The Optical Transmission Characteristic of Hollow Carbon-Coated Fe₃O₄ Colloidal Photonic Crystal

The optical transmission characteristics for the hollow carbon-coated Fe₃O₄ colloidal photonic crystal have been calculated with the finite-difference time-domain (FDTD) method. We analyze the influence of the factors on the photonic band gap (PBG) that include lattice constant a, the number of the particles in propagating direction N_y, the thickness of carbon layer H_c and Fe₃O₄ cluster layer H_f, and the thickness ratio of the two layers. The results show that the PBGs red shift and the bandwidth first increases and then decreases with the increasing a. In the situation of increasing N_y, the PBG changes from irregular to uniform, followed by the oscillations on both sides of the PBG growing in number and the deepened PBG in the low-frequency region. The PBGs move toward the low frequency direction with the increase of H_c, and the optimal value of H_c for the uniform color response is 10 nm ∼ 25 nm. The PBGs red shift with the increasing H_f, and the first bandwidth increases while the second decreases. The optimal H_f for the ideal PBG is 35 nm ∼ 55 nm. The stop bands move to the high-frequency direction with the increasing thickness ratio (H_c : H_f), and the best ratio is 10 nm : 55 nm for the complete PBG and wider bandwidth.