Physics and applications of photonic crystals

In this article, we investigate how the photonic band gaps and the variety of band dispersions of photonic crystals can be utilized for various applications and how they further give rise to completely novel optical phenomena. The enhancement of spontaneous emission through coupled cavity waveguides in a one-dimensional silicon nitride photonic microcrystal is investigated. We then present the highly directive radiation from sources embedded in two-dimensional photonic crystals. The manifestation of novel and intriguing optical properties of photonic crystals are exemplified experimentally by the negative refraction and the focusing of electromagnetic waves through a photonic crystal slab with subwavelength resolution.     

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     

Intensity depending on object distance in a two-dimensional photonic crystal

The propagation of electromagnetic (EM) waves in two-dimensional triangular-lattice photonic crystals (PCs) is investigated through dispersion characteristics analysis and numerical simulation of field pattern. The designed PC structure can exhibit all angle negative refraction in the second band. A flat superlens formed from such a PC has been designed and its imaging properties have been investigated systematically. Good-quality images and focusing, with relative refractive index of ?1, have been observed in this system for TE mode waves. In contrast to the images in near-field region for the lowest valence band, non-near-field images, explicitly following the well-known wave-beam negative refraction law, have been demonstrated. The relation between the intensity of the image and the object distance has also been discussed in this paper. The extensive applications of such a phenomenon to optical devices are anticipated.     

对全入射角负折射二维光子晶体结构和电磁参量的研究

利用二维光子晶体的等频线分析原理和平面波展开方法,得到了使二维光子晶体产生全入射角负折射(All-Angle Negative Refraction,AANR)现象时,入射电磁波的频率取值范围.同时,分析了AANR频率范围随着结构参量(晶格类型、介质棒半径与晶格周期的比值)和电磁参量(介质柱介电常量、本底介电常量、入射电磁波偏振方向)变化的行为.结果表明:固定组成光子晶体的一种介质的介电常量,另一介质的介电常量只有达到一定阈值,才有可能使光子晶体出现AANR现象.在给定两种介质介电常量的条件下,存在使AANR频率范围最大化的结构参量和电磁参量.     

Focusing Systems Based on Two-Dimensional Photonic Crystals

Russian Physics Journal - Methods of focusing electromagnetic waves based on the use of two-dimensional photonic crystals formed by metal and dielectric elements are considered. In the first case,...     

十二重准晶光子结构中的负折射与成像

最近实验证明周期性的光子晶体中存在电磁波的负折射现象，并且观测到亚波长成像．然而，这些研究主要集中在剧期性结构中，对非周期结构的研究还没有相关的报道。文章报道了一种新的理论和实验结果：非周期性十二重准晶光子结构同样存在负折射，并且可以实现超透镜的远场成像。具有这些特性的光子准晶可以广泛的应用于光集成器件中。     

Imaging properties of triangular lattice photonic crystal at multi-bands

The propagation of electromagnetic (EM) waves in two-dimensional triangular-lattice photonic crystals (PCs) is investigated through dispersion characteristics analysis and numerical simulation of field pattern. The designed PC structure can exhibit all angle negative refraction in the second and the eighth band. A flat superlen formed from such a PC has been designed and its imaging properties have been investigated systematically. Both in band 2 and band 8, a quite high quality image in the opposite side of the slab can be found.     

含负折射率材料的一维光子晶体的光学传输特性

采用光学传输矩阵方法,模拟研究了由正折射率材料和负折射率材料交替组成的一维光子晶体的光学传输特性.计算了这种含负折射率材料的一维光子晶体的透射谱和色散关系.结果表明,在正入射时,含负折射率材料的光子晶体的带隙要比传统的光子晶体要大得多,并具有狭窄的透射带,从光学薄膜理论的色散关系出发解释了形成上述现象的原因.讨论了在不同的偏振模式下,光以中心波长入射时,反射率随着入射角度的变化关系.发现含负折射率材料的一维光子晶体具有更好的角度特性,可以用来实现对中心波长的全方位反射.     

基于一维金属光子晶体平凹镜的柱矢量光束亚波长聚焦

柱矢量光束具有柱对称性的偏振分布,其独特的光场分布和聚焦特性被广泛应用于光学微操纵及光学成像等领域,并迅速向亚波长尺度拓展.通常,亚波长尺度聚焦采用等离激元透镜实现,但存在光场调控的偏振态局限性.而借助光子晶体的负折射效应,不仅能够实现亚波长聚焦或成像,而且应对正交偏振态同时有效.采用对电磁波具有更强调控能力的一维金属光子晶体结构,计算得到的能带结构和等频曲线表明其负折射效应在特定波段对正交偏振态同时有效.在此基础上设计出一维金属光子晶体柱对称平凹镜结构,通过有限元算法模拟显示了可见光波段的径向和旋向偏振光的同时亚波长聚焦行为.进一步的结果表明,改变柱矢量光束的偏振组分能够直接有效地调节焦场空间分布及偏振分布特性.所提出的平凹镜结构能够实现对任意偏振组分的柱矢量光束的亚波长尺度聚焦,且该结构的设计对于各波段情况均有参考意义.该研究结果对小尺度粒子的光学微操纵、超分辨率成像等相关领域具有潜在的应用价值.     

Negative refraction at infrared wavelengths in a two-dimensional photonic crystal

We report on the first experimental evidence of negative refraction at telecommunication wavelengths by a two-dimensional photonic crystal field. Samples were fabricated by chemically assisted ion beam etching in the InP-based low-index constrast system. Experiments of beam imaging and light collection show light focusing by the photonic crystal field. Finite-difference time-domain simulations confirm that the observed focusing is due to negative refraction in the photonic crystal area.     

正方介质柱光子晶体中异常传输现象研究

研究了电磁波在二维正方介质柱光子晶体中的传输,发现处于第一频带部分带隙的电磁波在不同界面切割方向上不同角度入射时可分别产生全反射及复杂异常折射现象如自准直现象、负折射现象.首先利用平面波展开法从理论上研究正方介质柱正方晶格光子晶体的频带结构及等频线,然后通过时域有限差分法来仿真研究光子晶体在第一频带部分带隙的传输特性.当光子晶体的界面切割沿着ΓX方向时,由于光子晶体内无本征模能够被有效地激发,入射波束被完全反射,这与光子带隙导致的全反射具有本质的不同;当光子晶体的界面切割方向沿着ΓM时,归因于其扁平的等频线,一定角度范围内入射的波束在光子晶体内几乎沿同方向传输即产生自准直现象.     

Quantum photonic crystals—Quantytes

Optical properties and structural characteristics of quantum photonic crystals??quantytes??are investigated. Quantytes are crystalline structures with periodically arranged quantum dots of dielectrics, ferroelectrics, magnets, or metals. They feature so-called stop bands in which anomalous reflection of electromagnetic radiation from the photonic crystal surface is observed. It is found that quantytes are characterized by a negative refractive index and anomalous deceleration of electromagnetic waves in some spectral ranges. Possible uses of quantytes as devices for recording and reading of optical information, optical elements with negative refraction, selective mirrors, and narrow-band light filters are discussed.     

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.     

Alternative approach to realize all-angle negative refraction and far-field imaging effects via two-dimensional all-solid photonic crystals

We systematically investigate the band structures, equifrequency surfaces, and the intensity distributions of Poynting vector in two-dimensional Si/SiO₂ all-solid photonic crystals with different lattice types. It is found that all-angle negative refraction with effective refractive index of nearly ? 1 and far-field imaging effects can be achieved from all-solid photonic crystals. And more important thing is that, the all-solid photonic crystals can realize all-angle negative refraction at lower frequencies and provide far-field images with higher quality compared with normal air–dielectric photonic crystals. Such improved performance provides an alternative approach to realize all-angle negative refraction in super-lens and super-prisms applications.     

Subwavelength resolution in a two-dimensional photonic-crystal-based superlens

We experimentally and theoretically demonstrate single-beam negative refraction and superlensing in the valence band of a two-dimensional photonic crystal operating in the microwave regime. By measuring the refracted electromagnetic waves from a slab shaped photonic crystal, we find a refractive index of -1.94 that is very close to the theoretical value of -2.06. A scanning transmission measurement technique is used to measure the spatial power distribution of the focused electromagnetic waves that radiate from a point source. The full width at half maximum of the focused beam is measured to be 0.21 lambda, which is in good agreement with the finite difference time domain method simulations. We also report a subwavelength resolution for the image of two incoherent point sources, which are separated by a distance of lambda/3.     

Negative refraction and left-handed properties in two-dimensional photonic crystals

We report on the negative refraction and left-handed behavior of two-dimensional photonic crystals. For the triangular two-dimensional photonic crystals there are two saddle points and a key point in the first Brillouin zone for the second band, which play important role to determine the refraction phenomena. There is no determined relation between the left-handed behavior and the negative refraction. The refraction phenomena depend on the band structure and the configuration of the incident light. For the first configuration, the first Brillouin zone can be divided into three parts. In part I there are negative refraction and left-handed behaviors. In part II there are normal refraction and left-handed behaviors. In part III there are normal refraction and right-handed behaviors. For the second configuration, the first Brillouin zone can only be divided into two parts. For these complex refraction phenomena, it is meaningless to define the phase refractive index, and it is necessary to define the effective refraction index by a Snell-like formula, and the value of the effective index is determined by the configuration and the band structure.     

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.     

Blur Reduction in the Focal Plane of Optical Receivers by Exploiting the Negative Refractive Behavior of Photonic Crystals

We present a passive method for reducing the size of a focal spot blurred by wavefront distortions in an optical system. The key to this reduction lies in the rather unique behavior of photonic crystals to exhibit negative refraction. First, we review the design of such a photonic crystal structure and analyze its dispersion property to find the proper condition where negative refraction occurs. The predictions derived from theoretical infinite structures are confirmed by rigorous electromagnetic analysis using both the finite-difference time-domain (FDTD) and rigorous coupled wave analysis (RCWA) methods in combination with more realistic finite structures. Second, we discuss an unconventional approach to exploit the negative refractive behavior in reducing the focal spot area spread caused by a blurred wavefront. A proof-of-principle calculation of this approach is performed with the ray trace method to visualize the reduction of the illumination area while preserving the propagation angle of the incoming beam. Finally, we investigate the crystal’s performance when its two-dimensional structure is exposed to conical illumination.     

用转移矩阵法数值研究二维正方介质柱光子晶体的传输特性

利用转移矩阵方法对二维正方介质柱光子晶体的传输特性进行了研究,数值计算研究了不同晶格、同一晶格柱体截面面积不同、放置方位角不同时光子晶体的传输特性。数值结果表明光子禁带的宽度与中心频率和晶格结构有很大关系,正方晶格更易形成平坦光子禁带,柱体截面面积大,则形成的禁带较宽,在其他因素相同的条件下柱体放置的方位角对光子禁带有重要影响。数值研究表明在正方介质柱下设计宽平坦光子禁带时,可以首先考虑正方晶格结构,其次设法使柱体截面尽量大一些,最后可通过柱体放置方位角来微调光子禁带的宽度与中心频率以达到设计要求。     

Negative Refraction and Near-Field Imaging of an Elliptical-Rod Photonic Crystal Slab in the Second Band

Negative refraction and imaging properties of the electromagnetic wave through a two-dimensional photonic crystal （PC） slab, which consists of a square lattice of elliptical dielectric rods immersed in the air background, is studied by the plane-wave expansion method and the finite-difference time-domain method. A point source placed in the vicinity of the PC slab can form a good-quality image spot through the PC slab for the incident frequencies within the second photonic band. The calculated result also shows that negative refraction occurs in this kind of PC slab.