A saturable absorber (SA) is constructed using a fiber taper embedded in a carbon nanotube/polymer composite. A fiber taper is made by heating and pulling a small part of standard optical fiber. At the taper's waist light is guided by the glass-air interface, with an evanescent field protruding out of the taper. Carbon nanotubes mixed with an appropriate polymer host material are then wrapped around the fiber taper to interact with the evanescent field. Saturable absorption is possible due to the unique optical properties of the carbon nanotubes. The device can be used in mode-locked lasers where it initiates and stabilizes the pulses circulating around the laser cavity. The SA can be used in various laser cavities, and can enable different pulse evolutions such as solitons, self-similar pulses and dissipative solitons. Other applications include but are not limited to optical switching, pulse cleanup and pulse compression.