Influence of EOM sideband modulation noise on space-borne gravitational wave detection

Clock noise is one of the dominant noises in the space -borne gravitational wave (GW) detection. To suppress this noise, the clock noise -calibrated time-delay-interferometry (TDI) technique is proposed. In this technique, an inter -spacecraft clock tone transfer chain is necessary to obtain the comparison information of the clock noises in two spacecraft, during which an electro-optic-modulator (EOM) is critical and used to modulate the clock noise to the laser phase. Since the EOM sideband modulation process introduces the extra modulation noise, it may limit the experimental demonstration of the suppression effect of the clock noise, and further affect the space -borne GW detection. To solve this problem, it is significant to put forward the modulation noise requirement and test whether the experimental components meet or not. In this work, based on the typical Michelson TDI algorithm and the fundamental noise requirement of GW detectors, the analytic expression of the modulation noise requirement is strictly derived, relaxing the specification compared to the commonly used rough assessments. Furthermore, a method is provided to experimentally test EOM modulation noise, and a commercial EOM (iXblue-NIR-10 GHz) is tested. The experimental results show that it can meet the requirement of the typical GW detection mission LISA in the whole scientific frequency bandwidth by taking the optimal combination of the data streams.