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We present and apply two complementary calculation methods used in phononic crystal studies: the finite difference time domain (FDTD) method and the plain wave method (PWM). The FDTD technique allows to simulate the time dependence of a wave packet of vibrational modes propagating through a composite and to determine the transmission coefficient. The PWM method is used for the determination of the phononic dispersion relation in systems with discrete translational symmetry. We use both methods for investigating the effect of periodic interface perturbations on the spectrum of longitudinal vibrational modes in 1D phononic crystals composed of semiconducting materials. The material parameters in the composites under consideration are modulated in the nanoscale.

Phononic Band Gaps in One-dimensional Phononic Crystals with Nanoscale Periodic Corrugations at Interfaces. FDTD and PWM Simulations