title: Principles of calculating the dynamical response of misaligned complex resonant optical interferometers
abstract: In the long-baseline laser interferometers for measuring gravitational waves 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 resonators with light storage times approaching 100 m. We present a basic formalism to calculate the frequency dependence of periodic variations in angular alignment and longitudinal displacement of the resonator mirrors. The electromagnetic field is decomposed into a superposition of higher-order spatial modes, Fourier frequency components, and polarization states. Alignment fluctuations and length variations of free-space propagation are represented by matrix operators that act on the multicomponent state vectors of the field.
authors.affiliation: LIGO Hanford Observatory, Richland, Washington 99352, USA. sigg_d@ligo.mit.edu
authors.initials: D
authors.lastname: Sigg
authors.initials: N
authors.lastname: Mavalvala