Directivity of a Source Inside an Ultrarefractive Slab

This letter derives an analytical formula that establishes a relationship between the quality factor (Q factor) at normal incidence and the directivity of an electromagnetic source located inside an ultrarefractive medium. The study explores the impact of the ultrarefractive medium on the radiation characteristics of the source, providing a comprehensive analysis of how the medium affects both the Q factor and the directivity. The derived formula is compared to the standard formula for Fabry–Perot cavity antennas, offering valuable insights into the design of efficient antenna systems and wireless propagation models in complex media. Applications of the work are discussed in the context of high gain antennas. Numerical results are presented to validate the derived formula and highlight its practical implications.