Response of Interferometric Detectors to Scalar Gravitational Waves

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We rigorously analyze the frequency response functions and antenna sensitivity patterns of three types of interferometric detectors to scalar mode of gravitational waves which is predicted to exist in the scalar-tensor theory of gravity. By a straightforward treatment, we show that the antenna sensitivity pattern of the simple Michelson interferometric detector depends strongly on the wave length λ SGW of the scalar mode of gravitational waves if λ SGW is comparable to the arm length of the interferometric detector. For the Delay-Line and Fabry-Perot interferometric detectors with arm length much shorter than λ SGW, however, the antenna sensitivity patterns depend weakly on λ SGW even though λ SGW is comparable to the effective path length of those interferometers. This agrees with the result obtained by Maggiore and Nicolis.