We give an analytical demonstration of the possibility to realize a simple magnonic demultiplexer based on induced transparency resonances. The demultiplexer consists on an Y-shaped waveguide with an input line and two output lines. Each line contains two grafted stubs at a given position far from the input line. We derive in closed form the analytical expressions for selective transfer of a single propagating mode through one line keeping the other line unaffected. This is performed through magnonic induced transparency resonances (MIT) characterized by a resonance squeezed between two transmission zeros. The existence of a complete transmission beside a zero transmission, enables to select a given frequency on one output line, by canceling the transmission on the second line as well as the reflection in the input line. Also, we show that despite the existence of a bifurcation of the input line on two output lines, the transmission through each line can be written following a Fano line shape. In addition, in order to understand better the scattering properties of the filtered resonances, we give the analytical expressions of Fano parameter q and quality factor Q of the MIT resonance in each line. The spatial distribution of the spin waves associated to different MIT resonances is performed through an analysis of the magnetization of these modes. Also, the effect of attenuation on the transmission spectra and the quality of demultiplexing is also discussed. The theoretical results are performed using the Green’s function approach which enables to deduce in closed form, the transmission and reflection coefficients as well as the densities of states.
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