Triturating versatile carbon materials as saturable absorptive nano powders for ultrafast pulsating of erbium-doped fiber lasers

Yung-Hsiang Lin; Chun-Yu Yang; Sheng-Fong Lin; Gong-Ru Lin

doi:10.1364/OME.5.000236

1. Introduction

In addition to the mature compound semiconductor based saturable absorber mirrors (SESAMs), carbon based materials have emerged as the promising fast saturable absorbers for mode-locking various fiber lasers. In 2004, the single-wall carbon nanotube (SWCNT) was the premier candidate to induce the passive mode-locking of the erbium-doped fiber lasers (EDFLs) [1–5]. The advantages of the SWCNT, including large optical nonlinearity, fast carrier relaxation time (~1 ps), and high damage threshold, meet the demand of being a passive mode-locker. However, the energy band gap of SWCNT inversely changes with its diameter, providing that the operable wavelength of saturable absorption strictly depends on the SWCNT's diameter. The tuning range of saturable absorption for the SWCNT can be up to ~200 nm from its peak resonance. Such a diameter dependent saturable absorption feature can be engineered to make the SWCNT suitable for operating at a variety of wavelengths. Later on, the thick graphene with 2 to 11 layer numbers were preliminarily used to mode-lock the EDFL in 2009 [6]. The graphene with a 2D honeycomb lattice structure of carbon atoms is formed by sp² hybridization, which possesses the unique properties and gradually shows the great impacts on several optotelectronic applications [7, 8]. In particular, this zero-bandgap Dirac material with its valance band and conduction band overlapping at K and K' points in the Brillouin zone forms a “Dirac cone”, which leads to a linear dispersion and an approximately wavelength-independent linear optical absorption from visible to the near infrared wavelengths, accompanying with an average visible transmittance of πα = 2.3% (α denotes the fine structure constant) for the atomic-layer graphene. However, the optical absorption changes dramatically in the UV and far infrared regions [9–11]. Under intense optical illumination, the Pauli blocking effect forbidden the photoelectron transition from valence band to conduction band, and makes the saturable absorption of graphene [12, 13]. When considering the graphene as a saturable absorber, which further offers the massless Dirac fermions with faster relaxation time within 200 fs [13] than SESAMs and SWCNT, the ultra-wideband tuning range due to its zero-bandgap energy, and especially the controllable saturable absorption [5] as compared to the SWCNT. Afterwards, versatile graphene based materials including atomic layer graphene [6, 8, 11, 14–17], graphene nano-sheet [18–23], graphene-doped polymer [24–30], graphene aqueous solution [31], and graphene oxide [32–34] have been fabricated by different methods, such as mechanic exfoliation [35, 36], chemical vapor deposition [5, 14–17, 21, 22, 29], dispersion in chemical polymer [24–28] and chemical solution [30], etc. These novel saturable absorbers have been applied to many kinds of passively mode-locked fiber lasers with erbium (Er)- [6, 8, 11, 14–35], ytterbium (Yb)- [36] and thulium (Tm)-doped fibers [37], and with linear [23, 38] or ring cavity architectures [6, 8, 11, 14–37], respectively. In addition, the graphene based saturable absorbers have also been employed to passively mode-lock several kinds of solid-state lasers, including Nd:YAG laser [39], Yb:KGW laser [40], Cr:forsterite laser [41], Tm:YAlO₃ laser and [42], and Cr:ZnSe laser [43].

More recently, the other carbon based materials such as graphite [44–46] and charcoal [47] with their nano-scale forms have also shown their potential to passively mode-lock the EDFLs. Lin et al. confirmed that the graphite nano-particles composed of multilayer graphene also possess the saturable absorption effect [44–46]. These graphite nano-sheets, nano-particles, or nano-flakes can be obtained by different methods including mechanical trituration [34–36, 44–46], sonication [23] or electrochemical exfoliation [48] of bulk graphite foil. These approaches have provided some advantages such as the comparable characteristics with simplified preparation and easier transferring process than graphene. On the other hand, the charcoal nano-particles directly polished from pencils were also observed to exhibit the similar saturable absorption property with graphite nano-particle [47]. The charcoal nano-particle powder consist very few graphene components, which also show the ability to passively mode-lock the EDFL [47]. Being a saturable absorber, the structural defects inside the charcoal nano-particle are found as one detrimental factor to degrade its mode-locking ability. Therefore, the passively mode-locked EDFL performance by using charcoal nano-particle was reported to be worse than that by using pure graphene or graphite nano-particles. Up to now, versatile carbon based materials have shown their potentials to mode-lock the EDFLs. Particularly, these carbon based materials are structurally different and some of them are even amorphous with only few graphene contents. However, the detailed parametric analyses and comparisons between these nano-scale carbon based materials with different structural forms, such as the relationship between their structural and optical properties were seldom investigated. It is thus essential to investigate the mode-locking abilities of these crystalline or amorphous carbon materials with different forms of structure. In addition, it is also important to figure out if there are different and dominated mode-locking mechanisms in the EDFLs started by using the aforementioned carbon based saturable absorbers with different phase structures.

In this work, the passive mode-locking mechanisms and performances of the EDFLs using five kinds of nano-scale carbon based materials as saturable absorbers are compared. These carbon based nano-scale powders includes few-layer graphene nano-sheets, graphite, graphene oxide, carbon black and charcoal nano-particles. The structural characteristics of these carbon incorporated nano-scale powders are investigated by X-ray diffraction (XRD) and Raman scattering spectroscopy. The optical properties including linear absorption and nonlinear saturable absorption are also analyzed, which help to calculate some key parameters such as saturation power, modulation coefficient and modulation depth required for optimizing the passively mode-locked EDFL. With a specific design by using high-gain EDF and a relatively large negative group delay dispersion (GDD) in the EDFL cavity, the effects of self-amplitude modulation (SAM, induced by saturable absorber) and self-phase modulation (SPM, induced by EDF and SMF) on the passive mode-locking of EDFL are clarified. Although the structural defects accompanied with different carbon incorporated nano-scale powders are induced during fabrication to affect the SAM mechanism in the EDFL. The strong nonlinear SPM and GDD compensation can cooperate to take over the pulse shortening force, which further compress the EDFL pulsewidth to sub-500 fs, no matter what kind of the carbon incorporated nano-scale powders is used as the saturable absorber in the EDFL.

2. Experimental setup

In experiment, five carbon based materials with their nano-scale forms were employed as the saturable absorbers of the homemade high-gain EDFL. The commercially available few-layer graphene (from Gotop Electronic Technology Co. Ltd.) was deposited on Cu foil by using thermal chemical vapor deposition (CVD) system. Subsequently, the few-layer graphene was transferred to the end-face of a single-mode fiber (SMF) patchcord from the Cu foil. The fabrications of the other four carbon based powders, including the graphite (from Alfa Aesar Co.), the graphene oxide (from Conary Enterprise Co., Ltd.), the carbon black (from Taiwan Taimax Co.), and the charcoal (from IKEN Co.), were performed by using the chemical solvent for the dispersion of these carbon based powders after mechanical triturating of the commercially available bulks. Afterwards, the aqueous solutions containing these carbon based powders were dipped onto the end-face of different SMF patchcords, and the samples were heated in an oven to remove the dispersive solvent. The natural adhesion of carbon based materials on the end-face of the SMF preserves these nano-scale saturable absorbers between patchcord connectors in the EDFL cavity. Figure 1(a) shows the photographs of the few-layer graphene on Cu foil, and the nano-scale powders of graphite, graphene oxide, carbon black, and charcoal after fine polishing. Figure 1(b) demonstrates the scanning electron microscopy (SEM) images of the graphite, graphene oxide, carbon black, and charcoal nano-particles. The average sizes of all nano-particles are confirmed within 500 nm.

Fig. 1 (a) The photographs and (b) the SEM images of graphene on Cu foil, graphite, graphene oxide, carbon black, and charcoal nano-particles.

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Figure 2 demonstrates the configuration of the passively mode-locked EDFL. In the EDFL system, a 2-m high-gain erbium-doped fiber (EDF, nLIGHT Liekki Er80-8/125) served as the gain medium, which was bi-directionally pumped by a 980 nm laser diode (LD) (forward) and a 1480 nm LD (backward). Two suitable wavelength division multiplexers (WDMs, 980/1550 and 1480/1550) were employed to deliver the pumping powers. An isolator was used to determine the circulation direction of optical pulse, and a polarizer controller (PC) set in front of the saturable absorber played the role to optimize the circulation polarization. A 5/95 fiber coupler was inserted to provide 5% output and 95% feedback. An autocorrelator (Femtochrome FR-103XL), an optical spectrum analyzer (Ando AQ6317B) and a digital oscilloscope (Tektronix, TDS 2022) were utilized to measure the pulsewidth, the optical spectrum and the pulse train of the passively mode-locked EDFL. The gain of the erbium-doped fiber amplifier (EDFA) with a 2-m long EDF is 21 dB under an incident power of 0 dBm. The five optical microscope (OM) images shown in the lower part of Fig. 2 demonstrate five different nano-scale carbon based saturable absorbers adhered on the end-face of SMF patchcords. The coverage ratios of the carbon based nano-particle powders were carefully controlled to make the transmittances of all saturable absorber coated fiber patchcords nearly identical to one another (T = 0.87~0.9). According to the Haus master equation [49], when the pulse is formed by the SAM effect of saturable absorber, the linear absorption of saturable absorber plays the role to affect the pulse formation. Therefore, the transmittance of five saturable abosrbers should be kept identical such that the similar linear loss can be maintained, and only the effect of nonlinear saturable absorption will be taken for comparison.

Fig. 2 The configuration of the graphite nano-sheet based passively mode-locked EDFL system.

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3. Results and discussion

3.1 Raman scattering and X-ray diffraction spectra of few-layer graphene nano-sheets, graphite, graphene oxide, carbon black and charcoal nano-particles

Raman scattering spectroscopy and XRD spectroscopy are two powerful techniques to investigate the structural properties of carbon based materials. For the Raman scattering spectroscopy, a CW 532-nm solid-state laser (Coherent, Verdi V10) was utilized as the pumping source. Five carbon materials were placed on the same Si substrate for the measurements. The Raman scattering signals were collected and analyzed by the Raman spectroscopy system (Horiba, T64000). For the Raman spectra, three prominent peaks related to graphene structure in five carbon based materials, including the D band at ~1380 cm⁻¹, the G band at ~1580 cm⁻¹, and the 2D band at ~2670 cm⁻¹, can be observed and compared in Fig. 3(a).The C-C sp² network of graphene plane generates an intense G band located at 1580 cm⁻¹. The structural defects and impurities in graphene can be observed from the appearance of D band at 1380 cm⁻¹, that is correlated with the zone boundary phonon. The second-order zone boundary phonon in graphene induces a 2D band wavenumber around 2670 cm⁻¹, which is highly sensitive with the layer number of graphene [50–52]. Ferrari et al. reported that when a single-layer graphene increases it layer number to form graphite, the 2D peak intensity is attenuated associated with its bandwidth significantly broadened. Moreover, the 2D band gradually separates to multi-peaks, because the interaction of each graphene plane splits the electronic bands [50–52].

Fig. 3 (a) The Raman scattering spectra and (b) the XRD spectra of few-layer graphene, graphite nano-particle, graphene oxide nano-particle, carbon black nano-particle and charcoal nano-particle.

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For a few-layer graphene (with layer numbers: 2~3), the D and G bands are appeared at 1360 and 1580 cm⁻¹, respectively. The intensity ratio of D band over G band (I_D/I_G) is identified to investigate the amount of structural defect and disorder. The I_D/I_G value of the few-layer graphene is as small as 0.06. The 2D band at 2670 cm⁻¹ shows an intensity ratio of I_2D/I_G of 0.9. In comparisons, the I_D/I_G value of graphite nano-particle show a comparable value of 0.08, (slightly larger than that of few-layer graphene). The defects existed outside the graphite nano-particles result from the mechanical polishing process. For graphene oxide nano-particle, the D band intensity increases by one order of magnitude to give a large I_D/I_G of 0.8, which is caused by the extensive oxidation process. Both the Raman spectra of carbon black and charcoal nano-particles exhibit the relatively broad G bands to indicate the amorphous graphite phase. When defects and disorders exist in the carbon based materials with graphite structure, a D' band around 1620 cm⁻¹ is induced as the shoulder of G band, which not only enlarges the bandwidth of G peak [53], but also raise the intensity of D band. The carbon black and charcoal nano-particles exhibit I_D/I_G ratio nearly identical to that of graphene oxide, which all exhibit the weak 2D bands with I_2D/I_G ratios of 0.17-0.23 due to the weak graphene crystallinity. For these amorphous graphite structures, the up-shift of 2D band with an enlarged bandwidth can be also observed [50]. All of the corresponding intensity ratios for different nano-scale carbon based powders are summarized in Table 1.

Table 1. The Raman scattering intensity ratios of I_2D/I_G and I_D/I_G, and the {002} XRD peak position (θ_D) and linewidth (Δθ) of the carbon based nano-scale materials

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The crystallinity of five different nano-scale carbon based materials are also examined by XRD, as shown in Fig. 3(b). The (002)-oriented diffraction peaks are observed for all the carbon based materials, where the diffraction peaks are dominated by the graphite crystallinity in the direction perpendicular to the hexagonal planes [54–56]. The few-layer graphene exhibits a broad peak around 25° due to the short crystalline range along the perpendicular direction [57]. The interlayer spacing and crystallite size can change the diffraction angle and the linewidth. For a natural graphite, an {002} diffraction peak is located at 26.6° to indicate the interlayer spacing d₀₀₂ of 0.334 nm [55]. In contrast, the {002} peak of the graphite nano-particle is slightly shifted to 26.2° due to the enlarging interlayer spacing. During the triturating process, the mechanical stress makes versatile defects generated inside the graphite nano-particle, such as layer rotation, layer translation and layer curvature, etc [56]. The distortions of graphene layer also cause the variation on interlayer spacing. For graphene oxide nano-particle, the {002} diffraction peak shows a distinct angle shift to 10.75°, because the expansion on interlayer spacing of graphene oxide is even larger than that of graphite nano-particle due to the invasion of oxygen. However, the peak linewidth is slightly increased to 0.8° indicating that the crystallite size distribution of graphene oxide nano-particle is comparable with that of graphite nano-particle. In contrast, the triturated carbon black and charcoal nano-particles shift the azimuth angles of the {002}-oriented XRD peaks to 25.05° and 26°, with their corresponding linewidths broadened to 4.39° and 7.84°. The small crystallite size inside these nano-scale carbon materials greatly expands the linewidth, and the structural defects lead to a small diffraction angle shift. These drawbacks of the carbon materials could slightly degrade their optical properties as being the saturable absorbers. The related XRD parameters of the carbon based materials are also included in Table 1.

3.2 Nonlinear transmittance and absorbance of few-layer graphene nano-sheets, graphite, graphene oxide, carbon black and charcoal nano-particles

When illuminating graphene with low optical intensity, the photo-excitation transfers the electrons from valence band to conduction band. The electron-hole recombination subsequently occurs to reinstate the original electron and hole distribution after the formation of Fermi-Dirac distribution. Under intensive optical illumination, the graphene possesses a nonlinear saturable absorbance due to the Pauli blocking effect, which reduces the photoelectron transition to increase the optical transmittance. The increasing electrons fill all of the near-band-edge states in the conduction band eventually, and no more electrons can be up-transmitted due to the band filling. This phenomenon ceases the photoelectron transition in graphene, saturates the optical absorption and increases the optical transmittance due to the Pauli blocking effect [6, 58]. The total optical absorbance of a saturable absorber can be separated into nonlinear absorbance q_non and linear absorbance q_lin. The related saturable transmittance can be expressed as [45, 46]:

T = \exp (- q_{t o t a l}) = \exp (- \frac{q_{n o n}}{1 + I_{P e a k} / I_{s a t}} - q_{l i n}),

where I_Peak and I_sat represent the incident intensity and the saturation intensity, respectively. Under small-signal approximation, the absorbance q in Eq. (1) can be modified to obtain the modulation depth, as given by [46]:

q = \frac{q_{n o n}}{1 + I_{P e a k} / I_{s a t}} + q_{l i n} = (q_{n o n} + q_{l i n}) (1 - \frac{γ I_{P e a k}}{(q_{n o n} + q_{l i n})}) = (q_{n o n} + q_{l i n}) (1 - M_{D}) .

With the modulation coefficient defined as γ = q_non/I_sat, and an approximation solution of Eq. (2) is derived by (1 + I_peak/I_sat)⁻¹≒1-I_Peak/I_sat. M_D denotes the modulation depth.

To obtain the nonlinear transmittances of five carbon based materials, a pulsed fiber laser with central wavelength of 1570 nm and a pulsewidth of 700 fs was utilized as the pumping source. The repetition frequency of the pulsed laser was 40 MHz. In the measurement, each carbon based material was adhered on the connector end-face of the SMF patchcord. By increasing the pumping power, the nonlinear transmittances of saturable absorbers were observed. No other nonlinear effects were detected during the measurement [6, 25]. Figure 4(a) provides the nonlinear transmittances of the carbon based materials. With precisely controlled coverage ratios of the carbon based nano-scale powders on the SMF end-faces, the optical transmittances under low incident power are around 0.87~0.91. By increasing the input power, the nonlinear transmittance of the few-layer graphene saturates at 0.965, with the corresponding parameters determined as q_non = 0.054, q_lin = 0.033 and I_sat = 0.8 MW/cm². The graphite and graphene oxide nano-particles show slightly reduced saturable transmittances of 0.957 and 0.935, accompanied with their saturation intensities (I_sat) enlarged to 1.15 and 1.55 MW/cm², respectively. In comparison, the carbon black and charcoal nano-particles also exhibit the saturable transmittance at even higher incident intensities, indicating that the saturation intensities of these nano-scale carbon materials are much higher as compared to few-layer graphene (I_sat = 3.52 MW/cm² for carbon black and I_sat = 6.1 MW/cm² for charcoal). On the other hand, the term q_non/(q_non + q_lin) is defined to realize the weighting of saturable absorbance in the q_total. For the few-layer graphene, the non-saturable loss is small to make 0.61 of saturable absorbance in total absorption. In contrast, the carbon black and charcoal nano-particles, decrease their q_non/(q_non + q_lin) weighting factors to 0.343 and 0.272, respectively. These observations indicate that the defects existed in the nano-scale carbon based powders inevitably increase the non-saturable loss and degrade the influence of saturable absorbance in total optical absorption [6].

Fig. 4 (a) The nonlinear transmittance and (b) the normalized absorbance of few-layer graphene, graphite nano-particle, graphene oxide nano-particle, carbon black nano-particle and charcoal nano-particle. The abscissas are in log-scale.

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As a result, the Fig. 4(b) provides the normalized saturable absorbance of the carbon based materials. The absorbance is difined as -ln(I_out/I_in), where I_out and I_in are the output power and input power, respectively. Among five nano-scale carbon based saturable absorbers, the few-layer graphene possesses the largest modulation depth of 60%. For the graphite and graphene oxide nano-particles, the modulation depths slightly decay to 55% and 45%, respectively. The carbon black and charcoal nano-particles exhibit the lower modulation depths of 30% and 23%, respectively.

Table 2 summarizes the characteristic parameters related to the linear and nonlinear absorbances of five different nano-scale carbon based saturable absorbers. In summary, the few-layer graphene exhibits the smallest non-saturable loss to provide the largest q_non/(q_non + q_lin), which makes the few-layer graphene having the highest modulation depth. The large non-saturable loss in the nano-scale carbon materials would inevitably suppresses the modulation depth to degrade the passively mode-locked EDFL performances. Because five different carbon powders all contribute to the similar absorption loss (q_non + q_lin), therefore, the EDFLs with these carbon based saturable absorbers show similar mode-locking thresholds. When considering the SAM as the dominated mechanism for mode-locking the EDFL, the modulation depth of saturable absorber plays an important role on both the pulse formation and the pulse shortening. In principle, the SAM mode-locked EDFL pulsewidth τ_SAM exhibits a proportionality with τ_SAM = (2D_g/γ|A₀|²)^1/2, where D_g and A₀ denote the gain dispersion and pulse amplitude, γ = q_non/I_sat represents the modulation coefficient [59]. That is, high nonlinear absorption and low saturation intensity of saturable absorber can enhance the pulse shortening force in the EDFL. If the pulse formation is determined by the SAM effect, the EDFL system with few-layer graphene can produce the shortest pulse due to its highest modulation depth (M_D = 60%). In contrast, the nano-scale carbon materials with lower modulation depth, such as carbon black (M_D = 30%) and charcoal nano-particles (M_D = 23%), would form the much broader pulses.

Table 2. The characteristic parameters of saturable absorbance of the carbon based materials.

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3.3 Passively mode-locked EDFLs with few-layer graphene nano-sheets, graphite, graphene oxide, carbon black and charcoal nano-particles

When the pumping currents of two LDs simultaneously increase to 900 mA, the pumping powers of the 980 nm LD and 1480 nm LD enlarge to 290 and 200 mW, respectively, as shown in Fig. 5(a).The Fig. 5(b) compares the output power responses of the EDFLs with different nano-scale carbon based saturable absorbers. When operating two pumping LDs at 70 mA, only the 980-nm LD which provides a pumping power of 19 mW to induce the gain of EDFL at nearly threshold condition, all of the EDFLs with different saturable absorbers start the continuous-wave (CW) lasing. Due to the precise control on the linear loss of the EDFL cavity and saturable absorbers, it is found that the threshold conditions of all EDFLs with different nano-scale carbon based materials are approximately the same. However, the power to current slope as well as the quantum efficiency of the passively mode-locked EDFL with highly crystalline few-layer graphene is still higher than those with other disordered carbon based saturable absorbers.

Fig. 5 (a) The pumping power vs. the pumping current of two LDs (orange: 980 nm; gray: 1480 nm). (b) The output power of EDFL systems vs. the pumping powers of two LDs (Upper abscissa: 1480-nm LD pumping power (mW); Lower abscissa: 980-nm LD pumping power (mW)).

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Figures 6(a) and 6(b) demonstrate the autocorrelation traces and the optical spectra of the passively mode-locked EDFLs with five nano-scale carbon based saturable absorbers. All the passively mode-locked EDFLs are operated under the same condition with the 980- and 1480-nm LD pumping powers of 290 and 200 mW. With the few-layer graphene saturable absorber, the passively mode-locked EDFL performs the minimal pulsewidth of 305 fs, the widest spectral full-width at half maximum (FWHM) of 8.05 nm, and the central wavelength of 1572 nm. The larger non-saturable loss and the lower modulation depth of saturable absorbers significantly broaden the EDFL pulsewidth. As evidence, the EDFLs mode-locked by using graphite, graphene oxide and carbon black nano-particles gradually broaden their pulsewidths to 335, 370 and 415 fs, with the corresponding FWHMs of 7.51, 7.05 and 6.49 nm, respectively. The widest pulsewidth of 435 fs is produced by using the charcoal nano-particle as a saturable absorber, the FWHM is 6.04 nm and the central wavelength is around 1570 nm. The central wavelengths are blue shifted to 1572-1570 nm. Because the linear transmittance of graphene (0.92) is slightly higher than other carbon based saturable absorbers [graphite nano-particle (0.9), graphene-oxide nano-particle (0.88), carbon black nano-particle (0.87), charcoal nano-particle (0.87)]. The increasing cavity loss could reduce the cavity gain so as to slightly blue-shift the central wavelength [47]. The time-bandwidth products (TBPs) of all the passively mode-locked EDFLs are nearly 0.315, because the EDFLs are operated under the same GDD and SPM effects by slightly detuning the pumping condition to optimize the pulse compression in each case. The GDD is −0.156 ps² by considering the dispersion coefficients of 2-m EDF (β_2,EDF = −20 ps²/km) and 5.8-m SMF (β_2,SMF = −20 ps²/km) [60–62]. The SPM coefficient δ is calculated as 0.01 W⁻¹ by considering the nonlinear refractive index of EDF (n_2,EDF = 3x10⁻²⁰ m²/W) and SMF (n_2,SMF = 2.96x10⁻²⁰ m²/W) [63, 64].

Fig. 6 (a) The autocorrelation traces, (b) the optical spectra and (c) the oscilloscope traces of the passively mode-locked EDFLs with few-layer graphene, graphite nano-particle, graphene oxide nano-particle, carbon black nano-particle and charcoal nano-particle.

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With the soliton pulse formed by the GDD and SPM, the Kelly sidebands occurred on the shoulder of optical spectra can be observed. During multiple round-trip circulation, the phase-matching condition between the perturbed solitons and the radiated dispersive waves would contribute to the constructive interferences at specific wavelengths and form the sharpened peaks on the optical spectrum. Typically, the frequency spacing of the Kelly sidebands is correlated with soliton length, soliton pulsewidth, and cavity length. In addition, the sideband frequencies are also correlated with the cavity GDD [46, 65, 66]. In experiment, the GDD effects from the laser cavity are kept as the same for all the passively mode-locked EDFLs with different saturable absorbers. It is observed that the frequency spacing of the Kelly sidebands are slightly increased from 1.25 to 1.28 THz with the broadening pulsewidth from 305 to 435 fs (summarized in Table 3).In a more general form, the theoretically derived frequency spacing of Kelly sidebands is described as [46, 65, 66]:

Δ ω_{m} = \pm \frac{2 \ln (1 + \sqrt{2})}{τ_{p}} \sqrt{m \frac{8 Z_{0}}{Z_{E D F L}} - 1} = \pm 2 \ln (1 + \sqrt{2}) \sqrt{4 π m {| \sum_{i = 1}^{n} β_{i} L_{i} |}^{- 1} - \frac{q_{n o n} {| A_{p e a k} |}^{2}}{2 D_{g} P_{s a t}}},

where τ_p denotes the soliton pulsewidth, m the order of Kelly sidebands, Z₀ the periodical length of soliton, βL the GDD contributed by different components, A_peak the peak amplitude of the soliton pulse, D_g the gain dispersion of the EDFL. The Eq. (3) interprets that such an increment is mainly attributed to the shortened pulsewidth or the lengthened soliton period. However, this is not always sustained as the soliton period, it is also a function of its pulsewidth. In more detail, both the reduced GDD, the enlarged pulse intensity in the EDFL, and the enhanced nonlinear absorbance of the saturable absorber can expand the frequency spacing of Kelly sidebands.

Table 3. The comparison of the passively mode-locked EDFLs with different saturable absorbers.

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On the other hand, the oscilloscopes monitored pulse-strains of the passively mode-locked EDFLs with the carbon based materials are shown in Fig. 6(c). The repetition frequency and the repetition time are determined as constants of 28 MHz and 35 ns, which are dominated by the EDFL cavity length of 7.8 m. The peak fluctuation of the soliton pulse is denoted as the carrier-amplitude jitter of CAJ = (σ/I_ave) in unit of %, with σ representing the standard deviation of peak pulse intensity and I_ave the average pulse intensity, which can be used to quantify the equalization of pulse intensity and the stability of the EDFL system [67]. All of the EDFLs passively mode-locked by different nano-scale carbon based saturable absorbers show the stabilized mode-locking with very small CAJ values around 1.6-1.7% (see Table 3). The highly crystalline graphene can generate the stabilized EDFL systems with a CAJ value around 1.63-1.66%. In contrast, the disordered nano-scale carbon materials produce the EDFL system with a slightly high CAJ values of >1.68%. In this work, the long-term operations of passively mode-locked EDFLs with five carbon based saturable absorbers could be maintained for at least 6 hours. The steady pulse trains from the EDFLs passively mode-locked with five carbon based saturable absorbers were obtained by monitoring the pulse-trains on the oscilloscope, while no amplitude fluctuation was observed during the operation. The EDFLs can be arbitrarily turned on and off by several times during operation, and there was no thermal damage occurred on these saturable absorbers after the passively mode-locked operation of the EDFLs.

3.4 Roles of SAM, SPM and GDD on the mode-locked pulse starting compression in the EDFL with different nano-scale carbon based saturable absorbers

It is observed that the EDFL can be passively mode-locked by all kinds of the nano-scale carbon materials based saturable absorbers with versatile structural and phase forms, including few-layer graphene nano-sheets, graphite, graphene oxide, carbon black and charcoal nano-particles. Nevertheless, the origin and the dominated mechanism of the mode-locking in the EDFLs with different saturable absorbers have not yet been well understood, which is mandatory for establishing the designing rule on selecting the appropriate materials.

First of all, the evolutions of autocorrelation trace and optical spectra of the passively mode-locked EDFL with five different saturable absorbers under different pumping currents are shown in Fig. 7.The mode-locking thresholds of the EDFLs with all of the nano-scale carbon based materials are ranged between 100~200 mA without distinct deviation, which can be confirmed by the appearances of pulsed autocorrelation trace associated with a broadened spectrum. By increasing the pumping currents of two LDs from 200 to 900 mA, the EDFL pulsewidth shows a significant decreasing trend at the LD pumping current below 600 mA, and the pulse shortening speed gradually slows down after pumping the LD at current larger than 700 mA. In contrast, the optical FWHM gradually broadens. This phenomenon indicates that gain enhancement can increase the oscillating mode number to reduce the pulsewidth; However, the gain enhancement no longer dominates the pulse compression after enlarging the pumping current to a critical level. It turns out that the mode-locking mechanism could be transferred when pumping the EDFL from low to high gain regime.

Fig. 7 (a) The autocorrelation traces and (b) the optical spectra of the passively mode-locked EDFLs with few-layer graphene under different pumping currents of 900 mA (red), 800 mA (orange), 700 mA (magenta), 600 mA (olive), 500 mA (Dark yellow), 400 mA (blue), 300 mA (purple), 200 mA (Navy), 100 mA (Dark gray), and 70 mA (black).

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The broadened optical spectrum also elucidates that the phase of the pulse is not only perturbed by the GDD effect, once the increasing pumping power significantly enlarges the optical pulse intensity and shortens the pulsewidth. The intensity-dependent SPM effect with enhanced pulse intensity is induced to cause a positive chirp, which generates new frequency components in lasing spectrum and plays the dominant role to reshape the pulse under the cooperation with GDD in the EDFL cavity. As a result, the Figs. 8(a) and 8(b) illustrate the evolutions on pulsewidth and linewidth determined from autocorrelation trace and optical spectra of the passively mode-locked EDFLs with five different nano-scale carbon based saturable absorbers under different pumping currents. By increasing the pumping currents of two LDs from 200 to 900 mA, the EDFL mode-locked by few-layer graphene shortens pulsewidth from 490 to 305 fs, associated with its spectral linewidth broadened from 5.39 to 8.05 nm (at central wavelength of 1572 nm). The TBP of nearly 0.315 indicates that a stabilized and transform-limited soliton can be formed by pumping the EDFL at 200 mA or larger. The graphite and graphene oxide nano-particles induced mode-locking can also compress the EDFL pulsewidths from 520 to 335 fs and from 547 to 370 fs, corresponding to the spectral linewidths broadened from 5 to 7.51 nm and from 4.74 to 7.05 nm, respectively. The carbon black and charcoal nano-particles only shorten the EDFL pulsewidth from 573 to 415 fs and from 585 to 435 fs, accompanied with their spectral linewidth broadened from 4.41 to 6.49 nm and from 4.2 to 6.04 nm, respectively. The EDFLs mode-locked with these nano-scale carbon nano-particles gradually blue-shift their central wavelengths from 1572 to 1570 nm, and result in TBPs of slightly higher than 0.315. Although the mode-locking abilities (absorption loss and modulation depth) of these nano-scale carbon based saturable absorbers are different, the passively mode-locked EDFLs with all kinds of the nano-scale carbon based saturable absorbers can still compress their pulsewidth down to sub-500 fs.

Fig. 8 The variations of (a) EDFL pulsewidth and (b) FWHM with the carbon based materials under the operations of two LDs' pumping powers (Upper abscissa: 1480-nm LD pumping power (mW); lower abscissa: 980-nm LD pumping power (mW)).

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To observe the effects of the SPM induced chirp and the intra-cavity GDD on the pulse shortening, the master equation for describing the pulse formation is given by Eq. (4) [46, 49, 68, 69].

T_{R} \frac{\partial A (T, t)}{\partial T} = {[g - l_{0} + D_{g, f} \frac{\partial^{2}}{\partial t^{2}} + γ {| A_{0} |}^{2}]}_{S A M} A (T, t) + j {[D \frac{\partial^{2}}{\partial t^{2}} - δ {| A_{0} |}^{2}]}_{S P M} A (T, t) .

For passive mode-locking, the solution of the circulated pulse A(T,t) inside the EDFL ring cavity is considered as a hyperbolic secant function. During the circulation, the pulse amplitude is correlated with the cavity gain g, the cavity loss l₀, the gain and filter dispersion D_g,f, and the loss modulation of saturable absorber. On the other hand, the phase of the circulated pulse is modified by the GDD and SPM effects. With the strong GDD and SPM effects, not only the pulse amplitude but also the phase are perturbed by the chirp, thus giving a chirped wave function A_c(T,t) as:

A_{c} (T, t) = A {[sech(\frac{t}{τ})]}^{(1 + j β)} e^{j ϕ T / T_{R}},

where β and ϕ denote the chirp and the round-trip phase shift, respectively. β is affected by the normalized dispersion of D_N = D/D_g,f and the normalized nonlinear SPM factor δ_N = δ/γ, as expressed as:

β = - \frac{3}{2} (\frac{- 1 + δ_{N} D_{N}}{δ_{N} + D_{N}}) \pm \sqrt{{[\frac{3}{2} (\frac{- 1 + δ_{N} D_{N}}{δ_{N} + D_{N}})]}^{2} + 2} .

When the negative chirp from the GDD effect is almost compensated by the positive chirp from the SPM effect, the passively mode-locked EDFL pulsewidth τ can be further compressed, as given by:

τ = \frac{τ_{0}}{2} (2 - β^{2} - 3 β D_{N}),

where τ₀ is the original pulsewidth of the passively mode-locked EDFL formed by the saturable absorber.

A simulation of the pulse compression ratio is shown in Fig. 9 with Eq. (7). At initial stage, the SAM from the saturable absorber is the main and only mechanism to dominate the pulse formation. Therefore, both the absorption loss and the modulation depth are the dominant factors to determine the pulse shaping. After the formation of stabilized pulse-train, the cooperation of negative GDD and large SPM effects starts the second-stage pulse shortening to further compress the pulsewidth, whereas the saturable absorber only functions as a mode-locking stabilizer. Note that if the intra-cavity intensity enlarges to induce a strong SPM, there will be a complicated correlation between round-trip phase shift β and normalized dispersion D_N that leads to a minimized pulsewidth occurred at a slightly negative GDD but not a fully compensated dispersion condition.

Fig. 9 Pulse compression ratio versus intra-cavity GDD at a given SPM factor.

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Previously, Agrawal has defined a governing factor N to evaluate the relative importance or the weighting scale between GDD and SPM effects in the EDFL cavity, as given by [70]:

N = \sqrt{\frac{L_{G D D}}{L_{S P M}}} = \sqrt{(\frac{δ_{E D F}}{L_{E D F}} + \frac{δ_{S M F}}{L_{S M F}}) \frac{P_{p e a k} τ^{2}}{| β_{2} |}},

where L_GDD is the dispersion length and L_SPM is the nonlinear length, δ_EDF and δ_SMF are the SPM coefficients of EDF and SMF, P_peak denotes the peak power and τ the pulsewidth. The SPM effect dominates the pulse compression when N>>1, whereas the GDD effect is the only effect to control the pulsewidth at N<<1. For N≅1 in the anomalous dispersion condition, the cooperation of GDD and SPM dominate the pulse compression to form a soliton pulse.

According to Fig. 7(b), the prominent Kelly sidebands appear even under the pumping currents as low as 300 mA, which indicates that GDD and SPM contribute similar perturbations to the pulse at such low pumping condition. Assuming that the output power of the EDFL is 2.6 mW and the circulated power within the EDFL cavity is thus 50 mW. In this situation, the N value is approximately 8 (δ_EDF = 0.25x10⁻² W⁻¹, δ_SMF = 1x10⁻² W⁻¹, P_peak = 3.6 kW, β₂ = −20 ps²/km). Furthermore, Fig. 10 shows the relationship between the governing factor N and the pumping currents of the EDFL. The calculations from experimental results reveal that the N value arises from 8 to 11.9 (close to a saturated value) with the increasing pumping current, which means that the enhanced pulse intensity only strengthens the SPM effect but has very minor influence on the intra-cavity GDD effect. In addition, the saturation trend of the N factor is observed to indicate that the pulse compression is also limited at extremely high pumping conditions. The increasing SPM effect can further compress the pulse, but the pulse compression is limited with a maximum of up to 2~3. In contrast, the extremely large SPM effect would also distort the phase to make the unstable pulse-train even with a stabilized mode-locker [58].

Fig. 10 The governing factor N versus the driving current of pumping LD in the EDFL passively mode-locked by using different carbon materials based saturable absorbers.

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4. Conclusion

Five triturating nano-scale carbon materials, including few-layer graphene, graphite, graphene oxide, carbon black and charcoal nano-particles are employed as the saturable absorbers to passively mode-lock the EDFLs. The structural and optical properties, and key parameters related to the mode-locking performances of these five nano-scale carbon based saturable absorbers are compared. By using Raman scattering spectroscopy, the few-layer graphene shows the largest I_2D/I_G ratio of 0.9 and the smallest I_D/I_G ratio of 0.06, to indicate the less graphene layer number and the pure crystallinity. For the other carbon based materials, the increasing graphene layer number lead to a decreasing I_2D/I_G ratio. Moreover, defects and disorders existed in the other carbon based materials significantly raise the I_D/I_G ratio. As compared to the few-layer graphene, the enlarged interlayer spacing of graphite nano-particle caused by the polishing process slightly shift the {002}-oriented XRD peak to 26.2°. The oxygen invasion into the graphene oxide nano-particle leads to a prominent angle shift to 10.75°. However, the linewidth of these two nano-scale carbon based materials are still confined to indicate their high crystallinity. For the disordered carbon black and charcoal nano-particles, the {002} diffraction angles shift to 25.05° and 26° with broadened linewidth of 4.39° and 7.84°, respectively.

By analyzing the linear and nonlinear transmittance of these nano-scale carbon materials, the modulation coefficient significantly reduces from 0.068 (few-layer graphene) to 0.006 (charcoal nano-powder), corresponding to the decreasing modulation depth from 60% to 23% and the increasing saturation intensity from 0.8 to 6.1 MW/cm², respectively. This is mainly attributed to their disordered structure with enlarged interlayer spacing and diminished graphene content. Nevertheless, it is observed that the EDFLs can still be passively mode-locked by all kinds of the nano-scale carbon materials based saturable absorbers with versatile structural and phase forms. But five carbon based materials would induce different SAM effects. The few-layer graphene can generate the shortest pulsewidth of 305 fs, and the widest FWHM of 8.05 nm due to the lowest linear absorbance and the largest modulation depth. The EDFLs mode-locked by graphite, graphene oxide and carbon black nano-particles gradually broaden the pulsewidths to 335, 370 and 415 fs, with less broadened linewidths of 7.51, 7.05 and 6.49 nm, respectively. The widest pulsewidth of 435 fs is produced by mode-locking the EDFL with charcoal nano-particle, providing a spectral linewidth of only 6.04 nm. The TBPs of all passively mode-locked EDFLs are nearly 0.315.

All of the EDFLs passively mode-locked by these nano-scale carbon powders show the transform-limited pulsewidths of less than 500 fs at L-band. The roles of the SAM and SPM effects played in such a high-gain EDFL mode-locked with disordered nano-scale carbon powders have been clarified. Under high-gain operation, the saturable absorber only functions as a weak starter and stabilizer for passive mode-locking. After forming an intense pulse by the saturable absorber, the strong SPM mechanism turns to dominate the pulse shortening force of the EDFL, and the minimized pulsewidth occurs at a slightly negative GDD but not a fully compensated dispersion. The increasing intra-cavity power only enlarges the SPM but contributes a trivial effect on the intra-cavity GDD. This makes the governing factor N increased from 8 to 11.9 by enlarging the pumping current from 300 to 900 mA. Therefore, these observations have disclosed a new era of high-gain EDFL passively mode-locked by all kinds of nano-scale carbon based saturable absorbers. All of the nano-scale carbon material based saturable absorbers need no longer possessing high crystallinity and uniform size distribution, which play the roles like the mode-locking initiators and stabilizers instead of serving as the pulse compressor.

Acknowledgments

This work was supported by the Ministry of Science and Technology, Taiwan, R.O.C., and the Excellent Research Projects of National Taiwan University, Taiwan, under grants NSC 100-2221-E-002-156-MY3, NSC 101-2221-E-002-071-MY3, MOST 103-2221-E002-042-MY3, 103R89081 and 103R89083.

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	Few-layer graphene	Graphite nano-particle	Graphene oxide nano-particle	Carbon black nano-particle	Charcoal nano-particle
*q_non*	0.054	0.057	0.059	0.048	0.037
*q_lin*	0.033	0.047	0.068	0.092	0.099
$q_{n o n} \frac{1}{q_{n o n} + q_{l i n}}$	0.61	0.548	0.464	0.343	0.272
I_sat (MW/cm²)	0.80	1.15	1.55	3.52	6.10
γ	0.068	0.05	0.038	0.014	0.006
M_D	60%	55%	45%	30%	23%

	Few-layer graphene	Graphite nano-particle	Graphene oxide nano-particle	Carbon black nano-particle	Charcoal nano-particle
*q_non*	0.054	0.057	0.059	0.048	0.037
*q_lin*	0.033	0.047	0.068	0.092	0.099
$q_{n o n} \frac{1}{q_{n o n} + q_{l i n}}$	0.61	0.548	0.464	0.343	0.272
I_sat (MW/cm²)	0.80	1.15	1.55	3.52	6.10
γ	0.068	0.05	0.038	0.014	0.006
M_D	60%	55%	45%	30%	23%

Triturating versatile carbon materials as saturable absorptive nano powders for ultrafast pulsating of erbium-doped fiber lasers

Abstract

1. Introduction

2. Experimental setup

3. Results and discussion

3.1 Raman scattering and X-ray diffraction spectra of few-layer graphene nano-sheets, graphite, graphene oxide, carbon black and charcoal nano-particles

3.2 Nonlinear transmittance and absorbance of few-layer graphene nano-sheets, graphite, graphene oxide, carbon black and charcoal nano-particles

3.3 Passively mode-locked EDFLs with few-layer graphene nano-sheets, graphite, graphene oxide, carbon black and charcoal nano-particles

3.4 Roles of SAM, SPM and GDD on the mode-locked pulse starting compression in the EDFL with different nano-scale carbon based saturable absorbers

4. Conclusion

Acknowledgments

References and links

Cited By

Figures (10)

Tables (3)

Equations (8)

Optical Materials Express

	Few-layer graphene	Graphite nano-particle	Graphene oxide nano-particle	Carbon black nano-particle	Charcoal nano-particle
I_D/I_G	0.06	0.08	0.8	0.8	0.67
I_2D/I_G	0.9	0.3	0.25	0.23	0.17
θ_D	25.4°	26.2°	10.75°	25.05°	26°
Δθ	11°	0.47°	0.8°	4.39°	7.84°

	Few-layer graphene	Graphite nano-particle	Graphene oxide nano-particle	Carbon black nano-particle	Charcoal nano-particle
Pulsewidth (fs)	305	335	370	415	435
FWHM (nm)	8.05	7.51	7.05	6.49	6.04
Wavelength (nm)	1572	1571	1571	1570	1570
TBP	0.315	0.315	0.315	0.32	0.32
Δυ of Kelly sidebands (THz)	1.25	1.26	1.27	1.27	1.28
CAJ (%)	1.64	1.66	1.63	1.69	1.70