Two-dimensional tunable magnetic photonic crystals

We have calculated the photonic band structure for a cubic block of magnetically saturated ferrite material having a triangular array of circular holes that is under the influence of an external static magnetic field ${\mathbf{H}}_{\mathrm{ex}}{=H}_{\mathrm{ex}}\mathbf{z}$ applied in the hole direction. In this two-dimensional magnetic photonic crystal, the saturated magnetism can affect the transverse electric (TE) mode whose electric field lies in the z axis, but not the transverse magnetic mode. The photonic band gaps of the TE mode shift to lower frequencies and their widths become narrower compared to the case when the relative magnetic permeability $\mu =\mathrm{1.0.}\mathrm{}$ Both the position and the width of the photonic band gap increase in frequency as $H_{\mathrm{ex}}$ increases and the gap never becomes larger than that for $\mu =\mathrm{1.0.}\mathrm{}$