Broadening the Bandwidth of Epsilon-Near-Zero Metamaterials with Embedded Square Frames

A narrow frequency bandwidth of epsilon-near-zero metamaterials limits the use of many optical, microwave, and electronic devices. In this paper, we propose a recipe to broaden the operational bandwidth by employing a structure of properly tailored square frames nested within each other. To illustrate this effect, we derive the effective permittivity for the considered frame geometry. Then, we show that combining constituent materials with loss and materials with gain enables us to achieve the effective permittivity over a frequency band as small as desired. This technique may prove valuable for various applications including invisibility cloaks, camouflage, shielding, and sensorics.