Parametric resonance in a vibrating cavity

We present, the analysis of parametric resonance based on the constniction of classical optical paths. in onedimensional cavities The recursive formulas for field cnergy are given. We separate the mechanism of particle production from the resonance amplification of radiation. The photoproduction is a purely quantum effect, dcscribed hy anomalies in recursive formulas. The resonance enhancement is rather a classical picture of fociising and amplifying beams of photons due to Doppler effect. Thc special role of SL(2, R) symmetry is indicat,ed.