SCATTERING MATRIX ANALYSIS OF 4-CAVITY INTERFEROMETERS FOR GRAVITATIONAL-WAVE DETECTION

Analysis of the most general laser interferometer gravitational detect ors (LIGDs) are given in terms of the scattering parameters of the ind ividual components. Each arm of the interferometer may contain a numbe r of lossy, partially reflecting, reciprocal or non-reciprocal compone nts or layers, forming a complex cavity. Similarly the beamsplitter ca n introduce a partial scattering of the incident light from any surfac e to any arm of the interferometer. The method is applied to the previ ously analysed dual and compound recycling interferometers, as illustr ative examples. In the previous works it is generally assumed that the so-called power and signal recycling circuits are decoupled. This is only true if, in the absence of the gravitational field, the light fro m the two main arms of the interferometer entering the detector arm is totally cancelled. In the present analysis this assumption need not b e made. The effect of any deviation from the null condition can hence be easily studied. Birefringence is not considered in this paper, but the analysis can easily be extended to include the birefringence in th e beamsplitter or polarization effects of other components.