Superprism properties in 2D polymer photonic crystals at high normal frequencies

The superprism effects of higher bands, i.e., for normal frequencies of higher than one, in two-dimensional (2D) polymer photonic crystals (PCs) are investigated. It is shown that in a polymer PC of triangular symmetry with filling factor of about 31%, the gradual transition of the hexagonal into triangular equi-frequency dispersion contours leads to a strong superprism in the 6th band at a normal frequency of 1.2. This dispersion is more prominent than those observed in the lower bands in 2D PCs. Also, this requires a lattice constant longer than the concerned wavelength. Furthermore, in a 2D polymer PC with a filling factor of about 83% a strong discontinuous superprism effect occurs at normal frequencies higher than one, which is due to an abrupt transition between two modes with the refraction angles of opposite signs. The effect can be exploited for switching applications as demonstrated in the paper.     

波状结构二维光子晶体负折射现象的研究

结合波状结构二维(2D)光子晶体(PC)与入射介质两者的等频面结构分析了PC内部的负折射现象，采用时域有限差分(FDTD)方法模拟了高斯光束在波状结构2DPC内的负折射，分别得到了折射角/入射角以及折射角/入射波长之间的关系曲线，当入射角为45°，入射波段在1485—1530nm区域时，波状结构2DPC的负折射角与入射波长近似呈线性变化关系，并带有明显的PC超棱镜效应，采用端面投影方法对波状结构2DPC的入射端面和出射端面进行处理，改善了负折射时的透过率. 关键词： 光子晶体 负折射 等频面     

Optical and electro-optical properties of photonic crystals based on polymer-dispersed liquid crystals

Two-dimensional (2-D) square lattice (SL) photonic crystals (PCs) are fabricated, and their optical/electro-optical properties are studied. The PCs are based on polymer-dispersed liquid crystals (PDLC) that are formed using two-beam interference with double exposures. The PC structure that is observed using a scanning electron microscope matches with the calculated interference pattern. The results of optical/electro-optical studies demonstrate that superprism and negative refraction effects occur at certain incident angles over a range of frequencies and are consistent with the simulated ones. Moreover, the negative refraction efficiency is electrically controllable.     

双曲色散型单轴左手介质中的折射

研究了横磁波在各向同性右手介质和双曲色散型单轴左手介质界面处波矢和能流的折射。计算发现,当入射角在很大范围内变化时,波矢的折射角和能流的折射角几乎不变。调节光轴角可使波矢折射角和能流折射角随入射角变化不敏感的现象更明显,经分析计算给出光轴角的调节范围。这一现象是由双曲色散型单轴左手介质的各向异性及负的主折射率引起的,可以用来实现光束准直、光束整合、光束压缩以及方便的光束耦合。如果光从双曲色散型单轴左手介质向各向同性右手介质入射,还能实现超棱镜(superprism)现象。计算了横磁波穿越界面时的透过率,证实双曲色散型单轴左手介质可能实现上述应用。     

单轴晶体中的负折射现象研究

分析了在各向同性介质和单轴晶体界面实现负折射的最佳条件。计算发现,通过调节光轴角和各向异性参量可以使得负折射现象更为明显,获得最佳光轴角和最大入射临界角。各向异性强的晶体实现负折射的入射角范围可能会很大。讨论了单轴晶体中和负折射率介质中的负折射现象的区别：负折射率介质中的负折射是由负的折射率引起的,单轴晶体中是由于各向异性决定的。同时还发现单轴晶体中的能流负折射现象不能实现Pendry在理论上所预言的完美透镜。     

Manipulating light flow with one-dimensional photonic crystals of an electromagnetically induced transparency medium

The band structures and equifrequency contours of one-dimensional photonic crystals (PCs), which consist of an electromagnetically induced transparency (EIT) medium and a common dielectric medium, can be dramatically changed by tuning the coupling field intensity (or coupling Rabi frequency, CRF) of the EIT medium. It is found that for a probe light at a fixed frequency, either positive or negative refraction in the EIT PC can be realized with a proper CRF. The behavior of a Gaussian beam (probe light) obliquely incident on such an EIT PC slab is simulated numerically. The probe light beam transmitted from the slab can be shifted transversely in a large range, and negative refraction enhances this effect. The present scenario can be applied in some areas such as quantum optical and photonic device designs.     

Superprism effect in a metal-clad terahertz photonic crystal slab

We report an experimental demonstration of the superprism effect in a photonic crystal slab at terahertz frequencies. For a 10% frequency variation around 0.28 THz, the refraction angle at the output facet of a wedge-shaped photonic crystal varies by about 15 degrees. A comparison with the predictions of a band structure calculation demonstrates that a three-dimensional treatment, accurately modeling the finite slab thickness and the metallic boundary conditions, is required for even a qualitative agreement with the experimental observations.     

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.     

Efficient tunable negative refraction photonic crystal achieved by an elliptic rod lattice with a nematic liquid crystal

Photonic crystals (PCs) have many potential applications because of their ability to control light-wave propagation. We have investigated the electromagnetic wave propagation inside an elliptic rod PC slab by means of finite-difference time-domain simulations. The band structure of the PC composed of elliptic rod in the square and triangular lattices is studied by solving Maxwell's equations using the plane wave expansion method. Numerical simulations show that the refractive angle can be tuned greatly by rotating the directors of elliptic rod in the PC slab. Furthermore, an optical switch based on elliptic rod PC structures with nematic liquid crystals was proposed. In the on/off switching system, the partial band gap can be controlled when the normalized operation frequency is 0.28. The modulation induced by liquid crystals created a sharp switching in the photonic devices. Such a mechanism of negative refraction PCs should open up a new application for designing components in photonic integrated circuits.     

Optically tunable superprism effect in nonlinear photonic crystals

An analysis of the tunable superprism effect in a two-dimensional nonlinear photonic crystal is presented. We show that, by shifting the photonic bands of the crystal through the Kerr effect induced by a pump beam, one can tune the refraction angle of a transmitted signal beam over tens of degrees. We also demonstrate that the optical power required to tune the refracted angle is dramatically reduced if the frequency of the pump beam is close to a bandgap edge.     

The superprism effect using large area 2D-periodic photonic crystal slabs

The “superprism effect” is an effect observed in photonic crystal structures whereby the direction of light propagation is extremely sensitive to the wavelength and angle of incidence. To realize the superprism effect, new structures are presented which rely on the sensitivity of the phase velocity in a two-dimensional (2D) photonic crystal slab to observe angular magnification outside the photonic crystal medium. Constant frequency contour calculations for a photonic crystal slab of finite thickness are used to predict the phase velocity superprism effect. Further analysis using 2D finite-difference time-domain simulations indicate that a large area photonic crystal and wide excitation beam are necessary for clear observation of the superprism effect. A fabrication technique is demonstrated to achieve the structure's required nanometer-sized features over centimeter-scale areas.     

Polarization- and direction-independent defect modes in a wide incident-angle range within Bragg gaps by photonic heterostructures containing negative-index materials

We propose a type of photonic heterostructure by combining dielectric one-dimensional (1D) defective photonic crystals (PCs) and magnetic 1D defective PCs. Both of the two PCs consist of alternating positive-index-material (PIM) layers with a negative-index-material (NIM) defect layer. It is demonstrated by transfer matrix method that there is a polarization- and direction-independent defect mode in a wide incident-angle range within Bragg gaps in the heterostructure. The field distributions prove that the dielectric 1D defective PC benefits to achieve the approximately omnidirectional defect mode for TE waves while the magnetic 1D defective PC benefits for TM waves. Such a structure is useful for designing polarization-independent and omnidirectional or large incident angle narrow-passband filters in optical devices.     

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提出碰撞吸收型等离子体的等效折射指数,重新计算了折射角,并与利用常规方法得到的折射角进行了比较。分析了等离子体密度和碰撞频率对折射角的影响。考察了斜入射电磁波在吸收型等离子体中的折射特性,并以一维非均匀碰撞吸收型等离子体为例,对斜入射电磁波的反射特性进行了考察。结果表明,等效折射指数的概念涵盖了入射角度的影响,在考察斜入射时更准确、便捷。     

二维光子晶体的特殊色散特性研究

为了研究光场在二维光子晶体中的传播特性,本文应用平面波展开法,得到了二维三角晶格光子晶体的能带结构,在此基础上,运用时域有限差分法,分析了在一定入射角度下,特定频率的光束在光子晶体中的负折射现象,由于应用光子晶体的自准直效应,光束束腰在传播过程中展宽较小。研究了由于能带交折、重叠而产生的特殊色散特性和超棱镜效应,给出了光子晶体内外的磁场强度的分布,得到了极高的角色散度。文章的研究结果对研究基于光子晶体超棱镜效应的波分复用器,具有指导意义。     

Tunable superprism and polarization splitting in a liquid crystal infiltrated two-dimensional photonic crystal made of silicon oxynitride

Tunable superprism and polarization splitting effects, based on liquid-crystal infiltrated two-dimensional photonic crystal with SiON as a background material, are demonstrated. Owing to the strong birefringence of the liquid crystal, the dispersion curves of the two polarizations are distinctly different, resulting in large splitting between the two polarizations. Extremely large splitting, as large as 80 degrees, can be obtained. Moreover, the splitting can be tuned to a substantial degree when the optic axis of the liquid crystal is reoriented. Fully controllable, incident-angle-dependent and wavelength-dependent superprism effects are also demonstrated. This large swing in the refraction can be completely switched off by reorientation of the optic axis of the liquid crystal, thus to resemble bulk media refraction.     

Giant Faraday rotation in graphene/MnF<Subscript>2</Subscript> photonic crystals

The effect of graphene on the Faraday rotation (FR) in dielectrics/antiferromagnetic photonic crystals (D/AF PCs) is investigated by using the forth-order transfer matrix, in which the graphene (Gr) is embedded on the surface of AF. When the incident light is vertical to the surface of D/Gr/AF PCs, Gr will present anisotropic properties, in which the optical conductivity is characterized by the tensor. The numerical simulations show that the FR angle almost is enhanced by one order compared with the ones of D/AF PCs when the number of D/Gr/AF in the PC is 9. In addition, the maxima and positions of the FR angles can be adjusted by changing the external magnetic field strength. On the other hand, the effects of the Fermi energy of Gr on the FR also are discussed since it can be tuned by controlling the applied back-gate voltage. These results may be valuable in the design of THz devices.     

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.     

利用含负折射率材料的光子晶体实现角度滤波器

利用光子晶体的共振隧穿效应，并结合由负折射材料引起的零平均折射率带隙，设计出一种新型的角度滤波器，使得对于某一频率范围内的入射电磁波仅在特定入射角度的波能够全透，而其他角度的波不能透过.这将在微波器件乃至光学器件上有广泛应用. 关键词： 光子晶体 负折射率材料 共振隧穿     

异质三周期光子晶体的光子带隙特性

利用传输矩阵法研究了由TiO₂和SiO₂两种材料构成的异质三周期一维光子晶体的传光特性,发现该结构能在波长为200~ 2 000 nm的范围内形成7处比较明显的光子带隙,并且波长越大,带隙的宽度越大。重点研究了这种结构的光子晶体的透射谱线与入射角度、介质层数及介质层厚度的关系,发现该结构形成的光子带隙的大小和位置对介质层的循环周期数不敏感,但对入射角度和介质层的厚度很敏感。     

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.