Computing Projected Band Diagrams for Photonic Crystals

In this article, we focus on computing the projected band diagrams of photonic crystals. This step is crucial for determining waveguide mode characteristics and designing photonic crystal slabs. Photonic crystals are materials with periodic structures that can control light propagation within specific wavelength ranges. By calculating projected band diagrams, we gain deeper insights into the band structure of photonic crystals, enabling more precise waveguide mode design and photonic crystal slab fabrication. The implementation typically involves using plane wave expansion methods to solve Maxwell's equations in periodic structures, where eigenvalue solvers compute the frequency eigenvalues for different wavevectors along high-symmetry directions in the Brillouin zone. Key computational steps include defining the unit cell geometry, setting dielectric constant distributions, and applying boundary conditions through Fourier space transformations. When performing these calculations, careful analysis and computation are essential to ensure result accuracy and reliability, particularly in handling convergence criteria and numerical stability of the eigenvalue solutions.