Real and Imaginary Properties of Epsilon-Near-Zero Materials

From the fundamental principle of causality we show that epsilon-near-zero (ENZ) materials with a 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 nonradiative damping of the 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 materials.