Meshfree Methods for Multiphysics Simulations of Natural and Artificial Crystals: Electronic, Photonic, and Acoustic Band-Structure Calculations

摘要

We present a novel meshfree framework for real-space band-structure calculations of semiconductors, photonic crystals, and phononic crystals. General formulation of periodic meshfree shape function is proposed in order to reproduce the periodicity in those materials. Matrix eigen-equations for the Schroedinger equation, the Maxwell equations, and the elastic wave equation are then solved. Numerical examples include the electronic structure of strained compound semiconductor, the strain-tunable band-gap modification of photonic crystal, and acoustic band-gap materials. Our results demonstrate that the meshfree method can be a promising tool for various strain-induced multiphysics problems of natural and artificial crystals.