Adaptation of Babinet's Principle for Complementary Antennas in a Dielectric Half-Space

Babinet's principle is widely known to relate the impedances of complementary structures. However, the usefulness of the principle is fundamentally limited by the requirement that the complementary structures be in homogeneous media-preventing its use for modern printed-circuit-board-style constructed antennas with a dielectric backing. This letter shows a modification of Babinet's principle to describe the impedance relationship of complementary structures in a dielectric half-space, providing a deeper theoretical understanding of complementary structure behavior. This provides a first step toward an analytical solution for the Babinet's principle applied to finite dielectric backings.