Cholesteric elastomer waveguides doped with metallic nanospheres: exhibiting metamaterial-like behaviour under transverse elongation

The propagation of electromagnetic waves through a cholesteric elastomer slab doped with a small amount of randomly distributed metallic nanospheres, which is subjected to transverse elongation, is considered. The nanocomposite dielectric response formed by the cholesteric and the nanospheres is described using a Maxwell Garnett formalism. The real and imaginary parts of the dispersion relation are calculated numerically by solving Maxwell’s equations, subjected to the corresponding boundary conditions. The presence of two peaks in the imaginary part of the wave number of the hybrid system, caused by the plasmonic resonance of the metal, is observed. The group velocity versus frequency is also calculated, revealing two intervals where this quantity opposes the wave vector, giving rise to behaviour similar to that of a metamaterial waveguide. The behaviour is confirmed by the calculation of the Poynting vector, where the energy travels in the opposite direction to the wave vector.