We consider, in the frame of long-wavelength Heisenberg model, the effect of a pinning field on the spin wave band gaps and transmission spectra of a simple magnonic device. This simple device is composed of an infinite one dimensional (1D) monomode waveguide (the backbone) along which N (N’) side resonators are grafted at two sites. Using a Green’s function method, we obtained closed-form expressions for the transmission coefficients for various systems of this kind. The amplitude, the phase, and the phase time of the transmission are discussed as a function of frequency and the strength of the pinning field parameter. In the presence of the pinning field at the ends of the side branches, the transmission probability may exhibit resonances of the Fano type. It is shown that the transition from strong to weak pinning leads to Fano line shapes with gradually smaller asymmetry. This also results in a modification of the position and the width of the resonance but the transmission amplitude remain unaffected. Furthermore, it is shown that the presence of the pinning field causes systematic collapse of certain Fano resonances. These results may provide useful means for the design of narrow-frequency optical or microwave filters. |
