Pendular Fabry-Pérot cavities as a paradigm for the dynamics of systems with delays

Abstract

We consider the dynamics of the suspended mirror of a pendular Fabry-Pérot cavity, taking into account the delays due to the finiteness of the velocity of light. We obtain an approximate equation for the asymptotic motion which allows a simple analysis of the behavior of the mirror and in particular of the instabilities that cavities with a large enough finesse or length can develop. The results, which are of relevance in cases of actual interest, can in principle be tested using presently available cavities. A pendular Fabry-Pérot cavity then appears as a perhaps ideal example of a delay system where theory, numerical, and laboratory experiments can be compared.