By Daniel Frederic Sievenpiper

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3 In the above equation, C is a constant. 2 explicitly, taking into account the three field components that are known to be zero for TM waves. Assume that the surface is surrounded by free space with ε = ε 0 and µ = µ 0 . 6, we can find an expression relating k, α, and ω. 9 This represents the dispersion relation for TM surface waves, but the same expression applies to TE surface waves. It is equivalent to stating the total wave vector as a sum of its components, as shown below. 9 with the impedance that we derived for TM surface waves, which is restated here for convenience.

In a narrow band around the LC resonance, the impedance is very high. In this frequency range, currents on the surface radiate very efficiently, and the structure suppresses the propagation of both types of surface waves. Having high surface impedance, it also reflects external electromagnetic waves without the phase reversal that occurs on a flat conductor. By using lumped elements, we retain the reflection phase and surface wave properties of the quarter-wave corrugated slab, while reducing the overall thickness to a small fraction of a wavelength.

These depend on the value of each element, as well as their arrangement. 3 Effective circuit used to model the surface impedance For the two-layer structures, the value of each capacitor is given by the fringing capacitance between neighboring co-planar metal plates. This can be derived using conformal mapping, a common technique for solving two-dimensional electrostatic field distributions. 4. 4 A pair of semi-infinite plates separated by a gap From the theory of conformal mapping, the electric flux function for this geometry is described by the following function.