Magnonic analogue of electromagnetic induced transparency in detuned magnetic circuit

A simple magnetic device consisting of two dangling side stubs grafted at the same site along a waveguide is designed to obtain a magnonic analogue of electromagnetic induced transparency (EIT) resonance. By detuning the lengths of the two stubs, a resonance can be squeezed between two transmission zeros induced by the two resonators. We give detailed analytical expressions for the transmission and reflection coefficients of the whole structure as a function of those of the individual resonators taken alone. The destructive interference between the waves in the two resonators may give rise to a sharp resonance peak with high Q factor in the transmission. We give an explicit expression of the transmission coefficient around the EIT resonance following a Fano-like form. In particular, we give an explicit expression of the position, width and Fano parameter of the resonances as a function of the detuning between the stubs. The analytical results are obtained by means of the Green's function method.