Résumé
Based on the theory of macroscopic quantum electrodynamics, we generalize the expression of theCasimir force for nonreciprocal media. The essential ingredient of this result is the Green’s tensor betweentwo nonreciprocal semi-infinite slabs, including a reflexion matrix with four coefficients that mixes opticalpolarizations. This Green’s tensor does not obey Lorentz’s reciprocity and thus violates time-reversal symmetry.The general result for the Casimir force is analyzed in the retarded and nonretarded limits, concentrating on theinfluences arising from reflections with or without change of polarization. In a second step, we apply our generalresult to a photonic topological insulator whose nonreciprocity stems from an anisotropic permittivity tensor,namely InSb. We show that there is a regime for the distance between the slabs where the magnitude of theCasimir force is tunable by an external magnetic field. Furthermore, the strength of this tuning depends on theorientation of the magnetic field with respect to the slab surfaces.