Effect of instrumental response time in exponential-decay-based cavity ring-down techniques for high reflectivity measurement

Exponential-decay based cavity ring-down (CRD) techniques, such as the pulsed-CRD and continuous-wave (cw) CRD employing a fast switch to shut down the laser beam, are widely used for high reflectivity measurement. In this paper the influence of the response time of the experimental apparatus on the high reflectivity measurement is investigated theoretically and experimentally. Theoretical expressions taking into account the instrumental response time are given for both pulsed- and cw-CRD techniques, respectively. By establishing a simple cw-CRD setup employing detectors with different response time, the influence of the instrumental response time on the high reflectivity measurement is experimentally investigated. By applying a multi-parameter estimation technique to determine simultaneously the cavity decay time and the overall response time of the experimental apparatus via fitting the experimental CRD signal to the corresponding theoretical model, the influence of a long instrumental response time on the reflectivity determination is eliminated. The reflectivities of the cavity mirror measured with detectors with different rise time are in excellent agreement. On the other hand, the error of high reflectivity measurement increases with the increasing rise/fall time of the apparatus in cases that the CRD signals obtained by detectors with relatively slow rise time are simply treated with a single exponential decay fitting procedure.