Essential parameter in the formation of photonic band gaps

Abstract

It is generally believed that the spatial periodic variation of a dielectric constant $\ensuremath{\epsilon}$ or refractive index $\sqrt{\ensuremath{\mu}\ensuremath{\epsilon}}$ can give rise to photonic band gaps. However, through microwave experiments of microstrip lines with a periodic array of holes, we demonstrate that the wave impedance, which depends on $\sqrt{\ensuremath{\mu}/\ensuremath{\epsilon}}$, is an essential parameter, giving photonic band gaps rather than the refractive index. We explain physically the effect of the magnetic permeability $\ensuremath{\mu}$ on photonic band gaps, already reported.