Electromagnetic Duality and Exceptional-Point Transitions in Non-Hermitian RH/LH LC Bilayers

An analytical non-Hermitian bilayer composed of coupled right-handed and left-handed LC lattices is investigated. The uncoupled lattices exhibit exact dual dispersions characterized by complementary direct and inverse excitation spectra. When the layers are coupled through a purely imaginary interlayer coupling, the resulting non-Hermitian Hamiltonian undergoes exceptional-point transitions that separate regions with purely real eigenenergies from regions with complex eigenenergies. It is shown that the spectral splitting is progressively transferred from the real-energy sector to the imaginary-energy sector, giving rise to hybridized modes with finite lifetimes. The corresponding relaxation time, which is directly related to the mobility of the excitations, is governed by the imaginary-energy splitting and diverges at the exceptional-point boundary. These findings establish a direct connection between electromagnetic duality, non-Hermitian spectral properties, and transport phenomena in mesoscopic networks. Possible extensions of the present approach may be relevant for artificial circuit platforms, including Josephson-junction arrays.