An optical fiber amplifier having improved gain and reduced noise, and an optical amplifier which restrains an unnecessary polarization component in the signal output light, maintains polarization of a signal light and performs optical amplification in which a polarizer is connected between a first optical fiber and a second optical fiber. The facility reads an arbitrary number of the tags contained by the series of messages. The first machine can transfer the constraint descriptor to a second machine that is capable of using the constraint descriptor to access documents that satisfy the set of constraints. Once the grinding wheel is positioned on the shaft, a nut is tightened onto the threaded bottom portion of the shaft to tighten the wheel against the shoulder.