Position-independent normal-mode splitting in cavities filled with zero-index metamaterials.

We study the normal-mode splitting when an oscillator is placed in a two-dimensional photonic crystal microcavity embedded with an impedance-matched or an impedance-mismatched zero-index medium (ZIM). Because of the (nearly) uniform localized fields in the ZIM, the normal-mode splitting remains (almost) invariant no matter where the oscillator is. When a split ring resonator is coupled to a transmission-line- based effective ZIM at various locations, nearly position-independent mode splitting is observed.