We investigate dynamic effective anisotropy in photonic crystals (PCs) through a combination of an effective medium theory, which is a high-frequency homogenisation (HFH) method explicitly developed to operate for short-waves, numerical simulations and through microwave experiments. The HFH yields accurate prediction of the effective anisotropic properties of periodic structures when the typical wave wavelength is on the order of the array pitch, specifically we investigate a square array of pitch 2 cm consisting of dielectric rods of radius 0.5 cm and refractive index n = √ 6 within an air matrix. This behaves as an effective medium, with strong artificial anisotropy, at a frequency corresponding to a flat band emerging from a Dirac-like point in transverse magnetic (TM) polarization (i.e. longitudinal electric field parallel to the rod axis); highly-directive emission for an electric source placed inside this PC is predicted at critical frequencies. The artificial anisotropy can be shown to coincide with a change of character of the underlying effective equation from isotropic to unidirective, with markedly different values for the effective equation tensor. In transverse electric polarization, we note an even more radical change of character of the underlying effective equation from elliptic to hyperbolic near a frequency at which an inflection point occurs in dispersion curves. Delicate microwave experiments are performed in both polarizations for such a PC consisting of 80 rods and demonstrate that a directive emission in the form of a + (resp. an X) is indeed seen experimentally at the predicted frequency 9.5 GHz in TM polarization (resp. 6 GHz in TE polarization). These are clearly dynamic effects since in the quasi-static regime the PC just behaves as an isotropic medium.

Abstract:We consider the cloaking properties of electromagnetic wired media deduced from arbitrary coordinate transformations. We propose an interpretation of invisibility via sub-wavelength imaging features. The quality of cloaking is assessed by the level of deformation of the image of a P-shaped source through the stretched wired media: the lesser the image deformation, the more effective the cloaking. We numerically and experimentally demonstrate a tetrahedral wired cloak with longer edge length about 7cm at a frequency of 1GHz (the cloak is thus subwavelength). The wired cloak has two functionalities: it can serve as a high-resolution imaging system over long distances, and it can also perform space transformations such as, but not limited to, cloaking at a single operation frequency.