Study Of Shift Operator Method In FDTD Analysis And Related Techniques

The Shift Operator (SO) method applied for frequency-dispersive media in FDTD analysis is studied and discussed in a deep going way. The SO-FDTD is perfected and developed to be a general method in analyzing the electromagnetic property of isotropic dispersive media, and extended to the case of anisotropic dispersive media. Moreover, based on the SO method, a general technique handing thin isotropic dispersive layer with the FDTD method, a general uniaxial anisotropic perfectly matched layer(UPML) absorbing boundary condition for isotropic dispersive medium and a general material independent perfectly matcher layer(MIPML) absorbing boundary condition for dispersive medium, are introduced.The SO-FDTD is developed to be a general method in analyzing the electromagnetic property of isotropic dispersive media. The SO method is expounded and perfected by proving that high-order time derivative can be expressed as a function of shift operator. It is proved that the complex constitutive parameter (permittivity, permeability) of three kinds of general dispersive media model, i.e. Debye model, Lorentz model, Drude model, may be described by rational polynomial fraction in jω, and then, by introducing shift operator, the constitutive relation between D and E, B and H are derived in discrete time domain and the recursive formulations for D and E, B and H available for FDTD computation are obtained. The recursive formulations for E and B, H and D, which is the FDTD formulations of Maxwell curl equations, are uniform in isotropic dispersive media, therefore, the SO-FDTD method is applied to the general isotropic dispersive medium case, in additionally, the uniform recursive formulations and program of the method can be deduced and written.The SO method is extended to the case of anisotropic dispersive medium by taking magnetized plasma and magnetized ferrite as example, respectively. Based on the constitutive parameter tensor in principal system, the permittivity and permeability tensor in plasma and ferrite subject to an external dc magnetic field in any direction are derived, in which the transfer matrix between the principal and the laboratory system is used. The constitutive parameter tensor in laboratory system is then described by rational polynomial fraction in jω, and then the recursive formulation for D and E, B and H available for FDTD computation is obtained by using shift operator. The present method is simple and effectual in simulating the electromagnetic scatter of magnetized plasma and ferrite.A general FDTD algorithm handing thin isotropic dispersive medium layers is presented. For the layer which is thinner than a Yee's cell, a new electromagnetic nodes modified method is introduced. The equivalent constitutive parameter and constitutive relation on modified node are obtained by weighted averaging of the electric displacement or magnetic induction vector according to the volume fraction of dispersive medium in the FDTD cell including thin layer, hereinto, thin layer with metal base is an exceptive case. In this exceptive case, the equivalent permittivity on modified node of tangential electric field component are obtained by weighted integrating the tangential electric displacement vector in longitudinal neighborhood of the modified node, the size of the neighborhood is half or one cell when the layer is thicker or thinner than half cell. Finally, the recursive formulation for electromagnetic-field quantities on modified node is gained by using SO-FDTD method, in this way, the recursive formulation is general for three kinds of dispersive media model.A general UPML absorbing boundary condition (ABC) for isotropic dispersive medium is proposed. Based on the theory of UPML absorbing boundary for non-dispersive medium, the theory of the general UPML ABC is deduced. Taking into account the characteristic that the constitutive parameter of common dispersive media model can be expressed by fractional polynomials of jω, and combining with the SO-FDTD method, a FDTD ABC available for three kinds of general isotropic dispersive medium models, i.e. Debye model, Lorentz model and Drude model, is given.A general MIPML ABC for dispersive medium is introduced. It is proved that MIPML can be applied for truncating isotropic dispersive medium by deducing the impedance matching condition and nonreflecting condition, and the parameter setting method is presented too. The recursive formulation for electromagnetic-field quantities in the ABC is gained then by using SO-FDTD method, therefore, this MIPML ABC method is general for isotropic dispersive media. Moreover, taken magnetized plasma and magnetized ferrite as example, the MIPML ABC method is extended to the truncating of anisotropic dispersive medium by proving the impedance matching condition and nonreflecting condition, the parameter setting method and the SO-FDTD recursive formulation of electromagnetic-field quantities in the ABC are presented at the same time.