Modeling the behavior of light within left-handed metamaterials

Recent material science advances have allowed scientists and engineers to reliably create left-handed metamaterials in which the resulting index of refraction is negative. It is well established that the index of refraction can be directly related to the speed of light within a medium. Typically, the magnetic permeability is negligible for most refractive materials and can essentially be ignored. However, in situations where the permittivity and permeability are both negative over the same frequency window, the resulting index of refraction can, likewise, become negative. When light enters a medium with a higher refractive index the phase velocity slows, extrapolating this, a negative refractive index suggests that the phase velocity would reverse. Note that this would not violate causality, which is governed by the group velocity. An interesting aspect of a negative, or a "left-handed" metamaterial is that the refracted wave will bend opposite to the normal when compared to that of a material having a ”standard” index in which n is greater than 1. The exotic behavior of light within materials having a negative refractive index requires scientists to consider how such media would impact the properties of optics should they become integrated into common devices. In this manuscript the properties of metamaterials are briefly reviewed. This manuscript then attempts to model the behavior of a left-handed metamaterial incorporated into a Distributed Bragg Reflector, determining that despite having an overall larger difference in refractive indices, the reflector containing the lefthanded metamaterial is predicted to behave in a similar manner to that constructed from common, positive index materials. The material science applications of left-handed metamaterials is then discussed.