文摘
Optical filters are one of the essential optical elements in telecommunication systems, signal processing devices, and spectrometers. The design principle of conventional filters is based on the classical theory of optics; for example, the transfer-matrix method is applied in Fabry–Pérot cavities. Because of their large thickness, such filters follow the multiplication rule of probability: if light passes through the two filters in turn, the final transmission spectrum is the product of the two individual spectra. This property makes it difficult to design a new filter having multipass-bands because such a filter cannot be constructed from a combination of the existing filters having single pass-band. Here we propose an alternative type of band-pass filter that operates under the addition rule of probability, wherein the final transmission spectrum is simply the sum of the individual spectra. We show that the strong plasmonic coupling between the slits and heterostructured epsilon-near-zero (ENZ) films gives rise to the addition rule. Therefore, a filter with a desired transmission spectrum can be easily configured from a combination of well-known filters. We demonstrate that the narrow bandwidth of the ENZ materials and plasmonic distant coupling between the slits and ENZ film contribute to the mutually exclusive condition for the addition rule. Furthermore, through developing an LC circuit model for the band-pass filters, we succeed in predicting the resonance positions in the transmission spectra. We believe that our novel findings can pave the way toward overcoming the current limitations of filter technologies by significantly reducing the time required to design and manufacture optical filters.