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.
© 2000 Optical Society of America
(030.4070) Coherence and statistical optics : Modes
(120.2230) Instrumentation, measurement, and metrology : Fabry-Perot
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(220.1140) Optical design and fabrication : Alignment
Daniel Sigg and Nergis Mavalvala, "Principles of calculating the dynamical response of misaligned complex resonant optical interferometers," J. Opt. Soc. Am. A 17, 1642-1649 (2000)