Dirichlet-to-Neumann Mapping Method for Bandgap Analysis in 2D Superconducting Photonic Crystals

Abstract

This study employs the Dirichlet-to-Neumann (DtN) method to analyze superconducting photonic crystals (SPCs). By building a DtN operator for the unit cell lattice, we develop an eigenvalue framework to calculate photonic bandgap structures in niobium (Nb) and yttrium barium copper oxide (YBCO) SPCs. This boundary-only discretization approach (avoiding full structural meshing) enhances computational efficiency. We systematically analyze temperature effects on bandgap properties and cutoff frequencies below YBCO’s critical temperature. Results of numerical experiments confirm the DtN method’s reliability and efficiency for studying SPC bandgap characteristics.