LSE- and LSM-mode sheet impedances of thin conductors

The sheet resistance of very thin conductors is commonly taken as R=1/σt. We show that the sheet impedance, defined as the ratio of the tangential electric field at the surface of the conductor to the conduction current per unit length in the conductor, depends on the field distribution. The LSE (TE-to-y) and LSM (TM-to-y) modes used in the spectral domain immittance approach have sheet impedances which are distinct for vanishingly small or large values of the wavenumber γ in the medium surrounding a thin conductor. In the limit γ→0 and t/δ≪1, Z_sh^LSE approaches R=1/σt while Z_sh^LSM→2/σt. In the limit γ→∞ and t/δ≪1, Z_sh^LSE approaches R=2/σt and Z_sh^LSM approaches R=1/σt. When t/δ≫1, the sheet impedance approaches the surface impedance Z_s=(1+j)/σδ and is independent of the field distribution