Influence of line defects on focusing in a two-dimensional photonic-crystal flat lens

We investigate in detail the influence of line defects on focusing of electromagnetic waves in a two-dimensional photonic-crystal flat lens. Through simulations, we find that a focusing can always be observed when a line defect in the lens is introduced along the light transmission direction and the width of the line defect is less than \lambda /2. However, there appear two focusings when the width of the line defect is more than \lambda /2. When the line defect is introduced along the direction perpendicular to the transmission, there is always one focusing.     

二维正方各向异性碲圆柱光子晶体完全禁带中缺陷模的FDTD计算分析和设计

用FDTD方法计算了二维正方晶胞各向异性碲圆柱光子晶体的点缺陷模.为了得到TE,TM模式在完全禁带中具有相同共振频率的缺陷模,对中心点缺陷半径Rd以及中心附近对称位置的点缺陷半径Rn做了一系列微调.计算表明,TM模对于Rn的变化不敏感,而TE模随着Rn的改变出现了明显的规则的移动趋势.通过计算分析,发现对应于f=0.4的背景(R=0.3568a),当Rd=0.55a,Rn=0.26a时在完全禁带中TE和TM的缺陷模具有相同的共振频率ω0=0.2466ωe(其中ωe=2πca,a为晶格常数) 关键词： 时域有限差分法 光子晶体 缺陷模 各向异性     

Towards focusing using photonic crystal flat lens

We report on the numerical simulation and fabrication of a two-dimensional flat lens based on negative refraction in photonic crystals. The slab acting as a lens is made of an hole array (operating at the wavelength of 1.5 μm) etched in a InP/InGaAsP/InP semiconductor layer. We first study the key issues for the achievement of a negative refractive index taking advantage of folding of dispersion branches with main emphasis in dispersion properties rather than the opening of forbidden gaps. The diffraction and refraction regimes are analysed according to the comparison of the wave-vector with respect to the relevant dimensions of the hole array. In the second stage, we illustrate technological challenges in terms of e-beam lithography on a sub-micron scale and deep reactive ion etching for an indium phosphide based technology.     

Theoretical demonstration of the hybrid focusing points of sonic crystal flat lenses and possible applications

We demonstrate the hybrid focusing points of sonic crystals for a multi-source array applied to flat sonic crystal lenses. The contributions of different point source couples form hybrid focusing points. Ray-trace analyses are conducted for acoustic flat lenses with multi-source configurations. The finite-difference time-domain (FDTD) simulation of flat lenses with multi-source configurations demonstrates the establishment of pure and hybrid focusing points in a pyramidal constellation. The number of focusing points in the pyramidal constellation depends on the number of point sources. We propose an acoustic device for fine-tuning the location of a far-field hybrid focusing point and discuss its benefits for acoustic energy focusing application.     

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     

点缺陷二维光子晶体波导的出射光集束

光子晶体器件在高密度集成光通信中有广泛的应用,为解决光子晶体波导出射光场的空间控制,采用时域有限差分法分析光子晶体波导结构的缺陷传播特性,提出基于点缺陷优化波导结构,通过在波导出射口两侧加上点缺陷,出射光方向性有显著提高,实现三点光源干涉系统的光集束。模拟结果表明缺陷态越靠近能带结构中央,共振腔的耦合效率越高;相反,缺陷态越靠近能带结构边缘位置,则共振腔耦合效率越低,因此,选取禁带区域四分之一处对应的点缺陷,可以有效实现波导出射的光集束。     

点缺陷二维光子晶体波导的出射光集束

光子晶体器件在高密度集成光通信中有广泛的应用,为解决光子晶体波导出射光场的空间控制,采用时域有限差分法分析光子晶体波导结构的缺陷传播特性,提出基于点缺陷优化波导结构,通过在波导出射口两侧加上点缺陷,出射光方向性有显著提高,实现三点光源干涉系统的光集束。模拟结果表明缺陷态越靠近能带结构中央,共振腔的耦合效率越高;相反,缺陷态越靠近能带结构边缘位置,则共振腔耦合效率越低,因此,选取禁带区域四分之一处对应的点缺陷,可以有效实现波导出射的光集束。     

Point defect states of a hollow cylinder in two-dimensional phononic crystal

Point defect states in two-dimensional phononic crystal of a hollow mercury cylinder in a water host are studied.An improved plane expansion method combined with the supercell technique is used to calculate the band gaps and the pressure distribution at the defect position.The sonic pressure of defect modes shows that the waves are localized at or near the defect.As the filing fraction increases,more defect modes appear in the band gaps.     

Numerical study on characteristic of two-dimensional metal/dielectric photonic crystals

An improved plan-wave expansion method is adopted to theoretically study the photonic band diagrams of twodimensional(2D) metal/dielectric photonic crystals.Based on the photonic band structures,the dependence of flat bands and photonic bandgaps on two parameters(dielectric constant and filling factor) are investigated for two types of 2D metal/dielectric(M/D) photonic crystals,hole and cylinder photonic crystals.The simulation results show that band structures are affected greatly by these two parameters.Flat bands and bandgaps can be easily obtained by tuning these parameters and the bandgap width may reach to the maximum at certain parameters.It is worth noting that the hole-type photonic crystals show more bandgaps than the corresponding cylinder ones,and the frequency ranges of bandgaps also depend strongly on these parameters.Besides,the photonic crystals containing metallic medium can obtain more modulation of photonic bands,band gaps,and large effective refractive index,etc.than the dielectric/dielectric ones.According to the numerical results,the needs of optical devices for flat bands and bandgaps can be met by selecting the suitable geometry and material parameters.     

二维蜂窝格子光子晶体的远场成像特性及界面对成像质量的影响

利用有限时域差分法研究了一种二维蜂窝格子光子晶体的远场亚波长成像特性，发现和折射率为-1时的负折射成像规律符合得很好.但是由于晶格结构本身的特性，入射光以大角度入射时，这种结构的耦合效率很低，影响了像的强度和质量.通过适当改变界面上介质柱的半径的方法可以提高耦合效率，进而有效提高成像的质量和强度.     

Wavelength dependence of focusing properties of two-dimensional photonic quasicrystal flat lens

We investigated the wavelength dependence of the focusing properties of a germanium-cylinder-based two-dimensional (2D) decagonal Penrose-type photonic quasicrystal (PQC) flat lens for the first time, to the best of our knowledge. We found that near the second bandgap and in the high-frequency side (between the bandgap boundary and the first light intensity peak) of the pass band, the flat lens can exhibit a focusing effect for a point light source and that the focusing wavelengths can directly be drawn from the photonic band structure. For all the focusing wavelengths, the summation of the object distance and the image distance is less than the thickness of the flat lens when the object distance is half the thickness of the flat lens. As the wavelength increases, the image distance, the image quality, and the effective refractive index of the flat lens increase, whereas the image power of the point light source decreases. The effective refractive index of the flat lens is less than -1.     

基于布里渊区谱的二维光子晶格线性缺陷模式分析

结合均匀光子晶格的衍射关系和晶格中正负缺陷的布里渊区谱特性,探讨了光诱导二维光子晶格中线性缺陷模式的形成条件,对布里渊区中各点的缺陷模式进行了模拟分析,并得到了光子带隙结构中“嵌入点”X₁点的正、负缺陷模式.结果表明：对于二维缺陷,只有当衍射关系曲面中沿两个正交的横向波矢方向同时为正常（反常）衍射的区域才能存在正（负）缺陷模式;而对于一维缺陷,只要在一个横向波矢方向上存在正常（反常）衍射的区域就可以支持正（负）缺陷模式,因此在某些特殊点处,正和负的缺陷模式可以同时存在.X₁点正缺陷模式的存在预示着自聚焦非线性同样可以支持带内孤子.研究结果有助于对光子晶格中晶格孤子（特别是带内孤子）的理解和进一步研究. 关键词： 光诱导光子晶格 光子带隙 线性缺陷态     

Scatterer radius dependence of focusing properties in two-dimensional photonic quasicrystal flat lens

The focusing properties of a germanium decagonal photonic quasicrystal flat lens with different scatterer radii have been analyzed. For different wavelengths and polarization modes, the lenses have different scatterer radius thresholds resulting in different focusing properties. For a point source of light in the transverse-electric mode, we found dual-focusing occurs along the symmetry axis within a range of scattering radii. As scatterer radius increases, the dual-focusing image power and far-field-focusing image quality diminish, whereas near-field-focusing image quality, dual-focusing image distance, and the summed object-image distance all increase.     

一种紧凑的、可调的、基于缺陷共振的光开关

采用平面波展开法(PWM)和时域有限差分(FDTD)法,研究光在含点缺陷的光子晶体波导中的传输特性.计算结果表明,通过引入两共振腔(点缺陷),处于共振频率附近的光波将被完全反射回光子晶体波导.由于共振频率随点缺陷的折射率的变化而改变,这种现象可用来设计可调光开关. 关键词： 光子晶体波导 缺陷共振 光开关 透射率     

Focal shift for off-axial partially coherent flat topped beams passing a thin lens

Focal shift is evaluated for partially coherent off-axis flat topped beams propagated through a thin lens. We have shown that the focal shift decreases as the off-axis parameter (x₀) increases and, for fully coherent flat topped beams, focal shift is enhanced as the order of flat topped beam decreases, but the partially coherent one does not show this behavior. Also we have shown that there is a critical point for partially coherent flat topped beams. We investigated the dependency of focal shift in thin lens on correlation length and focal length.     

Controlling the focusing properties of a triangular-lattice metallic photonic-crystal slab：

This paper studies the focusing properties of a two-dimensional photonic crystal (PC) slab consisting of a triangular lattice of metallic cylinders immersed in a dielectric background. Through the analysis of the equifrequency-surface contours and the field patterns of a point source placed in the vicinity of the PC slab, it finds that both the image distance and image quality can be controlled by simply adjusting the refractive index of the background material.     

Effects of wave propagation anisotropy on the wave focusing by negative refractive sonic crystal flat lenses

<正>In this study,wave propagation anisotropy in a triangular lattice crystal structure and its associated waveform shaping in a crystal structure are investigated theoretically.A directional variation in wave velocity inside a crystal structure is shown to cause bending wave envelcpes.The authors report that a triangular lattice sonic crystal possesses six numbers of a high symmetry direction,which leads to a wave convergence caused by wave velocity anisotropy inside the crystal.However,two of them are utilized mostly in wave focusing by an acoustic flat lens.Based on wave velocity anisotropy,the pseudo ideal imaging effect obtained in the second band of the flat lens is discussed.     

Extraordinary resonance transmission of two-dimensional terahertz metallic photonic crystals without defect

In this paper, we have demonstrated a kind of extraordinary transmission in the photonic first pass band of two-dimensional terahertz metallic photonic crystals: in the regime of low-middle metal filling radio, resonances among the metallic cylinders lead to sharp and high resonance peaks of Lorentz type, layer dependency of the peak numbers. The effect of positional disorders of metallic cylinders has been investigated as well. Based on a simple model proposed in this paper, we can intuitively understand the extraordinary transmission and roughly estimate resonance frequencies. Our results agree qualitatively with the experimental data reported in Appl. Phys. Lett. 65, 645.     

光脉冲通过含有色散与增益型缺陷的一维光子晶体的传播

研究了光脉冲通过含有色散和增益型缺陷的一维光子晶体的传播行为.缺陷的色散与增益性质用Lorentz振子模型描述.随着振子强度的变化，脉冲峰的传播呈现极慢光速和超光速的传播行为，但能量速度小于真空中的光速c.脉冲峰的超前与落后是各Fourier分量在介质中获得了不同的相移和幅度改变后重新相干叠加的结果. 关键词： 光子晶体 缺陷 光脉冲传播 能量速度     

Light propagation properties of two-dimensional photonic crystal channel filters with elliptical micro-cavities

Light propagation through a channel filter based on two-dimensional photonic crystals with elliptical-rod defects is studied by the finite-difference time-domain method. Shape alteration of the defects from the usual circle to an ellipse offers a powerful approach to engineer the resonant frequency of channel filters. It is found that the resonant frequency can be flexibly adjusted by just changing the orientation angle of the elliptical defects. The sensitivity of the resonant wavelength to the alteration of the oval rods' shape is also studied. This kind of multi-channel filter is very suitable for systems requiring a large number of output channel filters.