Theoretic Research And Numerical Simulation Of Negative Refractive Index Materials

The negative refractive index materials are characterized by simultaneous negative permittivity and permeability, so the refractive index of this materials are negative. When the electromagnetic wave propagate in this materials, the electric field vector E, magnetic field vector H and wave vector k form a left-handed set, so we called this materials "left-handed materials"(LHM). In this materials the wave vector k (phase velocity) and Poynting vector S are anti-parallel, so there are novel electromagnetic properties, for example, the negative Snell's law, negative Doppler effect, negative Cherenkov radiation, et al. In 2001, Smith, et al. proposed and tested that the new meta-materials consisting of periodic structure can simultaneous have negative permittivity and permeability in the microwave range, so the feasibility of manufacturing this meta-materials is proved. Because the left-handed materials have many unique physics characteristics, there are much interesting in the academe.In this paper, our research stress on the physics properties and application of the left-handed materials by the theoretic analysis and numerical simulation. In the second section, the propagation of the electromagnetic in the slab lens consisting of negative refractive materials is simulated by finite-difference time-domain method (FDTD). The perfect lens phenomenon is analyzed and approved by the FDTD. In the third section, the band structure and the transmittance of the one dimensional photonic crystals consisting of negative and positive refractive index materials are analyzed by the transfer matrix method (TMM). In the fourth section, the negative refraction phenomena of light propagation in the two dimensional photonic crystals are simulated by FDTD.The main research works and conclusion are as following:1. The finite-difference time-domain (FDTD) method was introduced into the simulation of the physics phenomena of the negative refractive index materials (NIM). The Drude model was introduced to indirectly defining the permittivityεand permeabilityμ, in order to avoid instability of the leapfrog in time domain caused by directly defining the negative values of the permittivityεand permeabilityμ. By introducing the Drude model to the Maxwell equations, the time-domain difference equations in the NIMs and the exponential difference equations in the PML absorbing boundary of TM model EW were induced. Based on these time-domain difference equations, the perfect lens phenomenon of the slab lens consisting of the NIMs was simulated. The simulation results show the perfect lens phenomenon only occur when theε_r =μ_r =-1 and ignoring the dispersion of the materials.When theε_r≠-1 andμ_r≠-1 or take the dispersion into account, theperfect lens phenomenon was disappear, but the paraxial focusing of the wave energy occurs. In addition, it was proved that the wave vector k and Poynting vector S are anti-parallel in the NIMs by comparing with the EW wave propagation phenomenon in the normal materials. These results were consistent with the theoretically analyzing, so proved the correctness of our simulation results.2. The influences of the one dimensional photonic crystals consisting of the negative and positive refractive index materials on the action spectrum were studied in this section. The dispersive relation (i.e. the photonic band gap structure) of this one dimensional photonic crystals consisting of the negative and positive refractive index materials were calculated by the TMM. From the calculation results, it wasfound that there was the zero-n|- gap, besides the Bragg gap. The transmittances of the period d and the period d×2/3 of the one dimensional photonic crystals consisting of the negative and positive refractive index materials were calculated respectively. It can be found that the zero-n|- gap didn't changed but the Bragg gap shifted to higher frequency range by comparing two transmittances of the period d and the period d×2/3. It can be proved that the Bragg gap is an intrinsic consequence of periodicity and the gap frequency is tied with the size of period, but the zero-n|- gap is independent of the size of periodicity. Lastly, the influences of the thickness changing on the transmittance were calculated. From the calculation results, it canbe found that the zero - n|- gap didn't changed but the Bragg gap is destroyed, when the thickness of the negative and positive materials randomly changed.3. In the fourth chapter, the negative refraction phenomenon in two-dimension (2D) photonic crystals (PCs) is investigated with the band structure calculation and equal frequency surface (EFS) of PCs. The frequency range of negative refraction phenomenon appearing is gained. The band structure and equal frequency surface (EFS) of triangle air-hole two dimensional PCs were calculated by the plane wave expansion method (PWE). The FDTD was used to simulate the propagation of light at the interface and inside of the photonic crystals. It is concluded that the negative refraction phenomena in two-dimension photonic crystals were real observed in the specific frequency range. Based on above analyzing, the negative refractive phenomenon of the prism-lens consisting of 2D air-column PCs was simulating and the obvious negative refractive phenomenon was observed. Furthermore, the negative refractive phenomenon of the slab-lens consisting of 2D triangle column PCs was simulating and the obvious negative refractive phenomenon was observed in the frequency range obtained from the band structure and the EFS method.