The interaction of dual-micro-cavity defect modes in a one-dimensional photonic crystal consisting of graphene layers is studied by using the transfer matrix method. The numerical relation of resonances and splitting condition of them are determined in this structure. Results show that for specific repetition numbers of surrounding and middle cells of the structure, a defect mode is split into two completely separated modes. Also, threshold states for merging the defect modes are determined for different amounts of these parameters. In addition, the transmission coefficients and the Faraday rotation angles of these states are calculated and compared with each other. By calculation of light intensity distribution inside the structure at resonance wavelengths, we present consistent qualitative interpretation of the analytical results. The information achieved by this research can be useful to fabricate a variety of graphene-based photonic systems and magneto-optical integrated devices such as miniaturized isolators and circulators.

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