Abstract

A photonic crystal fiber (PCF) with high-quality graphene nano-particles uniformly dispersed in the hole cladding are demonstrated to passively mode-lock the erbium-doped fiber laser (EDFL) by evanescent-wave interaction. The few-layer graphene nano-particles are obtained by a stabilized electrochemical exfoliation at a threshold bias. These slowly and softly exfoliated graphene nano-particle exhibits an intense 2D band and an almost disappeared D band in the Raman scattering spectrum. The saturable phenomena of the extinction coefficient β in the cladding provides a loss modulation for the intracavity photon intensity by the evanescent-wave interaction. The evanescent-wave mode-locking scheme effectively enlarges the interaction length of saturable absorption with graphene nano-particle to provide an increasing transmittance ΔT of 5% and modulation depth of 13%. By comparing the core-wave and evanescent-wave mode-locking under the same linear transmittance, the transmittance of the graphene nano-particles on the end-face of SMF only enlarges from 0.54 to 0.578 with ΔT = 3.8% and the modulation depth of 10.8%. The evanescent wave interaction is found to be better than the traditional approach which confines the graphene nano-particles at the interface of two SMF patchcords. When enlarging the intra-cavity gain by simultaneously increasing the pumping current of 980-nm and 1480-nm pumping laser diodes (LDs) to 900 mA, the passively mode-locked EDFL shortens its pulsewidth to 650 fs and broadens its spectral linewidth to 3.92 nm. An extremely low carrier amplitude jitter (CAJ) of 1.2-1.6% is observed to confirm the stable EDFL pulse-train with the cladding graphene nano-particle based evanescent-wave mode-locking.

© 2013 Optical Society of America

1. Introduction

In addition to the graphene based saturable absorbers [19] for the passively mode-locked fiber lasers, the graphene nano-particle has shown its potential to be the mode-locker for erbium-doped fiber lasers (EDFLs) [1012]. Because graphite is easily cleaved due to the weak coupling of van der Waals forces between each graphene plane, a convenient polishing method to triturate the graphene nano-particle from highly oriented pyrolytic graphite (HOPG) foil was demonstrated previously [10, 11]. The graphene nano-particle exhibits similar optical properties with graphene, such as fast carrier relaxation time, wideband absorption and superior thermal conductivity etc. In addition to reduce the size of graphene nano-particle for detuning the coverage ratio at the interacting cross-section area, the effect of layer number of the graphite or graphene on the saturable absorption was investigated to optimize the mode-locking performance. Bao et al. have studied that reducing the graphene layer number can enhance the mode-locking force of graphene saturable absorber, as attributed to the enlarged modulation depth and decreased linear absorbance. A stabilized and shortened mode-locking pulse is obtained by using an atomic-layer graphene as compared to that by a multilayer graphene [1, 13].

At current stage, the size shrinkage, layer number reduction and uniformity of graphene nano-particle can only be roughly controlled by the polishing conditions of mechanical trituration. In the case of fabricating graphene nano-particle saturable absorber, the few-layer and multilayer graphene nano-particles are co-existed after the mechanical polish process. Therefore, the layer number of graphene nano-particle must be decreased when considering it as a saturable absorber. Besides, the uniformity of graphene nano-particles is mandatory to precisely control the coverage ratio as well as linear insertion loss on the fiber end-face. These drawbacks were left the unsolved issues up to now. Recently, the electrochemical exfoliation has emerged as a simple solution-processed fabrication for obtaining few-layer graphene nano-particles from the graphite foil [1416]. Su et al. used the electrochemical exfoliation to fabricate a large-scale and few-layer graphene sheet by setting the graphite foil as an electrode under a bias voltage of + 10V [14]. However, the nonuniform graphene sheet with numerous structural defects is caused by the fast exfoliation mechanism at such high bias voltage.

On the other hand, most of the carbon based saturable absorbers [28] were sandwiched between two fiber patchcords to provide the loss modulation [28, 1733]. Sun et al. set a graphene-polymer composite obtained by a wet-chemical method between two fiber patchcords to passively mode-lock the EDFL with a 460-fs pulsewidth [4]. Zhang et al. placed the atomic-layer graphene between two SMF patchcords to generate a mode-locked EDFL soliton with 30-nm wavelength tunability [18]. Similar wavelength tunability at C- and L-bands with the insertion of a space between SMF patchcord connectors has also been reported in other kinds of fiber lasers [19, 20]. This patchcord/absorber/patchcord scheme is compact; however, the interaction is limited by the saturable absorber thickness. Increasing the thickness of saturable absorber in this scheme inevitably leads to a large insertion loss to increase the mode-locking threshold [34], and the thermal damage of graphene materials caused by the directly propagated laser beam also set a constrain for high-power operation. More recently, the EDFL passively mode-locked by evanescent-wave saturable absorption with graphene is developed to concurrently solve the reaction length and thermal damage problems [3540]. Song et al. reported the 1.3-ps pulsewidth with the evanescent-field saturable absorption by graphene at cladding region, which endures an intracavity power of up to 21 dBm without damaging the graphene [35]. Luo et al. demonstrated a graphene-deposited fiber taper to obtain the multi-wavelength mode-locked EDFL with 8.8-ps pulsewidth [37]. Choi et al. utilized a graphene-injected hollow optical fiber (HOF) to achieve the evanescent-wave mode-locking of EDFL with 510-fs pulsewidth [38]. Although the reacting length is lengthened, the interaction area is still limited on one-side of the taper fiber or on the single hole of HOF. This greatly lengthens the device and causes additional cavity loss.

In this work, the high-quality few-layer graphene nano-particle is obtained by using the stabilized electrochemical exfoliation at a threshold bias condition. The decreasing exfoliation rate significantly and precisely controls the layer number of the graphene nano-particles. Raman scattering spectroscopy is performed to determine the structural quality and layer number of graphene nano-particle. By syphoning the graphene nano-particles into a multi-core photonic crystal fiber (PCF), the evanescent-wave of the EDFL interacts with the graphene nano-particle uniformly in the hole cladding region. The multi-core PCF contains more graphene nano-particles in a shorter segment, which can strengthen the nonlinear saturable absorption as compared to that in a one-core HOF. By inserting the graphene nano-particle doped PCF with an interaction length of 200 μm, the evanescent-wave mode-locking of EDFL with low pumping threshold, sub-picosecond pulsewidth and ultra-low carrier amplitude jitter is demonstrated.

2. Experiment setup

Figure 1 illustrates the flow chart of electrochemical exfoliation, centrifugation, and syphoning of the graphene nano-particles into the PCF. In the electrochemical exfoliation, the HOPG foil and a Pt wire are respectively served as the anode and the cathode in the electrolyte of sulfuric acid aqueous solution, which is prepared by diluting 96% sulfuric acid and 100 mL of deionized water. The exfoliation process is operated by applying different DC bias voltages of + 3 and + 6V. When operating at a bias of + 6V, the HOPG foil is rapidly split and dissociated into small particles. The roughly exfoliated graphite stacks are observed right after turn-on the DC power supply. In contrast, the operation under a threshold bias of + 3V spends more than 20 sec to start the exfoliation after turn-on the DC power supply, and the exfoliated graphene nano-particles are more delicate. Subsequently, the graphene nano-particle aqueous solution is filtered to remove the large graphene sheets by a porous filter, and the percolated graphene nano-particles are preserved in acetone solution. After the ultrasonic agitation of graphene nano-particle contained in acetone solution for 10 min, the centrifugation of graphene nano-particle solution can separate small particles as the supernatants but deposit the large particles in the bottom.

 

Fig. 1 The flow chart of electrochemical exfoliation and extraction of graphene nano-particle into the PCF. The inset is the SEM image of graphene nano-particles.

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The supernatants are syphoned into the PCF (NKT, LMA-10) to make the graphene nano-particles dispersed in the PCF. To avoid the modification of guiding mode in the PCF filled with the acetone solution in the hole cladding region, the passive mode-locking of EDFL is performed after evaporating the acetone solution in an oven at 70° for 1 hour. The SEM image confirms the sizes of graphene nano-particles are around 400 nm. The slowly exfoliated graphene nano-particle obtained with low bias voltage is the preferred candidate to be used in the EDFL system. In addition, the centrifugation is a necessary process to collect the uniform and delicate graphene nano-particles after the electrochemical exfoliation, because the few-layer graphene nano-particle with small size induces low insertion loss but high modulation depth. Afterwards, the PCF with dispersed graphene nano-particles is spliced with another PCF. The evanescent-wave interaction improves the nonlinear interaction length and increases the tolerance of high intra-cavity power. The advantages of the fabrication process are simple, convenient and high reproducibility.

Figure 2 demonstrates the experimental setup of the passively mode-locked EDFL. This system utilizes an erbium-doped fiber (EDF, nLIGHT Liekki Er80-8/125) as the gain medium, which is bi-directionally pumped by a 980-nm laser diode (LD, forward) and a 1480-nm LD (backward) through two wavelength-division multiplexers (WDMs). The circulated direction is determined by an isolator and the intra-cavity polarization is controlled by a polarization controller (PC). A 95/5 coupler is inserted to provide 5% output and feedback 95% of intra-cavity power. The EDFL consists of a 2-m long EDF with dispersion coefficient β2,EDF of −20 ps2/km, and a 6.2-m long SMF with β2,SMF of −20 ps2/km [12, 41]. In the inset of Fig. 2, the photographs show the optical microscopy images of PCF. The top-view of PCF indicates that the hole diameter is 3.1 μm with the spacing between each hold of 7.1 μm. The length of PCF is 200 μm as shown in the side-view image. The dispersion coefficient β2,PCF of the PCF is about −40 ps2/km.

 

Fig. 2 The experimental setup of the passively mode-locked EDFL. Inset: the photographs of the PCF (left: top-view, right: side-view).

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3. Results and discussions

Figure 3(a) compares the Raman scattering spectra of the original HOPG foil and the electrochemically exfoliated graphene nano-particles obtained at bias voltages of + 3 and + 6V. The HOPG foil exhibits two prominent Raman signals at 1580 and 2730 cm−1, which represent G band and 2D band originated from the sp2 carbon network and the second-order double resonance [11,12,4245]. As the graphene layer number increases to form graphite, the 2D band intensity significantly reduces with a broadening linewidth and an asymmetric spectral shape. The divided phonon branches contribute different phonon frequencies that could lead to the splitting of 2D band [42]. After the electrochemical exfoliation at a bias of + 6V, the exfoliated graphene nano-particle shows a relatively broadened G band and an attenuated 2D band. To quantify, the intensity ratio of 2D band over G band (I2D/IG) is about 0.35. In addition, a distinct D band with an intensity ratio of D band over G band (ID/IG) of 1.57 is observed, which is mainly caused by the structural defects occurred outside the graphene nano-particle [11, 12]. The defects are inevitably generated outside the graphene nano-particle when the graphene nano-particles are rapidly exfoliated from the HOPG foil, such as cracks, vacancies, stretches and bending, as shown in Fig. 4.

 

Fig. 3 Raman spectra of the HOPG foil and the electrochemically exfoliated graphene nano-particles operated under bias voltages of + 6 and + 3V.

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Fig. 4 The schematic diagrams of the electrochemically exfoliated graphene nano-particles with bias voltages of + 6 and + 3V.

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Most of the defects are tensile strains after the electrochemical exfoliation, which lead to the red-shift of the Raman scattering peak wavenumber at 2D band [43, 45]. In contrast, the G band of the graphene nano-particle obtained under the exfoliated operation with bias voltage of + 3V becomes intense and sharp, and the 2D band increases it intensity with an enlarging I2D/IG ratio of 0.54, whereas the D band is approximately disappeared to show a dramatically decreased ID/IG ratio of 0.12. This observation indicates that the crystalline quality of graphene nano-particle can be improved and the size (or layer number) of graphene nano-particle is also reduced by decreasing the bias voltage, as shown in Fig. 4. Because the graphene nano-particles are slowly and softly exfoliated from the graphite foil under the stable exfoliation bias of + 3V, as compared to the operation of + 6V bias voltage. To be the saturable absorber, the large graphene nano-particle with plenty of defects obtained by the operation of + 6V bias voltage is not a good candidate due to the insufficient modulation depth and the enlarged absorption loss [12]. Therefore, the electrochemical exfoliation operated under + 3V bias voltage is suitable to fabricate few-layer graphene nano-particle with better crystalline quality.

Subsequently, the linear transmittance of graphene nano-particles in PCF is measured and shown in Fig. 5(a). By illuminating with a tunable continuous-wave (CW) laser (Agilent 8164A) at 1570 nm, the linear transmittance of graphene nano-particles in PCF is determined as 0.56, which is attributed to the linear absorption of graphene nano-particle, the coupling loss and the attenuation from PCF (main contribution of up to 2 dB). To compare the evanescent-wave mode-locking with the core-region wave mode-locking, the acetone solution with dispersed graphene nano-particles is dropped on the end-face of SMF patchcord. After the evaporation of acetone solution, the free-standing graphene nano-particles on the end-face of SMF can be obtained. The linear transmittance of 0.54 is shown in Fig. 5(b), which originates from the large coverage ratio and the enlarged sizes caused by the self-aggregation of graphene nano-particles. The linear transmittance of graphene nano-particles in the PCF is kept approximately the same with the one by confining the graphene nano-particles on the end-face of SMF. However, embedding the graphene nano-particles in the PCF would benefit from a better nonlinear absorption with higher modulation depth, which will be discussed in the next section.

 

Fig. 5 Linear transmittance of (a) graphene nano-particles in PCF and (b) graphene nano-particles on the end-face of SMF.

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The saturable absorption of graphene nano-particles under high power excitation due to Pauling blocking effect occurs under feedback light circulation in the EDFL cavity [1012]. Figure 6(a) and 6(b) demonstrate the nonlinear transmittance and the normalized absorbance of graphene nano-particles in PCF and graphene nano-particles on the end-face of SMF, respectively. The nonlinear transmittance is detected under a pulsed laser with wavelength of 1570 nm and pulsewidth of 700 fs. For the graphene nano-particles in PCF, the transmittance enlarges from 55% to 60% with an increasing ΔT of 5%, and the normalized absorbance shows a decreasing trajectory with a modulation depth of 13% by increasing the pumping power from 0.1 to 41 mW. In contrast, for the graphene nano-particles on the end-face of SMF, the transmittance enlarges from 0.54 to 0.578 with the corresponding increment of ΔT = 3.8% and the modulation depth of 10.8%. In comparison with the interaction of core-wave and graphene nano-particles, the evanescent-wave interaction contributes higher modulation depth due to the longer nonlinear interaction length. As a result, the characteristic parameters related to the saturable transmittance of graphene nano-particle in the PCF are numerically simulated by the following equation:

T=exp(qnon1+Pin/Psatqlin),
where qnon and qlin denote the nonlinear and linear absorbance, Pin and Psat are the input power and the saturable power, respectively. For the graphene nano-particles in PCF, the parameters of qnon, qlin and Psat are 0.09, 0.515 and 1 mW; For the graphene nano-particles on the end-face of SMF, the parameters of qnon, qlin and Psat are 0.073, 0.545 and 1.3 mW. In brief, the electrochemical exfoliation can fabricate smaller graphene nano-particle than using the direct mechanical polish, furthermore, which makes the exfoliated graphene nano-particles easily and uniformly distributed in the hole-cladding of the PCF. Therefore, it contributes to a higher nonlinear absorbance and a lower power required by using the evanescent-wave interaction induced saturable absorption. Besides, imprinting the graphene nano-particles on the end-face of SMF would easily cause the self-aggregation to form the multi-layer stacked graphene nano-particle, which inevitably leads to a higher linear absorbance.

 

Fig. 6 Nonlinear transmittance and normalized absorbance of (a) graphene nano-particles in PCF and (b) graphene nano-particles on the end-face of SMF.

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The schematic diagram of the evanescent-wave mode-locking for inducing the pulse formation with graphene nano-particles dispersed in hole-cladding region of the PCF is shown in Fig. 7. Assuming that the graphene nano-particle dispersed in the PCF has a nonlinear absorption coefficient given by

αnon,G=α0,G1+Ie,t/Ie,satIe,t=Ie,sat(α0,Gαnon,G1)
where αo,G is the nonlinear absorption component, Ie,t represents the evanescent-wave intensity and Ie,sat denotes the saturable intensity of graphene nano-particles.

 

Fig. 7 The schematic diagram of evanescent-wave mode-locked pulse propagation through the PCF doped with graphene nano-particles in hole-cladding region.

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Within the hole-cladding region of the PCF, the evanescent-wave exponentially decays with the radial distance (x) away from the core/cladding interface, and the evanescent-wave intensity can be described as [46]

Ie,t=I0e2βx,
where I0 and β denote the intracavity pulse intensity and the extinction coefficient factor. With the aid of graphene nano-particles, the extinction coefficient factor is re-written as:
β=2πncλ(sin2θi(nc/ni)21)1/2=2πλ{ni2[nc0+ncIe,sat(α0,Gαnon,G(It)1)]2}1/2,
where ni and nc are the core refractive index and the effective cladding refractive index. nc is determined by the dispersed graphene nano-particles which can be expressed as nc0 + nc.It with nc representing the nonlinear refractive index. According to the Z-scan measurement of the graphene materials given by Zhang et al., the nonlinear refractive index nc also exhibits an intensity dependent behavior, that is, the nc decreases and eventually saturates to a value of 6x10−6 (W/cm2)−1 [47]. This consequently results in the saturable phenomena for both the extinction coefficient β and the field confinement factor Γ given by [48]:

Γ=0d/2Ecore2(x)dx0d/2Ecore2(x)dx+d/2Ecladding2(x)dx.

The saturable phenomena of the extinction coefficient β determines the decay length (1/2β) of the evanescent wave, which results in a Kerr-lens like refractive index change along the transverse direction of the PCF fiber, thus providing a loss modulation for the intracavity photon intensity. According the schematic diagram shown in Fig. 8, the decay length decreases to perform the low evanescent-wave intensity when β increases, whereas the decay length increases with reducing β value to broaden the evanescent-wave field. Such a phenomenon occurs back and forth by the saturable-absorption of graphene nano-particles distributed in the hole-cladding region of the PCF.

 

Fig. 8 Schematic diagram of evanescent field modulation with varied extinction coefficient.

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To perform the evanescent-wave interaction for starting the passively mode-locked EDFL, the graphene nano-particle injected hollow optical fiber (HOF) [38] with a length of 59 mm has been inserted into the EDFL ring cavity. In our case, because more graphene nano-particles can be siphoned into the multi-core PCF to enhance the nonlinear interaction, the PCF with a length of only 200-μm is required to produce the evanescent-wave interaction with ΔT of 5%. The attenuation loss caused by the PCF can certainly be decreased and a large GDD caused by the PCF can also be avoided by shortening the PCF, simultaneously. However, there is a trade-off between the degradation of saturable absorption and aforementioned effects. Figure 9(a) and 9(b) show the Pout vs. Pin transfer response and the power gain curves of the EDFA with increasing both the pumping currents of 980-nm LD and 1480 nm-LD from 700 to 900 mA. A continuous-wave laser with a wavelength of 1570 nm is passing through the EDFA to measure the power gain at different pumping currents. The pumping power of 980-nm LD enlarges from 235 to 290 mW, and the pumping power of 1480-nm LD enlarges from 153 to 200 mW by increasing the pumping current from 700 to 900 mA. The Gain curves of the EDFA are simulated by G = G0/(1 + Pin/Psat), where G0 is the small signal gain, Pin and Psat are the input power and the saturated power of EDFA, respectively. G0 rises from 8.42 to 8.62, and Psat enlarges from 0.55 to 0.65 with increasing the pumping currents of 980-nm LD and 1480-nm LD simultaneously.

 

Fig. 9 (a) Pout-Pin curves and (b) the Gain curves of the EDFA under different pumping currents.

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Figure 10(a) and 10(b) depict the autocorrelation traces and the optical spectra of the passively mode-locked EDFLs under different pumping power. The autocorrelation traces and the optical spectra are measured by an autocorrelator (Femtochrome, FR-103XL) and an optical spectrum analyzer (Ando, AQ6317B), respectively. By simultaneously increasing the pumping currents of 980-nm and 1480-nm LDs from 700 to 900 mA, the enhanced net optical gain increases the synchronous oscillating modes [34]. As a result, the passively mode-locked EDFL pulsewidth slightly shrinks from 668 to 650 fs with the corresponding spectral full-width at half maximum (FWHM) broadened from 3.75 to 3.92 nm. The wavelength of the EDFL in all cases remains unchanged at 1567.6 nm. The time-bandwidth products (TBPs) of the EDFLs are around 0.315, and the group delay dispersion (GDD) of the laser cavity is approximately −0.164 ps2/km. In the anomalous dispersion condition, the soliton pulse formation is periodically perturbed by the linear effect of GDD and the nonlinear effect of self-phase modulation (SPM) [12, 49].

 

Fig. 10 (a) The autocorrelation traces and (b) optical spectra of the passively mode-locked EDFLs under different pumping current.

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The soliton mode-locking operation and the occurrence of Kelly sidebands on the shoulder of optical spectra are observed in the EDFL system. To confirm the optimized performances of passively mode-locked EDFL started by the graphene nano-particles doped in PCF, both the pulse shape and the optical spectrum are simulated by using Haus master equation with the experimentally obtained parameters. The master equation is given by [12]:

TRTA(T,t)=[G01+|A|2/PG,satl+Dg2t2qnon(T,t)1+|A|2/PsatiD2t2+iδ|A|2]A(T,t),
where TR and A(T,t) represent the round-trip time and the pulse amplitude, G0 and l denote the cavity gain and the cavity loss, Dg is the gain dispersion, D, qnon, and δ denote the cavity dispersion, the saturable loss and the self-phase modulation (SPM) coefficient, respectively. The round-trip circulation number of the equation is set up to 10000 for stabilizing the pulse formation. Figure 11(a) and 11(b) demonstrate the simulated autocorrelation traces and the optical spectra under different pumping currents. By simultaneously increasing the pumping current of 980-nm and 1480-nm LDs from 700 to 900 mA, the simulated pulse shapes show the pulsewidth shortening from 683 to 655 fs, with the spectral FWHM broadening from 3.71 to 3.86 nm, which are well correlated with the experimental results.

 

Fig. 11 (a) The simulated autocorrelation traces and (b) optical spectra of the passively mode-locked EDFLs under different pumping current.

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At last, the stabilization of the evanescent-wave mode-locking performance is monitored by characterizing the peak power fluctuation among the adjacent mode-locked pulses. The inset of Fig. 12 exhibits the oscilloscope traces of the passively mode-locked EDFLs under different pumping currents. The repetition time of the EDFL is 40 ns with the corresponding repetition rate of 25 MHz. By using the evanescent-wave mode-locking, the location of graphene nano-particles in the hole-cladding region of the PCF can ensure the high intracavity power in the core region without suffering from any thermal dissipation, which generates a highly stabilized mode-locking of EDFL at a larger output power. The quality of pulse-amplitude equalization can be determined by calculating the carrier amplitude jitter (CAJ) of the measured mode-locked pulse-train in time domain, which is defined as a ratio of the standard deviation (σ) on peak pulse intensity to the average pulse intensity (Iave), CAJ = (σ/Iave)x100% [50]. The extremely low CAJ values of around 1.23%~1.66% are obtained for different pumping cases and shown in Fig. 12, indicating a very small peak power fluctuation for the evanescent-wave mode-locked EDFL started with the graphene nano-particles doped in the hole-cladding region of the PCF. The operating lifetime of such an evanescent-wave mode-locked EDFL can be stably operated up to 12 hours, which is at least 1.5 times longer than the same system using the core-region mode-locking with same graphene nano-particle based saturable absorber. This observation confirms the stabilization of the evanescent-wave mode-locked EDFL.

 

Fig. 12 The CAJ values and the oscilloscope traces of the passively mode-locked EDFLs under different pumping currents.

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4. Conclusion

The high-quality graphene nano-particles obtained by the stabilized electrochemical exfoliation are uniformly dispersed in the hole-cladding region of a PCF to passively mode-lock the EDFL by evanescent-wave interaction. The electrochemical exfoliation operated at a threshold voltage of + 3V effectively reduces the structural defects and produces few-layer graphene nano-particle. Because the graphene nano-particles are slowly and softly exfoliated from the graphite foil under the operation of low bias voltage. In comparison with the operation under higher bias, the Raman scattering spectrum of the graphene nano-particle under + 3V exhibits an intense and sharp 2D band, whereas the defect related D band is approximately disappeared. The graphene nano-particles are siphoned into the hole cladding of PCF to induce the saturable absorption. The saturable phenomena of the extinction coefficient β in the cladding results in a Kerr-lens like refractive index change along the transverse direction of the PCF fiber, thus providing a loss modulation for the intracavity photon intensity. It contributes the increasing transmittance from 55% to 60% with ΔT of 5%, and the normalized absorbance shows a decreasing trajectory with the modulation depth of 13%. In contrast, the graphene nano-particles on the end-face of SMF under the same linear transmittance only provide a modulation depth of 10.8%. The evanescent-wave mode-locking with graphene nano-particles in hole-cladding of PCF provides higher modulation depth and lower linear loss than those imprinted on the SMF end-face, because the graphene nano-particles uniformly distributed in the PCF can enlarge interaction length and avoid self-aggregation. By simultaneously increasing the pumping current, the net optical gain enhances to shorten the passively mode-locked EDFL pulsewidth to 650 fs. The corresponding spectral linewidth broadens to 3.92 nm, leading to a transform limit operation with time-bandwidth of nearly 0.315. The temporal/spectral waveforms with Kelly sidebands are well simulated by using the Haus master equation. The extremely low carrier amplitude jitter of 1.23% indicates a very small peak power fluctuation for the evanescent-wave mode-locked EDFL started with the graphene nano-particle doped in the hole-cladding region of the PCF. A stabilized operation up to 12 hrs is confirmed to be 1.5 times longer than the core-wave mode-locking case, which ensures the handling of high intracavity power away from the thermal damage via the evanescent-wave interaction with the graphene nano-particles doped in the hole-cladding region of the PCF.

Acknowledgment

This work was supported by National Science Council and National Taiwan University under grants NSC101-2622-E-002-009-CC2, NSC101-2221-E-002-071-MY3 and NTU102R89083.

References and links

1. Q. L. Bao, H. Zhang, 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]  

2. 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, 3874–3899 (2009).

3. H. Zhang, Q. L. Bao, D. Y. Tang, L. Zhao, and K. P. Loh, “Large energy soliton erbium-doped fber laser with a graphene-polymer composite mode locker,” Appl. Phys. Lett. 95(14), 141103 (2009). [CrossRef]  

4. Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010). [CrossRef]   [PubMed]  

5. D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. C. Ferrari, “Sub 200 fs pulse generation from a graphene mode-locked fiber laser,” Appl. Phys. Lett. 97(20), 203106 (2010). [CrossRef]  

6. Y. M. Chang, H. Kim, J. H. Lee, and Y. W. Song, “Multilayered graphene efficiently formed by mechanical exfoliation for nonlinear saturable absorbers in fiber mode-locked lasers,” Appl. Phys. Lett. 97(21), 211102 (2010). [CrossRef]  

7. A. Martinez, K. Fuse, and S. Yamashita, “Mechanical exfoliation of graphene for the passive mode-locking of fiber lasers,” Appl. Phys. Lett. 99(12), 121107 (2011). [CrossRef]  

8. P. L. Huang, S. C. Lin, C. Y. Yeh, H. H. Kuo, S. H. Huang, G.-R. Lin, L. J. Li, C. Y. Su, and W. H. Cheng, “Stable mode-locked fiber laser based on CVD fabricated graphene saturable absorber,” Opt. Express 20(3), 2460–2465 (2012). [CrossRef]   [PubMed]  

9. G. Sobon, J. Sotor, and K. M. Abramski, “All-polarization maintaining femtosecond Er-doped fiber laser mode-locked by graphene saturable absorber,” Laser Phys. Lett. 9(8), 581–586 (2012). [CrossRef]  

10. G.-R. Lin and Y.-C. Lin, “Directly exfoliated and imprinted graphite nano-particle saturable absorber for passive mode-locking erbium-doped fiber laser,” Laser Phys. Lett. 8(12), 880–886 (2011). [CrossRef]  

11. Y. H. Lin and G.-R. Lin, “Free-standing nano-scale graphite saturable absorber for passively mode-locked erbium doped fiber ring laser,” Laser Phys. Lett. 9(5), 398–404 (2012). [CrossRef]  

12. Y. H. Lin and G.-R. Lin, “Kelly sideband variation and self four-wave-mixing in femtosecond fiber soliton laser mode-locked by multiple exfoliated graphite nano-particles,” Laser Phys. Lett. 10(4), 045109 (2013). [CrossRef]  

13. Q. L. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. Shen, Q. H. Xu, D. Y. Tang, and K. P. Loh, “Monolayer graphene as a saturable absorber in a mode-locked laser,” Nano Res. 4(3), 297–307 (2011). [CrossRef]  

14. C. Y. Su, A. Y. Lu, Y. Xu, F. R. Chen, A. N. Khlobystov, and L. J. Li, “High-quality thin graphene films from fast electrochemical exfoliation,” ACS Nano 5(3), 2332–2339 (2011). [CrossRef]   [PubMed]  

15. J. Lu, J.-X. Yang, J. Wang, A. Lim, S. Wang, and K. P. Loh, “One-pot synthesis of fluorescent carbon nanoribbons, nanoparticles, and graphene by the exfoliation of graphite in ionic liquids,” ACS Nano 3(8), 2367–2375 (2009). [CrossRef]   [PubMed]  

16. D. Wei, L. Grande, V. Chundi, R. White, C. Bower, P. Andrew, and T. Ryhänen, “Graphene from electrochemical exfoliation and its direct applications in enhanced energy storage devices,” Chem. Commun. (Camb.) 48(9), 1239–1241 (2012). [CrossRef]   [PubMed]  

17. H. Zhang, D. Y. Tang, L. M. Zhao, Q. L. Bao, and K. P. Loh, “Large energy mode locking of an erbium-doped fiber laser with atomic layer graphene,” Opt. Express 17(20), 17630–17635 (2009). [CrossRef]   [PubMed]  

18. H. Zhang, D. Y. Tang, L. M. Zhao, Q. Bao, K. P. Loh, B. Lin, and S. C. Tjin, “Compact graphene mode-locked wavelength-tunable erbium-doped fiber lasers: from all anomalous dispersion to all normal dispersion,” Laser Phys. Lett. 7(8), 591–596 (2010). [CrossRef]  

19. G.-R. Lin, J.-Y. Chang, Y.-S. Liao, and H.-H. Lu, “L-band erbium-doped fiber laser with coupling-ratio controlled wavelength tunability,” Opt. Express 14(21), 9743–9749 (2006). [CrossRef]   [PubMed]  

20. G.-R. Lin and I.-H. Chiu, “Femtosecond wavelength tunable semiconductor optical amplifier fiber laser mode-locked by backward dark-optical-comb injection at 10 GHz,” Opt. Express 13(22), 8772–8780 (2005). [CrossRef]   [PubMed]  

21. Q. L. Bao, H. Zhang, J. X. Yang, S. Wang, D. Y. Tang, R. Jose, S. Ramakrishna, C. T. Lim, and K. P. Loh, “Graphene-polymer nanofiber membrane for ultrafast photonics,” Adv. Funct. Mater. 20(5), 782–791 (2010). [CrossRef]  

22. H. Zhang, D. Y. Tang, R. J. Knize, L. Zhao, Q. L. Bao, and K. P. Loh, “Graphene mode locked, wavelength-tunable, dissipative soliton fber laser,” Appl. Phys. Lett. 96(11), 111112 (2010). [CrossRef]  

23. A. Martinez, K. Fuse, B. Xu, and S. Yamashita, “Optical deposition of graphene and carbon nanotubes in a fiber ferrule for passive mode-locked lasing,” Opt. Express 18(22), 23054–23061 (2010). [CrossRef]   [PubMed]  

24. H. Kim, J. H. Cho, S. Y. Jang, and Y. W. Song, “Deformation immunized optical deposition of graphene for ultrafast pulsed lasers,” Appl. Phys. Lett. 98(2), 021104 (2011). [CrossRef]  

25. A. Martinez, K. Fuse, and S. Yamashita, “Mechanical exfoliation of graphene for the passive mode-locking of fiber lasers,” Appl. Phys. Lett. 99(12), 121107 (2011). [CrossRef]  

26. J.-C. Chiu, C.-M. Chang, B.-Z. Hsieh, S.-C. Lin, C.-Y. Yeh, G.-R. Lin, C.-K. Lee, J.-J. Lin, and W.-H. Cheng, “Pulse shortening mode-locked fiber laser by thickness and concentration product of carbon nanotube based saturable absorber,” Opt. Express 19(5), 4036–4041 (2011). [CrossRef]   [PubMed]  

27. J. Sotor, G. Sobon, and K. M. Abramski, “Scalar soliton generation in all-polarization-maintaining, graphene mode-locked fiber laser,” Opt. Lett. 37(11), 2166–2168 (2012). [CrossRef]   [PubMed]  

28. K. N. Cheng, Y. H. Lin, S. Yamashita, and G.-R. Lin, “Harmonic order dependent pulsewidth shortening of a passively mode-locked fiber laser with carbon nanotube saturable absorber,” IEEE Photon. J 4(5), 1542–1552 (2012). [CrossRef]  

29. G. Sobon, J. Sotor, and K. M. Abramski, “All-polarization maintaining femtosecond Er-doped fiber laser mode-locked by graphene saturable absorber,” Laser Phys. Lett. 9(8), 581–586 (2012). [CrossRef]  

30. G. Sobon, J. Sotor, and K. M. Abramski, “Passive harmonic mode-locking in Er-doped fiber laser based on graphene saturable absorber with repetition rates scalable to 2.22 GHz,” Appl. Phys. Lett. 100(16), 161109 (2012). [CrossRef]  

31. J. Du, S. M. Zhang, H. F. Li, Y. C. Meng, X. L. Li, and Y. P. Hao, “L-Band passively harmonic mode-locked fiber laser based on a graphene saturable absorber,” Laser Phys. Lett. 9, 896–900 (2012).

32. Y. C. Meng, S. Zhang, X. Li, H. Li, J. Du, and Y. P. Hao, “Multiple-soliton dynamic patterns in a graphene mode-locked fiber laser,” Opt. Express 20(6), 6685–6692 (2012). [CrossRef]   [PubMed]  

33. K. N. Cheng, Y. H. Lin, and G.-R. Lin, “Single- and double-walled CNT based saturable absorbers for passively mode-locking erbium-doped fiber laser,” Laser Phys. 23(4), 045105 (2013). [CrossRef]  

34. Y. H. Lin, Y. C. Chi, and G.-R. Lin, “Nanoscale charcoal powder induced saturable absorption and mode-locking of a low-gain erbium-doped fiber-ring laser,” Laser Phys. Lett. 10(5), 055105 (2013). [CrossRef]  

35. 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]  

36. Z. B. Liu, X. He, and D. N. Wang, “Passively mode-locked fiber laser based on a hollow-core photonic crystal fiber filled with few-layered graphene oxide solution,” Opt. Lett. 36(16), 3024–3026 (2011). [CrossRef]   [PubMed]  

37. Z. Q. Luo, J. Z. Wang, M. Zhou, H. Y. Xu, Z. P. Cai, and C. C. Ye, “Multiwavelength mode-locked erbium-doped fiber laser based on the interaction of graphene and fiber-taper evanescent field,” Laser Phys. Lett. 9(3), 229–233 (2012). [CrossRef]  

38. S. Y. Choi, D. K. Cho, Y. W. Song, K. Oh, K. Kim, F. Rotermund, and D. I. Yeom, “Graphene-filled hollow optical fiber saturable absorber for efficient soliton fiber laser mode-locking,” Opt. Express 20(5), 5652–5657 (2012). [CrossRef]   [PubMed]  

39. J. Z. Wang, Z. Luo, M. Zhou, C. C. Ye, H. Fu, Z. P. Cai, H. H. Cheng, H. Y. Xu, and W. Qi, “Evanescent-light deposition of graphene onto tapered fibers for passive Q-switch and mode-locker,” IEEE Photon. J. 4(5), 1295–1305 (2012). [CrossRef]  

40. 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]  

41. G.-R. Lin, C. L. Pan, and Y. T. Lin, “Self-steepening of prechirped amplified and compressed 29-fs fiber laser pulse in large-mode-area erbium-doped fiber amplifier,” J. Lightwave Technol. 25(11), 3597–3601 (2007). [CrossRef]  

42. A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene Layers,” Phys. Rev. Lett. 97(18), 187401 (2006). [CrossRef]   [PubMed]  

43. Z. H. Ni, T. Yu, Y. H. Lu, Y. Y. Wang, Y. P. Feng, and Z. X. Shen, “Uniaxial strain on graphene: Raman spectroscopy study and band-gap opening,” ACS Nano 2(11), 2301–2305 (2008). [CrossRef]   [PubMed]  

44. M. J. Allen, V. C. Tung, and R. B. Kaner, “Honeycomb carbon: a review of graphene,” Chem. Rev. 110(1), 132–145 (2010). [CrossRef]   [PubMed]  

45. O. Frank, M. Mohr, J. Maultzsch, C. Thomsen, I. Riaz, R. Jalil, K. S. Novoselov, G. Tsoukleri, J. Parthenios, K. Papagelis, L. Kavan, and C. Galiotis, “Raman 2D-band splitting in graphene: theory and experiment,” ACS Nano 5(3), 2231–2239 (2011). [CrossRef]   [PubMed]  

46. E. Hecht, Optics (Addison Wesley, 4th Edition).

47. H. Zhang, S. Virally, Q. L. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37(11), 1856–1858 (2012). [CrossRef]   [PubMed]  

48. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics. (Wiley, New York, 1991).

49. G.-R. Lin, I.-H. Chiu, and M. C. Wu, “1.2-ps mode-locked semiconductor optical amplifier fiber laser pulses generated by 60-ps backward dark-optical comb injection and soliton compression,” Opt. Express 13(3), 1008–1014 (2005). [CrossRef]   [PubMed]  

50. G.-R. Lin, J. J. Kang, and C. K. Lee, “High-order rational harmonic mode-locking and pulse-amplitude equalization of SOAFL via reshaped gain-switching FPLD pulse injection,” Opt. Express 18(9), 9570–9579 (2010). [CrossRef]   [PubMed]  

References

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  1. Q. L. Bao, H. Zhang, 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]
  2. 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, 3874–3899 (2009).
  3. H. Zhang, Q. L. Bao, D. Y. Tang, L. Zhao, and K. P. Loh, “Large energy soliton erbium-doped fber laser with a graphene-polymer composite mode locker,” Appl. Phys. Lett. 95(14), 141103 (2009).
    [Crossref]
  4. Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
    [Crossref] [PubMed]
  5. D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. C. Ferrari, “Sub 200 fs pulse generation from a graphene mode-locked fiber laser,” Appl. Phys. Lett. 97(20), 203106 (2010).
    [Crossref]
  6. Y. M. Chang, H. Kim, J. H. Lee, and Y. W. Song, “Multilayered graphene efficiently formed by mechanical exfoliation for nonlinear saturable absorbers in fiber mode-locked lasers,” Appl. Phys. Lett. 97(21), 211102 (2010).
    [Crossref]
  7. A. Martinez, K. Fuse, and S. Yamashita, “Mechanical exfoliation of graphene for the passive mode-locking of fiber lasers,” Appl. Phys. Lett. 99(12), 121107 (2011).
    [Crossref]
  8. P. L. Huang, S. C. Lin, C. Y. Yeh, H. H. Kuo, S. H. Huang, G.-R. Lin, L. J. Li, C. Y. Su, and W. H. Cheng, “Stable mode-locked fiber laser based on CVD fabricated graphene saturable absorber,” Opt. Express 20(3), 2460–2465 (2012).
    [Crossref] [PubMed]
  9. G. Sobon, J. Sotor, and K. M. Abramski, “All-polarization maintaining femtosecond Er-doped fiber laser mode-locked by graphene saturable absorber,” Laser Phys. Lett. 9(8), 581–586 (2012).
    [Crossref]
  10. G.-R. Lin and Y.-C. Lin, “Directly exfoliated and imprinted graphite nano-particle saturable absorber for passive mode-locking erbium-doped fiber laser,” Laser Phys. Lett. 8(12), 880–886 (2011).
    [Crossref]
  11. Y. H. Lin and G.-R. Lin, “Free-standing nano-scale graphite saturable absorber for passively mode-locked erbium doped fiber ring laser,” Laser Phys. Lett. 9(5), 398–404 (2012).
    [Crossref]
  12. Y. H. Lin and G.-R. Lin, “Kelly sideband variation and self four-wave-mixing in femtosecond fiber soliton laser mode-locked by multiple exfoliated graphite nano-particles,” Laser Phys. Lett. 10(4), 045109 (2013).
    [Crossref]
  13. Q. L. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. Shen, Q. H. Xu, D. Y. Tang, and K. P. Loh, “Monolayer graphene as a saturable absorber in a mode-locked laser,” Nano Res. 4(3), 297–307 (2011).
    [Crossref]
  14. C. Y. Su, A. Y. Lu, Y. Xu, F. R. Chen, A. N. Khlobystov, and L. J. Li, “High-quality thin graphene films from fast electrochemical exfoliation,” ACS Nano 5(3), 2332–2339 (2011).
    [Crossref] [PubMed]
  15. J. Lu, J.-X. Yang, J. Wang, A. Lim, S. Wang, and K. P. Loh, “One-pot synthesis of fluorescent carbon nanoribbons, nanoparticles, and graphene by the exfoliation of graphite in ionic liquids,” ACS Nano 3(8), 2367–2375 (2009).
    [Crossref] [PubMed]
  16. D. Wei, L. Grande, V. Chundi, R. White, C. Bower, P. Andrew, and T. Ryhänen, “Graphene from electrochemical exfoliation and its direct applications in enhanced energy storage devices,” Chem. Commun. (Camb.) 48(9), 1239–1241 (2012).
    [Crossref] [PubMed]
  17. H. Zhang, D. Y. Tang, L. M. Zhao, Q. L. Bao, and K. P. Loh, “Large energy mode locking of an erbium-doped fiber laser with atomic layer graphene,” Opt. Express 17(20), 17630–17635 (2009).
    [Crossref] [PubMed]
  18. H. Zhang, D. Y. Tang, L. M. Zhao, Q. Bao, K. P. Loh, B. Lin, and S. C. Tjin, “Compact graphene mode-locked wavelength-tunable erbium-doped fiber lasers: from all anomalous dispersion to all normal dispersion,” Laser Phys. Lett. 7(8), 591–596 (2010).
    [Crossref]
  19. G.-R. Lin, J.-Y. Chang, Y.-S. Liao, and H.-H. Lu, “L-band erbium-doped fiber laser with coupling-ratio controlled wavelength tunability,” Opt. Express 14(21), 9743–9749 (2006).
    [Crossref] [PubMed]
  20. G.-R. Lin and I.-H. Chiu, “Femtosecond wavelength tunable semiconductor optical amplifier fiber laser mode-locked by backward dark-optical-comb injection at 10 GHz,” Opt. Express 13(22), 8772–8780 (2005).
    [Crossref] [PubMed]
  21. Q. L. Bao, H. Zhang, J. X. Yang, S. Wang, D. Y. Tang, R. Jose, S. Ramakrishna, C. T. Lim, and K. P. Loh, “Graphene-polymer nanofiber membrane for ultrafast photonics,” Adv. Funct. Mater. 20(5), 782–791 (2010).
    [Crossref]
  22. H. Zhang, D. Y. Tang, R. J. Knize, L. Zhao, Q. L. Bao, and K. P. Loh, “Graphene mode locked, wavelength-tunable, dissipative soliton fber laser,” Appl. Phys. Lett. 96(11), 111112 (2010).
    [Crossref]
  23. A. Martinez, K. Fuse, B. Xu, and S. Yamashita, “Optical deposition of graphene and carbon nanotubes in a fiber ferrule for passive mode-locked lasing,” Opt. Express 18(22), 23054–23061 (2010).
    [Crossref] [PubMed]
  24. H. Kim, J. H. Cho, S. Y. Jang, and Y. W. Song, “Deformation immunized optical deposition of graphene for ultrafast pulsed lasers,” Appl. Phys. Lett. 98(2), 021104 (2011).
    [Crossref]
  25. A. Martinez, K. Fuse, and S. Yamashita, “Mechanical exfoliation of graphene for the passive mode-locking of fiber lasers,” Appl. Phys. Lett. 99(12), 121107 (2011).
    [Crossref]
  26. J.-C. Chiu, C.-M. Chang, B.-Z. Hsieh, S.-C. Lin, C.-Y. Yeh, G.-R. Lin, C.-K. Lee, J.-J. Lin, and W.-H. Cheng, “Pulse shortening mode-locked fiber laser by thickness and concentration product of carbon nanotube based saturable absorber,” Opt. Express 19(5), 4036–4041 (2011).
    [Crossref] [PubMed]
  27. J. Sotor, G. Sobon, and K. M. Abramski, “Scalar soliton generation in all-polarization-maintaining, graphene mode-locked fiber laser,” Opt. Lett. 37(11), 2166–2168 (2012).
    [Crossref] [PubMed]
  28. K. N. Cheng, Y. H. Lin, S. Yamashita, and G.-R. Lin, “Harmonic order dependent pulsewidth shortening of a passively mode-locked fiber laser with carbon nanotube saturable absorber,” IEEE Photon. J 4(5), 1542–1552 (2012).
    [Crossref]
  29. G. Sobon, J. Sotor, and K. M. Abramski, “All-polarization maintaining femtosecond Er-doped fiber laser mode-locked by graphene saturable absorber,” Laser Phys. Lett. 9(8), 581–586 (2012).
    [Crossref]
  30. G. Sobon, J. Sotor, and K. M. Abramski, “Passive harmonic mode-locking in Er-doped fiber laser based on graphene saturable absorber with repetition rates scalable to 2.22 GHz,” Appl. Phys. Lett. 100(16), 161109 (2012).
    [Crossref]
  31. J. Du, S. M. Zhang, H. F. Li, Y. C. Meng, X. L. Li, and Y. P. Hao, “L-Band passively harmonic mode-locked fiber laser based on a graphene saturable absorber,” Laser Phys. Lett. 9, 896–900 (2012).
  32. Y. C. Meng, S. Zhang, X. Li, H. Li, J. Du, and Y. P. Hao, “Multiple-soliton dynamic patterns in a graphene mode-locked fiber laser,” Opt. Express 20(6), 6685–6692 (2012).
    [Crossref] [PubMed]
  33. K. N. Cheng, Y. H. Lin, and G.-R. Lin, “Single- and double-walled CNT based saturable absorbers for passively mode-locking erbium-doped fiber laser,” Laser Phys. 23(4), 045105 (2013).
    [Crossref]
  34. Y. H. Lin, Y. C. Chi, and G.-R. Lin, “Nanoscale charcoal powder induced saturable absorption and mode-locking of a low-gain erbium-doped fiber-ring laser,” Laser Phys. Lett. 10(5), 055105 (2013).
    [Crossref]
  35. 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]
  36. Z. B. Liu, X. He, and D. N. Wang, “Passively mode-locked fiber laser based on a hollow-core photonic crystal fiber filled with few-layered graphene oxide solution,” Opt. Lett. 36(16), 3024–3026 (2011).
    [Crossref] [PubMed]
  37. Z. Q. Luo, J. Z. Wang, M. Zhou, H. Y. Xu, Z. P. Cai, and C. C. Ye, “Multiwavelength mode-locked erbium-doped fiber laser based on the interaction of graphene and fiber-taper evanescent field,” Laser Phys. Lett. 9(3), 229–233 (2012).
    [Crossref]
  38. S. Y. Choi, D. K. Cho, Y. W. Song, K. Oh, K. Kim, F. Rotermund, and D. I. Yeom, “Graphene-filled hollow optical fiber saturable absorber for efficient soliton fiber laser mode-locking,” Opt. Express 20(5), 5652–5657 (2012).
    [Crossref] [PubMed]
  39. J. Z. Wang, Z. Luo, M. Zhou, C. C. Ye, H. Fu, Z. P. Cai, H. H. Cheng, H. Y. Xu, and W. Qi, “Evanescent-light deposition of graphene onto tapered fibers for passive Q-switch and mode-locker,” IEEE Photon. J. 4(5), 1295–1305 (2012).
    [Crossref]
  40. 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]
  41. G.-R. Lin, C. L. Pan, and Y. T. Lin, “Self-steepening of prechirped amplified and compressed 29-fs fiber laser pulse in large-mode-area erbium-doped fiber amplifier,” J. Lightwave Technol. 25(11), 3597–3601 (2007).
    [Crossref]
  42. A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene Layers,” Phys. Rev. Lett. 97(18), 187401 (2006).
    [Crossref] [PubMed]
  43. Z. H. Ni, T. Yu, Y. H. Lu, Y. Y. Wang, Y. P. Feng, and Z. X. Shen, “Uniaxial strain on graphene: Raman spectroscopy study and band-gap opening,” ACS Nano 2(11), 2301–2305 (2008).
    [Crossref] [PubMed]
  44. M. J. Allen, V. C. Tung, and R. B. Kaner, “Honeycomb carbon: a review of graphene,” Chem. Rev. 110(1), 132–145 (2010).
    [Crossref] [PubMed]
  45. O. Frank, M. Mohr, J. Maultzsch, C. Thomsen, I. Riaz, R. Jalil, K. S. Novoselov, G. Tsoukleri, J. Parthenios, K. Papagelis, L. Kavan, and C. Galiotis, “Raman 2D-band splitting in graphene: theory and experiment,” ACS Nano 5(3), 2231–2239 (2011).
    [Crossref] [PubMed]
  46. E. Hecht, Optics (Addison Wesley, 4th Edition).
  47. H. Zhang, S. Virally, Q. L. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37(11), 1856–1858 (2012).
    [Crossref] [PubMed]
  48. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics. (Wiley, New York, 1991).
  49. G.-R. Lin, I.-H. Chiu, and M. C. Wu, “1.2-ps mode-locked semiconductor optical amplifier fiber laser pulses generated by 60-ps backward dark-optical comb injection and soliton compression,” Opt. Express 13(3), 1008–1014 (2005).
    [Crossref] [PubMed]
  50. G.-R. Lin, J. J. Kang, and C. K. Lee, “High-order rational harmonic mode-locking and pulse-amplitude equalization of SOAFL via reshaped gain-switching FPLD pulse injection,” Opt. Express 18(9), 9570–9579 (2010).
    [Crossref] [PubMed]

2013 (4)

Y. H. Lin and G.-R. Lin, “Kelly sideband variation and self four-wave-mixing in femtosecond fiber soliton laser mode-locked by multiple exfoliated graphite nano-particles,” Laser Phys. Lett. 10(4), 045109 (2013).
[Crossref]

K. N. Cheng, Y. H. Lin, and G.-R. Lin, “Single- and double-walled CNT based saturable absorbers for passively mode-locking erbium-doped fiber laser,” Laser Phys. 23(4), 045105 (2013).
[Crossref]

Y. H. Lin, Y. C. Chi, and G.-R. Lin, “Nanoscale charcoal powder induced saturable absorption and mode-locking of a low-gain erbium-doped fiber-ring laser,” Laser Phys. Lett. 10(5), 055105 (2013).
[Crossref]

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]

2012 (14)

Z. Q. Luo, J. Z. Wang, M. Zhou, H. Y. Xu, Z. P. Cai, and C. C. Ye, “Multiwavelength mode-locked erbium-doped fiber laser based on the interaction of graphene and fiber-taper evanescent field,” Laser Phys. Lett. 9(3), 229–233 (2012).
[Crossref]

S. Y. Choi, D. K. Cho, Y. W. Song, K. Oh, K. Kim, F. Rotermund, and D. I. Yeom, “Graphene-filled hollow optical fiber saturable absorber for efficient soliton fiber laser mode-locking,” Opt. Express 20(5), 5652–5657 (2012).
[Crossref] [PubMed]

J. Z. Wang, Z. Luo, M. Zhou, C. C. Ye, H. Fu, Z. P. Cai, H. H. Cheng, H. Y. Xu, and W. Qi, “Evanescent-light deposition of graphene onto tapered fibers for passive Q-switch and mode-locker,” IEEE Photon. J. 4(5), 1295–1305 (2012).
[Crossref]

J. Sotor, G. Sobon, and K. M. Abramski, “Scalar soliton generation in all-polarization-maintaining, graphene mode-locked fiber laser,” Opt. Lett. 37(11), 2166–2168 (2012).
[Crossref] [PubMed]

K. N. Cheng, Y. H. Lin, S. Yamashita, and G.-R. Lin, “Harmonic order dependent pulsewidth shortening of a passively mode-locked fiber laser with carbon nanotube saturable absorber,” IEEE Photon. J 4(5), 1542–1552 (2012).
[Crossref]

G. Sobon, J. Sotor, and K. M. Abramski, “All-polarization maintaining femtosecond Er-doped fiber laser mode-locked by graphene saturable absorber,” Laser Phys. Lett. 9(8), 581–586 (2012).
[Crossref]

G. Sobon, J. Sotor, and K. M. Abramski, “Passive harmonic mode-locking in Er-doped fiber laser based on graphene saturable absorber with repetition rates scalable to 2.22 GHz,” Appl. Phys. Lett. 100(16), 161109 (2012).
[Crossref]

J. Du, S. M. Zhang, H. F. Li, Y. C. Meng, X. L. Li, and Y. P. Hao, “L-Band passively harmonic mode-locked fiber laser based on a graphene saturable absorber,” Laser Phys. Lett. 9, 896–900 (2012).

Y. C. Meng, S. Zhang, X. Li, H. Li, J. Du, and Y. P. Hao, “Multiple-soliton dynamic patterns in a graphene mode-locked fiber laser,” Opt. Express 20(6), 6685–6692 (2012).
[Crossref] [PubMed]

D. Wei, L. Grande, V. Chundi, R. White, C. Bower, P. Andrew, and T. Ryhänen, “Graphene from electrochemical exfoliation and its direct applications in enhanced energy storage devices,” Chem. Commun. (Camb.) 48(9), 1239–1241 (2012).
[Crossref] [PubMed]

P. L. Huang, S. C. Lin, C. Y. Yeh, H. H. Kuo, S. H. Huang, G.-R. Lin, L. J. Li, C. Y. Su, and W. H. Cheng, “Stable mode-locked fiber laser based on CVD fabricated graphene saturable absorber,” Opt. Express 20(3), 2460–2465 (2012).
[Crossref] [PubMed]

G. Sobon, J. Sotor, and K. M. Abramski, “All-polarization maintaining femtosecond Er-doped fiber laser mode-locked by graphene saturable absorber,” Laser Phys. Lett. 9(8), 581–586 (2012).
[Crossref]

Y. H. Lin and G.-R. Lin, “Free-standing nano-scale graphite saturable absorber for passively mode-locked erbium doped fiber ring laser,” Laser Phys. Lett. 9(5), 398–404 (2012).
[Crossref]

H. Zhang, S. Virally, Q. L. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37(11), 1856–1858 (2012).
[Crossref] [PubMed]

2011 (9)

O. Frank, M. Mohr, J. Maultzsch, C. Thomsen, I. Riaz, R. Jalil, K. S. Novoselov, G. Tsoukleri, J. Parthenios, K. Papagelis, L. Kavan, and C. Galiotis, “Raman 2D-band splitting in graphene: theory and experiment,” ACS Nano 5(3), 2231–2239 (2011).
[Crossref] [PubMed]

A. Martinez, K. Fuse, and S. Yamashita, “Mechanical exfoliation of graphene for the passive mode-locking of fiber lasers,” Appl. Phys. Lett. 99(12), 121107 (2011).
[Crossref]

G.-R. Lin and Y.-C. Lin, “Directly exfoliated and imprinted graphite nano-particle saturable absorber for passive mode-locking erbium-doped fiber laser,” Laser Phys. Lett. 8(12), 880–886 (2011).
[Crossref]

Q. L. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. Shen, Q. H. Xu, D. Y. Tang, and K. P. Loh, “Monolayer graphene as a saturable absorber in a mode-locked laser,” Nano Res. 4(3), 297–307 (2011).
[Crossref]

C. Y. Su, A. Y. Lu, Y. Xu, F. R. Chen, A. N. Khlobystov, and L. J. Li, “High-quality thin graphene films from fast electrochemical exfoliation,” ACS Nano 5(3), 2332–2339 (2011).
[Crossref] [PubMed]

H. Kim, J. H. Cho, S. Y. Jang, and Y. W. Song, “Deformation immunized optical deposition of graphene for ultrafast pulsed lasers,” Appl. Phys. Lett. 98(2), 021104 (2011).
[Crossref]

A. Martinez, K. Fuse, and S. Yamashita, “Mechanical exfoliation of graphene for the passive mode-locking of fiber lasers,” Appl. Phys. Lett. 99(12), 121107 (2011).
[Crossref]

J.-C. Chiu, C.-M. Chang, B.-Z. Hsieh, S.-C. Lin, C.-Y. Yeh, G.-R. Lin, C.-K. Lee, J.-J. Lin, and W.-H. Cheng, “Pulse shortening mode-locked fiber laser by thickness and concentration product of carbon nanotube based saturable absorber,” Opt. Express 19(5), 4036–4041 (2011).
[Crossref] [PubMed]

Z. B. Liu, X. He, and D. N. Wang, “Passively mode-locked fiber laser based on a hollow-core photonic crystal fiber filled with few-layered graphene oxide solution,” Opt. Lett. 36(16), 3024–3026 (2011).
[Crossref] [PubMed]

2010 (10)

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]

Q. L. Bao, H. Zhang, J. X. Yang, S. Wang, D. Y. Tang, R. Jose, S. Ramakrishna, C. T. Lim, and K. P. Loh, “Graphene-polymer nanofiber membrane for ultrafast photonics,” Adv. Funct. Mater. 20(5), 782–791 (2010).
[Crossref]

H. Zhang, D. Y. Tang, R. J. Knize, L. Zhao, Q. L. Bao, and K. P. Loh, “Graphene mode locked, wavelength-tunable, dissipative soliton fber laser,” Appl. Phys. Lett. 96(11), 111112 (2010).
[Crossref]

A. Martinez, K. Fuse, B. Xu, and S. Yamashita, “Optical deposition of graphene and carbon nanotubes in a fiber ferrule for passive mode-locked lasing,” Opt. Express 18(22), 23054–23061 (2010).
[Crossref] [PubMed]

H. Zhang, D. Y. Tang, L. M. Zhao, Q. Bao, K. P. Loh, B. Lin, and S. C. Tjin, “Compact graphene mode-locked wavelength-tunable erbium-doped fiber lasers: from all anomalous dispersion to all normal dispersion,” Laser Phys. Lett. 7(8), 591–596 (2010).
[Crossref]

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. C. Ferrari, “Sub 200 fs pulse generation from a graphene mode-locked fiber laser,” Appl. Phys. Lett. 97(20), 203106 (2010).
[Crossref]

Y. M. Chang, H. Kim, J. H. Lee, and Y. W. Song, “Multilayered graphene efficiently formed by mechanical exfoliation for nonlinear saturable absorbers in fiber mode-locked lasers,” Appl. Phys. Lett. 97(21), 211102 (2010).
[Crossref]

M. J. Allen, V. C. Tung, and R. B. Kaner, “Honeycomb carbon: a review of graphene,” Chem. Rev. 110(1), 132–145 (2010).
[Crossref] [PubMed]

G.-R. Lin, J. J. Kang, and C. K. Lee, “High-order rational harmonic mode-locking and pulse-amplitude equalization of SOAFL via reshaped gain-switching FPLD pulse injection,” Opt. Express 18(9), 9570–9579 (2010).
[Crossref] [PubMed]

2009 (5)

Q. L. Bao, H. Zhang, 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]

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, 3874–3899 (2009).

H. Zhang, Q. L. Bao, D. Y. Tang, L. Zhao, and K. P. Loh, “Large energy soliton erbium-doped fber laser with a graphene-polymer composite mode locker,” Appl. Phys. Lett. 95(14), 141103 (2009).
[Crossref]

H. Zhang, D. Y. Tang, L. M. Zhao, Q. L. Bao, and K. P. Loh, “Large energy mode locking of an erbium-doped fiber laser with atomic layer graphene,” Opt. Express 17(20), 17630–17635 (2009).
[Crossref] [PubMed]

J. Lu, J.-X. Yang, J. Wang, A. Lim, S. Wang, and K. P. Loh, “One-pot synthesis of fluorescent carbon nanoribbons, nanoparticles, and graphene by the exfoliation of graphite in ionic liquids,” ACS Nano 3(8), 2367–2375 (2009).
[Crossref] [PubMed]

2008 (1)

Z. H. Ni, T. Yu, Y. H. Lu, Y. Y. Wang, Y. P. Feng, and Z. X. Shen, “Uniaxial strain on graphene: Raman spectroscopy study and band-gap opening,” ACS Nano 2(11), 2301–2305 (2008).
[Crossref] [PubMed]

2007 (1)

2006 (2)

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene Layers,” Phys. Rev. Lett. 97(18), 187401 (2006).
[Crossref] [PubMed]

G.-R. Lin, J.-Y. Chang, Y.-S. Liao, and H.-H. Lu, “L-band erbium-doped fiber laser with coupling-ratio controlled wavelength tunability,” Opt. Express 14(21), 9743–9749 (2006).
[Crossref] [PubMed]

2005 (2)

Abramski, K. M.

G. Sobon, J. Sotor, and K. M. Abramski, “All-polarization maintaining femtosecond Er-doped fiber laser mode-locked by graphene saturable absorber,” Laser Phys. Lett. 9(8), 581–586 (2012).
[Crossref]

J. Sotor, G. Sobon, and K. M. Abramski, “Scalar soliton generation in all-polarization-maintaining, graphene mode-locked fiber laser,” Opt. Lett. 37(11), 2166–2168 (2012).
[Crossref] [PubMed]

G. Sobon, J. Sotor, and K. M. Abramski, “All-polarization maintaining femtosecond Er-doped fiber laser mode-locked by graphene saturable absorber,” Laser Phys. Lett. 9(8), 581–586 (2012).
[Crossref]

G. Sobon, J. Sotor, and K. M. Abramski, “Passive harmonic mode-locking in Er-doped fiber laser based on graphene saturable absorber with repetition rates scalable to 2.22 GHz,” Appl. Phys. Lett. 100(16), 161109 (2012).
[Crossref]

Allen, M. J.

M. J. Allen, V. C. Tung, and R. B. Kaner, “Honeycomb carbon: a review of graphene,” Chem. Rev. 110(1), 132–145 (2010).
[Crossref] [PubMed]

Andrew, P.

D. Wei, L. Grande, V. Chundi, R. White, C. Bower, P. Andrew, and T. Ryhänen, “Graphene from electrochemical exfoliation and its direct applications in enhanced energy storage devices,” Chem. Commun. (Camb.) 48(9), 1239–1241 (2012).
[Crossref] [PubMed]

Bae, M.-K.

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]

Bao, Q.

H. Zhang, D. Y. Tang, L. M. Zhao, Q. Bao, K. P. Loh, B. Lin, and S. C. Tjin, “Compact graphene mode-locked wavelength-tunable erbium-doped fiber lasers: from all anomalous dispersion to all normal dispersion,” Laser Phys. Lett. 7(8), 591–596 (2010).
[Crossref]

Bao, Q. L.

H. Zhang, S. Virally, Q. L. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37(11), 1856–1858 (2012).
[Crossref] [PubMed]

Q. L. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. Shen, Q. H. Xu, D. Y. Tang, and K. P. Loh, “Monolayer graphene as a saturable absorber in a mode-locked laser,” Nano Res. 4(3), 297–307 (2011).
[Crossref]

Q. L. Bao, H. Zhang, J. X. Yang, S. Wang, D. Y. Tang, R. Jose, S. Ramakrishna, C. T. Lim, and K. P. Loh, “Graphene-polymer nanofiber membrane for ultrafast photonics,” Adv. Funct. Mater. 20(5), 782–791 (2010).
[Crossref]

H. Zhang, D. Y. Tang, R. J. Knize, L. Zhao, Q. L. Bao, and K. P. Loh, “Graphene mode locked, wavelength-tunable, dissipative soliton fber laser,” Appl. Phys. Lett. 96(11), 111112 (2010).
[Crossref]

H. Zhang, D. Y. Tang, L. M. Zhao, Q. L. Bao, and K. P. Loh, “Large energy mode locking of an erbium-doped fiber laser with atomic layer graphene,” Opt. Express 17(20), 17630–17635 (2009).
[Crossref] [PubMed]

Q. L. Bao, H. Zhang, 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]

H. Zhang, Q. L. Bao, D. Y. Tang, L. Zhao, and K. P. Loh, “Large energy soliton erbium-doped fber laser with a graphene-polymer composite mode locker,” Appl. Phys. Lett. 95(14), 141103 (2009).
[Crossref]

Basko, D. M.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

Bonaccorso, F.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

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, 3874–3899 (2009).

Bower, C.

D. Wei, L. Grande, V. Chundi, R. White, C. Bower, P. Andrew, and T. Ryhänen, “Graphene from electrochemical exfoliation and its direct applications in enhanced energy storage devices,” Chem. Commun. (Camb.) 48(9), 1239–1241 (2012).
[Crossref] [PubMed]

Cai, Z. P.

Z. Q. Luo, J. Z. Wang, M. Zhou, H. Y. Xu, Z. P. Cai, and C. C. Ye, “Multiwavelength mode-locked erbium-doped fiber laser based on the interaction of graphene and fiber-taper evanescent field,” Laser Phys. Lett. 9(3), 229–233 (2012).
[Crossref]

J. Z. Wang, Z. Luo, M. Zhou, C. C. Ye, H. Fu, Z. P. Cai, H. H. Cheng, H. Y. Xu, and W. Qi, “Evanescent-light deposition of graphene onto tapered fibers for passive Q-switch and mode-locker,” IEEE Photon. J. 4(5), 1295–1305 (2012).
[Crossref]

Casiraghi, C.

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene Layers,” Phys. Rev. Lett. 97(18), 187401 (2006).
[Crossref] [PubMed]

Chang, C.-M.

Chang, J.-Y.

Chang, Y. M.

Y. M. Chang, H. Kim, J. H. Lee, and Y. W. Song, “Multilayered graphene efficiently formed by mechanical exfoliation for nonlinear saturable absorbers in fiber mode-locked lasers,” Appl. Phys. Lett. 97(21), 211102 (2010).
[Crossref]

Chen, F. R.

C. Y. Su, A. Y. Lu, Y. Xu, F. R. Chen, A. N. Khlobystov, and L. J. Li, “High-quality thin graphene films from fast electrochemical exfoliation,” ACS Nano 5(3), 2332–2339 (2011).
[Crossref] [PubMed]

Cheng, H. H.

J. Z. Wang, Z. Luo, M. Zhou, C. C. Ye, H. Fu, Z. P. Cai, H. H. Cheng, H. Y. Xu, and W. Qi, “Evanescent-light deposition of graphene onto tapered fibers for passive Q-switch and mode-locker,” IEEE Photon. J. 4(5), 1295–1305 (2012).
[Crossref]

Cheng, K. N.

K. N. Cheng, Y. H. Lin, and G.-R. Lin, “Single- and double-walled CNT based saturable absorbers for passively mode-locking erbium-doped fiber laser,” Laser Phys. 23(4), 045105 (2013).
[Crossref]

K. N. Cheng, Y. H. Lin, S. Yamashita, and G.-R. Lin, “Harmonic order dependent pulsewidth shortening of a passively mode-locked fiber laser with carbon nanotube saturable absorber,” IEEE Photon. J 4(5), 1542–1552 (2012).
[Crossref]

Cheng, W. H.

Cheng, W.-H.

Chi, Y. C.

Y. H. Lin, Y. C. Chi, and G.-R. Lin, “Nanoscale charcoal powder induced saturable absorption and mode-locking of a low-gain erbium-doped fiber-ring laser,” Laser Phys. Lett. 10(5), 055105 (2013).
[Crossref]

Chiu, I.-H.

Chiu, J.-C.

Cho, D. K.

Cho, J. H.

H. Kim, J. H. Cho, S. Y. Jang, and Y. W. Song, “Deformation immunized optical deposition of graphene for ultrafast pulsed lasers,” Appl. Phys. Lett. 98(2), 021104 (2011).
[Crossref]

Choi, S. Y.

Chundi, V.

D. Wei, L. Grande, V. Chundi, R. White, C. Bower, P. Andrew, and T. Ryhänen, “Graphene from electrochemical exfoliation and its direct applications in enhanced energy storage devices,” Chem. Commun. (Camb.) 48(9), 1239–1241 (2012).
[Crossref] [PubMed]

Debnath, P.

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]

Du, J.

J. Du, S. M. Zhang, H. F. Li, Y. C. Meng, X. L. Li, and Y. P. Hao, “L-Band passively harmonic mode-locked fiber laser based on a graphene saturable absorber,” Laser Phys. Lett. 9, 896–900 (2012).

Y. C. Meng, S. Zhang, X. Li, H. Li, J. Du, and Y. P. Hao, “Multiple-soliton dynamic patterns in a graphene mode-locked fiber laser,” Opt. Express 20(6), 6685–6692 (2012).
[Crossref] [PubMed]

Feng, Y. P.

Z. H. Ni, T. Yu, Y. H. Lu, Y. Y. Wang, Y. P. Feng, and Z. X. Shen, “Uniaxial strain on graphene: Raman spectroscopy study and band-gap opening,” ACS Nano 2(11), 2301–2305 (2008).
[Crossref] [PubMed]

Ferrari, A. C.

D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. C. Ferrari, “Sub 200 fs pulse generation from a graphene mode-locked fiber laser,” Appl. Phys. Lett. 97(20), 203106 (2010).
[Crossref]

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

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, 3874–3899 (2009).

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene Layers,” Phys. Rev. Lett. 97(18), 187401 (2006).
[Crossref] [PubMed]

Frank, O.

O. Frank, M. Mohr, J. Maultzsch, C. Thomsen, I. Riaz, R. Jalil, K. S. Novoselov, G. Tsoukleri, J. Parthenios, K. Papagelis, L. Kavan, and C. Galiotis, “Raman 2D-band splitting in graphene: theory and experiment,” ACS Nano 5(3), 2231–2239 (2011).
[Crossref] [PubMed]

Fu, H.

J. Z. Wang, Z. Luo, M. Zhou, C. C. Ye, H. Fu, Z. P. Cai, H. H. Cheng, H. Y. Xu, and W. Qi, “Evanescent-light deposition of graphene onto tapered fibers for passive Q-switch and mode-locker,” IEEE Photon. J. 4(5), 1295–1305 (2012).
[Crossref]

Fuse, K.

A. Martinez, K. Fuse, and S. Yamashita, “Mechanical exfoliation of graphene for the passive mode-locking of fiber lasers,” Appl. Phys. Lett. 99(12), 121107 (2011).
[Crossref]

A. Martinez, K. Fuse, and S. Yamashita, “Mechanical exfoliation of graphene for the passive mode-locking of fiber lasers,” Appl. Phys. Lett. 99(12), 121107 (2011).
[Crossref]

A. Martinez, K. Fuse, B. Xu, and S. Yamashita, “Optical deposition of graphene and carbon nanotubes in a fiber ferrule for passive mode-locked lasing,” Opt. Express 18(22), 23054–23061 (2010).
[Crossref] [PubMed]

Galiotis, C.

O. Frank, M. Mohr, J. Maultzsch, C. Thomsen, I. Riaz, R. Jalil, K. S. Novoselov, G. Tsoukleri, J. Parthenios, K. Papagelis, L. Kavan, and C. Galiotis, “Raman 2D-band splitting in graphene: theory and experiment,” ACS Nano 5(3), 2231–2239 (2011).
[Crossref] [PubMed]

Geim, A. K.

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene Layers,” Phys. Rev. Lett. 97(18), 187401 (2006).
[Crossref] [PubMed]

Godbout, N.

Grande, L.

D. Wei, L. Grande, V. Chundi, R. White, C. Bower, P. Andrew, and T. Ryhänen, “Graphene from electrochemical exfoliation and its direct applications in enhanced energy storage devices,” Chem. Commun. (Camb.) 48(9), 1239–1241 (2012).
[Crossref] [PubMed]

Han, W.-S.

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]

Hao, Y. P.

Y. C. Meng, S. Zhang, X. Li, H. Li, J. Du, and Y. P. Hao, “Multiple-soliton dynamic patterns in a graphene mode-locked fiber laser,” Opt. Express 20(6), 6685–6692 (2012).
[Crossref] [PubMed]

J. Du, S. M. Zhang, H. F. Li, Y. C. Meng, X. L. Li, and Y. P. Hao, “L-Band passively harmonic mode-locked fiber laser based on a graphene saturable absorber,” Laser Phys. Lett. 9, 896–900 (2012).

Hasan, T.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. C. Ferrari, “Sub 200 fs pulse generation from a graphene mode-locked fiber laser,” Appl. Phys. Lett. 97(20), 203106 (2010).
[Crossref]

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, 3874–3899 (2009).

He, X.

Hsieh, B.-Z.

Huang, P. L.

Huang, S. H.

Jalil, R.

O. Frank, M. Mohr, J. Maultzsch, C. Thomsen, I. Riaz, R. Jalil, K. S. Novoselov, G. Tsoukleri, J. Parthenios, K. Papagelis, L. Kavan, and C. Galiotis, “Raman 2D-band splitting in graphene: theory and experiment,” ACS Nano 5(3), 2231–2239 (2011).
[Crossref] [PubMed]

Jang, S. Y.

H. Kim, J. H. Cho, S. Y. Jang, and Y. W. Song, “Deformation immunized optical deposition of graphene for ultrafast pulsed lasers,” Appl. Phys. Lett. 98(2), 021104 (2011).
[Crossref]

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]

Jiang, D.

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene Layers,” Phys. Rev. Lett. 97(18), 187401 (2006).
[Crossref] [PubMed]

Jose, R.

Q. L. Bao, H. Zhang, J. X. Yang, S. Wang, D. Y. Tang, R. Jose, S. Ramakrishna, C. T. Lim, and K. P. Loh, “Graphene-polymer nanofiber membrane for ultrafast photonics,” Adv. Funct. Mater. 20(5), 782–791 (2010).
[Crossref]

Kaner, R. B.

M. J. Allen, V. C. Tung, and R. B. Kaner, “Honeycomb carbon: a review of graphene,” Chem. Rev. 110(1), 132–145 (2010).
[Crossref] [PubMed]

Kang, J. J.

Kavan, L.

O. Frank, M. Mohr, J. Maultzsch, C. Thomsen, I. Riaz, R. Jalil, K. S. Novoselov, G. Tsoukleri, J. Parthenios, K. Papagelis, L. Kavan, and C. Galiotis, “Raman 2D-band splitting in graphene: theory and experiment,” ACS Nano 5(3), 2231–2239 (2011).
[Crossref] [PubMed]

Khlobystov, A. N.

C. Y. Su, A. Y. Lu, Y. Xu, F. R. Chen, A. N. Khlobystov, and L. J. Li, “High-quality thin graphene films from fast electrochemical exfoliation,” ACS Nano 5(3), 2332–2339 (2011).
[Crossref] [PubMed]

Kim, H.

H. Kim, J. H. Cho, S. Y. Jang, and Y. W. Song, “Deformation immunized optical deposition of graphene for ultrafast pulsed lasers,” Appl. Phys. Lett. 98(2), 021104 (2011).
[Crossref]

Y. M. Chang, H. Kim, J. H. Lee, and Y. W. Song, “Multilayered graphene efficiently formed by mechanical exfoliation for nonlinear saturable absorbers in fiber mode-locked lasers,” Appl. Phys. Lett. 97(21), 211102 (2010).
[Crossref]

Kim, K.

Knize, R. J.

H. Zhang, D. Y. Tang, R. J. Knize, L. Zhao, Q. L. Bao, and K. P. Loh, “Graphene mode locked, wavelength-tunable, dissipative soliton fber laser,” Appl. Phys. Lett. 96(11), 111112 (2010).
[Crossref]

Kockaert, P.

Koo, J.

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]

Kuo, H. H.

Lazzeri, M.

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene Layers,” Phys. Rev. Lett. 97(18), 187401 (2006).
[Crossref] [PubMed]

Lee, C. K.

Lee, C.-K.

Lee, J.

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]

Lee, J. H.

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]

Y. M. Chang, H. Kim, J. H. Lee, and Y. W. Song, “Multilayered graphene efficiently formed by mechanical exfoliation for nonlinear saturable absorbers in fiber mode-locked lasers,” Appl. Phys. Lett. 97(21), 211102 (2010).
[Crossref]

Li, H.

Li, H. F.

J. Du, S. M. Zhang, H. F. Li, Y. C. Meng, X. L. Li, and Y. P. Hao, “L-Band passively harmonic mode-locked fiber laser based on a graphene saturable absorber,” Laser Phys. Lett. 9, 896–900 (2012).

Li, L. J.

P. L. Huang, S. C. Lin, C. Y. Yeh, H. H. Kuo, S. H. Huang, G.-R. Lin, L. J. Li, C. Y. Su, and W. H. Cheng, “Stable mode-locked fiber laser based on CVD fabricated graphene saturable absorber,” Opt. Express 20(3), 2460–2465 (2012).
[Crossref] [PubMed]

C. Y. Su, A. Y. Lu, Y. Xu, F. R. Chen, A. N. Khlobystov, and L. J. Li, “High-quality thin graphene films from fast electrochemical exfoliation,” ACS Nano 5(3), 2332–2339 (2011).
[Crossref] [PubMed]

Li, X.

Li, X. L.

J. Du, S. M. Zhang, H. F. Li, Y. C. Meng, X. L. Li, and Y. P. Hao, “L-Band passively harmonic mode-locked fiber laser based on a graphene saturable absorber,” Laser Phys. Lett. 9, 896–900 (2012).

Liao, Y.-S.

Lim, A.

J. Lu, J.-X. Yang, J. Wang, A. Lim, S. Wang, and K. P. Loh, “One-pot synthesis of fluorescent carbon nanoribbons, nanoparticles, and graphene by the exfoliation of graphite in ionic liquids,” ACS Nano 3(8), 2367–2375 (2009).
[Crossref] [PubMed]

Lim, C. T.

Q. L. Bao, H. Zhang, J. X. Yang, S. Wang, D. Y. Tang, R. Jose, S. Ramakrishna, C. T. Lim, and K. P. Loh, “Graphene-polymer nanofiber membrane for ultrafast photonics,” Adv. Funct. Mater. 20(5), 782–791 (2010).
[Crossref]

Lin, B.

H. Zhang, D. Y. Tang, L. M. Zhao, Q. Bao, K. P. Loh, B. Lin, and S. C. Tjin, “Compact graphene mode-locked wavelength-tunable erbium-doped fiber lasers: from all anomalous dispersion to all normal dispersion,” Laser Phys. Lett. 7(8), 591–596 (2010).
[Crossref]

Lin, G.-R.

Y. H. Lin and G.-R. Lin, “Kelly sideband variation and self four-wave-mixing in femtosecond fiber soliton laser mode-locked by multiple exfoliated graphite nano-particles,” Laser Phys. Lett. 10(4), 045109 (2013).
[Crossref]

Y. H. Lin, Y. C. Chi, and G.-R. Lin, “Nanoscale charcoal powder induced saturable absorption and mode-locking of a low-gain erbium-doped fiber-ring laser,” Laser Phys. Lett. 10(5), 055105 (2013).
[Crossref]

K. N. Cheng, Y. H. Lin, and G.-R. Lin, “Single- and double-walled CNT based saturable absorbers for passively mode-locking erbium-doped fiber laser,” Laser Phys. 23(4), 045105 (2013).
[Crossref]

K. N. Cheng, Y. H. Lin, S. Yamashita, and G.-R. Lin, “Harmonic order dependent pulsewidth shortening of a passively mode-locked fiber laser with carbon nanotube saturable absorber,” IEEE Photon. J 4(5), 1542–1552 (2012).
[Crossref]

Y. H. Lin and G.-R. Lin, “Free-standing nano-scale graphite saturable absorber for passively mode-locked erbium doped fiber ring laser,” Laser Phys. Lett. 9(5), 398–404 (2012).
[Crossref]

P. L. Huang, S. C. Lin, C. Y. Yeh, H. H. Kuo, S. H. Huang, G.-R. Lin, L. J. Li, C. Y. Su, and W. H. Cheng, “Stable mode-locked fiber laser based on CVD fabricated graphene saturable absorber,” Opt. Express 20(3), 2460–2465 (2012).
[Crossref] [PubMed]

G.-R. Lin and Y.-C. Lin, “Directly exfoliated and imprinted graphite nano-particle saturable absorber for passive mode-locking erbium-doped fiber laser,” Laser Phys. Lett. 8(12), 880–886 (2011).
[Crossref]

J.-C. Chiu, C.-M. Chang, B.-Z. Hsieh, S.-C. Lin, C.-Y. Yeh, G.-R. Lin, C.-K. Lee, J.-J. Lin, and W.-H. Cheng, “Pulse shortening mode-locked fiber laser by thickness and concentration product of carbon nanotube based saturable absorber,” Opt. Express 19(5), 4036–4041 (2011).
[Crossref] [PubMed]

G.-R. Lin, J. J. Kang, and C. K. Lee, “High-order rational harmonic mode-locking and pulse-amplitude equalization of SOAFL via reshaped gain-switching FPLD pulse injection,” Opt. Express 18(9), 9570–9579 (2010).
[Crossref] [PubMed]

G.-R. Lin, C. L. Pan, and Y. T. Lin, “Self-steepening of prechirped amplified and compressed 29-fs fiber laser pulse in large-mode-area erbium-doped fiber amplifier,” J. Lightwave Technol. 25(11), 3597–3601 (2007).
[Crossref]

G.-R. Lin, J.-Y. Chang, Y.-S. Liao, and H.-H. Lu, “L-band erbium-doped fiber laser with coupling-ratio controlled wavelength tunability,” Opt. Express 14(21), 9743–9749 (2006).
[Crossref] [PubMed]

G.-R. Lin and I.-H. Chiu, “Femtosecond wavelength tunable semiconductor optical amplifier fiber laser mode-locked by backward dark-optical-comb injection at 10 GHz,” Opt. Express 13(22), 8772–8780 (2005).
[Crossref] [PubMed]

G.-R. Lin, I.-H. Chiu, and M. C. Wu, “1.2-ps mode-locked semiconductor optical amplifier fiber laser pulses generated by 60-ps backward dark-optical comb injection and soliton compression,” Opt. Express 13(3), 1008–1014 (2005).
[Crossref] [PubMed]

Lin, J.-J.

Lin, S. C.

Lin, S.-C.

Lin, Y. H.

Y. H. Lin and G.-R. Lin, “Kelly sideband variation and self four-wave-mixing in femtosecond fiber soliton laser mode-locked by multiple exfoliated graphite nano-particles,” Laser Phys. Lett. 10(4), 045109 (2013).
[Crossref]

Y. H. Lin, Y. C. Chi, and G.-R. Lin, “Nanoscale charcoal powder induced saturable absorption and mode-locking of a low-gain erbium-doped fiber-ring laser,” Laser Phys. Lett. 10(5), 055105 (2013).
[Crossref]

K. N. Cheng, Y. H. Lin, and G.-R. Lin, “Single- and double-walled CNT based saturable absorbers for passively mode-locking erbium-doped fiber laser,” Laser Phys. 23(4), 045105 (2013).
[Crossref]

Y. H. Lin and G.-R. Lin, “Free-standing nano-scale graphite saturable absorber for passively mode-locked erbium doped fiber ring laser,” Laser Phys. Lett. 9(5), 398–404 (2012).
[Crossref]

K. N. Cheng, Y. H. Lin, S. Yamashita, and G.-R. Lin, “Harmonic order dependent pulsewidth shortening of a passively mode-locked fiber laser with carbon nanotube saturable absorber,” IEEE Photon. J 4(5), 1542–1552 (2012).
[Crossref]

Lin, Y. T.

Lin, Y.-C.

G.-R. Lin and Y.-C. Lin, “Directly exfoliated and imprinted graphite nano-particle saturable absorber for passive mode-locking erbium-doped fiber laser,” Laser Phys. Lett. 8(12), 880–886 (2011).
[Crossref]

Liu, Z. B.

Loh, K. P.

Q. L. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. Shen, Q. H. Xu, D. Y. Tang, and K. P. Loh, “Monolayer graphene as a saturable absorber in a mode-locked laser,” Nano Res. 4(3), 297–307 (2011).
[Crossref]

Q. L. Bao, H. Zhang, J. X. Yang, S. Wang, D. Y. Tang, R. Jose, S. Ramakrishna, C. T. Lim, and K. P. Loh, “Graphene-polymer nanofiber membrane for ultrafast photonics,” Adv. Funct. Mater. 20(5), 782–791 (2010).
[Crossref]

H. Zhang, D. Y. Tang, R. J. Knize, L. Zhao, Q. L. Bao, and K. P. Loh, “Graphene mode locked, wavelength-tunable, dissipative soliton fber laser,” Appl. Phys. Lett. 96(11), 111112 (2010).
[Crossref]

H. Zhang, D. Y. Tang, L. M. Zhao, Q. Bao, K. P. Loh, B. Lin, and S. C. Tjin, “Compact graphene mode-locked wavelength-tunable erbium-doped fiber lasers: from all anomalous dispersion to all normal dispersion,” Laser Phys. Lett. 7(8), 591–596 (2010).
[Crossref]

H. Zhang, D. Y. Tang, L. M. Zhao, Q. L. Bao, and K. P. Loh, “Large energy mode locking of an erbium-doped fiber laser with atomic layer graphene,” Opt. Express 17(20), 17630–17635 (2009).
[Crossref] [PubMed]

J. Lu, J.-X. Yang, J. Wang, A. Lim, S. Wang, and K. P. Loh, “One-pot synthesis of fluorescent carbon nanoribbons, nanoparticles, and graphene by the exfoliation of graphite in ionic liquids,” ACS Nano 3(8), 2367–2375 (2009).
[Crossref] [PubMed]

H. Zhang, Q. L. Bao, D. Y. Tang, L. Zhao, and K. P. Loh, “Large energy soliton erbium-doped fber laser with a graphene-polymer composite mode locker,” Appl. Phys. Lett. 95(14), 141103 (2009).
[Crossref]

Q. L. Bao, H. Zhang, 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]

Lu, A. Y.

C. Y. Su, A. Y. Lu, Y. Xu, F. R. Chen, A. N. Khlobystov, and L. J. Li, “High-quality thin graphene films from fast electrochemical exfoliation,” ACS Nano 5(3), 2332–2339 (2011).
[Crossref] [PubMed]

Lu, H.-H.

Lu, J.

J. Lu, J.-X. Yang, J. Wang, A. Lim, S. Wang, and K. P. Loh, “One-pot synthesis of fluorescent carbon nanoribbons, nanoparticles, and graphene by the exfoliation of graphite in ionic liquids,” ACS Nano 3(8), 2367–2375 (2009).
[Crossref] [PubMed]

Lu, Y. H.

Z. H. Ni, T. Yu, Y. H. Lu, Y. Y. Wang, Y. P. Feng, and Z. X. Shen, “Uniaxial strain on graphene: Raman spectroscopy study and band-gap opening,” ACS Nano 2(11), 2301–2305 (2008).
[Crossref] [PubMed]

Luo, Z.

J. Z. Wang, Z. Luo, M. Zhou, C. C. Ye, H. Fu, Z. P. Cai, H. H. Cheng, H. Y. Xu, and W. Qi, “Evanescent-light deposition of graphene onto tapered fibers for passive Q-switch and mode-locker,” IEEE Photon. J. 4(5), 1295–1305 (2012).
[Crossref]

Luo, Z. Q.

Z. Q. Luo, J. Z. Wang, M. Zhou, H. Y. Xu, Z. P. Cai, and C. C. Ye, “Multiwavelength mode-locked erbium-doped fiber laser based on the interaction of graphene and fiber-taper evanescent field,” Laser Phys. Lett. 9(3), 229–233 (2012).
[Crossref]

Martinez, A.

A. Martinez, K. Fuse, and S. Yamashita, “Mechanical exfoliation of graphene for the passive mode-locking of fiber lasers,” Appl. Phys. Lett. 99(12), 121107 (2011).
[Crossref]

A. Martinez, K. Fuse, and S. Yamashita, “Mechanical exfoliation of graphene for the passive mode-locking of fiber lasers,” Appl. Phys. Lett. 99(12), 121107 (2011).
[Crossref]

A. Martinez, K. Fuse, B. Xu, and S. Yamashita, “Optical deposition of graphene and carbon nanotubes in a fiber ferrule for passive mode-locked lasing,” Opt. Express 18(22), 23054–23061 (2010).
[Crossref] [PubMed]

Massar, S.

Maultzsch, J.

O. Frank, M. Mohr, J. Maultzsch, C. Thomsen, I. Riaz, R. Jalil, K. S. Novoselov, G. Tsoukleri, J. Parthenios, K. Papagelis, L. Kavan, and C. Galiotis, “Raman 2D-band splitting in graphene: theory and experiment,” ACS Nano 5(3), 2231–2239 (2011).
[Crossref] [PubMed]

Mauri, F.

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene Layers,” Phys. Rev. Lett. 97(18), 187401 (2006).
[Crossref] [PubMed]

Meng, Y. C.

J. Du, S. M. Zhang, H. F. Li, Y. C. Meng, X. L. Li, and Y. P. Hao, “L-Band passively harmonic mode-locked fiber laser based on a graphene saturable absorber,” Laser Phys. Lett. 9, 896–900 (2012).

Y. C. Meng, S. Zhang, X. Li, H. Li, J. Du, and Y. P. Hao, “Multiple-soliton dynamic patterns in a graphene mode-locked fiber laser,” Opt. Express 20(6), 6685–6692 (2012).
[Crossref] [PubMed]

Meyer, J. C.

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene Layers,” Phys. Rev. Lett. 97(18), 187401 (2006).
[Crossref] [PubMed]

Mohr, M.

O. Frank, M. Mohr, J. Maultzsch, C. Thomsen, I. Riaz, R. Jalil, K. S. Novoselov, G. Tsoukleri, J. Parthenios, K. Papagelis, L. Kavan, and C. Galiotis, “Raman 2D-band splitting in graphene: theory and experiment,” ACS Nano 5(3), 2231–2239 (2011).
[Crossref] [PubMed]

Ni, Z.

Q. L. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. Shen, Q. H. Xu, D. Y. Tang, and K. P. Loh, “Monolayer graphene as a saturable absorber in a mode-locked laser,” Nano Res. 4(3), 297–307 (2011).
[Crossref]

Q. L. Bao, H. Zhang, 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]

Ni, Z. H.

Z. H. Ni, T. Yu, Y. H. Lu, Y. Y. Wang, Y. P. Feng, and Z. X. Shen, “Uniaxial strain on graphene: Raman spectroscopy study and band-gap opening,” ACS Nano 2(11), 2301–2305 (2008).
[Crossref] [PubMed]

Novoselov, K. S.

O. Frank, M. Mohr, J. Maultzsch, C. Thomsen, I. Riaz, R. Jalil, K. S. Novoselov, G. Tsoukleri, J. Parthenios, K. Papagelis, L. Kavan, and C. Galiotis, “Raman 2D-band splitting in graphene: theory and experiment,” ACS Nano 5(3), 2231–2239 (2011).
[Crossref] [PubMed]

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene Layers,” Phys. Rev. Lett. 97(18), 187401 (2006).
[Crossref] [PubMed]

Oh, K.

Pan, C. L.

Papagelis, K.

O. Frank, M. Mohr, J. Maultzsch, C. Thomsen, I. Riaz, R. Jalil, K. S. Novoselov, G. Tsoukleri, J. Parthenios, K. Papagelis, L. Kavan, and C. Galiotis, “Raman 2D-band splitting in graphene: theory and experiment,” ACS Nano 5(3), 2231–2239 (2011).
[Crossref] [PubMed]

Parthenios, J.

O. Frank, M. Mohr, J. Maultzsch, C. Thomsen, I. Riaz, R. Jalil, K. S. Novoselov, G. Tsoukleri, J. Parthenios, K. Papagelis, L. Kavan, and C. Galiotis, “Raman 2D-band splitting in graphene: theory and experiment,” ACS Nano 5(3), 2231–2239 (2011).
[Crossref] [PubMed]

Ping, L. K.

Piscanec, S.

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene Layers,” Phys. Rev. Lett. 97(18), 187401 (2006).
[Crossref] [PubMed]

Polavarapu, L.

Q. L. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. Shen, Q. H. Xu, D. Y. Tang, and K. P. Loh, “Monolayer graphene as a saturable absorber in a mode-locked laser,” Nano Res. 4(3), 297–307 (2011).
[Crossref]

Popa, D.

D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. C. Ferrari, “Sub 200 fs pulse generation from a graphene mode-locked fiber laser,” Appl. Phys. Lett. 97(20), 203106 (2010).
[Crossref]

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

Privitera, G.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

Qi, W.

J. Z. Wang, Z. Luo, M. Zhou, C. C. Ye, H. Fu, Z. P. Cai, H. H. Cheng, H. Y. Xu, and W. Qi, “Evanescent-light deposition of graphene onto tapered fibers for passive Q-switch and mode-locker,” IEEE Photon. J. 4(5), 1295–1305 (2012).
[Crossref]

Ramakrishna, S.

Q. L. Bao, H. Zhang, J. X. Yang, S. Wang, D. Y. Tang, R. Jose, S. Ramakrishna, C. T. Lim, and K. P. Loh, “Graphene-polymer nanofiber membrane for ultrafast photonics,” Adv. Funct. Mater. 20(5), 782–791 (2010).
[Crossref]

Riaz, I.

O. Frank, M. Mohr, J. Maultzsch, C. Thomsen, I. Riaz, R. Jalil, K. S. Novoselov, G. Tsoukleri, J. Parthenios, K. Papagelis, L. Kavan, and C. Galiotis, “Raman 2D-band splitting in graphene: theory and experiment,” ACS Nano 5(3), 2231–2239 (2011).
[Crossref] [PubMed]

Rotermund, F.

Roth, S.

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene Layers,” Phys. Rev. Lett. 97(18), 187401 (2006).
[Crossref] [PubMed]

Rozhin, A. G.

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, 3874–3899 (2009).

Ryhänen, T.

D. Wei, L. Grande, V. Chundi, R. White, C. Bower, P. Andrew, and T. Ryhänen, “Graphene from electrochemical exfoliation and its direct applications in enhanced energy storage devices,” Chem. Commun. (Camb.) 48(9), 1239–1241 (2012).
[Crossref] [PubMed]

Scardaci, V.

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene Layers,” Phys. Rev. Lett. 97(18), 187401 (2006).
[Crossref] [PubMed]

Shen, Z.

Q. L. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. Shen, Q. H. Xu, D. Y. Tang, and K. P. Loh, “Monolayer graphene as a saturable absorber in a mode-locked laser,” Nano Res. 4(3), 297–307 (2011).
[Crossref]

Shen, Z. X.

Q. L. Bao, H. Zhang, 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]

Z. H. Ni, T. Yu, Y. H. Lu, Y. Y. Wang, Y. P. Feng, and Z. X. Shen, “Uniaxial strain on graphene: Raman spectroscopy study and band-gap opening,” ACS Nano 2(11), 2301–2305 (2008).
[Crossref] [PubMed]

Sobon, G.

J. Sotor, G. Sobon, and K. M. Abramski, “Scalar soliton generation in all-polarization-maintaining, graphene mode-locked fiber laser,” Opt. Lett. 37(11), 2166–2168 (2012).
[Crossref] [PubMed]

G. Sobon, J. Sotor, and K. M. Abramski, “All-polarization maintaining femtosecond Er-doped fiber laser mode-locked by graphene saturable absorber,” Laser Phys. Lett. 9(8), 581–586 (2012).
[Crossref]

G. Sobon, J. Sotor, and K. M. Abramski, “Passive harmonic mode-locking in Er-doped fiber laser based on graphene saturable absorber with repetition rates scalable to 2.22 GHz,” Appl. Phys. Lett. 100(16), 161109 (2012).
[Crossref]

G. Sobon, J. Sotor, and K. M. Abramski, “All-polarization maintaining femtosecond Er-doped fiber laser mode-locked by graphene saturable absorber,” Laser Phys. Lett. 9(8), 581–586 (2012).
[Crossref]

Song, Y. W.

S. Y. Choi, D. K. Cho, Y. W. Song, K. Oh, K. Kim, F. Rotermund, and D. I. Yeom, “Graphene-filled hollow optical fiber saturable absorber for efficient soliton fiber laser mode-locking,” Opt. Express 20(5), 5652–5657 (2012).
[Crossref] [PubMed]

H. Kim, J. H. Cho, S. Y. Jang, and Y. W. Song, “Deformation immunized optical deposition of graphene for ultrafast pulsed lasers,” Appl. Phys. Lett. 98(2), 021104 (2011).
[Crossref]

Y. M. Chang, H. Kim, J. H. Lee, and Y. W. Song, “Multilayered graphene efficiently formed by mechanical exfoliation for nonlinear saturable absorbers in fiber mode-locked lasers,” Appl. Phys. Lett. 97(21), 211102 (2010).
[Crossref]

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]

Song, Y.-W.

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]

Sotor, J.

G. Sobon, J. Sotor, and K. M. Abramski, “Passive harmonic mode-locking in Er-doped fiber laser based on graphene saturable absorber with repetition rates scalable to 2.22 GHz,” Appl. Phys. Lett. 100(16), 161109 (2012).
[Crossref]

G. Sobon, J. Sotor, and K. M. Abramski, “All-polarization maintaining femtosecond Er-doped fiber laser mode-locked by graphene saturable absorber,” Laser Phys. Lett. 9(8), 581–586 (2012).
[Crossref]

G. Sobon, J. Sotor, and K. M. Abramski, “All-polarization maintaining femtosecond Er-doped fiber laser mode-locked by graphene saturable absorber,” Laser Phys. Lett. 9(8), 581–586 (2012).
[Crossref]

J. Sotor, G. Sobon, and K. M. Abramski, “Scalar soliton generation in all-polarization-maintaining, graphene mode-locked fiber laser,” Opt. Lett. 37(11), 2166–2168 (2012).
[Crossref] [PubMed]

Su, C. Y.

P. L. Huang, S. C. Lin, C. Y. Yeh, H. H. Kuo, S. H. Huang, G.-R. Lin, L. J. Li, C. Y. Su, and W. H. Cheng, “Stable mode-locked fiber laser based on CVD fabricated graphene saturable absorber,” Opt. Express 20(3), 2460–2465 (2012).
[Crossref] [PubMed]

C. Y. Su, A. Y. Lu, Y. Xu, F. R. Chen, A. N. Khlobystov, and L. J. Li, “High-quality thin graphene films from fast electrochemical exfoliation,” ACS Nano 5(3), 2332–2339 (2011).
[Crossref] [PubMed]

Sun, Z.

D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. C. Ferrari, “Sub 200 fs pulse generation from a graphene mode-locked fiber laser,” Appl. Phys. Lett. 97(20), 203106 (2010).
[Crossref]

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

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, 3874–3899 (2009).

Tan, P. H.

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, 3874–3899 (2009).

Tang, D. Y.

Q. L. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. Shen, Q. H. Xu, D. Y. Tang, and K. P. Loh, “Monolayer graphene as a saturable absorber in a mode-locked laser,” Nano Res. 4(3), 297–307 (2011).
[Crossref]

H. Zhang, D. Y. Tang, L. M. Zhao, Q. Bao, K. P. Loh, B. Lin, and S. C. Tjin, “Compact graphene mode-locked wavelength-tunable erbium-doped fiber lasers: from all anomalous dispersion to all normal dispersion,” Laser Phys. Lett. 7(8), 591–596 (2010).
[Crossref]

H. Zhang, D. Y. Tang, R. J. Knize, L. Zhao, Q. L. Bao, and K. P. Loh, “Graphene mode locked, wavelength-tunable, dissipative soliton fber laser,” Appl. Phys. Lett. 96(11), 111112 (2010).
[Crossref]

Q. L. Bao, H. Zhang, J. X. Yang, S. Wang, D. Y. Tang, R. Jose, S. Ramakrishna, C. T. Lim, and K. P. Loh, “Graphene-polymer nanofiber membrane for ultrafast photonics,” Adv. Funct. Mater. 20(5), 782–791 (2010).
[Crossref]

H. Zhang, D. Y. Tang, L. M. Zhao, Q. L. Bao, and K. P. Loh, “Large energy mode locking of an erbium-doped fiber laser with atomic layer graphene,” Opt. Express 17(20), 17630–17635 (2009).
[Crossref] [PubMed]

H. Zhang, Q. L. Bao, D. Y. Tang, L. Zhao, and K. P. Loh, “Large energy soliton erbium-doped fber laser with a graphene-polymer composite mode locker,” Appl. Phys. Lett. 95(14), 141103 (2009).
[Crossref]

Q. L. Bao, H. Zhang, 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]

Thomsen, C.

O. Frank, M. Mohr, J. Maultzsch, C. Thomsen, I. Riaz, R. Jalil, K. S. Novoselov, G. Tsoukleri, J. Parthenios, K. Papagelis, L. Kavan, and C. Galiotis, “Raman 2D-band splitting in graphene: theory and experiment,” ACS Nano 5(3), 2231–2239 (2011).
[Crossref] [PubMed]

Tjin, S. C.

H. Zhang, D. Y. Tang, L. M. Zhao, Q. Bao, K. P. Loh, B. Lin, and S. C. Tjin, “Compact graphene mode-locked wavelength-tunable erbium-doped fiber lasers: from all anomalous dispersion to all normal dispersion,” Laser Phys. Lett. 7(8), 591–596 (2010).
[Crossref]

Torrisi, F.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. C. Ferrari, “Sub 200 fs pulse generation from a graphene mode-locked fiber laser,” Appl. Phys. Lett. 97(20), 203106 (2010).
[Crossref]

Tsoukleri, G.

O. Frank, M. Mohr, J. Maultzsch, C. Thomsen, I. Riaz, R. Jalil, K. S. Novoselov, G. Tsoukleri, J. Parthenios, K. Papagelis, L. Kavan, and C. Galiotis, “Raman 2D-band splitting in graphene: theory and experiment,” ACS Nano 5(3), 2231–2239 (2011).
[Crossref] [PubMed]

Tung, V. C.

M. J. Allen, V. C. Tung, and R. B. Kaner, “Honeycomb carbon: a review of graphene,” Chem. Rev. 110(1), 132–145 (2010).
[Crossref] [PubMed]

Virally, S.

Wang, D. N.

Wang, F.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. C. Ferrari, “Sub 200 fs pulse generation from a graphene mode-locked fiber laser,” Appl. Phys. Lett. 97(20), 203106 (2010).
[Crossref]

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, 3874–3899 (2009).

Wang, J.

J. Lu, J.-X. Yang, J. Wang, A. Lim, S. Wang, and K. P. Loh, “One-pot synthesis of fluorescent carbon nanoribbons, nanoparticles, and graphene by the exfoliation of graphite in ionic liquids,” ACS Nano 3(8), 2367–2375 (2009).
[Crossref] [PubMed]

Wang, J. Z.

Z. Q. Luo, J. Z. Wang, M. Zhou, H. Y. Xu, Z. P. Cai, and C. C. Ye, “Multiwavelength mode-locked erbium-doped fiber laser based on the interaction of graphene and fiber-taper evanescent field,” Laser Phys. Lett. 9(3), 229–233 (2012).
[Crossref]

J. Z. Wang, Z. Luo, M. Zhou, C. C. Ye, H. Fu, Z. P. Cai, H. H. Cheng, H. Y. Xu, and W. Qi, “Evanescent-light deposition of graphene onto tapered fibers for passive Q-switch and mode-locker,” IEEE Photon. J. 4(5), 1295–1305 (2012).
[Crossref]

Wang, S.

Q. L. Bao, H. Zhang, J. X. Yang, S. Wang, D. Y. Tang, R. Jose, S. Ramakrishna, C. T. Lim, and K. P. Loh, “Graphene-polymer nanofiber membrane for ultrafast photonics,” Adv. Funct. Mater. 20(5), 782–791 (2010).
[Crossref]

J. Lu, J.-X. Yang, J. Wang, A. Lim, S. Wang, and K. P. Loh, “One-pot synthesis of fluorescent carbon nanoribbons, nanoparticles, and graphene by the exfoliation of graphite in ionic liquids,” ACS Nano 3(8), 2367–2375 (2009).
[Crossref] [PubMed]

Wang, Y.

Q. L. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. Shen, Q. H. Xu, D. Y. Tang, and K. P. Loh, “Monolayer graphene as a saturable absorber in a mode-locked laser,” Nano Res. 4(3), 297–307 (2011).
[Crossref]

Wang, Y. Y.

Z. H. Ni, T. Yu, Y. H. Lu, Y. Y. Wang, Y. P. Feng, and Z. X. Shen, “Uniaxial strain on graphene: Raman spectroscopy study and band-gap opening,” ACS Nano 2(11), 2301–2305 (2008).
[Crossref] [PubMed]

Wei, D.

D. Wei, L. Grande, V. Chundi, R. White, C. Bower, P. Andrew, and T. Ryhänen, “Graphene from electrochemical exfoliation and its direct applications in enhanced energy storage devices,” Chem. Commun. (Camb.) 48(9), 1239–1241 (2012).
[Crossref] [PubMed]

White, R.

D. Wei, L. Grande, V. Chundi, R. White, C. Bower, P. Andrew, and T. Ryhänen, “Graphene from electrochemical exfoliation and its direct applications in enhanced energy storage devices,” Chem. Commun. (Camb.) 48(9), 1239–1241 (2012).
[Crossref] [PubMed]

Wu, M. C.

Xu, B.

Xu, H. Y.

J. Z. Wang, Z. Luo, M. Zhou, C. C. Ye, H. Fu, Z. P. Cai, H. H. Cheng, H. Y. Xu, and W. Qi, “Evanescent-light deposition of graphene onto tapered fibers for passive Q-switch and mode-locker,” IEEE Photon. J. 4(5), 1295–1305 (2012).
[Crossref]

Z. Q. Luo, J. Z. Wang, M. Zhou, H. Y. Xu, Z. P. Cai, and C. C. Ye, “Multiwavelength mode-locked erbium-doped fiber laser based on the interaction of graphene and fiber-taper evanescent field,” Laser Phys. Lett. 9(3), 229–233 (2012).
[Crossref]

Xu, Q. H.

Q. L. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. Shen, Q. H. Xu, D. Y. Tang, and K. P. Loh, “Monolayer graphene as a saturable absorber in a mode-locked laser,” Nano Res. 4(3), 297–307 (2011).
[Crossref]

Xu, Y.

C. Y. Su, A. Y. Lu, Y. Xu, F. R. Chen, A. N. Khlobystov, and L. J. Li, “High-quality thin graphene films from fast electrochemical exfoliation,” ACS Nano 5(3), 2332–2339 (2011).
[Crossref] [PubMed]

Yamashita, S.

K. N. Cheng, Y. H. Lin, S. Yamashita, and G.-R. Lin, “Harmonic order dependent pulsewidth shortening of a passively mode-locked fiber laser with carbon nanotube saturable absorber,” IEEE Photon. J 4(5), 1542–1552 (2012).
[Crossref]

A. Martinez, K. Fuse, and S. Yamashita, “Mechanical exfoliation of graphene for the passive mode-locking of fiber lasers,” Appl. Phys. Lett. 99(12), 121107 (2011).
[Crossref]

A. Martinez, K. Fuse, and S. Yamashita, “Mechanical exfoliation of graphene for the passive mode-locking of fiber lasers,” Appl. Phys. Lett. 99(12), 121107 (2011).
[Crossref]

A. Martinez, K. Fuse, B. Xu, and S. Yamashita, “Optical deposition of graphene and carbon nanotubes in a fiber ferrule for passive mode-locked lasing,” Opt. Express 18(22), 23054–23061 (2010).
[Crossref] [PubMed]

Yan, Y.

Q. L. Bao, H. Zhang, 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]

Yang, J. X.

Q. L. Bao, H. Zhang, J. X. Yang, S. Wang, D. Y. Tang, R. Jose, S. Ramakrishna, C. T. Lim, and K. P. Loh, “Graphene-polymer nanofiber membrane for ultrafast photonics,” Adv. Funct. Mater. 20(5), 782–791 (2010).
[Crossref]

Yang, J.-X.

J. Lu, J.-X. Yang, J. Wang, A. Lim, S. Wang, and K. P. Loh, “One-pot synthesis of fluorescent carbon nanoribbons, nanoparticles, and graphene by the exfoliation of graphite in ionic liquids,” ACS Nano 3(8), 2367–2375 (2009).
[Crossref] [PubMed]

Ye, C. C.

J. Z. Wang, Z. Luo, M. Zhou, C. C. Ye, H. Fu, Z. P. Cai, H. H. Cheng, H. Y. Xu, and W. Qi, “Evanescent-light deposition of graphene onto tapered fibers for passive Q-switch and mode-locker,” IEEE Photon. J. 4(5), 1295–1305 (2012).
[Crossref]

Z. Q. Luo, J. Z. Wang, M. Zhou, H. Y. Xu, Z. P. Cai, and C. C. Ye, “Multiwavelength mode-locked erbium-doped fiber laser based on the interaction of graphene and fiber-taper evanescent field,” Laser Phys. Lett. 9(3), 229–233 (2012).
[Crossref]

Yeh, C. Y.

Yeh, C.-Y.

Yeom, D. I.

Yu, T.

Z. H. Ni, T. Yu, Y. H. Lu, Y. Y. Wang, Y. P. Feng, and Z. X. Shen, “Uniaxial strain on graphene: Raman spectroscopy study and band-gap opening,” ACS Nano 2(11), 2301–2305 (2008).
[Crossref] [PubMed]

Zhang, H.

H. Zhang, S. Virally, Q. L. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37(11), 1856–1858 (2012).
[Crossref] [PubMed]

Q. L. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. Shen, Q. H. Xu, D. Y. Tang, and K. P. Loh, “Monolayer graphene as a saturable absorber in a mode-locked laser,” Nano Res. 4(3), 297–307 (2011).
[Crossref]

H. Zhang, D. Y. Tang, R. J. Knize, L. Zhao, Q. L. Bao, and K. P. Loh, “Graphene mode locked, wavelength-tunable, dissipative soliton fber laser,” Appl. Phys. Lett. 96(11), 111112 (2010).
[Crossref]

Q. L. Bao, H. Zhang, J. X. Yang, S. Wang, D. Y. Tang, R. Jose, S. Ramakrishna, C. T. Lim, and K. P. Loh, “Graphene-polymer nanofiber membrane for ultrafast photonics,” Adv. Funct. Mater. 20(5), 782–791 (2010).
[Crossref]

H. Zhang, D. Y. Tang, L. M. Zhao, Q. Bao, K. P. Loh, B. Lin, and S. C. Tjin, “Compact graphene mode-locked wavelength-tunable erbium-doped fiber lasers: from all anomalous dispersion to all normal dispersion,” Laser Phys. Lett. 7(8), 591–596 (2010).
[Crossref]

H. Zhang, D. Y. Tang, L. M. Zhao, Q. L. Bao, and K. P. Loh, “Large energy mode locking of an erbium-doped fiber laser with atomic layer graphene,” Opt. Express 17(20), 17630–17635 (2009).
[Crossref] [PubMed]

Q. L. Bao, H. Zhang, 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]

H. Zhang, Q. L. Bao, D. Y. Tang, L. Zhao, and K. P. Loh, “Large energy soliton erbium-doped fber laser with a graphene-polymer composite mode locker,” Appl. Phys. Lett. 95(14), 141103 (2009).
[Crossref]

Zhang, S.

Zhang, S. M.

J. Du, S. M. Zhang, H. F. Li, Y. C. Meng, X. L. Li, and Y. P. Hao, “L-Band passively harmonic mode-locked fiber laser based on a graphene saturable absorber,” Laser Phys. Lett. 9, 896–900 (2012).

Zhao, L.

H. Zhang, D. Y. Tang, R. J. Knize, L. Zhao, Q. L. Bao, and K. P. Loh, “Graphene mode locked, wavelength-tunable, dissipative soliton fber laser,” Appl. Phys. Lett. 96(11), 111112 (2010).
[Crossref]

H. Zhang, Q. L. Bao, D. Y. Tang, L. Zhao, and K. P. Loh, “Large energy soliton erbium-doped fber laser with a graphene-polymer composite mode locker,” Appl. Phys. Lett. 95(14), 141103 (2009).
[Crossref]

Zhao, L. M.

H. Zhang, D. Y. Tang, L. M. Zhao, Q. Bao, K. P. Loh, B. Lin, and S. C. Tjin, “Compact graphene mode-locked wavelength-tunable erbium-doped fiber lasers: from all anomalous dispersion to all normal dispersion,” Laser Phys. Lett. 7(8), 591–596 (2010).
[Crossref]

H. Zhang, D. Y. Tang, L. M. Zhao, Q. L. Bao, and K. P. Loh, “Large energy mode locking of an erbium-doped fiber laser with atomic layer graphene,” Opt. Express 17(20), 17630–17635 (2009).
[Crossref] [PubMed]

Zhou, M.

Z. Q. Luo, J. Z. Wang, M. Zhou, H. Y. Xu, Z. P. Cai, and C. C. Ye, “Multiwavelength mode-locked erbium-doped fiber laser based on the interaction of graphene and fiber-taper evanescent field,” Laser Phys. Lett. 9(3), 229–233 (2012).
[Crossref]

J. Z. Wang, Z. Luo, M. Zhou, C. C. Ye, H. Fu, Z. P. Cai, H. H. Cheng, H. Y. Xu, and W. Qi, “Evanescent-light deposition of graphene onto tapered fibers for passive Q-switch and mode-locker,” IEEE Photon. J. 4(5), 1295–1305 (2012).
[Crossref]

ACS Nano (5)

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

C. Y. Su, A. Y. Lu, Y. Xu, F. R. Chen, A. N. Khlobystov, and L. J. Li, “High-quality thin graphene films from fast electrochemical exfoliation,” ACS Nano 5(3), 2332–2339 (2011).
[Crossref] [PubMed]

J. Lu, J.-X. Yang, J. Wang, A. Lim, S. Wang, and K. P. Loh, “One-pot synthesis of fluorescent carbon nanoribbons, nanoparticles, and graphene by the exfoliation of graphite in ionic liquids,” ACS Nano 3(8), 2367–2375 (2009).
[Crossref] [PubMed]

Z. H. Ni, T. Yu, Y. H. Lu, Y. Y. Wang, Y. P. Feng, and Z. X. Shen, “Uniaxial strain on graphene: Raman spectroscopy study and band-gap opening,” ACS Nano 2(11), 2301–2305 (2008).
[Crossref] [PubMed]

O. Frank, M. Mohr, J. Maultzsch, C. Thomsen, I. Riaz, R. Jalil, K. S. Novoselov, G. Tsoukleri, J. Parthenios, K. Papagelis, L. Kavan, and C. Galiotis, “Raman 2D-band splitting in graphene: theory and experiment,” ACS Nano 5(3), 2231–2239 (2011).
[Crossref] [PubMed]

Adv. Funct. Mater. (2)

Q. L. Bao, H. Zhang, 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]

Q. L. Bao, H. Zhang, J. X. Yang, S. Wang, D. Y. Tang, R. Jose, S. Ramakrishna, C. T. Lim, and K. P. Loh, “Graphene-polymer nanofiber membrane for ultrafast photonics,” Adv. Funct. Mater. 20(5), 782–791 (2010).
[Crossref]

Adv. Mater. (1)

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, 3874–3899 (2009).

Appl. Phys. Lett. (9)

H. Zhang, Q. L. Bao, D. Y. Tang, L. Zhao, and K. P. Loh, “Large energy soliton erbium-doped fber laser with a graphene-polymer composite mode locker,” Appl. Phys. Lett. 95(14), 141103 (2009).
[Crossref]

D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. C. Ferrari, “Sub 200 fs pulse generation from a graphene mode-locked fiber laser,” Appl. Phys. Lett. 97(20), 203106 (2010).
[Crossref]

Y. M. Chang, H. Kim, J. H. Lee, and Y. W. Song, “Multilayered graphene efficiently formed by mechanical exfoliation for nonlinear saturable absorbers in fiber mode-locked lasers,” Appl. Phys. Lett. 97(21), 211102 (2010).
[Crossref]

A. Martinez, K. Fuse, and S. Yamashita, “Mechanical exfoliation of graphene for the passive mode-locking of fiber lasers,” Appl. Phys. Lett. 99(12), 121107 (2011).
[Crossref]

H. Zhang, D. Y. Tang, R. J. Knize, L. Zhao, Q. L. Bao, and K. P. Loh, “Graphene mode locked, wavelength-tunable, dissipative soliton fber laser,” Appl. Phys. Lett. 96(11), 111112 (2010).
[Crossref]

H. Kim, J. H. Cho, S. Y. Jang, and Y. W. Song, “Deformation immunized optical deposition of graphene for ultrafast pulsed lasers,” Appl. Phys. Lett. 98(2), 021104 (2011).
[Crossref]

A. Martinez, K. Fuse, and S. Yamashita, “Mechanical exfoliation of graphene for the passive mode-locking of fiber lasers,” Appl. Phys. Lett. 99(12), 121107 (2011).
[Crossref]

G. Sobon, J. Sotor, and K. M. Abramski, “Passive harmonic mode-locking in Er-doped fiber laser based on graphene saturable absorber with repetition rates scalable to 2.22 GHz,” Appl. Phys. Lett. 100(16), 161109 (2012).
[Crossref]

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]

Chem. Commun. (Camb.) (1)

D. Wei, L. Grande, V. Chundi, R. White, C. Bower, P. Andrew, and T. Ryhänen, “Graphene from electrochemical exfoliation and its direct applications in enhanced energy storage devices,” Chem. Commun. (Camb.) 48(9), 1239–1241 (2012).
[Crossref] [PubMed]

Chem. Rev. (1)

M. J. Allen, V. C. Tung, and R. B. Kaner, “Honeycomb carbon: a review of graphene,” Chem. Rev. 110(1), 132–145 (2010).
[Crossref] [PubMed]

IEEE Photon. J (1)

K. N. Cheng, Y. H. Lin, S. Yamashita, and G.-R. Lin, “Harmonic order dependent pulsewidth shortening of a passively mode-locked fiber laser with carbon nanotube saturable absorber,” IEEE Photon. J 4(5), 1542–1552 (2012).
[Crossref]

IEEE Photon. J. (1)

J. Z. Wang, Z. Luo, M. Zhou, C. C. Ye, H. Fu, Z. P. Cai, H. H. Cheng, H. Y. Xu, and W. Qi, “Evanescent-light deposition of graphene onto tapered fibers for passive Q-switch and mode-locker,” IEEE Photon. J. 4(5), 1295–1305 (2012).
[Crossref]

J. Lightwave Technol. (1)

Laser Phys. (1)

K. N. Cheng, Y. H. Lin, and G.-R. Lin, “Single- and double-walled CNT based saturable absorbers for passively mode-locking erbium-doped fiber laser,” Laser Phys. 23(4), 045105 (2013).
[Crossref]

Laser Phys. Lett. (10)

Y. H. Lin, Y. C. Chi, and G.-R. Lin, “Nanoscale charcoal powder induced saturable absorption and mode-locking of a low-gain erbium-doped fiber-ring laser,” Laser Phys. Lett. 10(5), 055105 (2013).
[Crossref]

J. Du, S. M. Zhang, H. F. Li, Y. C. Meng, X. L. Li, and Y. P. Hao, “L-Band passively harmonic mode-locked fiber laser based on a graphene saturable absorber,” Laser Phys. Lett. 9, 896–900 (2012).

Z. Q. Luo, J. Z. Wang, M. Zhou, H. Y. Xu, Z. P. Cai, and C. C. Ye, “Multiwavelength mode-locked erbium-doped fiber laser based on the interaction of graphene and fiber-taper evanescent field,” Laser Phys. Lett. 9(3), 229–233 (2012).
[Crossref]

G. Sobon, J. Sotor, and K. M. Abramski, “All-polarization maintaining femtosecond Er-doped fiber laser mode-locked by graphene saturable absorber,” Laser Phys. Lett. 9(8), 581–586 (2012).
[Crossref]

H. Zhang, D. Y. Tang, L. M. Zhao, Q. Bao, K. P. Loh, B. Lin, and S. C. Tjin, “Compact graphene mode-locked wavelength-tunable erbium-doped fiber lasers: from all anomalous dispersion to all normal dispersion,” Laser Phys. Lett. 7(8), 591–596 (2010).
[Crossref]

G. Sobon, J. Sotor, and K. M. Abramski, “All-polarization maintaining femtosecond Er-doped fiber laser mode-locked by graphene saturable absorber,” Laser Phys. Lett. 9(8), 581–586 (2012).
[Crossref]

G.-R. Lin and Y.-C. Lin, “Directly exfoliated and imprinted graphite nano-particle saturable absorber for passive mode-locking erbium-doped fiber laser,” Laser Phys. Lett. 8(12), 880–886 (2011).
[Crossref]

Y. H. Lin and G.-R. Lin, “Free-standing nano-scale graphite saturable absorber for passively mode-locked erbium doped fiber ring laser,” Laser Phys. Lett. 9(5), 398–404 (2012).
[Crossref]

Y. H. Lin and G.-R. Lin, “Kelly sideband variation and self four-wave-mixing in femtosecond fiber soliton laser mode-locked by multiple exfoliated graphite nano-particles,” Laser Phys. Lett. 10(4), 045109 (2013).
[Crossref]

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]

Nano Res. (1)

Q. L. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. Shen, Q. H. Xu, D. Y. Tang, and K. P. Loh, “Monolayer graphene as a saturable absorber in a mode-locked laser,” Nano Res. 4(3), 297–307 (2011).
[Crossref]

Opt. Express (10)

P. L. Huang, S. C. Lin, C. Y. Yeh, H. H. Kuo, S. H. Huang, G.-R. Lin, L. J. Li, C. Y. Su, and W. H. Cheng, “Stable mode-locked fiber laser based on CVD fabricated graphene saturable absorber,” Opt. Express 20(3), 2460–2465 (2012).
[Crossref] [PubMed]

G.-R. Lin, J.-Y. Chang, Y.-S. Liao, and H.-H. Lu, “L-band erbium-doped fiber laser with coupling-ratio controlled wavelength tunability,” Opt. Express 14(21), 9743–9749 (2006).
[Crossref] [PubMed]

G.-R. Lin and I.-H. Chiu, “Femtosecond wavelength tunable semiconductor optical amplifier fiber laser mode-locked by backward dark-optical-comb injection at 10 GHz,” Opt. Express 13(22), 8772–8780 (2005).
[Crossref] [PubMed]

H. Zhang, D. Y. Tang, L. M. Zhao, Q. L. Bao, and K. P. Loh, “Large energy mode locking of an erbium-doped fiber laser with atomic layer graphene,” Opt. Express 17(20), 17630–17635 (2009).
[Crossref] [PubMed]

A. Martinez, K. Fuse, B. Xu, and S. Yamashita, “Optical deposition of graphene and carbon nanotubes in a fiber ferrule for passive mode-locked lasing,” Opt. Express 18(22), 23054–23061 (2010).
[Crossref] [PubMed]

J.-C. Chiu, C.-M. Chang, B.-Z. Hsieh, S.-C. Lin, C.-Y. Yeh, G.-R. Lin, C.-K. Lee, J.-J. Lin, and W.-H. Cheng, “Pulse shortening mode-locked fiber laser by thickness and concentration product of carbon nanotube based saturable absorber,” Opt. Express 19(5), 4036–4041 (2011).
[Crossref] [PubMed]

S. Y. Choi, D. K. Cho, Y. W. Song, K. Oh, K. Kim, F. Rotermund, and D. I. Yeom, “Graphene-filled hollow optical fiber saturable absorber for efficient soliton fiber laser mode-locking,” Opt. Express 20(5), 5652–5657 (2012).
[Crossref] [PubMed]

Y. C. Meng, S. Zhang, X. Li, H. Li, J. Du, and Y. P. Hao, “Multiple-soliton dynamic patterns in a graphene mode-locked fiber laser,” Opt. Express 20(6), 6685–6692 (2012).
[Crossref] [PubMed]

G.-R. Lin, I.-H. Chiu, and M. C. Wu, “1.2-ps mode-locked semiconductor optical amplifier fiber laser pulses generated by 60-ps backward dark-optical comb injection and soliton compression,” Opt. Express 13(3), 1008–1014 (2005).
[Crossref] [PubMed]

G.-R. Lin, J. J. Kang, and C. K. Lee, “High-order rational harmonic mode-locking and pulse-amplitude equalization of SOAFL via reshaped gain-switching FPLD pulse injection,” Opt. Express 18(9), 9570–9579 (2010).
[Crossref] [PubMed]

Opt. Lett. (3)

Phys. Rev. Lett. (1)

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene Layers,” Phys. Rev. Lett. 97(18), 187401 (2006).
[Crossref] [PubMed]

Other (2)

E. Hecht, Optics (Addison Wesley, 4th Edition).

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics. (Wiley, New York, 1991).

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Figures (12)

Fig. 1
Fig. 1 The flow chart of electrochemical exfoliation and extraction of graphene nano-particle into the PCF. The inset is the SEM image of graphene nano-particles.
Fig. 2
Fig. 2 The experimental setup of the passively mode-locked EDFL. Inset: the photographs of the PCF (left: top-view, right: side-view).
Fig. 3
Fig. 3 Raman spectra of the HOPG foil and the electrochemically exfoliated graphene nano-particles operated under bias voltages of + 6 and + 3V.
Fig. 4
Fig. 4 The schematic diagrams of the electrochemically exfoliated graphene nano-particles with bias voltages of + 6 and + 3V.
Fig. 5
Fig. 5 Linear transmittance of (a) graphene nano-particles in PCF and (b) graphene nano-particles on the end-face of SMF.
Fig. 6
Fig. 6 Nonlinear transmittance and normalized absorbance of (a) graphene nano-particles in PCF and (b) graphene nano-particles on the end-face of SMF.
Fig. 7
Fig. 7 The schematic diagram of evanescent-wave mode-locked pulse propagation through the PCF doped with graphene nano-particles in hole-cladding region.
Fig. 8
Fig. 8 Schematic diagram of evanescent field modulation with varied extinction coefficient.
Fig. 9
Fig. 9 (a) Pout-Pin curves and (b) the Gain curves of the EDFA under different pumping currents.
Fig. 10
Fig. 10 (a) The autocorrelation traces and (b) optical spectra of the passively mode-locked EDFLs under different pumping current.
Fig. 11
Fig. 11 (a) The simulated autocorrelation traces and (b) optical spectra of the passively mode-locked EDFLs under different pumping current.
Fig. 12
Fig. 12 The CAJ values and the oscilloscope traces of the passively mode-locked EDFLs under different pumping currents.

Equations (6)

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T = exp ( q n o n 1 + P i n / P s a t q l i n ) ,
α non,G = α 0,G 1+ I e , t / I e , s a t I e , t = I e , s a t ( α 0,G α non,G 1 )
I e , t = I 0 e 2 β x ,
β = 2 π n c λ ( sin 2 θ i ( n c / n i ) 2 1 ) 1 / 2 = 2 π λ { n i 2 [ n c 0 + n c I e , s a t ( α 0,G α non,G ( I t ) 1 ) ] 2 } 1 / 2 ,
Γ = 0 d / 2 E c o r e 2 ( x ) d x 0 d / 2 E c o r e 2 ( x ) d x + d / 2 E c l a d d i n g 2 ( x ) d x .
T R T A ( T , t ) = [ G 0 1 + | A | 2 / P G , s a t l + D g 2 t 2 q n o n ( T , t ) 1 + | A | 2 / P s a t i D 2 t 2 + i δ | A | 2 ] A ( T , t ) ,

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