The Optical Transmission Characteristic of Hollow Carbon-Coated $\hbox{Fe}_{3}\hbox{O}_{4}$ Colloidal Photonic Crystal

The optical transmission characteristics for the hollow carbon-coated
$\hbox{Fe}_{3}\hbox{O}_{4}$
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
$\hbox{Fe}_{3}\hbox{O}_{4}$
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
$\sim$
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
$\sim$
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.