Real and Imaginary Properties of Epsilon-near-Zero Materials
Mohammad H. Javani and Mark I. Stockman
Department of Physics and Astronomy and Center for Nano-Optics, Georgia State University, Atlanta, GA 30340, USA
Abstract: From the fundamental principle of causality we show that epsilon-near-zero (ENZ) materials with very low (asymptotically zero) intrinsic dielectric loss do necessarily possess a very low (asymptotically zero) group velocity of electromagnetic wave propagation. This leads to the loss function being singular and causes high non-radiative damping of optical resonators and emitters (plasmonic nanoparticles, quantum dots, chromophore molecules) embedded into them or placed at their surfaces. Rough ENZ surfaces do not exhibit hot spots of local fields suggesting that surface modes are overdamped. Reflectors and waveguides also show very large losses both for realistic and idealized ENZ.
Recently, materials at frequencies close to the bulk plasmon frequency, , which are characterized by dielectric permittivity being small enough, , and are usually referred to as Epsilon Near Zero (ENZ) materials, have attracted a great deal of attention, see, e.g., [1-3].
Their optical properties are expected to be quite remarkable: ENZ should totally reflect light at all angles, the phase velocity of light tends to infinity and, correspondingly, the light wave carries almost constant phase, the density of photonic states diverges at , a waveguide formed inside an ENZ material can confine light at deep sub-wavelength dimensions, there is no reflections even at sharp bands, and the unavoidable roughness of the waveguide walls does not significantly spoil the wave-guiding. As in many other cases in nanooptics \cite, dielectric losses present a significant problem deteriorating these unique properties and limiting useful applications of ENZ materials.
Following Ref. , we show that the fundamental principle of causality [as given by dictates that any ENZ material with a very low (asymptotically zero) loss at the observation frequency has necessarily asymptotically zero group velocity at that frequency. Physically, this leads to enhanced scattering and dissipative losses as given by the diverging energy-loss function. Paradoxically, a reduction of the intrinsic loss, , leads to an increase of energy-loss function and further deterioration of performance of reflectors and waveguides built from ENZ materials. Both analytically and numerically we have shown that a realistic ENZ material ITO at the bulk plasma frequency causes high reflection and propagation losses. The singular loss function is also responsible for anomalously strong optical damping of resonant systems (plasmonic nanoparticles, dye molecules, quantum dots, etc.) embedded into or positioned at the surfaces of ENZ materials. In contrast to plasmonic metals, there are no pronounced hot spots of local fields at rough ENZ surfaces. Structured dielectric media with practically zero loss in the optical region cannot function as true ENZ materials because of the singular response; they necessarily are diffractive photonic crystals, and not refractive effective media. Obviously, this anomalous loss of ENZ materials can be gainfully used in energy absorbers, which begets analogy with heating of plasmas at plasma frequency with charged particles or electromagnetic waves. These losses and singularities are fundamental, local properties of the ENZ media, which cannot be eliminated by micro- or nano-structuring.
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