We demonstrate a mode-locked erbium-doped fiber laser with a 1-microm InGaAs saturable absorber that produces 84-ps, 1-nJ transform-limited pulses. Measurements of the InGaAs multiple quantum well revealed a slow saturable absorber that is useful for passive mode locking. Optical fiber was added to extend the cavity and vary the repetition rate from 51 kHz to 5.4 MHz. The narrow spectral width of the laser output (<0.04 nm) permits amplification to 0.2 microJ/pulse with minimal pulse broadening. Pulse energies as large as 1.7 microJ can be achieved with pulse widths of <330 ps. Average powers of 0.5 W at megahertz repetition rates are demonstrated.