The generalized Fibonacci multiferroic superlattices (GFMS) are composed of single-phase multiferroic domains with simultaneous polarization and magnetization and are defined by the binary substitutional rule (B → BmA, A → B, m = 2, 3). We propose to construct a nonreciprocal multi-channel bandstop filter by the GFMS. The couplings between electromagnetic waves and lattice vibration of multiferroic material with ferroelectric and ferromagnetic (or antiferromagnetic) orders can be invoked either through piezoelectric or piezomagnetic effects and can lead to the creation of the polaritonic band structure. The plane wave expansion method with first-order approximation predicts the existence of multiple band gaps, and electromagnetic waves lying within the band gaps are prohibited, and the band gaps with respect to forward electromagnetic waves (FEWs) and backward electromagnetic waves (BEWs) are asymmetric. The forbidden band structures with FEWs and BEWs are calculated by the transfer matrix method and multiple frequency channels with unidirectional transmission of electromagnetic waves can be further confirmed. Nine and twenty transmission dips in transmission spectra for the BEWs in the frequency range of ω = 0.4 − 0.6 (17.06 GHz-25.59 GHz) are found in the GFMS with m = 2 and 3, respectively, in which the BEWs are prohibited while the FEWs can travel. Thus, the GFMS has all the conditions for the nonreciprocal multi-channel bandstop filter. Besides, the GFMS can also be applied to construct compact multi-channel one-way electromagnetic waveguides.
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