UPML-ABC of dispersive materials for the unconditionally stable 2-D WLP-FDTD method

In this paper, uniaxial anisotropic perfectly matched layer (UPML) absorbing boundary condition (ABC) of dispersive materials is presented for 2-D finite-difference time-domain(FDTD) method with weighted Laguerre polynomials (WLP). Taking advantage of the auxiliary differential equation (ADE) technique, our proposed algorithm avoids not only the complicated formulations but also the convolution integral. Using ADE scheme, the relationship between field components and auxiliary differential variables is derived in Laguerre domain. Substituting auxiliary differential variables into UPML-ABC, the electric field E of order q can be expressed directly by magnetic field H in Laguerre domain. Inserting magnetic field H of order q$ into electric field, and using central difference scheme, the formulations of uniaxial anisotropic dispersive media PML are obtained. One numerical example of wave propagation in 2-D dispersive materials is simulated. Numerical results validate the efficiency of the presented method.