  We investigate the magnon-photon couplings by employing a small magnet within
an irregular resonant cavity, which leads to a desirable nonreciprocity with a
big isolation ratio. Moreover, the higher-order couplings between the spin wave
modes with the polarized photon modes also exhibit the nonreciprocity. These
couplings between polarized photon and spin waves could be regarded as an
indirect multi-modes coupling between the ferromagnetic resonance (FMR) mode
and spin wave mode magnons mediated by the cavity mode photons. We also derive
a coupling matrix to predict the characteristics of this kind of indirect
coupling. The existence of the indirect couplings broaden the field range of
the nonreciprocity of the system. The achieved nonreciprocal multi-mode
magnon-photon couplings in a single system offer a feasible method to improve
the signal transmission quality.
