Apply FDTD/MRTD Method In Dispersive Medium

In electromagnetic field computation, it is difficult to have the analytical solutionof the problem. There are two reasons: one is the equations have the variety ofconditions; the other is that some equations don’t truly solve a analytical solution at all.Even the semi-analytical solution is hard to get. With the development of numericalmethods, numerical method has become an effective method to solve electromagneticproblems.This paper introduces the numerical methods which are applied in chiral mediumand dispersive medium. Focusing on the basic theory of finite difference time domainmethod, there are some work here: to get the discrete equations in different dimensions,to discuss the numerical stability of the finite difference time domain method, to getMur absorbing boundary conditions and add the incident source.Because the permittivity, permeability and chirality parameter of chiralmetamaterials (CMMs) are frequency-dependent, the wave equations that describecharacters of electromagnetic wave in CMMs are presented and discretized based onauxiliary differential equation (ADE) technique in Finite-Difference Time-Domain(FDTD) method. The total-field/scattered-field, Mur’s first order absorbing anddielectric boundary conditions for a chiral metamaterials slab are discussed in the paper.Numerical results show that cross-polarized reflected coefficient of the CMMs slab iszero. Negative index of refraction phenomenon and optical property of giant opticalactivity in chiral metamaterials slabs are illustrated with ADE-FDTD method. Theeffects to positive or negative phase velocity caused by media parameters of CMMs arestudied.The dispersive medium is permittivity or other constitutive parameters varyingwith frequency, for example, plasma, water, biological tissues, and radar absorbingmaterial. The dispersion phenomena will be produced when the grid is big in divided byFDTD method. When decreasing the mesh size, you need to consume more computermemory resources. For this contradiction, there is a new time-domain methodmulti-resolution analysis of the time domain (MRTD). Compared to FDTD method, in the case of a large grid dispersion phase error is small, thus reducing the burden on thecomputer. The MRTD equation will be used in the Cole-Cole dispersive medium. Therelative permittivity of the Cole-Cole dispersive medium has the form of a fractionalexponent, so using Z-transform and Taylor expansion to derive the Cole-Cole’s MRTDiteration. There are two examples to test the equation of MRTD. One is from water toair, and another is from muscle to air. Two examples demonstrate the feasibility of thisderivation.