Physical Bounds and Sum Rules for High-Impedance Surfaces

High-impedance surfaces are artificial surfaces synthesized from periodic structures. The high impedance is useful as it does not short circuit electric currents and reflects electric fields without phase shift. Here, a sum rule is presented that relates frequency intervals having high impedance with the thickness of the structure. The sum rule is used to derive physical bounds on the bandwidth for high-impedance surfaces composed by periodic structures above a perfectly conducting ground plane. Numerical examples are used to illustrate the result, and show that the physical bounds are tight.