Patch-antenna metamaterial has already proven to be a successful way to improve the performances of quantum detectors up to room temperature and to simplify the light-matter coupling geometry required to satisfy the constraints imposed by inter-sub-band selection rules. However, this structure can be further optimised in order to maximise the absorption of the incoming light and minimise the losses of photons. The optimization strategy presented in this work focuses on the study of the empty cavities, that is the double metal resonators without active region enclosed inside. It aims to determine the optimal geometrical parameters to reach the critical coupling regime, investigating how the array periodicity and the cavity thickness affect the response of the system to the external radiation.