Digital synthesis of multistage etalons based upon unequal cavity lengths

Fabry–Perot fiber etalons (FPEs) built from three or more reflectors are attractive for a variety of applications, including communication and sensing. In order to realize a desired transmission profile, usually multistage FPEs are designed with equal cavity lengths followed by a determination of the required reflectivities. As seen in previous works, however, fabricated reflectors may slightly differ from the designs, leading to a departure from the desired transmission profile of the FPE. Here, we show a novel digital synthesis of multistage etalons with off-the-shelf reflectors and unequal lengths of involved cavities. We find that, in contrast to equal cavity lengths, unequal lengths provide more poles in the z domain and hence more flexibility to achieve a desired multicavity FPE transmission response. For given reflectivities and by determining correct unequal lengths of a multicavity FPE with our synthesis technique, we demonstrate two design examples involving free spectral range enhancement and passband shaping. This work is generalizable to ring resonators and mirror- and fiber-Bragg-grating-based cavities, enabling the design and optimization of cavity systems for a wide range of applications, including lasers, sensors, and filters.