Absence of unidirectionally propagating surface plasmon-polaritons in nonreciprocal plasmonics

In the presence of an external magnetic field, the surface plasmon polariton that exists at the metal-dielectric interface is believed to support a unidirectional frequency range near the surface plasmon frequency, where the surface plasmon polariton propagates along one but not the opposite direction. Recent works have pointed to some of the paradoxical consequences of such a unidirectional range, including in particular the violation of the time-bandwidth product constraint that should otherwise apply in general in static systems. Here we show that such a unidirectional frequency range is nonphysical, using both a general thermodynamic argument, and a detailed calculation based on a nonlocal hydrodynamic Drude model for the metal permittivity. Our calculation reveals that the surface plasmon-polariton remains bidirectional for all frequencies. This work overturns a long-held belief in nonreciprocal photonics, and highlights the importance of quantum plasmonic concepts for the understanding of nonreciprocal plasmonic effects.