Calculation of Transmission and Reflection in 1D Photonic Crystals

This article discusses the calculation of transmission and reflection in one-dimensional photonic crystals. We explore the implementation using transverse magnetic (TM) mode simulations with perfectly matched layer (PML) boundary conditions. The computational framework employs the total-field/scattered-field (TFSF) method with Gaussian pulse excitation, where the incident wave is implemented through source conditions in the total-field region while scattered fields are computed in designated regions. The implementation involves optimizing the simulation parameters through careful selection of PML absorption coefficients and Gaussian pulse bandwidth to minimize numerical dispersion and boundary reflections. Key computational aspects include: implementing Maxwell's equations using finite-difference time-domain (FDTD) method with Yee grid arrangement for TM mode, where electric field components are updated using curl equations of magnetic fields with appropriate material parameters. The PML boundary conditions are implemented through modifiedupdate equations with stretched-coordinate perfectly matched layers to absorb outgoing waves without reflections. The TFSF formulation separates computational domains using connecting boundary conditions that inject incident fields while properly handling scattered wave propagation. These methodologies provide deep insights into the properties and behaviors of photonic crystals, enabling accurate simulation and prediction of their optical characteristics. We provide detailed explanations of each topic along with practical implementation examples and computational techniques, including code snippets demonstrating field update equations and boundary condition implementations. The optimization process involves parameter tuning through iterative simulations with performance metrics comparing numerical results with analytical solutions where available. This comprehensive approach helps readers better understand the fundamental concepts and technical implementations, contributing to advanced knowledge of photonic crystals and related computational methods in photonics research.