Mesoscopic magnetism in dielectric photonic crystal meta materials: topology and inhomogeneous broadening

We consider meta materials made from a two-dimensional dielectric rod-type photonic crystal. The magnetic response is studied within the recently developed homogenization theory and we in particular study the effects of topology and inhomogeneous broadening. While topology itself mainly affects the Mie resonance frequency we find that the dispersion in the topological radius R of the dielectric rods may lead to significant inhomogeneous broadening and suppression of the negative-mu phenomena for dR/R0 >> epsilon''/epsilon', with epsilon=epsilon'+i*epsilon'' being the relative dielectric function of the rods.