Optical cavity diffraction loss

The experimental setup is shown in Fig. 1.18. The laser pulses are coupled into the resonator by carefully designed mode-matching optics, which ensure that only the TEMoo modes of the cavity are excited. Diffraction losses are minimized by spherical mirrors, which also form the end windows of the absorption cell. If the absorbing species are in a molecular beam inside the cavity, the mirrors form the windows of the vacuum chamber. For a sufficiently short input pulse (Tp < 7r), the output consists of a sequence of pulses with a time separation Tr and with exponentially decreasing intensities, which are detected with a boxcar integrator. For longer pulses (Tp > 7r), these pulses overlap in time and one observes a quasi-continuous exponential decay of the transmitted intensity. Instead of input pulses, the resonator can also be illuminated with cw radiation, which is suddenly switched off at f = 0. 

Fig.12.3. Diffraction effects in optical cavities fractional power loss per transit as a function of the Fresnel number, F.., plane mirror cavity with circular apertures ., confocal spherical mirror...

The effects of non-parallelism of the mirrors in a nominally plane-parallel cavity have been studied by Fox and Li (1963). The diffraction loss is found to increase rapidly for only slight deviations from perfect alignment or from perfect optical quality of the windows and mirrors. 

We have seen in preceding sections that the diffraction losses in optical cavities can be reduced to negligible values by careful design. However, all practical resonators have finite losses associated with the output transmission at the mirrors and so the Q of the cavity, defined by... 

Assume a short laser pulse with input power Pq is sent through an optical resonator with two highly reflecting mirrors (reflectivities R = R2 = R, and transmission T = 1 — R — A 1, where A includes all losses of the cavity from absorption, scattering, and diffraction, except those losses introduced by the absorbing sample). The pulse will be reflected back and forth between the mirrors (Fig. 6.12), while for each round-trip a small fraction will be transmitted through the end mirror and reach the detector. The transmitted power of the first output pulse is... 

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