Pulse-Width Saturation and Kelly-Sideband Shift in a Graphene-Nanosheet Mode-Locked Fiber Laser with Weak Negative Dispersion Chun-Yu Yang, Yung-Hsiang Lin, Yu-Chieh Chi, Chung-Lun Wu, Jui-Yung Lo, and Gong-Ru Lin * Graduate Institute of Photonics and Optoelectronics, Department of Electrical Engineering, National Taiwan University, Number 1, Section 4, Roosevelt Road, Taipei 10617, Taiwan, Republic of China (Received 8 December 2014; revised manuscript received 18 March 2015; published 24 April 2015) The optimized soliton mode locking of the erbium-doped fiber laser (EDFL) and its pulse-shortening dynamic with the graphene nanosheet is demonstrated by precisely detuning the weakly negative group- delay dispersion (GDD) and maintaining strong self-phase-modulation (SPM), to obtain the shortest pulse width of 449 fs with a spectral linewidth of 6.02 nm. The pulse evolution with the mode-locking mechanism changing from the self-amplitude-modulation of the saturable absorber, to the soliton compression caused by the GDD and SPM is experimentally and numerically investigated in detail. Under high pumping powers, the enlarged up-chirp inside the EDFL cavity can induce a significant Kelly- sideband shift of up to 0.5 nm. The passively-mode-locked EDFL pulse width is controllable by detuning the GDD and SPM parameters, so that the pulse width can be compressed from 642 to 449 fs while reducing the negative GDD from -0.354 to -0.154 ps 2 . The compression ratio can be also improved by strengthening the SPM at this stage. DOI: 10.1103/PhysRevApplied.3.044016 I. INTRODUCTION Passive mode locking of lasers via saturable absorbers (SAs) is a general mechanism to implement the ultrafast laser system. Recently, carbon-based materials have shown their great potential for being promising saturable absorbers for passively-mode-locked fiber lasers, such as single- walled carbon nanotubes (SWCNTs) [1–7], graphene [8–10], graphite [11,12], and charcoal nanoparticles [13]. At the initial stage, the SWCNT-incorporated saturable absorber has emerged with the advantages of an ultrafast relaxation time of <1 ps, a high optical damage threshold, a large optical nonlinearity, and polarization insensitivity [2–4]. However, the direct-band-gap SWCNT exhibits discrete working wavelengths corresponding to its diam- eter, which elucidates that the SWCNT does not always absorb light when the incoming optical wavelength is mismatched with any of the discrete band gaps. It causes linear loss only in the mismatched wavelength region. That is, the SWCNT with a unitary diameter hardly performs the property of broadband operation in passively-mode-locked fiber lasers, and the broadband absorption relies strictly on collecting the dispersed SWCNTs with different diameters in a single saturable absorber [4]. Since the investigation of mechanically exfoliated atomic-layer graphene by Novoselov et al. in 2004 [14], versatile synthesis methodologies for graphene saturable absorbers have also emerged [15–17]. The advantages of graphene, including broadband absorption, ultrafast relax- ation, and low saturation intensity, make it a nice candidate of the low-threshold and wideband saturable absorber [15–17]. Hasan et al. demonstrated the first graphene mode-locked laser by synthesizing a polymer composite containing the exfoliated single- and few-layer graphene as the saturable absorber [18]. In addition, the atomic-layer graphene-based saturable absorber by using chemical vapor deposition (CVD) was further demonstrated by Bao et al. in 2009 [8]. The CVD-grown high-quality and large-area graphene can easily vary its layer number to provide an excellent saturable-absorption property for obtaining sub-ps pulse width from the passively-mode-locked erbium-doped fiber laser (EDFL) [19,20]. However, the CVD-grown graphene requires a rigorously controlled gaseous recipe, host matrix, and growth environment during synthesis. Various techniques are proposed for efficient synthesis of graphene materials, such as mechanical tritu- ration [10,21], graphene-oxide reduction [22], and solution- based electrochemical exfoliation [23], etc. Among these demonstrations, the chemical solution process is considered to be the most economical way to quantitatively fabricate single- or few-layer nanoscale graphene materials in an aqueous environment, while maintaining the good quality for excellent passive mode locking. According to the reports, the graphene saturable absorber possesses broadband absorption due to its zero-band-gap property, which has been experimentally characterized in passively-mode-locked or Q-switched lasers with wave- lengths ranging from 800 to 3000 nm [24–29]. In passively- mode-locked EDFL, the graphene saturable absorber can * Corresponding author. grlin@ntu.edu.tw PHYSICAL REVIEW APPLIED 3, 044016 (2015) 2331-7019=15=3(4)=044016(9) 044016-1 © 2015 American Physical Society