Controlling the transmitted field into a cylindrical cloak's hidden region

Constitutive parameters for simplified cylindrical cloaks have been developed such that epsilon(z)micro(theta) and epsilon(z)micro(r) match those of the ideal cylindrical cloak. Although they are not perfect, simplified cylindrical cloaks have been shown to inherit many of the power-bending properties of the ideal cloak. However, energy is transmitted into simplified cloaks hidden regions. Here, we develop a constraint equation that can be used to determine how closely field behavior within the simplified cylindrical cloak matches that of the ideal cloak. The deviation from this controlling equation can be reduced by controlling the cloaks parameter value, microtheta. As the deviation from our constraint equation is decreased, the field transmitted into the cloaks hidden region is reduced, resulting in less energy impinging on the cloaked object. This results in a smaller scattered field due to the presence of the cloaked object. However, the resulting impedance mismatch at r = b results in a significant scattered field by the cloak itself. Thus, we have found when using cylindrical cloaks that satisfy the ideal values of epsilon (z)micro(theta)and epsilon(z)micro(r) for scattering width reduction, it is more important to have a matched impedance at r = b than to have a smaller field transmitted into the cloaks hidden region. However, such cloaks scattering widths can vary significantly as a function of the object in the hidden region. A cloak with a matched impedance at r = b and that satisfies specific values for epsilon(z)micro(theta) and micro'theta performs reasonably well in terms of scattering width reduction in certain angular regions while being independent of the object in the hidden region.