Band structure calculation of one-dimensional periodic structures by a time-domain method based on matrix-exponential decomposition technique

A matrix-exponential decomposition based time-domain method for band structure calculations of one-dimensional (1D) periodic structures is developed. The method is more stable than the conventional finite-difference time-domain method, and particularly efficient for large-scale structures containing a defect with a high wave speed. The numerical examples for 1D quasi-periodic phononic crystal structures are presented to demonstrate the efficiency advantage of the method.