Epitaxy (MBE), and an additional substrate removal process is needed in some cases; high-energy heavy-ion implantation is required to introduce defect sites in order to reduce the device recovery time (typically a few nanoseconds) to the picosecond regime required for short-pulse laser mode-locking applications; since the SESAM is a reflective device, its use is restricted to only certain types of linear cavity topologies. Other laser cavity topologies such as the ring-cavity design, which requires a transmission-mode device, which offers advantages such as doubling the repetition rate for a given cavity length, and which is less sensitive to reflection-induced instability with the use of optical isolators, is not possible unless an optical circulator is employed, which increases cavity loss and laser complexity; SESAMs also suffer from a low optical damage threshold. But there had been no alternative saturable absorbing materials to compete with SESAMs for the passive mode-locking of fiber lasers. Recently, by the virtue of the saturable absorption properties in single wall carbon nanotubes (SWCNTs) in the near-infrared region with ultrafast saturation recovery times of ~1 picosecond, researchers have successfully produced a new type of effective saturable absorber quite different from SESAMs in structure and fabrication, and has, in fact, led to the demonstration of pico- or subpicosecond erbium-doped fiber (EDF) lasers. In these lasers, solid SWCNT saturable absorbers have been formed by direct deposition of SWCNT films onto flat glass substrates, mirror substrates, or end facets of optical fibers. However, the non-uniform chiral properties of SWNTs present inherent problems for precise control of the properties of the saturable absorber. Furthermore, the presence of bundled and entangled SWNTs, catalyst particles, and the formation of bubbles cause high nonsaturable losses in the cavity, despite the fact that the polymer host can circumvent some of these problems to some extent and afford ease of device integration. In addition, under large energy ultrashort pulses multi-photon effect induced oxidation occurs, which degrades the long term stability of the absorber. Graphene is a single two-dimensional (2D) atomic layer of carbon atom arranged in a hexagonal lattice. Although as an isolated film it is a zero bandgap semiconductor, it is found that like the SWCNTs, graphene also possesses saturable absorption. In particular, as it has no bandgap, its saturable absorption is wavelength independent. It is potentially possible to use graphene or graphene-polymer composite to make a wideband saturable absorber for laser mode locking. Furthermore, comparing with