FDTD simulation of interaction between a light and a photonic crystal structure
FDTD simulation of interaction between a plane electromagnetic wave and a globular PC, during pumping in its band gap
Various fundamental phenomena, such as electromagnetic wave interaction with structured optical media, photonic crystal (PC) structures, metamaterials, can be investigated by means of numerical solution of Maxwell equations using finite-difference time-domain method (FDTD). It is very useful in case of studying some special features of wave interaction with PC: wave propagation in complex media, band gap structure, optical field localization in PC volume and near its surface due to structural focusing phenomena. The last one leads to the strong localization of electric field near the PC surface during pumping in its band gap. This effect is of fundamental importance, since it exists not only in 2D and 3D PC structures, but also in acoustic and quasi-crystalline structures of different nature. It can be useful for making new high-efficient laser materials and nonlinear media based on PC structures, and also for new high-sensitive spectroscopic methods.
Evidently, the strong localization of optical field takes place near the PC surface, which is connected exactly with the structural focusing effect. Meanwhile, structural focusing cannot be explained by the Bloch theory of light-crystal interaction, because the wave front, interacted with PC, is considered to remain plane in this theory, whilst namely the coherent deformation of the wave front leads to structural focusing.
Transverse localized modes in PC fiber as the result of FDTD simulation
As it can be seen, light interaction with PC fiber also leads to the effects of optical field localization. These effects can play the significant role in nonlinear conversion in PCF, including supercontinuum generation.