Two-membrane etalon

Optomechanics with semi-transparent membrane multioscillators in a high-finesse cavity is an established solution for designing the dispersive interaction, and reaching many achievements, such as the study of nonlinear dynamics, heat transfer, and so on. The multioscillators are dielectric slabs, usually with low reflectivity, constituting an etalon. Here we propose the theoretical and experimental investigation of a low-finesse optical cavity formed by two (nominally identical) parallel semi-transparent membranes. The experiment consists in laser-driving the cavity, detecting interferometrically the field reflected by the etalon, and measuring the intensity of the transmitted field, for different distances within the two membranes. A complete characterization of the membrane sandwich is provided. Moreover, we develop an analytical model to describe the fields, which reproduces all the experimental results, under specific approximations. As expected, the model reproduces the known results when high-reflectivity, and/or fixed mirrors conditions are restored. This work paves the way for a complete and analytical model to describe multi-oscillators "membrane-in-the-middle"optomechanics.