Efficient Band Diagram Computation for Periodic Structures using Multiple Scattering Theory and Broadband Green’s Function (MST-BBGF)

PASSCODE: 521850

This dissertation presents a high-efficiency computational framework for analyzing electromagnetic band diagrams in three-dimensional (3D) periodic photonic crystals. Photonic crystals—engineered structures with periodic dielectric modulation—are widely used in optical communication, quantum photonics, and topological insulator design. However, computing their band structures remains challenging due to complex geometries, high-index contrasts, and near-field coupling.

To address these issues, this work introduces an advanced approach combining Multiple Scattering Theory (MST) with the Broadband Green’s Function (BBGF) method. The MST-BBGF technique formulates the problem as a compact eigenvalue system using vector spherical harmonics and Foldy-Lax equations. BBGF accelerates the evaluation of periodic Green’s functions, enabling fast and accurate broadband computation.

A key contribution is a general T-matrix extraction method using far-field scattering data from full-wave simulations. This modular T-matrix enables efficient modeling of arbitrarily shaped scatterers. The framework is validated through comparisons with FEM solvers, showing excellent agreement and significant speedup. Applications to dense photonic lattices and topological structures demonstrate the solver’s scalability, accuracy, and flexibility, offering a powerful tool for modern photonic device design and optimization.

CHAIR: Professor Leung Tsang