In Chapters 8-10 we considered primarily the two-mirror, standing-wave laser. The analysis was written to cover also the theoretically simpler ring (or three mirror) laser depicted in Fig. 8-2, which is constructed to support only a single, clockwise running wave characterized by the normal-mode function Un(z) = exp(iA^z) of Eq. (8.7). The relative simplicity of this unidirectional ring laser stems from the fact that the two-mirror field is com posed of two running waves traveling in opposite directions, as given by Eq. (10.25). Hence, for example, the standing-wave gas laser may exhibit a dip in intensity versus detuning (Lamb dip), as discussed in Sec. 10-1; the uni directional case does not, for only one velocity ensemble contributes gain regardless of tuning. Similarly, the two-mirror case can be affected by spatial hole burning by the standing-wave intensity (Sec. 8-2); the unidirectional laser cannot. The simple operation of the latter is, however, a special case of operation more general than that of the two-mirror, standing-wave laser, for without nonreciprocal losses or suitable mode inhibitory effects the ring laser supports running waves in both directions, clockwise and counterclockwise. Unlike the standing-wave field of Eq. (10.25), the oppositely directed running waves in this bidirectional ring laser may have unrelated amplitudes, phases, and frequencies. In particular, a clockwise rotation of the laser about an axis perpendicular to the plane of the mirrors Doppler-downshifts the frequency of the clockwise running wave and upshifts the counterclockwise running wave. The beat note between the two waves provides a measure of the rotation rate, leading to the use of the ring laser as a gyroscope. A representation equivalent to the independent running waves is that with cos Knz mode functions in addition to the sin KnZ functions of the two-mirror case.