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Received December 6, 1994 We have developed a new ring-down technique that does not require a shutter to turn a probe laser on and off. With a rapid cavity scan we can measure a simple exponential cavity decay from which a cavity finesse can be found. When the cavity is scanned slowly, the cavity decay exhibits an amplitude modulation, and an analytic expression is derived for this modulation. With this new technique we measured the ultraslow relative velocity of the mirrors (of the order of micrometers per second) as well as the linewidth (,100 kHz) of the probe laser. The recent development of an ultra-high-Q optical resonator has made possible many new exciting ex- periments, such as the experimental realization of the one-atom laser1 and normal mode splitting for a weakly excited absorbing atom in a cavity.2 In designing such experiments it is important to know the resonator finesse exactly. One way to measure the finesse is to probe the linewidth of the resonator transmission. Such a measurement is easily done if the resonator linewidth is much broader than the linewidth of the probe laser; if not, a direct measure- ment of the cavity decay is preferred. The cavity decay can be measured by use of the de- cay or ring-down of the field inside the resonator. In the standard ring-down scheme an electromagnetic- field pulse is stored in the empty cavity, and the subsequent decay of the field is monitored in time. The duration of this excitation pulse should be much shorter than the cavity decay time, so that the ex- citation can be considered to be a delta function. One prepares the excitation field from a cw laser field by turning a shutter, which is often an acousto- optic modulator, on and off. Initially the shutter is opened, and the cavity is permitted to drift slowly toward resonance. At resonance a field builds up quickly in the cavity. When the cavity transmission signal reaches a certain threshold, the acousto-optic modulator is switched off, and the subsequent field decay is measured as a function of time. This tech- nique was used in Ref. 3 to measure a finesse as high as 2 3 106 at 850 nm. In this Letter we report a much simpler but more powerful ring-down technique that requires neither a shutter nor a trigger circuit to turn the probe laser on and off at the right moment. Instead, we point out that, if the cavity is quickly scanned, it is resonant with the probe for only a brief moment. This short resonance time effectively simulates a delta-function excitation. By controlling the scan speed we can ad- just how much field can build up in the cavity before it tunes out of resonance with the laser field. The cavity is scanned repeatedly while the field decay is measured by a photodiode and displayed on an oscil- loscope in real time. The hallmark of this method is that the cavity decay curve shows an amplitude modulation that depends on the scan speed. Note that the cavity con- figuration in this study (two mirrors and a piezoelec- tric transducer between them) has been widely used in spectrum analyzers for more than a decade. It may be that the amplitude modulation in the cav- ity transmission may have been accidentally observed previously but misinterpreted as rf noise or some in- terference effect, as it was initially so even in our laboratory. Until now the cause for the amplitude modulation has not been well understood. Here we algebraically derive the period of the modulation to be roughly given by

Cavity ring-down technique and its application to the measurement of ultraslow velocities