Discrete Coordinate Transformation for Designing All-Dielectric Flat Antennas

Abstract

Transformation electromagnetics provides a practical approach to control electromagnetic fields at will. Based on this principle, novel devices such as the invisible cloak have been proposed. Here we examine the extension of this technique as applied to the design of flat devices in antenna systems. A method using discrete coordinate transformation is proposed, which allows the conversion of conventional devices with curved shapes into flat systems, while preserving their non-dispersive, isotropic, broadband, and lossless properties. Two specific design examples, a flat reflector and a flat lens embedded in free space, are presented. To avoid the loss and narrow bandwidth issues typically present in metamaterials, appropriate approximations and simplifications are introduced to make the all-dielectric devices, which are more practical to build. It is also shown that the discrete coordinate transformation is valid for both the E and H polarizations, as long as the local coordinates of the system remain near-orthogonal. Finite-Difference Time-Domain simulations are used to verify the performances of these designs, and show that the all-dielectric devices have similar broadband performances compared to the conventional ones, while possessing the advantages of flat profiles and small volumes.

Reconfigurable Reflectarrays and Array Lenses for Dynamic Antenna Beam Control: A Review

“…a refractive index less than 1), the dispersion associated with such materials is avoided yielding a potentially very broadband transformation device. This approach has been used to successfully design flat reflectors [108] and lenses [109][110] in principle.…”

Metasurface transformation for surface wave control

“…The entries of the transparent MTS reactance expressed in the TE-TM basis (3.7) can be represented as [30] 14) where the capacitances C n,m and the inductances L n,m can be found in analytical form as a function of the Fourier spectrum of the low-frequency irrotational and solenoidal components of the currents after using the asymptotic form of the spectral GF. The simplified representation in (3.14) is valid under the 'single accessible mode' condition, which implies [26] …”

Method for arbitrary phase transformation by a slab based on transformation optics and the principle of equal optical path

“…Further, in order to characterize the slab more clearly and commonly we introduce the effective average refractive index [32,33,37,38] in terms of the complex amplitude transmittance Eq. (4),…”

“…Then the slab can be considered as nonmagnetic and be realized by dielectrics only though the performance may be sacrificed a bit [37,38]. The effective refractive index on the transverse of the slab for different choices of a are shown in Figure 6(d) which has included the results in Figures 4(b)-(d).…”