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A large number of sensors work in the narrow bandpass circumstance. Meanwhile, some of them hold fine details merely along one and two dimensions. In order to efficiently simulate these sensors and devices, the one-step leapfrog hybrid implicit-explicit (HIE) algorithm with the complex envelope (CE) method and absorbing boundary condition is proposed in the narrow bandpass circumstance. To be more precise, absorbing boundary condition is implemented by the higher order convolutional perfectly matched layer (CPML) formulation to further enhance the absorption during the entire simulation. Numerical examples and their experiments are carried out to further illustrate the effectiveness of the proposed algorithm. The results show considerable agreement with the experiment and theory resolution. The relationship between the time step and mesh size can break the Courant–Friedrichs–Levy condition which indicates the physical size/selection mesh size. Such a condition indicates that the proposed algorithm behaviors are considerably accurate due to the rational choice in discretized mesh. It also shows decrement in simulation duration and memory consumption compared with the other algorithms. In addition, absorption performance can be improved by employing the proposed higher order CPML algorithm during the whole simulation.

In this paper, a complex-envelope (CE) scheme is introduced into the locally one-dimensional finite-difference time-domain (LOD-FDTD) method for the band-gap analysis of the plasma photonic crystal (PPC). The un-magnetized plasma, characterized by a complex frequency-dependent permittivity, is expressed by the Drude model and solved with a generalized auxiliary differential equation (ADE) technique. The CE scheme is also applied to the perfectly matched layer. Numerical examples show that the proposed CE-ADELOD- FDTD method provides much more accurate results than the traditional ADE-LOD-FDTD with the same CFL number. The reflection and transmission coefficients of the PPC are calculated and their dependence on the relative permittivity of dielectric, the plasma frequency, the collision frequency and the plasma layer thickness is studied. The results show that the photonic band gaps of the PPC could be tuned by adjusting the parameters.

Unconditionally stable complex envelope (CE) perfectly matched layer (PML) absorbing boundary conditions (ABCs) are presented for truncating the scalar wave-equation finite difference time domain (WE-FDTD) grids. The formulations are based on incorporating the alternating direction implicit (ADI) scheme into the CE FDTD implementations of the scalar wave-equation derived in the PML region at the domain boundaries. Numerical example carried out in two dimensional domain shows that the proposed formulations are more accurate than the classical ADI scalar wave equation PML formulations when it is used for modelling band limited electromagnetic applications.

This chapter contains sections titled: Introduction Maxwell's Equations Brief History of the Finite‐Difference Time‐Domain (FDTD) Method Finite‐Difference Time‐Domain (FDTD) Method Alternating‐Direction‐Implicit FDTD (ADI‐FDTD): Beyond the Courant Limit Complex‐Envelope ADI‐FDTD (CE‐ADI‐FDTD) Perfectly Matched Layer (PML) Boundary Conditions Uniaxial Perfectly Matched Layer (UPML) Absorbing Boundary Condition PML Parameters PML Boundary Conditions for CE‐ADI‐FDTD PhC Resonant Cavities 5 x 5 Rectangular Lattice PhC Cavity Triangular Lattice PhC Cavity Wavelength Division Multiplexing References