Transmission Simulation of Defect-Structured Photonic Crystals Using FDTD Method

We can employ the Finite-Difference Time-Domain (FDTD) method to simulate transmission phenomena in photonic crystals, particularly when investigating defect structures. This numerical approach solves Maxwell's equations through discrete spatial and temporal discretization, enabling accurate computation of electromagnetic wave propagation within complex material systems. The implementation typically involves Yee's grid algorithm for field component arrangement and leapfrog time-stepping scheme for numerical stability.

Through this methodology, we gain deeper insights into photonic crystals' optical characteristics, including photonic bandgaps and localized modes around defects. The simulation code generally requires defining material permittivity/permeability distributions, implementing perfectly matched layer (PML) boundary conditions, and calculating field evolution using staggered grid finite differences. Key functions involve updating electric and magnetic field components alternately through curl operations discretized via central difference schemes.

Consequently, this approach can be effectively applied to practical optical device design, enabling performance optimization and efficiency improvements through parametric studies of defect configurations and material properties.