An in-depth experimental investigation was conducted into the use of a graphene oxide-based saturable absorber implemented on a side-polished fiber platform for femtosecond pulse generation in the 2 μm region. First, it was experimentally shown that an all-fiberized thulium-holmium (Tm-Ho)-codoped fiber ring laser with reduced cavity length can produce stable femtosecond pulses by incorporating a graphene oxide-deposited side-polished fiber. Second, the measurement accuracy issue in obtaining a precise pulse-width value by use of an autocorrelator together with a silica fiber-based 2 μm-band amplifier was investigated. It showed that the higher-order soliton compression effect caused by the combination of anomalous dispersion and Kerr nonlinearity can provide incorrect pulse-width information. Third, an experimental investigation into the precise role of the graphene oxide-deposited side-polished fiber was carried out to determine whether its polarization-dependent loss (PDL) can be a substantial contributor to mode-locking through nonlinear polarization rotation. By comparing its performance with that of a gold-deposited side-polished fiber, the PDL contribution to mode-locking was found to be insignificant, and the dominant mode-locking mechanism was shown to be saturable absorption due to mutual interaction between the evanescent field of the oscillated beam and the deposited graphene oxide particles.
© 2013 OSA
Pulsed lasers operating at wavelengths of ~2 μm are a promising light source useful for a variety of applications such as gas detection , long-range LIDAR [2, 3], free-space optical communication , medical diagnostics , and laser surgery . They are also known to be suitable for material processing applications for plastics and glasses, which are not transparent in this spectral region. Due to a range of advantages over traditional free-space optics-based lasers in terms of beam quality, reliability, and environmental stability, optical fiber-based 2 μm pulsed lasers have been of high technical interest in recent years. Thulium (Tm), holmium (Ho), or Tm-Ho-codoped fiber is commonly used as a gain medium for 2 μm light emission.
The pulsed output from a laser cavity can be obtained by use of either Q-switching or mode-locking techniques. Since the temporal width and repetition rate of the output pulses obtainable from the Q-switching technique is limited, the mode-locking technique is known to be suitable for ultra-fast short pulse generation. For industrial and medical applications, the passive mode-locking technique is preferred to the active technique due to the possibility of achieving high peak power femtosecond pulses at a repetition rate less than tens of MHz without using external electrical signal sources. One of the key components for the implementation of self-started, passively mode-locked femtosecond pulsed fiber lasers is the saturable absorber.
The commonly used saturable absorbers have been based on semiconductors for a long time, and an alternative that is based on carbon nanotube (CNT) was reported in 2004 . Very recently, graphene, which has a honeycomb structure of single-layered carbon atoms, has been shown to be readily operable as a saturable absorption material for mode-locked, ultra-fast pulse generation [8–12].
The applicability of graphene-based saturable absorbers to 2 μm mode-locked pulse lasers has been intensively investigated as a hot issue in the ultra-fast laser field. Examples are mode-locking of a Tm:CNLGG laser , mode-locking of a Tm:YAlO3 laser , mode-locking of Tm-doped fiber lasers [15–19], and mode-locking of a Tm:Lu2O3 laser . Even if the efficacy of graphene-based saturable absorbers at wavelengths of 2 μm has been successfully verified through experimental demonstrations, there still remains an issue as to whether the combination between graphene-based saturable absorbers and fiber lasers can provide highly stable, femtosecond mode-locked pulses. No reports were found on femtosecond pulse generation at 2 μm wavelengths from a fiber laser cavity incorporating a graphene-based saturable absorber, even if solid state lasers are shown to be readily operable together with graphene-based saturable absorbers for producing high-quality femtosecond pulses . Most 2 μm femtosecond fiber lasers demonstrated so far used saturable absorbers based on semiconductors [21–23]. Very recently, a Tm-doped mode-locked laser based on the combined use of a nonlinear amplifying loop mirror and a CNT saturable absorber was demonstrated for producing femtosecond pulses . Note that recent works on mode-locking of 2 μm fiber lasers by graphene saturable absorbers were limited to the experimental demonstration of 1.2 ~3.6 ps pulses [15–19]. The limited temporal performance of the combination of a 2 μm optical fiber cavity and a graphene-based saturable absorber could be attributed to the difficulty in cavity dispersion control in the wavelength region.
In this work, we have further investigated the ultimate potential of the graphene oxide-based saturable absorber for the generation of femtosecond pulses at 2 μm wavelengths as an on-going study of other recent work . First, it is experimentally shown that a Tm-Ho-codoped fiber laser incorporating a graphene oxide-deposited side-polished fiber can readily produce stable femtosecond pulses by proper reduction of cavity length without additional dispersion compensation. Second, the measurement accuracy issue associated with the use of an autocorrelator together with an anomalously dispersive, silica fiber-based 2 μm-band amplifier for precise pulse-width measurement is investigated. Third, an experimental study on the precise role of the graphene oxide-deposited side-polished fiber within a fiberized cavity is carried out to determine whether its polarization-dependent loss (PDL) can be another substantial contributor to pulse formation through nonlinear polarization rotation or not.
For this experimental demonstration we chose to use graphene oxide as a saturable absorption material at 2 μm wavelengths due to its various advantages over graphene such as low-cost, solubility, and ease to handle . It is well known that graphene oxide has different optoelectronic properties compared to graphene . However, it is also known that the nonlinear saturable absorption performance of graphene oxide is almost comparable to that of graphene [26, 27]. We thus believe that high quality graphene is not essential to its application for mode-locked fiber lasers that require only the nonlinear saturable absorption function.
2. Experimental laser schematic
Figure 1(a) shows the laser schematic used in this experimental demonstration. The mode-locked cavity was composed of a 1 m long Tm-Ho-codoped fiber (Coractive, TH512) with an absorption of 13 dB/m at a pump wavelength of 1550 nm, an isolator, a 90:10 coupler, a polarization controller, a 1550/2000 nm wavelength division multiplexing (WDM) coupler, and a graphene oxide-deposited D-shaped fiber. The pump source for the mode-locked laser was a 1550 nm semiconductor laser diode with ~250 mW of power. The mode-locked laser output was extracted from the ring cavity via a 10% output port of a 90:10 fiber coupler. For the purpose of optimum laser performance we ensured the use of a single-mode fiber (SM2000) that is optimized at a wavelength of 2 μm for the construction of the ring cavity, except the Tm-Ho-codoped fiber. All of the components within the cavity were fusion-spliced; the total length of the ring cavity was ~6 m. The dispersion of the SM2000 and Tm-Ho-codoped fiber were measured to be −0.067(+/−0.005) ps2/m and −0.056(+/−0.005) ps2/m, respectively, at a wavelength of 1.95 μm. For these dispersion measurements, we launched 1 ps pulses into 2 m lengths of fiber and observed the temporal broadening by measuring autocorrelation traces. As a matter of fact, such a dispersion measurement technique allows for non-negligible measurement uncertainty.
Compared to the laser cavity in our previous work of Ref , the main difference is the optimization of the cavity in terms of propagation loss and dispersion. The gain medium was also changed from Tm-doped fiber into Tm-Ho-codoped fiber to increase pump absorption with a shorter gain fiber length. Note that the Tm-Ho-codoped fiber used in has a pump absorption of 13 dB/m at a wavelength of 1550 nm, whereas the Tm-doped fiber in Ref . has only 4.5 dB/m. Unlike Ref . we used a SM2000 fiber due to ease of handling for our laser construction in this work. It is well-known that the SM2000, which has a cut-off wavelength of 1.7 μm, is optimized for 2 μm operation . It has a much smaller bending loss than the conventional standard fiber of SMF28 even if it exhibits almost similar propagation loss and dispersion properties.
Using the measured dispersion values of the SM2000 and Tm-Ho-codoped fiber, we roughly estimated the total cavity dispersion at −0.391(+/−0.03) ps2. Compared to a recently demonstrated mode-locked Tm-doped fiber laser with a cavity length of 12.8 m and a cavity dispersion of −0.91(+/−0.08) ps2 , the cavity dispersion was substantially reduced by using a shorter length of gain medium and cutting off cavity fiber pigtails. The insertion losses of the coupler, isolator, and WDM were measured to be ~0.8, ~1.2, and ~0.5 dB, respectively, at 1.95 μm. The average power of the mode-locked laser output was measured to be ~1.6 mW. This value was measured at point A in Fig. 1(a).
The saturable absorber used in this experimental demonstration was prepared by depositing graphene oxide particles onto the flat side of a side-polished fiber. To prepare the side-polished fiber, one side of a SM2000 was polished while the fiber was fixed onto a V-grooved quartz block. Note that a standard single-mode fiber of SMF28 was used in our earlier study for the preparation of side-polished fiber . The distance between the flat side and the fiber core was measured at ~6 μm, as shown in the inset of Fig. 1(a). Further details on how to prepare the graphene oxide-deposited side-polished fiber are fully described elsewhere . The minimum insertion loss and PDL of the graphene oxide-deposited side-polished fiber were ~5 and ~1 dB, respectively, at 1.9 μm. Saturable absorption occurs due to the mutual interaction of graphene oxide particles and the evanescent field of the oscillating beam. The measured linear absorption curve for the coated graphene oxide layer is shown in Fig. 1(b). It is obvious from the figure that an absorption of ~15% exists in the 2 μm spectral region.
In order to figure out the nonlinear absorption performance of the prepared graphene oxide-deposited side-polished fiber we measured its absorption as a function of the input optical pulse peak power, as shown in Fig. 1(c). For this measurement we used a ~1-ps mode-locked fiber pulse laser operating at 1.93 μm. The saturation power was found to be ~14.83 W, which is three times larger than that of our previously reported graphene oxide-deposited side-polished fiber operating at 1.562 μm . The estimated modulation depth was ~7.1%, which is ~20% lower than that of the 1.562 μm graphene oxide-deposited side-polished fiber . The saturation pulse peak power (~14.83 W) required for the graphene oxide-deposited side-polished fiber within the cavity could be easily obtained with a pump power of ~250 mW.
3. Experimental femtosecond pulse generation from the cavity
Figure 2(a) shows the measured oscilloscope trace of the output pulses. The period of the output pulses was measured to be ~30.07 ns, which corresponds to a repetition rate of 33.25 MHz. This measured repetition rate was coincident with the estimated fundamental frequency of the implemented ring cavity. A close-up view of an output mode-locked pulse is also shown in the inset of Fig. 2(a) indicating that the temporal width of the output pulses must be less than ~60 ps, which is a minimum measurable pulse-width of our fast real-time oscilloscope (DSA71604C, Tektronix). The measured optical spectrum of the output pulses is shown in Fig. 2(b). The center wavelength and 3 dB bandwidth were measured to be ~1950 nm and ~6.9 nm, respectively. Kelly sidebands were clearly observed on the spectrum . Assuming that the pulses were in a transform-limited soliton form, the output pulse-width was expected to be ~578 fs using the time-bandwidth product value 0.317, of transform-limited hyperbolic secant pulses .
Before we carried out autocorrelation measurements to measure the precise pulse-width, we tried to figure out whether or not the output mode-locked pulses are transform-limited through the use of Kelly sideband spectral positions relative to the center wavelength of the pulses. Assuming that soliton pulses are chirp-free, the mth order of the Kelly sideband position relative to the center wavelength (Δλ) is given by the following well-known equation .
Using Eq. (1) with the experimental total cavity dispersion value of L|β2| = 0.391 ps2 the theoretical position of the first-order Kelly sideband relative to the center wavelength was calculated to be 9.58 nm in the case of transform-limited 578 fs pulses. Figure 3(a) shows the theoretically calculated Kelly sideband position relative to the center wavelength (Δλ) as a function of the temporal width of transform-limited pulses (TFWHM) for various Kelly sideband orders. The fact that our measured Δλ of ~8.4 nm for the first-order Kelly sideband is different from the theoretical value (~9.58 nm), implies that the output pulses of our laser are chirped . However, the precise amount of the chirp is still unknown, since its estimation requires a range of experimental parameter measurements, which are not straightforward, to be conducted. Note that it is well known that the Kelly sideband position is affected by the amount of chirp of the pulses .
The measured electrical spectrum of the output pulses is shown in Fig. 3(b). A strong signal peak with the fundamental repetition rate of ~33.25 MHz was clearly observed and the peak-to-background ratio was measured to be ~50 dB.
4. Autocorrelation measurement of the output pulses
In order to precisely measure the temporal width of the output pulses, we conducted an autocorrelation measurement using a second harmonic generation (SHG)-based autocorrelator (FR-103HS(XL)/IR, Femtochrome). One issue in this autocorrelation measurement was that the optical power of the mode-locked output pulses (average ~1.6 mW) was not high enough to induce an SHG signal within the autocorrelator used. An additional Tm-Ho-doped fiber amplifier with a total fiber length of 8 m, including a 2 m Tm-Ho-codoped fiber, was thus used just before the autocorrelator input, as shown in Fig. 1(a). For the purpose of achieving higher output power and better power conversion efficiency, we used a combination of erbium-ytterbium-codoped fiber amplifier and a distributed feedback laser diode operating at 1568 nm as a pump source. The maximum pump power was ~1.44 W. No isolator was used in this amplifier configuration to reduce the total amplifier fiber length. For proper adjustment of the polarization status of the amplified pulses that were fed into the autocorrelator input port, a polarization controller was attached to the output end of the amplifier. In using such a fiberized optical amplifier for amplification of subpicosecond pulses, one critical issue is the non-negligible temporal distortion of the amplified pulses due to dispersion and Kerr nonlinearity of the fiber amplifier. The amplifier dispersion was estimated to be −0.514(+/−0.04) ps2, which is larger than that of the cavity. Pump power was increased in an attempt to find the minimum average power of the amplified pulses for inducing a SHG signal in this autocorrelation measurement setup. It was found to be ~25 mW, which was obtained at a pump power of ~500 mW.
Figure 4(a) shows the measured optical spectra of the amplified optical pulses for various amplifier pump powers, whereas Fig. 4(b) shows the corresponding autocorrelation traces. The amplified pulses suffered from significant pulse-width broadening due to the dispersion of the 8-m long fiber amplifier. Taking into account both the fiber amplifier dispersion and the laser output chirp, the autocorrelation trace of the amplified pulses should have exhibited a temporal width larger than 2.35 ps. However, with pump power of ~500 mW, the 3 dB spectral bandwidth of the amplified pulses was observed to decrease to ~5 nm with a non-negligible spectral modulation. The pulse-width was measured to be only ~2 ps, which is smaller than the aforementioned value expected with the amplifier dispersion, assuming no fiber Kerr nonlinearity. This result means that the combined effect of anomalous dispersion and self-phase modulation within the fiber amplifier induced the soliton compression effect to shorten the temporal width of the amplified pulses to ~2 ps, even at pump power of 500 mW . The higher-order soliton compression effect was easily confirmed by the measured spectra and autocorrelation traces of the amplified pulses at higher pump powers, as shown in Fig. 4. At pump power of ~1.44 W, the amplified pulses exhibited a temporal width of ~590 fs with a small pedestal, which is a common feature of higher-order solitons . The pulse energy was estimated to be ~4.3 nJ. Figure 5 summarizes the measurement results of pulse-width and average optical power of the amplified pulses as a function of the amplifier pump power. Such a higher order soliton compression effect is inevitable in our measurement setup, since silica-based fiber always exhibits anomalous dispersion at 2 μm wavelengths irrespective of thulium and holmium ion doping. Therefore, we found that it would be very difficult to estimate the precise temporal width of the output pulses by using a simple method of subtracting the amount of dispersion-induced pulse-width broadening from the measured autocorrelation trace when an anomalously dispersive fiber amplifier is used in front of the autocorrelator.
Anyhow, one interesting result with the Tm-Ho-codoped fiber amplifier is that 590 fs soliton pulses with an energy of ~4.3 nJ could be obtained from an all-fiberized combination of a fiberized cavity and a fiber amplifier.
The previous demonstrations of mode-locked Tm-doped fiber lasers using graphene saturable absorbers have never reported such an issue associated with higher-order soliton compression in anomalously dispersive fiber amplifier-assisted autocorrelation measurement at 2 μm wavelengths [15–19]. As a matter of fact, it is unknown from published articles [16, 18, 19] including measured autocorrelation traces whether anomalously dispersive fiber amplifiers were employed for the autocorrelation measurements or not. The autocorrelation measurements [16, 18, 19] must have been conducted with high-sensitivity detectors without the help of fiber amplifiers. Nevertheless, the measurement accuracy limitation caused by the higher-order soliton compression effect needs to be taken into account whenever a fiberized autocorrelator is used together with an anomalously dispersive, silica-based 2 μm fiber amplifier.
5. Experimental investigation of the role of graphene oxide-deposited side-polished fiber
Even if it was known that the mode-locking mechanism in using a graphene oxide- or carbon nanotube-deposited side-polished fiber within a fiberized cavity is saturable absorption caused by the evanescent field interaction between the oscillated beam and the graphene oxide (or carbon nanotube) particles [34, 35], there has always been a question as to whether the PDL of the graphene oxide- (or carbon nanotube)-deposited side-polished fiber could be another significant contributor to mode-locking operation through nonlinear polarization rotation . It is well known that the side-polished fiber exhibits a non-negligible PDL due to surface wave-induced TM mode coupling  if a metallic layer including graphene and carbon nanotube is overlaid onto the flat side [38, 39].
In order to figure out the precise role of the graphene oxide-deposited side-polished fiber within our optical fiber-based laser cavity, we conducted another experiment with the same laser cavity shown in Fig. 1(a), in which the graphene oxide-deposited side-polished fiber was replaced with a gold-deposited side-polished fiber. Note that the cavity length incorporating the gold-deposited side-polished fiber is 5.9 m, which is slightly shorter than that incorporating the graphene oxide-deposited side-polished fiber. The length difference could be attributed to fiber shortening caused by iterative cleaving and splicing. The gold-deposited side-polished fiber was also prepared with SM2000, and the distance between the flat side and the fiber core was kept to ~6 μm to ensure the same structural condition as the graphene oxide-deposited side-polished fiber. The cross-sectional schematic and photo of the prepared gold-deposited side-polished fiber are shown in Fig. 6(a). Its measured insertion loss and PDL were ~6 and ~4 dB, respectively. Compared to the graphene oxide-deposited side-polished fiber the PDL of the gold-deposited side-polished fiber was observed to become substantially larger even if the insertion loss exhibited a small increase. It should be noticed that gold particles do not provide any evanescent field interaction-induced saturable absorption. Table 1 summarizes the insertion loss and PDL values of the side-polished fibers with graphene oxide and gold deposited.
Figure 6(b) shows the measured oscilloscope trace of the output pulses. An extremely unstable pulsation phenomenon was observed under the same pump power condition as the fiber laser incorporating the graphene oxide-deposited side-polished fiber. The pump power and cavity beam polarization were adjusted to find a stable mode-locking condition through nonlinear polarization rotation, but to no avail, as shown in this figure. Figure 7(a) shows the measured optical spectrum of the unstable output pulses, whereas its electrical spectrum is shown in Fig. 7(b). Unlike the well-defined hyperbolic secant spectral shape of the output pulses when using graphene oxide-deposited side-polished fiber (Fig. 2(b)), an unstable optical spectrum with a strong continuous-wave peak was observed as shown in Fig. 7(a). The poor quality of the output pulses was also confirmed in the electrical spectrum of Fig. 7(b) with substantial phase noise and side frequency components.
These results confirm that a 4 dB PDL is not high enough to induce nonlinear polarization rotation-induced mode-locking in the optical fiber-based laser cavity shown in Fig. 1(a). In other words, a much higher PDL value or a higher pump power is required for inducing passive mode-locking through nonlinear polarization rotation. This indicates that the graphene oxide-deposited side-polished fiber with only 1 dB used in the 1.95 μm femtosecond laser could not act as a cavity polarizer that is capable of inducing nonlinear polarization rotation-induced mode-locking in our laser cavity. Therefore, it can be inferred that the main mode-locking mechanism in our Tm-Ho-codoped fiber laser incorporating a graphene oxide-deposited side-polished fiber is saturable absorption caused by evanescent field interaction between the oscillated beam and the graphene oxide particles.
An in-depth experimental investigation was carried out into the use of a graphene oxide-deposited side-polished fiber as a 2 μm band passive mode-locker. It was shown that stable femtosecond mode-locked pulses could be generated from a Tm-Ho-codoped fiber laser with a length-reduced all-fiberized cavity. The accuracy limitation issue in the autocorrelation measurement, which was caused by higher-order soliton compression effect within an anomalously dispersive silica-based 2 μm fiber amplifier, was also discussed. Finally, it was found from a comparative study with graphene oxide- and gold-deposited side-polished fiber that the contribution of the PDL of our prepared graphene oxide-deposited side-polished fiber to mode-locking through nonlinear polarization rotation would be insignificant.
One additional and interesting result was that stable ~590 fs pulses with 4.3 nJ of energy has still been produced and experimentally measured from an all-fiberized combination of a Tm-Ho-codoped fiber cavity and a Tm-Ho-codoped fiber amplifier. It is believed that a graphene oxide-deposited saturable absorber is a cost-effective, all-fiberized mode-locker suitable for femtosecond pulse generation at 2 μm wavelengths.
This work was supported by the National Research Foundation (NRF) of Korea grant funded by the Ministry of Education, Science, and Technology (MEST), Republic of Korea (No. 2011-0028978, No. 2012R1A1B3000587). This work was also supported by the IT R&D program of MKE/KEIT. [10039226, Development of actinic EUV mask inspection tool and multiple electron beam wafer inspection technology]. This work was also supported by the KIST Institutional Program (2E23910).
References and links
1. F. J. McAleavey, J. O’Gorman, J. F. Donegan, B. D. MacCraith, J. Hegarty, and G. Mazé, “Narrow linewidth, tunable Tm3+ -doped fluoride fiber laser for optical-based hydrocarbon has sensing,” IEEE J. Sel. Top. Quantum Electron. 3(4), 1103–1111 (1997). [CrossRef]
2. S. W. Henderson, P. J. M. Suni, C. P. Hale, S. M. Hannon, J. R. Magee, D. L. Bruns, and E. H. Yuen, “Coherent laser radar at 2 μm using solid-state lasers,” IEEE Trans. Geosci. Electron. 31, 4–15 (1993).
3. G. D. Spiers, R. T. Menzies, J. Jacob, L. E. Christensen, M. W. Phillips, Y. Choi, and E. V. Browell, “Atmospheric CO2 measurements with a 2 μm airborne laser absorption spectrometer employing coherent detection,” Appl. Opt. 50(14), 2098–2111 (2011). [CrossRef]
4. M. Ebrahim-Zadeh and I. T. Sorokina, Mid-Infrared Coherent Sources and Applications (Springer, 2008).
5. B. E. Bouma, L. E. Nelson, G. J. Tearney, D. J. Jones, M. E. Brezinski, and J. G. Fujimoto, “Optical coherence tomographic imaging of human tissue at 1.55 μm and 1.81 μm using Er- and Tm-doped fiber sources,” J. Biomed. Opt. 3(1), 76–79 (1998). [CrossRef]
7. S. Y. Set, H. Yaguchi, Y. Tanaka, and M. Jablonski, “Laser mode locking using a saturable absorber incorporating carbon nanotubes,” J. Lightwave Technol. 22(1), 51–56 (2004). [CrossRef]
8. Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009). [CrossRef]
9. F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010). [CrossRef]
10. T. Hasan, Z. Sun, F. Wang, F. Bonaccorso, P. H. Tan, A. G. Rozhin, and A. C. Ferrari, “Nanotube-polymer composites for ultrafast photonics,” Adv. Mater. 21(38â€“39), 3874–3899 (2009). [CrossRef]
11. S. Yamashita, “A tutorial on nonlinear photonic applications of carbon nanotube and graphene,” J. Lightwave Technol. 30(4), 427–447 (2012). [CrossRef]
12. Z. Sun, T. Hasan, and A. C. Ferrari, “Ultrafast lasers mode-locked by nanotubes and graphene,” Physica E 44(6), 1082–1091 (2012). [CrossRef]
13. J. Ma, G. Q. Xie, P. Lv, W. L. Gao, P. Yuan, L. J. Qian, H. H. Yu, H. J. Zhang, J. Y. Wang, and D. Y. Tang, “Graphene mode-locked femtosecond laser at 2 μm wavelength,” Opt. Lett. 37(11), 2085–2087 (2012). [CrossRef]
14. J. Liu, Y. G. Wang, Z. S. Qu, L. H. Zheng, L. B. Su, and J. Xu, “Graphene oxide absorber for 2 μm passive mode-locking Tm:YAlO3 laser,” Laser Phys. Lett. 9(1), 15–19 (2012). [CrossRef]
15. J. Liu, S. Wu, J. Xu, Q. Wang, Q.-H. Yang, and P. Wang, “Mode-locked 2 μm thulium-doped fiber laser with graphene oxide saturable absorber,” in Proc. CLEO, JW2A.76 (2012).
16. M. Zhang, E. J. R. Kelleher, F. Torrisi, Z. Sun, T. Hasan, D. Popa, F. Wang, A. C. Ferrari, S. V. Popov, and J. R. Taylor, “Tm-doped fiber laser mode-locked by graphene-polymer composite,” Opt. Express 20(22), 25077–25084 (2012). [CrossRef]
17. Q. Q. Wang, T. Chen, B. Zhang, M. Li, Y. Lu, and K. P. Chen, “A mode-locked 1.91 μm fiber laser based on interaction between graphene oxide and evanescent field,” Appl. Phys. Express 5(11), 112702 (2012). [CrossRef]
18. Q. Wang, T. Chen, B. Zhang, M. Li, Y. Lu, and P. K. Chen, “All-fiber passively mode-locked thulium-doped fiber ring laser using optically deposited graphene saturable absorbers,” Appl. Phys. Lett. 102(13), 131117 (2013).
19. G. Sobon, J. Sotor, I. Pasternak, A. Krajewska, W. Strupinski, and K. M. Abramski, “Thulium-doped all-fiber laser mode-locked by CVD-graphene/PMMA saturable absorber,” Opt. Express 21(10), 12797–12802 (2013). [CrossRef]
20. A. A. Lagatsky, Z. Sun, T. S. Kulmala, R. S. Sundaram, S. Milana, F. Torrisi, O. L. Antipov, Y. Lee, J. H. Ahn, C. T. A. Brown, W. Sibbett, and A. C. Ferrari, “2 μm solid-state laser mode-locked by single-layer graphene,” Appl. Phys. Lett. 102(1), 013113 (2013). [CrossRef]
21. S. Kivisö and O. G. Okhotnikov, “600-fs mode-locked Tm-Ho-doped fiber laser synchronized to optical clock with optically driven semiconductor saturable absorber,” IEEE Photon. Technol. Lett. 23(8), 477–479 (2011). [CrossRef]
22. A. Wienke, F. Haxsen, D. Wandt, U. Morgner, J. Neumann, and D. Kracht, “Ultrafast, stretched-pulse thulium-doped fiber laser with a fiber-based dispersion management,” Opt. Lett. 37(13), 2466–2468 (2012). [CrossRef]
24. M. A. Chernysheva, A. A. Krylov, P. G. Kryukov, N. R. Arutyunyan, A. S. Pozharov, E. D. Obraztsova, and E. M. Dianov, “Thulium-doped mode-locked all-fiber laser based on NALM and carbon nanotube saturable absorber,” Opt. Express 20(26), B124–B130 (2012). [CrossRef]
27. J. Lee, J. Koo, P. Debnath, Y.-W. Song, and J. H. Lee, “A Q-switched, mode-locked fiber laser using a graphene oxide-based polarization sensitive saturable absorber,” Laser Phys. Lett. 10(3), 035103 (2013). [CrossRef]
29. S. M. Kelly, “Characteristic sideband instability of periodically amplified average soliton,” Electron. Lett. 28(8), 806–808 (1992). [CrossRef]
30. P. Lazaridis, G. Debarge, and P. Gallion, “Time-bandwidth product of chirped sech2 pulses: application to phase-amplitude-coupling factor measurement,” Opt. Lett. 20(10), 1160–1162 (1995). [CrossRef]
31. N. J. Smith, K. J. Blow, and I. Andonovic, “Sideband generation through perturbations to the average soliton model,” J. Lightwave Technol. 10(10), 1329–1333 (1992). [CrossRef]
33. G. P. Agrawal, Nonlinear Fiber Optics, 3rd Ed. (Academic Press, 2007).
34. Y.-W. Song, S.-Y. Jang, W.-S. Han, and M.-K. Bae, “Graphene mode-lockers for fiber lasers functioned with evanescent field interaction,” Appl. Phys. Lett. 96(5), 051122 (2010). [CrossRef]
35. Y.-W. Song, S. Yamashita, C. S. Goh, and S. Y. Set, “Carbon nanotube mode lockers with enhanced nonlinearity via evanescent field interaction in D-shaped fibers,” Opt. Lett. 32(2), 148–150 (2007). [CrossRef]
36. J. H. Im, S. Y. Choi, F. Rotermund, and D.-I. Yeom, “All-fiber Er-doped dissipative soliton laser based on evanescent field interaction with carbon nanotube saturable absorber,” Opt. Express 18(21), 22141–22146 (2010). [CrossRef]
37. D. G. Moodie and W. Johnstone, “Wavelength tunability of components based on the evanescent coupling from a side-polished fiber to a high-index-overlay waveguide,” Opt. Lett. 18(12), 1025–1027 (1993). [CrossRef]
39. Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011). [CrossRef]