Negative effective permeability in polaritonic photonic crystals

We find that a two-dimensional photonic crystal composed of polaritonic materials behaves as an effective medium with negative permeability in the micron wavelength range. The resonance in μeff is due to the large values of ε(ω) attained near the transverse phonon frequency ωT. The minimal wavelength for achieving an effective permeability less than −1 in a LiTaO3 crystal, obtained by optimizing the rod size and the lattice constant, is around 12μm, a range previously inaccessible using dielectric metamaterials. For certain dissipation levels, we find that other polaritonic media also exhibit a resonant effect with μeff<−1 for wavelengths ranging from 2 to ∼100μm.