The FDTD Method For Maxwell's Equations In Lorentz Metamaterials

Lorentz model is a widely used dispersion model in engineering,the paper fo-cuses on studying the finite difference time domain method of Maxwell's equations in Lorentz metamaterials.Maxwell's equations in Lorentz metamaterials are more complex than those in simple media and more difficult to analyze numerically.First-ly,we designed an effective finite difference time domain method for the governing equations of electromagnetic wave propagation in Lorentz metamaterials.Then,it is proved that the discrete scheme is stable,and the error optimal convergence order isO(T~2+h~2).Finally,numerical experiments are presented to support the theoretical analysis and apply our scheme to model many interesting phenomena happened when wave propagates in the Lorentz metamaterials:the reverse propa-gation of electromagnetic waves in negative refractive index metamaterials,and the total transmission and total reflection phenomena in zero refractive index metama-terials.