Optical response of a misaligned and suspended Fabry-Perot cavity

The response to a probe laser beam of a suspended, misaligned, and detuned optical cavity is examined. A five degree of freedom dynamical model of the fluctuations of the longitudinal and transverse mirror coordinates is presented. Classical and quantum mechanical effects of radiation pressure are studied with the help of the optical stiffness coefficients and the signals provided by an FM sideband technique and a quadrant detector, for generic values of the product $\ensuremath{\varpi}\ensuremath{\tau}$ of the fluctuation frequency times the cavity round trip. A simplified version is presented for the case of small misalignments. Mechanical stability, mirror position entanglement, and ponderomotive squeezing are accommodated in this model. Numerical plots refer to cavities under test at the so-called Pisa LF facility. The presented model can describe radiation pressure effects recently appeared in the VIRGO antenna and give a framework for designing the next generation of gravitational wave antennas where such effects would be of critical relevance.