Flat optics for leaky-waves on modulated metasurfaces: Adiabatic floquet-wave analysis

This paper presents a new theory for analyzing the leaky-wave (LW) mechanism supported by planar metasurfaces (MTSs) described by continuous, anisotropic, nonuniform, locally periodic boundary conditions (BCs), and excited by a vertical dipole at the interface. These BCs well represent a dense distribution of subwavelength metal patches of infinitesimal thickness, printed on a grounded slab. We denote succinctly this theoretical formulation as flat optics for LWs. This formulation is based on an adiabatic, asymptotic form of the Floquet theorem, introduced here for the first time. The adiabatic Floquet-wave analysis allows for: 1) describing the mechanism of global interaction between the cylindrical surface wave (SW) launched by the dipole and the modulated MTS; 2) introducing a generalized curvilinear-wavefront LW field that can be used for controlling the radiation-pattern shaping; 3) describing the local and global transfer of energy from SW to LW; 4) establishing an analytical relationship between the aperture field polarization and the anisotropic parameters of the MTS and 5) between the leakage parameter $alpha $ and the MTS modulation index. Concerning the latter point, a closed-form formula for $alpha $ is introduced, which allows for unprecedented control of the aperture field amplitude. The theoretical results are successfully validated by comparison with a full-wave analysis, showing impressive accuracy. In a companion paper published in this Journal issue, the present theory is used for the synthesis of a large class of planar aperture antennas.