The Dynamics of a Field in a Cavity with a Slowly Oscillating Metal Mirror

Resumo

We have examined analytically the behavior of an electromagnetic field in a cavity of one of two metal mirrors that is stationary, while the other mirror oscillates in the vicinity of its equilibrium position. The case in which the period of the mirror oscillations substantially exceeds the characteristic roundtrip time of the electromagnetic radiation in the cavity has been considered. To solve the problem, we have applied the method of two time scales. The method makes it possible to solve the problem by using the expansion with respect to a small parameter, for which the ratio of the cavity roundtrip time to the mirror-oscillation period is used. The solution to the problem in the zeroth-order approximation with respect to the small parameter has been obtained and examined. This solution has been shown to be correct up to the mirror-oscillation amplitude being on the order of the average cavity length. We have showed that this scheme can be used to gain and generate electromagnetic radiation. We have compared our results obtained for the oscillating mirror with the results of an exact solution of the problem when the mirror moves uniformly and rectilinearly. We have showed that, in these two cases, a change in the total field energy in the cavity is inversely proportional to the current value of the cavity length.