We demonstrate an erbium doped fiber ring laser mode-locked with a carboxymetylcellulose high-optical quality film with dispersed single-walled carbon nanotubes (SWCNT). The laser with large normal net cavity dispersion generates near bandwidth-limited picosecond inverse modified soliton pulses at 1.56 µm.
©2012 Optical Society of America
Over past decade single walled carbon nanotubes (SWCNTs) have been incorporated into laser schemes as saturable absorbers for mode-locked regime initiation replacing semiconductor saturable absorbers (SESAM), nonlinear polarization switches and nonlinear loop mirrors. Sub-picosecond recovery time and broad absorption spectra have made SWCNTs very attractive for applications in fiber lasers with different cavity geometries [1–5].
A cavity of most modern lasers generating ultrashort pulses consists of fiber segments with normal and anomalous group velocity dispersion (GVD). Internal dispersion management provides efficient control of the laser output characteristics such as pulse duration, energy and spectrum shape. Evolution of output pulse characteristics of erbium-doped SWCNT mode-locked fiber lasers via net cavity dispersion variation has been studied earlier in detail [6,7]. At the large anomalous net cavity GVD soliton like pulses are formed by balancing of the GVD and self-phase modulation (SPM). As overall cavity dispersion approaches to zero laser generates stretched pulses so-called dispersion managed solitons. Their output energy can be much higher than in the case of conservative soliton pulses .
Recently positive chirped pulses generated in mode-locked fiber lasers with large net normal dispersion cavities have been realized and thoroughly investigated . Moreover, by applying a dispersion management into a cavity with net normal GVD, the laser generates high-energy pulses of femtosecond-time scale dechirped by means of appropriate external dispersion delay line.
Here we report on the erbium-doped fiber ring laser with intracavity dispersion management mode-locked by a polymer film incorporating SWCNTs as a saturable absorber. Via appropriate intracavity dispersion management by means of low-loss normal dispersion germanium-silica fiber inclusion inside a ring, various lasing regimes were realized. We present for the first time to our knowledge normal dispersion fiber laser generating almost transform-limited picosecond pulses bearing inverse soliton behavior.
2. Experimental scheme of the erbium doped mode-locked fiber ring laser
Experimental setup of the all-fiber erbium ring laser with intracavity dispersion management is presented in Fig. 1 . Laser cavity is based on a 1.2 m-long step-index (∆n = 0.0049) erbium-doped alumina-silicate fiber (EDF) with a 10 μm core diameter and 11 dB/m nonsaturated absorption at a wavelength of 0.98 µm. EDF second-order dispersion was measured to be –23 ps2/km, that was very close to the SMF-28 fiber GVD value. EDF is pumped by a single-mode laser diode emitting 200 mW max output power at a wavelength of 0.98 μm through the wavelength division multiplexer (WDM).
To vary mode-locking regimes via appropriate intracavity dispersion management, low-loss single-mode germanium-silica (GeO2/SiO2) highly nonlinear fiber  with normal GVD of β2 = + 218 ps2/km at 1.56 μm was inserted into the ring. 75-molpercentage germanium oxide concentration in the GeO2/SiO2-fiber core along with 2.75 μm measured mode-field diameter gave rise to the γ~30 W−1·km−1 fiber nonlinearity value. Polarization controller (PC) provides additional adjustment of laser operation regime while the fiber-pigtailed isolator (ISO) ensures unidirectional generation in the ring.
A polymer film incorporating SWCNTs fixed between two angular-polished ferrules of APC optical connectors is placed in laser cavity in order to initiate mode-locked lasing. The SWCNTs were synthesized by the arc discharge method in the helium atmosphere with the help of the Ni – Y2O3 catalyst. Carbon nanotubes synthesized by this method have more pronounced red-shifted optical-absorption band comparing to the SWCNTs synthesized by the laser ablation CVD or HiPCO methods . Stable suspensions of individual SWCNTs in 1 wt% aqueous solution of carboxymetylcellulose (CMC) have been prepared by ultrasonication followed by ultracentrifugation and a slow evaporation of the solvent . Cellulose is an efficient surfactant and the matrix material simultaneously. Due to this fact, the only two components (cellulose and SWCNTs) are necessary in the suspension to create high-optical quality films . SWCNTs diameters were evaluated to range around 1.4 nm, while the thickness of films was ~10 µm. To obtain an appropriate amount of saturated losses for stable mode-locking operation, two CMC films were installed between optical ferrules simultaneously, giving total transmission value of almost 60% at 1.56 μm wavelength. Transmission spectra of single and tandem CMC films with dispersed arc-discharged SWCNTs are shown in Fig. 2 .
Fiber coupler positioned before saturable absorber provides 50% power output. Thus, entering SWCNTs-module radiation is partly weakened to prevent CMC film crushing during pulse energy increase.
3. Experimental results
Through the accurate PC adjustment, stable self-starting single-pulse mode-locked lasing was achieved in the above-mentioned laser at different GeO2/SiO2 fiber lengths. GeO2/SiO2 fiber was cut back from 1.2 m providing net cavity dispersion variation from + 0.194 ps2 to −0.068 ps2 while the pulse repetition frequency ranged between 42.4 and 57.1 MHz. Figure 3 presents the evolution of the autocorrelation trace FWHM, spectrum bandwidth at half-maximum value (FWHM) (Fig. 3(a)) along with time-bandwidth product and average power (Fig. 3(b)) through the intracavity GVD variation.
If net cavity dispersion was established to have anomalous value ranged between−0.068 ps2 and −0.024 ps2, laser generated soliton-like pulses with measured pulse intensity autocorrelation traces accurately fitted by corresponding soliton-type function . The autocorrelation trace FWHM varied in this case from 1.2 ps to 1.37 ps, giving a pulse length variation from 790 to 920 fs (Fig. 3). The spectrum FWHM reached maximum value of 6.5 nm in the middle of indicated GVD interval and dropped down to 4.5 nm at its ends. Pulse autocorrelation traces and spectra corresponding to different output average powers in the case of −0.068 ps2 net cavity dispersion are presented in Fig. 4 . It is evident that with pump growing, pulse-width decreased while the spectrum is broadened, which is in agreement with soliton-type pulse behavior . In addition, spectral Kelly side bands became more pronounced in laser spectrum proving a soliton generation too.
If the net cavity dispersion is close to zero value (ranging from −0.013 to + 0.013 ps2) laser generates long pulses with step-sided spectrum of almost 8.5 nm width at −10 dB level (Fig. 5 ). In this case, autocorrelation trace has the maximum width of 19 ps (blue curve on Fig. 5(a)). As it could be exactly fitted by Gaussian function, an estimated pulse length reached as much as ~13.5 ps. Time bandwidth product has increased up to 13.4 (Fig. 3), proving the generation of highly chirped laser pulses.
As it is seen in Fig. 5, during the average output power increase from 5.14 to 11.6 mW both autocorrelation trace and spectrum broadened insignificantly. Further pulse energy growth was stopped by a stochastic generation appearance at 1.53 μm.
Moving across zero intracavity GVD, we did not obtain stretched-pulse generation regime , but, instead of it, we realized chirped pulses with characteristic step-sided spectrum (Fig. 5). We consider the crucial reason of such untypical behavior originates from the usage of the highly nonlinear GeO2/SiO2 –fiber for dispersion management. The stretched-pulse generation regime implies strictly symmetrical pulse evolution in fiber segments with negative and positive dispersion. However, in this case, the cavity symmetry is strictly broken by including highly nonlinear GeO2/SiO2 –fiber, which prevents pulse breathing. Indeed, the nonlinear coefficient of SMF-28 fiber and its GVD parameter value are quiet small to give the same pulse evolution as it might be in the GeO2/SiO2 –fiber. Thus, near zero cavity dispersion large SPM impact results in the highly chirped pulses with step-sided spectrum. The GVD in this case could only linearize phase modulation inside the pulse. The situation looks like a pulse propagation along the fiber in the case of LD»LNL (nonlinear length is much shorter than dispersion length for given pulse) .
In the case of large normal net cavity dispersion, EDF-laser generated stable pulses with autocorrelation trace width slightly varied around 3 ps (Fig. 3). During cavity GVD increase, laser spectrum FWHM oscillated in rather narrow interval between 1 and 2 nm.
It should be noticed that the most of observed spectra contain side bands, which are similar to well-known Kelly side bands inherent to conservative solitons. Moreover, via pulse energy increase, spectral positions of these side bands were quietly preserved with regard to the central wavelengths of pulse spectra as it is seen in Fig. 6 . However, despite this similarity, generated pulses could not be considered as conservative solitons as net cavity dispersion in these cases was substantially normal. In addition, neither Gaussian function nor soliton-type one fitted output spectra accurately, especially their wings (Fig. 7 ).
The time-bandwidth product value ranged around ~0.3, which was significantly less than well-known value of 0.441 attributed to bandwidth-limited Gaussian pulses. Finally, as it is shown in Fig. 6, given pulse autocorrelation trace broadened from 2.8 to 4.2 ps while spectrum narrowed from 1.5 nm to 1 nm with output power increase in the range between 1.84 mW and 3 mW, giving rise to the absolutely inverse behavior in comparison with conservative solitons (Es~1/τs).
To specify generated pulses both in time (1) and frequency (2) domains following relations have been implied according to reference :13]. In this case, the corresponding second-order autocorrelation Eq. (3) is given by :13]. It is evidently seen in Fig. 7, that introduced functions quiet accurately fit both the pulse spectrum and autocorrelation trace.
One of the most striking things is that time bandwidth product value for transform-limited pulses characterized by Eqs. (1) and (2) is equal to 0.22 . If the net cavity dispersion was adjusted to be D2 = + 0.129 ps2, time bandwidth product for generated pulses (Fig. 7) turned out to be ∆ν·∆τ = 0.308 giving rise to slightly chirped pulses. It should be also mentioned, that increasing a pulse energy brought in the pulse length growing as well as spectrum FWHM reduction by almost the same factor (see Fig. 6), with a minor decreasing of the time-bandwidth product value (∆ν·∆τ = 0.277 for τp = 2.7 ps). Through the intracavity dispersion reduction, time-bandwidth product value was not varied substantially as it is seen in Fig. 3(b). Otherwise, when increasing the intracavity GVD, generated pulses became even more bandwidth-limited (∆ν·∆τ = 0.26 for D2 = + 0.194 ps2). Thus, we are able to claim generated pulses to be almost bandwidth-limited.
Spectral side bands origination we attribute to the four-wave mixing (FWM) influence on pulse propagating along highly nonlinear GeO2/SiO2 fiber . Indeed, at a given nonlinearity coefficients of GeO2/SiO2 fiber (γ~30 W−1·km−1) and both SMF-28 and EDF ones (γ ~1.4 W−1·km−1), sufficient FWM amplification in the short ring may occur only in GeO2/SiO2 fiber. Furthermore, being strongly phase-matching process, FWM is additionally promoted by the flattened second-order dispersion profile inherent to GeO2/SiO2 fiber near 1.56 μm. According to this fact, m-order side band position Δλm with regard to the pulse central wavelength λc could be estimated as follows:Fig. 7, using this equation for m-order side bands position approximation in the case of + 0.129 ps2 net cavity dispersion, gave rise to the quiet reasonable agreement with experimental data, if assuming coherence length to be equal to Lcoh = 0.92 m. It appeared to be almost equal to the GeO2/SiO2 fiber length (L = 0.9 m), verifying our assumption of FWM influence in GeO2/SiO2 fiber.
As the fiber coupler providing 50% power output is positioned directly before the section of the GeO2/SiO2 fiber (see Fig. 1), pulses, entering this section, possessed almost the same parameters as output ones. Thus, we were able to estimate nonlinear length Lnl for peak pulse power Ppeak according to well-known relation: Lnl = 1/(γ·Ppeak) . For net cavity dispersion of + 0.129 ps2 peak power was evaluated as Ppeak ≈22.1 W, giving ~1.5-m-long nonlinear length with corresponding nonlinear phase shift Δφnl equal to Δφnl~LGeO2/SiO2 /Lnl~0.19π. As it was mentioned above (see Fig. 6), while the average output power increased, pulse duration increased almost with the same rate. According to this fact, we may imply that nonlinear phase shift preserves its amount with the pulse energy growth, keeping SPM influence at a constant level.
The evaluation of pulse dispersion length Ld in GeO2/SiO2 fiber according to Ld = T02/β2  gave us the value of Ld as long as 8.9 m. Thus, taking into account second-order dispersion ratio (~10) of included into the cavity fibers, we may assume that pulse length is varied insignificantly during cavity roundtrip. In fact, pulse slightly breathes only one time when transmitting from positive to negative GVD fibers. The ratio of dispersion length to nonlinear one (N2 ~5.9) shows that SPM slightly dominates over GVD during pulse propagation along the highly nonlinear GeO2/SiO2 fiber.
Passing through the segment of GeO2/SiO2-fiber, pulses then launched to EDF in which they were amplified as well as their side bands. As a result, shorter wavelength side bands became more pronounced in pulse spectra as it is demonstrated in Fig. 6(b).
The presence of spectral side bands as well as inversely proportional dependence of the pulse energy to the pulse length allow us to distinguish almost bandwidth-limited pulses, generated by positive dispersion cavity laser, from Gaussian ones and, of cause, conservative solitons and to consider them as inverse modified solitons.
In conclusion, we have demonstrated erbium doped fiber ring laser mode-locked by CMC films incorporating SWCNTs. We present rather careful analysis of pulse characteristics evolution through the intracavity dispersion variation. In the case of large anomalous dispersion laser generated soliton-like pulses with shortest duration of 675 fs and spectrum FWHM of 5 nm. When an intracavity GVD was close to zero, EDF-laser emitted highly chirped long pulses with up to 14 ps length and rectangular-shaped spectrum of FWHM close to 8.5 nm. In addition, we demonstrate and carefully describe for the first time to our knowledge generation of newly developed almost transform-limited picosecond pulses in the case of large positive net cavity dispersion, showing quietly inverse soliton behavior. We claim them to be referred to as inverse modified solitons.
The authors would like to acknowledge I.A. Bufetov and V.M. Mashinsky from the Fiber Optics Research Center of RAS for fiber providing, as well as B.L. Davydov from the Institute of Radio engineering and Electronics of RAS for technical support.
References and links
1. S. Y. Set, H. Yaguchi, Y. Tanaka, M. Jablonski, Y. Sakakibara, A. Rozhin, M. Tokumoto, H. Kataura, Y. Achiba, and K. Kikuchi, “Mode-locked fiber lasers based on a saturable absorber incorporating carbon nanotubes,” in OFC’03 paper PD44 (2003).
2. K. Kashiwagi, S. Yamashita, and S. Y. Set, “Optically manipulated deposition of carbon nanotubes onto optical fiber end,” Jpn. J. Appl. Phys. 46(40), L988–L990 (2007). [CrossRef]
3. Y.-W. Song, S. Yamashita, C. S. Goh, and S. Y. Set, “Carbon nanotube mode lockers with enhanced nonlinearity via evanescent field interaction in D-shaped fibers,” Opt. Lett. 32(2), 148–150 (2007). [CrossRef] [PubMed]
5. A. Martinez, K. Zhou, I. Bennion, and S. Yamashita, “In-fiber microchannel device filled with a carbon nanotube dispersion for passive mode-lock lasing,” Opt. Express 16(20), 15425–15430 (2008). [CrossRef] [PubMed]
6. J. H. Im, S. Y. Choi, F. Rotermund, and D.-I. Yeom, “All-fiber Er-doped dissipative soliton laser based on evanescent field interaction with carbon nanotube saturable absorber,” Opt. Express 18(21), 22141–22146 (2010). [CrossRef] [PubMed]
7. N. Nishizawa, Y. Nozaki, E. Itoga, H. Kataura, and Y. Sakakibara, “Dispersion-managed, high-power, Er-doped ultrashort-pulse fiber laser using carbon-nanotube polyimide film,” Opt. Express 19(22), 21874–21879 (2011). [CrossRef] [PubMed]
9. E. M. Dianov and V. M. Mashinsky, “Germania-based core optical fibers,” J. Lightwave Technol. 23(11), 3500–3508 (2005). [CrossRef]
10. C. Journet, W. K. Maser, P. Bernier, A. Loiseau, M. Lamy de la Chapelle, S. Lefrant, P. Deniard, R. Lee, and J. E. Fischer, “Large-scale production of single-walled carbon nanotubes by the electric-arc technique,” Nature 388(6644), 756–758 (1997). [CrossRef]
11. E. D. Obraztsova, J.-M. Bonard, V. L. Kuznetsov, V. I. Zaikovskii, S. M. Pimenov, A. S. Pozarov, S. V. Terekhov, V. I. Konov, A. N. Obraztsov, and A. P. Volkov, “Structural measurements for single-wall carbon nanotubes by Raman scattering technique,” Nanostructured Mater. 12(1-4), 567–572 (1999). [CrossRef]
12. A. I. Chernov, E. D. Obraztsova, and A. S. Lobach, “Optical properties of polymer films with embedded single-wall carbon nanotubes,” Phys. Status Solidi B 244(11), 4231–4235 (2007). [CrossRef]
13. J.-C. M. Diels, J. J. Fontaine, I. C. McMichael, and F. Simoni, “Control and measurement of ultrashort pulse shapes (in amplitude and phase) with femtosecond accuracy,” Appl. Opt. 24(9), 1270–1282 (1985). [CrossRef] [PubMed]
14. J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (San Diego, Academic Press, 1996).
15. L. E. Nelson, D. J. Jones, K. Tamura, H. A. Haus, and E. P. Ippen, “Ultrashort-pulse fiber ring lasers,” Appl. Phys. B 65(2), 277–294 (1997). [CrossRef]
16. G. P. Agrawal, Nonlinear Fiber Optics, 3d ed. (San Francisco Academic Press, 2001).