Study Of Left-handed Materials And Modified FDTD Methods Based On Different Media Model

Presently,left-handed materials(LHMs)is one of the hot research interests for it has intensively potential application in the fields of Electromagnetics,Optics and Materials.However,for the newly artificial electromagnetic materials,these traditional theories,numerical methods and applications of electromagnetic fields need to be developed.Especially,by using the numerical methods to analyze the characteristics of the LHMs and the distributions of electromagnetic fields in the LHMs would greatly enhance the people's right understanding for these newly man-made materials and reduce the research time and costs.Besides,the variation of electromagnetic fields with time could be easily and clearly illustrated by recent drawing tools. Finite-difference time-domain(FDTD)method is directly derived by Maxwell's Equations which is widely used in many complex conditions.However,the traditional FDTD method would make the numerical simulation of LHMs divergence.In this thesis,finite-difference time-domain(FDTD)methods in different mathematic modeling LHMs are developed.Programs based on these modified algorithms are performed in order to analyze the electromagnetic fields in such LHMs. According a great quantity of calculations,the characteristics of different modeling LHMs are discussed.Some special LHMs structures or systems are proposed.Their potential applications are explored.The author's work is mainly focused on:1.The special characteristics and the basic theory of LHMs are introduced. Finite-difference time-domain(FDTD)method is grasped and applied masterly to the numerical analysis of electromagnetic problems.2.Traditional FDTD method is modified.Such modified FDTD method is successfully applied in the numerical calculation of LHMs.It could solve the numerical problem of traditional FDTD in LHMs simulation.3.TM and TE mode electromagnetic waves are separately concerned.The numerical expressions of the perfect-matched layer(PML)and such modified FDTD method in LHMs modeled by cold plasma model are derived.The permittivityε'_r and permeabilityμ'_r of back ground media are introduced.Two dimensional finite LHMs slab and infinite LHMs slab are numerically analyzed by such modified method.Besides,the refractional phenomena of electromagnetic waves in LHMs slab surface with different refraction-index are simulated.The extended Shell's law which electromagnetic waves satisfy in the LHMs could be verified by the numerical results.4.The much more real media model,Drude model,compared to the cold plasma model is introduced into the LHMs.The numerical expressions of the modified FDTD method in Drude model LHMs are derived in detail.The lossy LHMs slab is studied.The distributions of electromagnetic waves around such LHMs slab with different lossy factorγare calculated.An electromagnetic energy localizing system with such lossy LHMs slab is numerically analyzed.The characteristic of electromagnetic energy localization in such system could be proved by the numerical results.5.The most general model,Lorentz model,is introduced in LHMs.Based on the modified FDTD theory of chapter 3,chapter 4 and chapter 5,the numerical expressions of the modified FDTD method in Lorentz model LHMs are derived. The distributions of electromagnetic waves around such LHMs slab with different thickness are calculated.A multipoint focusing system with LHMs is discussed. According to the numerical results,these multipoint focuses certainly agree with the focusing theory of LHMs.Besides,a multi-layer LHMs system with multi-layer focusing characters is also discussed.A real metal-ring LHMs structure with the refraction-index approximately to -1 is designed which is applied to the multi-layer LHMs system.Ansoft is used to simulate the electromagnetic waves around the real LHMs.Great agreement could be seen between the FDTD results and the Ansoft results.6.Nonlinear LHMs is primarily discussed.The numerical expressions of the modified FDTD method in Nonlinear LHMs with Kerr effects are derived.The distribution of electromagnetic waves around such nonlinear LHMs slab is calculated steadily. Compare to the linear LHMs,the electromagnetic focus could also be observed in this nonlinear LHMs slab.The location of the focus would vary with the distance between the source and the nonlinear LHMs slab.