Analytically Expressed Dispersion Diagram of Unit Cells for a Novel Type of Holographic Surface

A novel type of surface-impedance modulation mechanism for designing of microstrip-technology-based surface-wave-excited holographic antennas is proposed. The advanced radiating geometry consists of quasi-periodic arrangement of unit cells operating in the leaky-wave region. Flexible design requires a considerable numerical effort determining the dispersion characteristics of any possible unit cell present in the geometry. In this context, an analytic determination of the dispersion diagram for a unit cell with a sinusoidal modulation of the effective dielectric constant in its inside is presented. In this particular case, the solution is expressed in terms of Mathieu functions. The good agreement between numerical data and analytic solutions for an open, unbounded microstrip structure allows introducing the principle of a novel type of holographic surface obtained by cascading unit cells with different modulation parameters, where the phase of the radiating field can be geometrically controlled.