Negative refraction in two-dimensional photonic crystals

We present some of our recent results for negative refraction in photonic crystals. The concept of negative refraction in photonic crystals is firstly introduced. Then, the propagation of electromagnetic waves in photonic crystals is systematically studied. By the layer Korringa–Kohn–Rostoker method, the coupling efficiency between external plane waves and the Bloch waves in photonic crystals is investigated. It is found that the coupling coefficient is highly angular dependent even for an interface between air with n=1 and a photonic crystal with effective index n_eff=-1. It is also shown that, for point imaging by a photonic crystal slab, owing to the negative refraction, the influence of the surface termination on the transmission and the imaging quality is significant. Finally, we present results experimentally demonstrating negative refraction in a two-dimensional photonic crystal at optical communication wavelengths. PACS 42.70.Qs; 41.85.Ct; 42.30.Va     

基于硅柱-磁性液体体系的光子晶体的可调谐负折射特性研究

本文研究了硅柱在MnFe₂O₄磁性液体背景中排列成六边形结构的二维光子晶体的可调谐负折射特性. 利用平面波展开法和时域有限差分法理论研究了硅柱-磁性液体体系二维光子晶体的带隙结构、等频曲线和负折射现象随外磁场强度的变化关系. 模拟结果表明, 硅柱-磁性液体体系二维光子晶体工作在TE模式时, 其负折射特性可由外磁场调节. 在固定背景溶液的磁性颗粒体积分数和入射光频率时, 所研究的折射光束的偏转角和光子晶体的负折射率绝对值随外磁场的增大而增大, 而在固定背景溶液的磁性颗粒体积分数和外磁场强度时, 负折射角和负折射率的绝对值随入射光归一化频率增大而减小. 固定外场强度和入射光频率时, 所研究结构的负折射特性随背景溶液的磁性颗粒体积分数增大而变弱.     

Polarization beam splitters based on a two-dimensional photonic crystal of negative refraction

A two-dimensional metallo-dielectric photonic crystal of negative refraction was designed for the application of polarization beam splitters. To match the refractive index of air, the effective refractive index of the designed photonic crystal is -1 for TE polarization and +1 for TM polarization. Two types of polarization beam splitter are presented.     

Amphoteric-like refraction in a two-dimensional photonic crystal

High-index contrast photonic crystals possess an intricate photonic band structure that is responsible for surprising phenomena as the surperprism effect, self-collimation, power splitting or negative refraction. Recently, it was reported that at the interface between an isotropic medium and a uniaxial crystal (or between two uniaxial crystals) a phenomenon known as amphoteric refraction, that is, positive as well as negative refraction, can take place. By means of a equifrequency contours analysis and finite-difference time-domain simulations, we show that a two dimensional photonic crystal can also present amphoteric refraction by properly choosing the lattice orientation and the termination. However, total transmission is difficult to achieve because a Bloch mode is excited inside the photonic crystal and the coupling efficiency from this mode to an external plane wave is lower than one.     

二维光子晶体负折射现象条件及特性研究

结合光子晶体带隙图和等频率线图分析了二维光子晶体中出现负折射现象的条件,得出了负折射现象出现的频率范围.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,验证了以上理论所给出的负折射出现的频段,观察到了明显的负折射现象.比较了不同介质、不同晶格结构光子晶体中不同频率的负折射行为.提出一种新结构的六角型二维三角晶格光子晶体分光镜的模型.     

Negative refraction and left-handed electromagnetism in microwave photonic crystals

We demonstrate the negative refraction of microwaves in a metallic photonic crystal prism. The spectral response of the photonic crystal prism, which manifests both positive and negative refraction, is in complete agreement with band-structure calculations and numerical simulations. The validity of Snell's law with a negative refractive index is confirmed experimentally and theoretically. The negative refraction observed corresponds to left-handed electromagnetism that arises due to the dispersion characteristics of waves in a periodic medium. This mechanism for negative refraction is different from that in metamaterials.     

All angle negative refraction with the effective phase index of-1

We theoretically studied a left-hand structure based on a two-dimensional (2D) photonic crystal (PC)with a negative refractive index. The propagation of electromagnetic waves in the proposed PC structure is investigated through dispersion characteristic analysis and numerical simulation of field pattern. The designed PC structure can exhibit all angle negative refraction, and the corresponding effective refractive indices along all directions are almost same and close to the ideal value of -1. A flat lens formed from such a PC has been designed and its imaging properties have been investigated systematically.     

二维空气孔型光子晶体负折射平板透镜的减反层

提出并优化了由单排渐变介质波导构成的二维空气孔型光子晶体负折射平板透镜表面的减反层，改善了成像质量.二维时域有限差分模拟计算结果表明，采用减反层后，在入射角小于23°的范围内，在使得有效折射率n_eff=-1的工作频率处，光子晶体表面对从空气一侧入射的平面波的反射率可降低到1％以下. 关键词： 光子晶体 负折射 平板透镜 减反层     

液晶光子晶体的负折射特性研究

可调光子晶体由于其潜在的应用价值成为现今光子晶体研究中的一个热点.本文提出了通过光诱导液晶来调节光子晶体负折射效应的方法,采用平面波展开法、等频图分析法和推广的斯涅尔定理分析了二维液晶正方晶格光子晶体负折射的可调节性.提出了一种新型的液晶光子晶体结构, 数值模拟结果表明:通过偏振光改变液晶指向矢可以调节该液晶光子晶体的负折射.与电场调制方法相比,该光控液晶取向技术具有响应速度快、结构简单的优点.这种可调光子晶体可用于制作光控路由或者应用于全光网络.     

A liquid refractive index detect method based on negative refraction phenomenon in 2D photonic crystal structure

This paper is mainly concerned with the investigation of negative refraction phenomenon dependent on the background refractive index in 2D photonic crystal, which consists of a hexagonal lattice of circular dielectric rods with Si. The paper presents the relationship between background refractive index and negative refraction. The relationship is investigated by using the finite-difference time-domain (FDTD) method on software RSoft. The results point out that the output power is added with the increase of the background refractive index. With the research, a new fluid refractive index detection method is proposed. Compared with other normal liquid refractive index analyzer reported, this detector has advantages of faster detection, less stray light interference and miniaturization.     

基于空气孔的光子晶体亚波长成像的特性研究

负折射率材料因为其奇异的特性成为广泛研究的对象,尤其是光子晶体平板的完美成像.本文采用空气孔在硅介质中周期性排列构成六角结构的光子晶体结构,用平面波展开法及FDTD方法,研究了该光子晶体的亚波长成像能力还研究了入射波长以及温度漂移对该光子晶体平面亚波长成像的影响.     

等效折射率为非-1时的亚波长成像

本文采用硅柱子周期性排列构成六角结构光子晶体,用平面波展开方法和FDTD方法研究表明,此结构光子晶体存在等效折射率接近-1的频率区域.在等效折射率趋于-1但不等于-1时,此光子晶体平板结构超透镜能形成一个非近场的像.模拟还发现,此结构平板光子晶体等效折射率为非-1时,可以亚波长成像. 关键词： 负折射 光子晶体 亚波长 成像     

一维掺杂光子晶体缺陷模的共振理论

为了得到一维掺杂光子晶体的共振理论,建立了一维掺杂光子晶体的谐振腔模型,利用谐振腔的共振条件推导出缺陷模频率满足的解析公式,从理论上解释了产生一维掺杂光子晶体缺陷模的物理机理.利用频率的解析公式对缺陷模的频率随入射角、杂质光学厚度以及杂质折射率的变化规律进行了研究,解释了一维掺杂光子晶体缺陷模的变化规律.与特征矩阵法的计算结果相比,其结果完全吻合,从而证明了共振理论的正确性,弥补了一维光子晶体研究中数值计算方法的不足.     

Negative refraction in photonic crystals

We demonstrate that light propagation in strongly modulated 2D/3D photonic crystals (PhCs) becomes refraction-like in the vicinity of the photonic bandgap, which is contrary to the fact that light propagation in weakly modulated PhCs is very different from refraction and thus the definition of refraction index becomes meaningless. Such a crystal behaves like a material having an effective refractive index controllable by the band structure. This situation is analogous to the effective-mass approximation in electron-band theory. The propagation states having a negative effective index exhibit unusual properties, such as mirror-like imaging effect, image-transfer effect. These properties are confirmed by finite-difference time-domain simulations.     

一维掺杂光子晶体缺陷模的共振理论

为了得到一维掺杂光子晶体的共振理论,建立了一维掺杂光子晶体的谐振腔模型,利用谐振腔的共振条件推导出缺陷模频率满足的解析公式,从理论上解释了产生一维掺杂光子晶体缺陷模的物理机理.利用频率的解析公式对缺陷模的频率随入射角、杂质光学厚度以及杂质折射率的变化规律进行了研究,解释了一维掺杂光子晶体缺陷模的变化规律.与特征矩阵法的计算结果相比,其结果完全吻合,从而证明了共振理论的正确性,弥补了一维光子晶体研究中数值计算方法的不足.     

Frequency bands of negative refraction in finite one-dimensional photonic crystals

We have discussed theoretically the negative refraction in finite one-dimensional (1D) photonic crystals (PCs) composed of alternative layers with high index contrast. The frequency bands of negative refraction are obtained with the help of the photonic band structure, the group velocity and the power transmittance, which are all obtained in analytical expression. There shows negative transverse position shift at the endface when negative refraction occurs, which is analysed in detail.     

一维光子晶体中的电磁模密度

阐述了电磁模密度(EDOM)的概念及其在描述光辐射中的重要作用.推导了有限大小的均匀介质和一维光子晶体EDOM的解析表达式,计算出由λ₀/4薄片构成的一维光子晶体的EDOM,明显看出一维光子晶体中EDOM受光子带结构调制的现象;分析了在带边缘处EDOM有极大增强的现象,其值近似正比于周期数N的平方和两种介质折射率差的平方,并用数值计算结果证实了这一特点.     

基于各向异性介质的偏振分束器

利用各向异性介质与各向同性介质构造了一维光子晶体,利用传输矩阵方法分析了它的能带结构,指出利用各向异性介质可以构造高消光比,全角度的偏振分束器件,并分析了它的理论基础.对影响偏振分束带宽的因素进行了分析.为进一步改进设计提出了方向.     

Homogenization of magnetodielectric photonic crystals

We calculate the low-frequency index of refraction of a medium which is homogeneous along axis z and possesses a periodic dependence of the permittivity epsilon(r) and permeability micro(r) in the x-y plane (2D magnetodielectric photonic crystal). Exact analytical formulas for the effective index of refraction for two eigenmodes with vector E or H polarized along axis z are obtained. We show that, unlike nonmagnetic photonic crystals where the E mode is ordinary and the H mode is extraordinary, now both modes exhibit extraordinary behavior. Because of this distinction, the magnetodielectric photonic crystals exhibit optical properties that do not exist for natural crystals. We also discuss the limiting case of perfectly conducting cylinders and clarify the so-called problem of noncommuting limits, omega-->0 and epsilon--> infinity.     

Dispersionless slow light by photonic crystal slab waveguide with innermost elliptical air holes

We report a low-loss photonic crystal slab waveguide formed by deforming the innermost circle air holes in the conventional photonic crystal slab waveguide into elliptical ones. We obtain the photonic bands and group index of guided modes in this photonic crystal waveguide by guided-mode expansion method and investigate the dependence of photonic bands and group index of guided modes on the parameters of the innermost elliptical air holes. The group velocity and group velocity dispersion of this waveguide strongly depend on the innermost elliptical air holes. Photonic crystal slab waveguide with the optimum innermost elliptical air holes possesses a wider single mode region below the light line, in which light can easily propagate without intrinsic loss. At the same time, the guided mode supported by this waveguide has nearly constant group velocity and vanishing group velocity dispersion in a 3-5 nm bandwidth.