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In this paper, we report the evidence for the possibility of achieving complex signal processing functionalities such as multiplexing/demultiplexing at high frequencies using phononic crystal (PnC) slabs. It is shown that such functionalities can be obtained by appropriate cross-coupling of PnC resonators and waveguides. PnC waveguides and waveguide-based resonators are realized and cross-coupled through two different methods of mechanical coupling (i.e., direct coupling and side coupling). Waveguide-based PnC resonators are employed because of their high-Q, compactness, large spurious-free spectral ranges, and the possibility of better control over coupling to PnC waveguides. It is shown that by modifying the defects in the formation of the resonators, the frequency of the resonance can be tuned

On chip complex signal processing devices using coupled phononic crystal slab resonators and waveguides