Investigation on invisibility cloaking without optical singularities

Abstract

Invisibility cloaking has become feasible thanks to the development of metamaterials and transformation optics. The material design usually requires inhomogeneous and anisotropic optical properties such as permittivity and permeability or refractive index. Optical singularity is one of the principle challenge in which the properties go to zero or infinity at certain locations in the device. This hinders implementation of cloaking in broad frequency and demands some approximation for experimental purposes. In this work, we investigate three approaches of invisibility cloaking whereby no optical singularity is required. They are non-Euclidean transformation optics, transmutation of conformal mapping device, and under carpet cloaking. The first approach is based on transformation optics using the so-called Maxwell?s fish-eye in design. Maxwell?s fish-eye refers to a certain refractive index profile with non-Euclidean nature. We propose transmutation of an existing conformal mapping device as the second approach; the principle is similar to transformation optics. The device is based on Zhukovski conformal mapping where two singularity points initially exist. Non-Euclidean structure of two kissing mirrored Maxwell?s fish-eyes are also embedded in the design. We show that both singularity points are eliminated at cost of slight increase in the anisotropy. These two approaches have Maxwell?s fish-eye which implies certain conditions for the frequency of the wave. The devices work at certain eigenmodes frequencies associated with the Maxwell?s fish-eye. We present derivation of design and some supporting simulation works at these frequencies. Lastly, under carpet cloaking works by making cloaked object under mirror to appear flat. It has advantage as the material do not need to be inhomogeneous. We will present the design derivation, implementation with alternating layers of aluminum oxide and air, and comparison with experimental data with TM-mode polarization at frequencies of 8 GHz, 10 GHz, and 12 GHz.