Principles of calculating the dynamical response of misaligned complex resonant optical interferometers

In the long-baseline laser interferometers for measuring gravitational wave s that are now under construction, understanding the dynamical response to small distortions such as angular alignment fluctuations presents a unique challenge. These interferometers comprise multiple coupled optical resonato rs with light storage times approaching 100 m. We present a basic formalism to calculate the frequency dependence of periodic variations in angular al ignment and longitudinal displacement of the resonator mirrors. The electro magnetic held is decomposed into a superposition of higher-order spatial mo des, Fourier frequency components, and polarization states. Alignment fluct uations and length variations of free-space propagation are represented by matrix operators that act on the multicomponent state vectors of the field. (C) 2000 Optical Society of America [S0740-3232(00)01509-X] OCIS codes: 12 0.3180, 120.2230, 030.4070, 220.1140.