Manipulation of Surface Waves through Metasurfaces

Metamaterials (MTMs) are artificial materials that are structured at a subwavelength scale to exhibit desired effective constitutive parameters. Achievable material parameters can include those not found in nature (Veselago, Sov Phys Usp 10(4):509, 1968, [1], Pendry, Phys Rev Lett 85:3966–3969, 2000, [2], Shelby et al., Science 292(5514):77–79, 2001, [3]). MTMs can be formed by periodic arrangements of many small inclusions in a dielectric host environment, so that the resulting effective medium possesses desired bulk properties.

As mentioned in the previous chapter, a simple anisotropic MTS can be obtained by periodically printing small elliptical patches on a grounded dielectric slab. Rotation of the ellipses with respect to the direction of SW propagation may provide control of the field polarization in circularly-polarized leaky-wave antennas or in TO SW-based devices.

The first part of this chapter proposes a formulation for the description of the equivalent reactance of MTS constituted by periodic small patches printed on a grounded dielectric slab. As already mentioned in the previous chapters, the printed elements are assimilated to homogenized scalar boundary conditions that can be represented by the circuit in Fig. 3.1. This scalar description is valid for printed elements with symmetric shapes (e.g. circular or square patches) and also for more complex elements with two axes of symmetry, provided the direction of propagation matches one of the symmetry axes of the printed elements (Fig. 3.1). A systematic way to extract a circuit description by a full-wave analysis is given by the pole-zero matching technique (Maci et al., IEEE Trans Antennas Propag 53(1):70–81, 2005, [1]), which requires the use of a Foster type expansion of the patch reactance. Derivation of a quasi-analytical representation of the circuit elements as a function of phasing is shown in the previous chapter for elliptical patches.

As already mentioned in Chap. 1, a modulated MTS may be obtained by gradually varying the geometry of the elements in contiguous cells, while maintaining the period unchanged and electrically small. Macroscopically, this results in a modulation of the IBC that, due to the small dimensions of the unit cell, can be assumed to be almost continuous and locally treated by assuming each element as immersed in a periodic environment. The spatial variability of the IBC imposes a deformation of the SW wavefront, which addresses the local wavevector along non-rectilinear paths.

Checkerboard metasurface (CBMS) consists of an infinitesimally thin layer of electrically small complementary square metallic patches and apertures (Fig. 5.1). The name MTS is adopted here because the periodicity d of the checkerboard lattice is small in terms of the wavelength so that the global effect is the same as that of a continuous impedance surface. Propagation of waves driven by impedance discontinuity has been investigated in Quarfoth and Sievenpiper (IEEE Trans Antennas Propag 61(7):3597–3606, 2013, [1]). The present solution can be viewed as an implementation of this concept. In fact, the behavior of the CBMS changes depending on whether the square patches’ vertexes are connected by short-circuits or separated by a small gap.

In this thesis we have theoretically and numerically examined the prospects of modulated metasurface (MTS) as a new platform for planar transformation optics devices, which allow one to manipulate the propagation of the supported surface waves (SWs). Such devices can be used as a part of flat lens antennas producing a fan-beam radiation pattern at microwaves, but can be also employed as components of optical circuits.