  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 context, linear three-mirror cavities
could be of interest because of the additional control that they can provide.
  In this paper, 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-peak" as a
function of cavity parameters, which is one of the key features of this system.
We show that the double-peak shape is almost freely adjustable, either in terms
of spacing between maxima, their relative height and their intrinsic width.
This is made possible by changing the mirrors' reflectivity coefficients and
their spacing. However, the amount of achievable realistic configurations is
limited by the stability conditions of the cavity. In particular, if the middle
mirror is not close enough to the center of the cavity, it could be difficult
to obtain a stable three-mirror cavity. Different geometries have been studied
to obtain a stable cavity system.
