The Optical Transmission Characteristic of Hollow Carbon-Coated <named-content content-type="math" xlink:type="simple"> <inline-formula> <tex-math notation="LaTeX">$\hbox{Fe}_{3}\hbox{O}_{4}$</tex-math></inline-formula></named-content> Colloidal Photonic Crystal

Abstract

The optical transmission characteristics for the hollow carbon-coated Fe 3 O 4 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 Fe 3 O 4 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 ðH c : H f Þ, and the best ratio is 10 nm : 55 nm for the complete PBG and wider bandwidth.