We conducted a detailed study of the stability of short, erbium-doped
fiber lasers fabricated with two UV-induced Bragg gratings written int
o the doped fiber. We find that the relative intensity noise of single
-longitudinal-mode fiber grating lasers is approximately 3 orders of m
agnitude lower than that of a single-frequency 1.523-mu m helium-neon
laser. The frequency noise spectrum contains few resonances, none of w
hich exceeds 0.6 kHz/Hz(1/2) rms; the integrated rms frequency noise f
rom 50 Hz to 63 kHz is 36 kHz. We also demonstrate a simple method for
monitoring the laser power and number of oscillating modes during las
er fabrication.