Role of Electric Permitivity and Magnetic Permeability for Left Handed Materials

Abstract

Left handed materials opens new horizon in modern optics. This motivates trying to build a theoretical model that can help in predicting new materials. The aim of this work is to how to control the physical properties so as to fabricate left handed materials. The model is based on using mathematical framework and physical reality by assuming the existence of medium electric and magnetic fields. The orientation of medium field with respect to the external ones is described by complex representation. The refractive index is expressed in terms of real and complex electric permittivity and magnetic permeability. It is found that the material become left handed if certain restrictions are imposed on the values and orientations of the medium fields with respect to the external ones. These restrictions requires the real components of the medium internal field to be larger than that of the external field and opposite to it. It also requires the normal velocity component of the medium generated field to be opposite to the incident one. The condition for left handed material can also be found by expressing the refractive index in terms of the electric permittivity and magnetic permeability components parallel and perpendicular to the external electric and magnetic fields. The model shows that the left handed material atoms should be in the form of electric and magnetic dipoles having certain values and certain orientations with respect to the internal field. The electric and magnetic fields generated by the medium must subtend angels with respect to the external field such that they oppose it and become larger than the external one. The refracted beam need to be also in the same medium of the incident beam.