Simulating the performance of michelson-and sagnac-based laser interferometric gravitational wave detectors in the presence of mirror tilt and curvature errors

We model the behaviour of single-bounce delay-line dual recycled Sagnac-based interferometer and compare its performance with that of single-bounce Michelson-based system. Geometric imperfections such as mirror tilt and curvature mismatch can strongly influence the performance of the Sagnac device due to the inherently smaller free spectral range (FSR) and higher order mode spacing. This leads to a greater number of higher order modes near, or within the signal band in the signal recycling cavity of the instrument. The important consequence of that is, in general, a greater sensitivity of a Sagnac system to nonideal parameters and imperfections of various kind affecting the performance of a real interferometer. A number of optical configurations have also been examined numerically to determine the best possible optical arrangement, in the presence of such geometric imperfections. We show that there is an optimum choice for the nominal radius of curvature of the end mirrors which results from balancing the loss due to mirror tilt against that due to curvature mismatch.