Total external reflection from metamaterials with ultralow refractive index

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Abstract
Metamaterials composed of metal-dielectric nanostructures are engineered to have an effective refractive index less than unity at optical wavelengths. The effect of total external reflection is demonstrated when light from vacuum is incident onto these materials at an angle exceeding the critical angle defined by Snell’s law. Novel approaches are discussed to derive the effective index of refraction from the reflection and refraction properties of finite slabs. The effect of losses and dispersion are analyzed in the visible range of frequencies by consideration of the measured properties of silver. The differences among ultralow refractive-index metamaterials, photonic bandgap materials, and metals are discussed. Remarkably, a bandgap is not required to obtain total external reflection.