A Generalized Dispersion Equation Combining Coupled Modes, Parity-Time Symmetry, and Leaky Waves Describing Non-Decaying Leaky Surface Waves

A generalized dispersion equation is derived featuring coupled mode theory, parity-time symmetry, and leaky wave antennas of arbitrary periodic modulation. It can be specialized to each of these cases individually or can describe a structure containing all three electromagnetic phenomena simultaneously in a single antenna. This very general dispersion equation is derived using both mode matching and the transverse resonance method, the latter lacking the ability to provide the field descriptions and wave impedances at the cost of computational simplicity. Using the dispersion equation, a sinusoidally modulated reactive sheet (SMRS) supported by an active impedance sheet backed dielectric spacer is designed. The active impedance sheet is designed to compensate the SMRS radiative leakage loss when coupled in close proximity. Due to the coupling, each spatial harmonic generated by the SMRS modulation is characterized by a purely real propagation constant and hence leaky wave radiation is generated from surface waves which do not decay. Due to the non-decaying nature of the surface waves, an input to output surface wave port-to-port |S21| would be unity despite an open far field channel being generated. The non-decaying leaky surface wave antenna is compared to the traditional PEC backed SMRS. The non-decaying leaky surface waves give rise to perfect aperture efficiency and the associated radiation pattern making it far superior to the traditional PEC backed SMRS case. Full-wave simulations corroborate the results. These types of antennas can make sensors probed from the far field where changes in S21 amplitude directly correlate to local changes in the waveguiding environment.