FDTD Method for Simulating TM Mode Propagation in 2D Photonic Crystals

The Finite-Difference Time-Domain (FDTD) method was implemented to simulate TM (Transverse Magnetic) mode propagation in 2D photonic crystals. The algorithm discretizes Maxwell's equations using central differences in both time and space domains, with electric and magnetic field components updated alternately through Yee's grid scheme. During computation, variations in material parameters such as refractive index, lattice periodicity, and structure thickness were observed to directly alter electromagnetic field distributions within the photonic crystal. This correlation enables inverse deduction of parameter changes by analyzing waveform evolution patterns. The implementation typically involves defining periodic boundary conditions for unit cells and incorporating perfectly matched layers (PML) to absorb outgoing waves. This intuitive approach provides a robust tool for investigating photonic crystal properties, with field visualization achieved through techniques like color-mapped intensity plots or animated time-sequence displays.