【作者】 宋磊；

【导师】 梅良模；

【作者基本信息】 山东大学 ， 无线电物理， 2007， 博士

【摘要】 负折射率材料是指介电常数ε和磁导率μ都小于零的介质材料,在这种介质中折射率n为负数。当电磁波在这种介质中传播时,电场矢量E、磁场矢量H和波矢k之间遵从左手系法则,所以负折射率材料又被称为“左手系材料”(LHM)。在负折射率材料中波矢k与能流密度S传播方向平行相反,由此导致了光的负折射、负Doppler效应和负Cherenkov辐射等一些反常的物理现象。2001年,Smith,et al.在微波波段首次发现利用特殊结构周期排列的复合介质能同时得到负介电常量ε和负磁导率μ,从而在试验上验证了制备这种材料的可行性。由于负折射率材料所表现出的众多物理特性,因此受到学术界极大的关注。本论文通过理论分析和数值模拟,重点研究了负折射率材料的相关物理性质和应用。研究内容包括用时域有限差分法(FDTD)数值模拟了电磁波在负折射率材料平板透镜中的传播,验证了负折射率材料平板透镜的完美成像现象。用传输矩阵法(Transfer-Matrix Method)分析了由正负折射率材料平板构成的一维光子晶体的带隙特性和传输参数。最后还用时域有限差分法仿真模拟了电磁波在二维光子晶体中传播时具有的负折射现象。本论文的研究工作和成果如下:1.将时域有限差分(FDTD)法引入了对负折射率材料的物理现象的仿真研究。为了避免仿真程序在迭代过程中由于直接定义介电常量和磁导率为负数而出现的不稳定现象,引入了色散Drude模型间接定义介电常量和磁导率的值。并将色散Drude模型带入Maxwell方程组,推导出了TM电磁波在负折射率材料中传播的时域差分方程以及其在PML吸收边界中的指数差分方程。根据推导出的时域差分方程,我们仿真了由负折射率介质构成的平板透镜的完美成像现象,从仿真结果可以发现只有在ε_r=μ_r=-1的情况下,并且不考虑负折射率介质色散的情况下,由负折射率材料构成的平板透镜才会出现完美透镜的现象,当ε_r≠-1和μ_r≠-1时或者色散不为零时,完美成像现象就不会出现。但负折射率平板透镜仍然对电磁波有着近轴聚焦效应,这类似于光子隧道的效果。另外通过与电磁波在正折射率介质构成的平板透镜中传播特性相比较,可以验证电磁波在负折射率材料中传播时,其波矢方向和坡印廷矢量方向是平行相反的。这和理论分析的结果是一致的。从而证明了我们仿真结果的正确性。2.研究了一维光子晶体中加入了负折射率材料后对光子禁带谱的影响。采用传输矩阵法(TMM,Transfer Matrix Method),计算了由正折射率材料和负折射率材料平板构成的一维光子晶体结构的色散曲线即光子禁带谱。通过计算发现,由正负折射率介质构成的一维光子晶体结构除了存在Bragg禁带以外,在其平均折射率为零时也存在禁带,即零折射率禁带((?)=0禁带)。我们分别计算了由正折射率介质和负折射率介质构成的周期为d和周期为d×2/3的一维光子晶体的透射率,通过比较二者的透过率图,我们可以发现zero-(?)禁带对应的频率没有改变,而Bragg禁带对应的频率向较高的频率区间偏移了。这说明Bragg禁带一维光子晶体的本身周期性有较强的依赖性,而zero-(?)禁带则对一维光子晶体的本身周期性没有什么依赖性。最后我们还计算了改变正负折射率介质构成的一维光子晶体的介质层的厚度对zero-(?)禁带和Bragg禁带的影响,通过比较我们发现改变介质层的厚度时,zero-(?)禁带没有什么明显的改变,而Bragg禁带则被破坏了。3.结合光子晶体带隙图和等频率线(面)图分析了二维光子晶体中出现负折射现象的条件,推导出了负折射现象出现的频率范围。采用平面波展开法计算三角晶格空气柱二维光子晶体的光子晶体带隙图和等频率线(EFS)图,验证了在以上理论所给出的负折射出现的频段。采用有限时域差分法模拟了光在光子晶体界面和内部的传输行为,模拟了光在空气柱楔型二维光子晶体中的负折射现象,在等频率图给出的归一化频率范围内观察到比较明显的负折射现象。另外,还模拟了光在二维介质柱三角晶格光子晶体平板中的负折射现象,在能带图和等频率图给出的频率范围内,同样观察到比较明显的负折射现象。通过上面的模拟分析可以看到,由能带图和等频率面图得到的二维光子晶体的负折射频率范围是正确的,在以上理论所给出的负折射出现的频率范围内,能够观察到明显的负折射现象。更多还原

【Abstract】 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.更多还原