PWE Calculation of Band Structures for Line Defects in 2D Square Lattice Photonic Crystals

This document provides MATLAB source code for calculating band structures of line defects in two-dimensional square lattice photonic crystals using the Plane Wave Expansion (PWE) method. The implementation serves as a valuable computational tool that enables researchers to analyze the properties and behavior of photonic crystals with various defect configurations. The code employs Fourier space transformations to solve Maxwell's equations numerically, utilizing eigenvalue solvers to determine photonic band gaps and defect state frequencies. Key algorithmic features include periodic boundary condition handling, dielectric constant matrix formulation, and efficient band structure visualization routines. Users can calculate band structures for different types of line defects and perform subsequent analysis on defect mode characteristics, including quality factors and field distributions. The modular code structure allows for customization of lattice parameters, defect geometries, and material properties. While the current implementation provides accurate results for fundamental defect studies, significant optimization potential exists for future versions. Possible enhancements include parallel computation for larger supercells, improved convergence algorithms, and adaptive meshing techniques to increase computational precision and efficiency. The code architecture supports straightforward integration of these advanced features.