Tunable Band-Pass Filters with Long Periodicity Using Cascaded Mach-Zehnder Interferometer Networks

This paper introduces a theoretical framework for designing and tuning band-pass filters with a highly extended periodicity using cascaded Mach-Zehnder Interferometer (MZI) networks. We show that a filter centered at frequency f0 with a bandwidth of FSR0 and an arbitrarily large free spectral range (FSR) can be built with a minimal number of MZIs by using stages with FSRs that are prime multiples of FSR0. Due to the inherent multi-spectral transparency of materials, this design ensures that only a single narrow passband is transparent. We derive the total power transmission for such a cascaded system and show that the filter’s overall periodicity is the product of the individual MZI transfer functions. Furthermore, we deduce the linear relationship between the applied differential voltage and the resulting frequency shift, offering a precise method for continuous spectral tuning without altering the filter’s intrinsic FSR. We propose a new, simplified electronic circuit that uses a single input current and series impedances for continuous resonant peak tuning and analyze the feasibility of such a design. This circuit improves practical implementation and allows for compensation of fabrication errors. This work offers crucial analytical tools and insights for developing advanced reconfigurable photonic integrated filters, essential for future optical communication and sensing systems.