Resonant behavior and stability of a linear three-mirror cavity

The implementation of Fabry–Perot cavities in gravitational-wave detectors has been pivotal to improving their sensitivity, allowing the observation of an increasing number of cosmological events with higher signal-to-noise ratio. Notably, Fabry–Perot cavities play a key role in the frequency-dependent squeezing technique, which provides a reduction of quantum noise over the whole observation frequency spectrum. In this paper, we first present how the adaptability of resonance properties of linear three-mirror cavities, and the real-time control we could have on it, would be interesting for frequency-dependant squeezing in future detectors, especially for Einstein Telescope project. In this view, we develop a complete model to describe the stability behavior and the properties of transmitted and reflected fields of a linear three-mirror cavity aiming to be used for design purposes. In particular, simulations are carried out to show the evolution of the characteristic double resonance peak they can show-off, which is one of the key features of this system, as a function of cavity parameters. We show that the double-peak shape is almost freely adjustable, either in terms of spacing between maxima, their relative amplitude and intrinsic width. This is made possible by changing the mirrors’ reflectivity coefficients and the sub-cavities microscopic/macroscopic lengths. However, the amount of achievable realistic configurations is limited by the stability conditions of the cavity. In particular, if the two sub-cavities do not have the same macroscopic length, it could be difficult to obtain a stable three-mirror cavity. Different geometries have been studied to obtain a stable system.