Effects of static and dynamic higher-order optical modes in balanced homodyne readout for future gravitational waves detectors

With the recent detection of gravitational waves (GWs), marking the start of the new field of GW astronomy, the push for building more sensitive laser-interferometric gravitational wave detectors (GWDs) has never been stronger. Balanced homodyne detection (BHD) allows for a quantum-noise (QN) limited readout of arbitrary light field quadratures, and has therefore been suggested as a vital building block for upgrades to Advanced LIGO and third-generation observatories. In terms of the practical implementation of BHD, we develop a full framework for analyzing the static optical high-order modes (HOMs) occurring in the BHD paths related to the misalignment or mode matching at the input and output ports of the laser interferometer. We find the effects of HOMs on the quantum-noise limited sensitivity is independent of the actual interferometer configuration; e.g. Michelson and Sagnac interferometers are affected in the same way. We show that misalignment of the output ports of the interferometer (output misalignment) only affects the high-frequency part of the quantum-noise limited sensitivity (detection noise). However, at low frequencies, HOMs reduce the interferometer response and the radiation pressure noise (back-action noise) by the same amount and hence the quantum-noise limited sensitivity is not negatively affected in that frequency range. We show that the misalignment of the laser into the interferometer (input misalignment) produces the same effect as output misalignment and additionally decreases the power inside the interferometer. We also analyze dynamic HOM effects, such as beam jitter created by the suspended mirrors of the BHD. Our analyses can be directly applied to any BHD implementation in a future GWD. Moreover, we apply our analytical techniques to the example of the speed meter proof-of-concept experiment under construction in Glasgow. We find that for our experimental parameters, the performance of our seismic isolation system in the BHD paths is compatible with the design sensitivity of the experiment.