The Effects of Spatial Dispersion on Power Flow Along a Printed-Circuit Tensor Impedance Surface

In this communication, expressions for the group velocity and the direction of power flow along an idealized tensor impedance boundary condition (TIBC) and a printed-circuit tensor impedance surface (PCTIS), are found. A PCTIS consists of a patterned metallic cladding over a grounded dielectric substrate. The patterned metallic cladding is modeled by a tensor impedance sheet. Expressions for the surface impedance of a TIBC and a PCTIS are reviewed. From these expressions, the group velocity and direction of power flow are derived as a function of transverse wave vector. A PCTIS exhibits spatial dispersion due to the electrical thickness of its substrate while a TIBC does not. As a result of this spatial dispersion, a PCTIS can have the same surface impedance as a TIBC for a given transverse wave vector, but a different direction of power flow. The expressions for direction of power flow along a TIBC and a PCTIS are verified with a full-wave electromagnetic solver.