Multiband filter at adjustable free spectral range by convolution of transfer functions according to the Vernier effect

In this study, the authors present the design, fabrication and characterisation of a filter multiband tunable consequence of a convolution product of two transfer functions. The device consists of two cavities arranged in tandem and realised in integrated optics. The second cavity is 10% shorter than the first one. These maximas of transmission are slightly moved away than those of the first one. The choice of the lengths of both close but uneven cavities put in the profit a Vernier effect between the two spectral characteristics the purpose of which is to increase the free spectral range (FSR), and therefore the tuning range. The filter design is discussed and its performance is introduced using measurements and simulations. Consequently, the process is validated by the design of a dual-band filter with the resulting FSR multiplied by a factor of six as compared with that of a single Fabry-Perot. These results were verified theoretically and experimentally.