Tunable negative-index photonic crystals using colloidal magnetic fluids

The model of using colloidal magnetic fluid to build tunable negative-index photonic crystal is established. The effective permittivity ε_e and permeability μ_e of the two-dimensional photonic crystal are investigated in detail. For transverse magnetic polarization, both ε _e and μ_e exhibit a Lorentz-type anomalous dispersion, leading to a region where ε_e and μ_e are simultaneously negative. Then, considering a practical case, in which the thickness of photonic crystal is finite, the band structures for odd modes are calculated by the plane wave expansion method and the finite-difference time-domain method. The results suggest that reducing the external magnetic field strength or slab thickness will weaken the periodic modulation strength of the photonic crystal. Simulation results prove that the negative-index can be tuned by varying the external magnetic field strength or the slab thickness. The work presented in this paper gives a guideline for realizing the flat photonic crystal lens with tunable properties at optical frequencies, which may have potential applications in tunable near-field imaging systems.