectral linewidth of the MLEDFL reaches a limit at about 6.00 nm. The time-bandwidth product (TBP) ranged between 0.315 and 0.33 which is relatively close to the theoretical value of 0.315 (the minimum TBP of a hyperbolic-secant-square pulse under transform limit). From the results shown in right part of the following figure, the total effective amount of SWCNTs is critical to the pulsation characteristics of the MLEDFL. At a optimized thickness of 136 μm (as obtained from the left part of the figure), the MLEDFL pulsewidth is further decreased from 480 to 420 fs as the concentration of SWCNTs SA increased from 0.125 to 0.5 wt%.
The SPM is induced when the intra-cavity peak power of the SWCNT/PVA passively mode-locked EDFL is relatively high. In our case, the pumping power is sufficiently high and the ASE power of the EDFA under free-running case is exceeding over 17 dBm, which means the intra-cavity peak power has entered the low-order soliton regime by considering the EDFL cavity itself. Nonetheless, it could possibly the the highly concentrated SWCNT based SA also introduces another SPM effect. Therefore, we take the SWCNT induced SPM process into consideration. The SPM effect is not caused by the SWCNT SA itself but due to the EDFA fiber ring cavity if the concentration of SA is not extremely high. Therefore, we discuss the effect of the SWCNT on the SPM to see if the SPM can be further enhanced by the SWCNT based SA in our case.
Figure 7(a) shows the corresponding intra-cavity energy versus TCP at single-pulse ML regime. The increasing TCP inevitably enlarges the involuntary non-saturable absorber loss and connection loss. As the losses increase, the pulse energy is decreased accordingly. Figure 7(b) interprets the estimated SPM versus TCP based on the area theorem, in which the increasing TCP greatly enhances the SPM and achieves the quasi-soliton MLEDFL operation. From the enhanced SPM, the nonlinear refractive index n2 was calculated at a level of 0.4-1x10−15 m2/W that was close to the values of 10−15-10−16 m2/W reported in literature [13,14]. This result also corroborates the accuracy of the estimation on SPM in our work. By substituting the fitting functions of the pulse energy and the estimated SPM into the Eq. (1) with constant GVD, the simulated pulsewidth is calculated and shown in Fig. 7.
The experimental data shows a good agreement with the simulated results, and the existence of a shortest pulsewidth is also predicted. It also corroborates that the existence of the maximum “effective” amount of SWCNTs in SWCNTs SA. With insufficient SWCNTs in SA, the less ML strength is contributing to the EDFL. Nonetheless, the more SWCNTs could arise the nonsaturable loss in the ring cavity. This observation is similar with the results given in previous works [10,11]. The exceeding concentration of SWCNTs made the re-aggregation of the bundled SWCNTs, such that the performance of the MLEDFL pulses became worse. In addition, the excessive thickness also enhances the absorption of the SWCNTs SA film due to the non-saturable loss and the connection loss. All these factors degrade the MLEDFL performance and broaden its pulsewidth. The shortest pulse can only be obtained under compromised TCP of the SWCNTs SA.
Furthermore, the enhancement of SPM is achieved by increasing the TCP of SWCNTs SA to sustain the soliton-like ML operation. The further pulse compression could be made by further enhancing SPM under soliton-like ML condition, however, the inevitably increased TCP following with the enhanced SPM could degrade the MLEDFL pulse in opposite. That is, the soliton pulse energy is eventually decreased due to the increasing connector and nonsaturable absorber losses. The trade-off between the SPM parameter and the soliton pulse energy determines the behavior of the soliton-like ML pulses based on area theorem. Through the active Z-scan measurement, the nonlinear refractive index of the nonlinear element could be easily measured and the trend of SPM could be estimated. If we also realized the trend of pulse energy through few samples in MLEDFL, the behavior of pulsewidth can be theoretically simulated to find out the optimized SWCNTs SA based on area theorem.
In conclusion, the dependence of TCP of SWCNTs SA on stabilizing and shortening pulsewidth in mode-locked fiber lasers (MLFLs) was investigated and measured. As the TCP of SWCNTs SA increased, the pulse energy decreased and SPM increased. The trade-off between decreasing pulse energy and increasing SPM determined the behavior of pulsewidth based on the area theorem. At optimized TCP of 70.93 (μm•wt%), it was found that the shortest pulsewidth of 418 fs and broad 3-dB spectral linewidth of 6 nm were obtained. In this study, the TCP represents the total amount of SWCNTs in SA, which can be used as one of important and key parameters to determine the shorter pulsewidth and broader 3-dB spectral linewidth of the passive MLFLs.
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