In this research, we give an analytical demonstration of the possibility to realize a simple phononic demultiplexer based on Fano and AIT resonances for application of wave routing. Our proposed demultiplexer contains a shaped waveguides with an input line and three output lines, each output line contains two resonators grafted at two positions far from the input line. We derive the analytical expressions for a selective transfer of a single propagation mode through one output line by keeping the other output lines unaffected. The AIT resonance; induced by two resonators inserted in the same position or by the segment that separates the two resonators, is characterized by a maximum transmission peak wedged between two transmission zeros. On the other hand, the existence of a maximum transmission peak beside a transmission zero enables to select a given frequency in the first output line, by canceling the transmission in the second and third output lines and the reflection in the input line, this resonance type is called Fano resonance in which the resonators lengths di2 and di4 must have the same values. These resonances are obtained by detuning the lengths of the two resonators. The position and the quality factor of these two resonances (Fano and AIT) are extremely sensitive to the geometrical parameters of the segments and resonators which should be chosen appropriately. Our results are found out using the Green function method. We demonstrate that our proposed three-channel demultiplexer can be used to design a multifunctional device that functions as a wave routing splitter for different frequencies coming from the input line in order to separate each frequency at each output line. This system is capable to realize various wave guiding characteristics with perfect transmissions and good quality factors of resonant modes.
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