Anisotropic photonic crystals: Generalized plane wave method and dispersion symmetry properties

This article presents a generalized vector plane wave expansion method, applicable to isotropic and anisotropic periodic dielectric media of arbitrary geometry and dimension. The influence of anisotropic material orientation on the symmetry properties of photonic crystal dispersion surface is discussed. It is shown that the overall Brillouin zone symmetry is formed by the intersection of the photonic crystal lattice symmetry and the symmetry determined by the anisotropic material orientation. This work explains how to define the irreducible Brillouin zone of a two-dimensional anisotropic photonic crystal and demonstrates that doing it correctly allows one to avoid erroneous results, when calculating band gap diagrams of anisotropic photonic crystals. With the help of the methods presented, the possibility of controlling the band gaps of anisotropic photonic crystals by means of external electric field is shown.     

Negative refraction in a honeycomb-lattice photonic crystal

In this paper we theoretically investigate a photonic crystal with dielectric rods in a honeycomb lattice. Two left-handed frequency regions are found in the second and third photonic band by using the plane wave expansion method to analyze the photonic band structure and equifrequency contours. Subwavelength imaging by the photonic crystal flat lens are systematically studied by numerical simulations using the multiple scattering method. Different from the photonic crystals with noncircular dielectric rods in air, this structure is almost isotropic at the optimal frequency for superlensing. As a comparison, flat slab focusing is also demonstrated at other frequencies in the two left-handed regions.     

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.     

由球形原子构成的多种周期性介电结构的光子能带计算

采用矢量平面波方法计算了由球形空气原子构成的体心立方结构和六角密堆结构的光子能带，两种结构下都看到了贯通整个布里渊区的禁带。本文预言周期性介电结构的最大折射率调制度和最大禁带宽度对应于同样的原子体积分数，而且这个最佳的原子体积分数是结构无关的。文中还计算了由各向异性介电小球构成的面心立方结构的光子能带并看到了禁带，这与各向同性介电小球构成的面心立方结构很不相同。     

FDTD study of subwavelength imaging by a photonic crystal slab

The problem of subwavelength imaging via a photonic crystal slab lens made of two-dimensional (2D) square arrays of parallel dielectric cylinders in air is studied and discussed theoretically. The finite-difference time-domain method is employed to investigate the unique features of imaging by such lens. We confirm earlier findings that a photonic crystal slab lens can provide the imaging of a point source. By analysing the transmission properties of the proposed structure, we demonstrate that inside the all-angle negative refraction, there are some favourable directions for waves to travel. We show that the surface termination of the photonic crystal is a key parameter to obtain a good quality image. The super-resolution of two sources separated by a distance less than the wavelength is also considered. It is shown that the achievable resolution is limited by the slab length.     

Electromagnetic wave propagation from a point source in air through a medium with a negative refractive index

Refraction of an electromagnetic wave from a point source to a medium with a negative refractive index is considered. An electric Hertz dipole that is located in air and directed parallel to a plane interface is considered as the point source. It is rigorously shown that the electromagnetic radiation propagated from the dipole into the medium with the negative refractive index is focused within a certain region in this medium. The sizes of the focusing region are determined. As a result, it is pointed out that the diffraction limit cannot be overcome by using homogeneous materials with negative refractive indices.     

Band gap properties of two-dimensional photonic crystals with rhombic lattice

A new structure of two-dimensional photonic crystals (PCs) with rhombic lattice is proposed in this paper. It provides more flexibility in the design of photonic crystal devices and makes the designer be able to choose a more suitable lattice angle to satisfy different demands. The first Brillouin zone (1st BZ) of this structure is discussed and the general wave vectors are derived. The plane wave expansion (PWE) method is used to analyze the band gap properties. The impact of different lattice angels on the band gaps is analyzed, and the band gap map is also given.     

基于蜷曲空间结构的近零折射率声聚焦透镜

研究基于蜷曲空间结构的近零折射率声聚焦透镜.根据近零折射率材料的声波方向选择机理,采用蜷曲空间结构为基本单元进行排列,设计具有特定入射与出射界面的几何结构,对透射声波的出射方向进行调控,实现了平面声波与柱面声波的聚焦效应,并深入讨论了透镜内部刚性散射体对声聚焦性能的影响.在此基础上,改变近零折射率透镜的出射界面,可以精确调控声波阵面的形状与方向.该类型透镜具有单一的单元结构、高聚焦性能及高鲁棒性等优点.研究结果为设计新型近零折射率声聚焦透镜提供了理论指导与实验参考,同时也为研究声波阵面的调控提供了新思路.     

二维斜方晶格光子晶体的第一布里渊区分析

二维斜方晶格光子晶体在光学聚焦器件及光子晶体波导中有重要的应用价值。对二维斜方晶格的第一布里渊区进行研究发现,保持斜方晶格基矢模长比R不变,改变倾斜角θ,第一布里渊区形状将在矩形和平行六边形间交替变化,所需的倒格矢也相应地变化,利用倒格矢正交临界条件可以对第一布里渊区的形状和所需的倒格矢进行划分。最后,利用平面波展开法对一种斜方晶格光子晶体进行带隙计算,验证了这种划分的正确性。     

基于近零折射率材料的声非对称聚焦透镜

研究基于近零折射率声子晶体的声非对称聚焦透镜。声非对称聚焦透镜的两侧分别为竖直平面与圆弧面结构,由于近零折射率材料的声波方向选择性,当声波从竖直平面一侧入射时,可以通过透镜,实现高性能声聚焦效应;而当声波从圆弧面一侧任意方向入射时,声波无法通过透镜,从而实现同时具有聚焦与非对称传输特性的声学透镜。在此基础上,改变透镜圆弧面的曲率半径,可以调控非对称透镜的正向聚焦焦点位置,且声非对称传输性能保持不变.此外,透镜内部的刚性散射体对声非对称聚焦性能的影响较小。研究结果表明所设计的声非对称聚焦透镜具有多功能、单一结构及高鲁棒性等优点,为设计新型近零折射率声学器件提供相应的理论方案与实验参考.      

Refraction of light in two-dimensional photonic crystals

Refraction of light at an interface between a homogeneous dielectric and a two-dimensional photonic crystal is studied. Using the isofrequency method, various cases of refraction, including a change in the magnitude and direction of the wave vector of the incident wave, in the refractive indices of the media, and in the mutual orientation of the interface and the translation vectors of the photonic crystal, are investigated. Different types of refraction and the possibilities for realizing negative and multiwave refraction are considered.     

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.     

A point radiator parallel to a plane layer with negative refractive index

Focusing of an electromagnetic wave radiated by a point source and transmitted through a plane layer filled with a medium with negative refractive index is considered. An elementary electric Hertzian dipole located in the air (or vacuum) parallel to the boundaries of the layer is considered as a point source of radiation. It is rigorously shown that, after transmitting through a layer with negative refractive index, the electromagnetic wave of the dipole is focused into a certain domain. The dimensions of the focusing region are investigated. The results of the investigation show that the use of homogeneous materials with negative refraction does not allow one to overcome the diffraction limit.     

Rainbow trapping using chirped all-dielectric periodic structures

We report a numerical investigation of rainbow trapping (light of different wavelengths) at different spatial locations in a newly designed two-dimensional photonic structure that is formed using chirping parameters in two-dimensional photonic crystals. Chirped parameters ensure trapping of certain light wavelengths inside these structures. To achieve broadband electromagnetic wave trapping, we properly adjust and chirp the position and dielectric filling factor of each unit cell within a photonic crystal structure. The low group velocity regions of the dielectric continuum bands at the Brillouin zone edge enable different wavelengths to be slowed and stopped along the propagation direction. The all-dielectric transparent material nature of the proposed structure realizes light trapping in different electromagnetic regions by spatially varying the effective refractive index of the structure.     

色散负折射特异介质的1维光子晶体缺陷态

在1维光子晶体中引入色散负折射特异介质,分析了其介电常数和磁导率在微波区（1～10 GHz）与频率的关系。分别对以色散负折射介质为缺陷的正折射率介质光子晶体及以正折射率介质为缺陷的正负折射率介质光子晶体进行了数值仿真,得出了均匀平面电磁波在正入射和斜入射时的透射谱。结果表明:在介电常数和磁导率均为负值的不同禁带中,分别出现了单、双缺陷模。利用透射谱的这一特点,可实现单、双通道滤波。     

Multi-band imaging and focusing of photonic crystal flat lens with scatterer-size gradient

In this Letter, a photonic crystal(PC) flat lens with a scatterer-size gradient is proposed, which simultaneously achieves imaging of the point source and sub-wavelength focusing of the plane wave in the first, second, and fifth bands. The imaging of the point source breaks through the diffraction limit in the second and fifth bands. The PC flat lens with the scatterer-size gradient is expected to be used in a new multifunctional optical imaging and focusing device, which improves the application potential of a PC flat lens.     

Optical third-harmonic generation in one-dimensional photonic crystals and microcavities

The formalism of nonlinear transfer matrices is used to develop a phenomenological model of a cubic nonlinear-optical response of one-dimensional photonic crystals and microcavities. It is shown that third-harmonic generation can be resonantly enhanced by frequency-angular tuning of the fundamental wave to the photonic band-gap edges and the microcavity mode. The positions and amplitudes of third-harmonic resonances at the edges of a photonic band gap strongly depend on the value and sign of the dispersion of refractive indexes of the layers that constitute the photonic crystal. Model calculations elucidate the role played by phase matching and spatial localization of the fundamental and third-harmonic fields inside a photonic crystal as the main mechanisms of enhancement of third-harmonic generation. The experimental spectrum of third-harmonic intensity of a porous silicon microcavity agrees with the calculated results.     

Optimized focusing properties of photonic crystal slabs

We propose an optimization procedure for focusing operation in finite two dimensional photonic crystal slabs. The device consists of a triangular lattice air holes etched in a semiconductor matrix at a nanometer scale to operate at 1.55 μm. To reach simultaneously an effective refractive index equal to −1 along with a very high transmission coefficient whatever optical wave incidence, the parameters as the lattice period and/or filling factor are precisely adjusted depending on the slab thickness. The method relies on Fabry-Perot resonances engineering in the air/crystal/air cavity constituting the lens.     

Design of photonic crystal superlens with improved image resolution

In this paper, we theoretically investigate the spatial resolution of a triangular two-dimensional photonic crystal superlens. We prove that this resolution can be improved by optimizing the air hole radius as well as the air hole shape. First, it is found that by decreasing the radius of the air holes, the spatial resolution is improved significantly. Next, we demonstrate that using elliptic air holes instead of circular air holes in a triangular two-dimensional photonic crystal can leads to good-quality images and focusing, with effective refractive index n_eff=−1 and enhanced image resolution. It is also shown that for the case of two sources, the resolution of such a photonic crystal lens can be made indeed better than the radiation wavelength.     

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.