We analytically derived an explicit condition for high-contrast plasmonic modulation and switchable routing in coupled graphene waveguides consisting of two coupled gated graphene sheets sandwiching a gyrotropic medium. The analytical condition intuitively predicts that by manipulating the graphene chemical potential and the gyration of the in-between medium we can combine robustness of the plasmonic routing to the deviation of design and material parameters due to imperfect fabrication and harsh environment with the extreme high contrast. Also, it predicts broadband tunability of the high-contrast plasmonic routing. The intuitive analytical condition reveals that the high contrast is achievable at a resonance gyration due to a magnetic resonance of nonreciprocal directional coupling. The magnetic resonance of nonreciprocity breaks a currently held preconception that the stronger magnetic field induces the stronger magnetically induced nonreciprocity. Numerical simulations demonstrate the robustness of the magnetic resonance of nonreciprocity and its tunability over a one-octave spanning spectral range. In practice, the chemical potential and the gyration can be manipulated by controlling the gate voltage of the graphene and the external magnetic field, respectively. Our findings would provide a robust and broadband tunable tool for high-contrast plasmonic modulator and switchable router and for probing of ultrafast magnetization dynamics.

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• Magneto-optical effect
• Surface plasmons
• Waveguides
• Graphene