The CFS-PML for 2-D WLP-FDTD method of dispersive materials

Abstract

This paper proposes the complex frequency shifted (CFS) perfectly matched layer (PML) of dispersive media for finite-difference time-domain (FDTD) method combined with weighted Laguerre polynomials (WLP). According to the property of Laguerre basis function, the relative dielectric constant ε _r (ω) of dispersive media and complex frequency shifted (CFS) PML parameters, auxiliary differential equation (ADE) technique is introduced. Based on the ADE technique, the relationship between field components and auxiliary differential variables is derived in Laguerre domain. Using ADE scheme, the relationship between electric flux density D and electric fieldE is derived in Laguerre domain. Substituting auxiliary differential variables into CPML absorbing boundary conditions, using auxiliary differential variables, electric flux density D of order q can be expressed directly by magnetic field H in Laguerre domain. Using the same procedure, magnetic field H of order q can be expressed directly by electric field E in Laguerre domain. Inserting H of order q$ into D , using the relationship between D and E , and using central difference scheme, the formulations for dispersive media are obtained. In order to validate the efficiency of the presented method, two numerical examples are simulated. Numerical results show that, compared with the Berenger PML (BPML) and nearly PML (NPML), the CFS-PML has about more than 24 dB improvement in terms of the maximum relative error and much lower reflection error for the late-time region.

Keywords

Auxiliary differential equation (ADE)dispersive materials finite-difference time-domain (FDTD)

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