Extraordinary refraction and dispersion in two-dimensional photonic-crystal slabs

Studies of the refraction and dispersion properties of two-dimensional (2D) photonic-crystal (PC) slab waveguides are reported. The photonic band structure is strongly modified in a slab PC, and only a small number of bands satisfy the guiding conditions imposed by the lack of translation symmetry in the direction perpendicular to the slab; however, it was found that a significant number of the guided modes retain the giant refraction and strong dispersion properties discovered previously in pure 2D PCs. A small change in incident angle resulted in a dramatic change in refraction angle. Furthermore, the dispersion surface exhibited a strong dependence on the frequency, resulting in a superprism effect similar to what has been predicted for pure 2D PCs. In the silicon-based slab PC studied, refraction angles as high as nearly 70 degrees were predicted for incident angles of less than 7 degrees , and frequency components differing by 3% were separated by 15 degrees . The demonstration of giant refraction and superprism phenomena in slab waveguide PCs open the possibility of developing new classes of optical devices that can, for example, be used to develop 2D optical integrated circuits for communications and computing.     

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.     

Impacts of uniaxial elongation on the bandstructures of two-dimensional sonic crystals and associated applications

Influences of uniaxial elongation along the [11] direction of triangular and [10] direction of square sonic crystals under the constraint of conserved unit cell area are investigated by examining band structures and equi-frequency contours. Lowest-lying band gap of the triangular lattice observed at high filling fractions diminishes for negative elongation (compression), whereas another band gap develops at lower frequencies whose width reaches appreciable values for moderate elongation. The band gap of the square lattice, which appears at high filling fractions, is modified slightly with elongation. Frequency ranges of the bands, and thus the group velocities along the high-symmetry directions, vary with elongation which may be useful in applications like slow sound propagation. Elongation is observed to modify the equi-frequency contours significantly through reducing the lattice symmetry. The most prominent impact is the transformation of closed contours into open ones, whereas the rest are stretched either along or normal to the elongation axis of the 1st Brillouin Zone. This observation is utilized to implement wide-band all-angle self-collimation and superprism effect, which are demonstrated through Finite-Element computations.     

Superprism effect in 1D photonic crystal

It is shown that superprism effect can be observed not only in 2D and 3D photonic crystal but also in 1D photonic crystal. To observe the effect a diffraction grating should be put on the top of the 1D PC. It is shown that the band gap more dramatically appears in 1D PC than in 2D PC. This effect makes all PBG effects including superprism effect more pronounced and also weakens the influence of losses.     

Spectroscopic manifestations of nitrite group intermolecular repulsion in PAN

It has been found that methylene stretching bands in polyacrylonitrile (PAN) occur at higher frequencies and have a lower intensity than in other hydrocarbon compounds. This is a spectroscopic manifestation of nitrile group intermolecular repulsion in PAN, which leads to helical winding of the polymer chains. The distortion of the elementary unit geometry occurs on spiraiization, changing the methylene band parameters. On heating, the polymer spiral unwinds, which restores the normal geometry, band position, and intensity. The unwinding of a polymer chain represents a thermal transition, occurring in PAN at a temperature of about 180°C. This transition is a necessary prerequisite for initiation of cyclization.     

Comparison of photonic bandgaps of two-dimensional periodic and quasi-periodic photonic crystals with different relative permittivity dielectric

Photonic bandgaps (PBGs) of two-dimensional (2D) triangular-lattice and square-lattice and decagonal quasi-periodic photonic crystals (PCs) have been analyzed, with a given scatterer radius and dielectric relative permittivity changing from 1 to 30 within air-cylinders-in-dielectric and dielectric-cylinders-in-air constructions. The results have shown that 2D quasi-periodic PC is more likely to generate PBG and complete PBG than 2D periodic PC. For the given scatterer radius and two constructions, PBG widths of the two types of 2D PCs vary little, whereas the corresponding center frequencies decrease in smooth “hyperbola-like” curves with dielectric relative permittivity increasing monotonically. The present results will guide the design of PBG-type microstructure photonic devices.     

Complete band gaps of phononic crystal plates with square rods

Much of previous work has been devoted in studying complete band gaps for bulk phononic crystal (PC). In this paper, we theoretically investigate the existence and widths of these gaps for PC plates. We focus our attention on steel rods of square cross sectional area embedded in epoxy matrix. The equations for calculating the dispersion relation for square rods in a square or a triangular lattice have been derived. Our analysis is based on super cell plane wave expansion (SC-PWE) method. The influence of inclusions filling factor and plate thickness on the existence and width of the phononic band gaps has been discussed. Our calculations show that there is a certain filling factor (f = 0.55) below which arrangement of square rods in a triangular lattice is superior to the arrangement in a square lattice. A comparison between square and circular cross sectional rods reveals that the former has superior normalized gap width than the latter in case of a square lattice. This situation is switched in case of a triangular lattice. Moreover, a maximum normalized gap width of 0.7 can be achieved for PC plate of square rods embedded in a square lattice and having height 90% of the lattice constant.     

Superprism effect in all-glass volumetric photonic crystals

This paper focuses on the superprism effect which can be obtained in low-contrast photonic crystals. The modelling is related to the newly developed method for all-dielectric photonic crystals. This places material constraints on the simulated crystals which limit the refractive index difference to 0.1 for all-glass photonic crystals and 0.6 for air-glass structures and forces us to focus on hexagonal lattices. The simulations show the existence of superprism effect in both types of structure for realistic glasses. In both cases various linear filling factors are studied in order to maximize the frequency range of the superprism effect. For the air-F2 glass structure it reaches 0.108 normalized frequencies and for the air-NC21 glass structure it reaches 0.99 normalized frequencies for TM polarization. For the double glass structures, the largest range is for the F2/NC21 photonic crystal and spans 0.012 normalized frequencies. In the F2/NC21 crystal the frequency range reaches 0.005 for TE polarization.     

Light confinement in 3D silicon doped with germanium (n-SixGe1−x) and silicon-on-insulator (SOI) photonic crystal structures

The numerical investigation of photonic band gaps (PBGs) for three-dimensional (3D) photonic crystals (PCs) of silicon doped with germanium (n-Si_xGe_1−x) and silicon-on-insulator (SOI) structures has been illustrated. The effect of germanium-doping (Ge-doping) concentration on the vertical confinement of the light and the band gap size has been presented. A 3D full vectorial plane wave was developed and employed to investigate design parameters of the 3D PC structure and to calculate dispersion relation for guided modes. Calculations of band structures for the triangular lattices of dielectric cylinders in air for quasi-3D PC structures have been performed.     

Collimation and enhancement of elastic transverse waves in two-dimensional solid phononic crystals

In this Letter, we numerically investigate the propagation characteristics of elastic transverse waves emitted by line sources embedded inside two-dimensional (2D) solid phononic crystals (PCs). The results show that collimation and enhancement of elastic transverse waves can be achieved at the band edge frequencies. We find that the collimation effect originates from the flat equifrequency contours (EFCs) at the band edge of appropriately designed 2D solid PCs. It is shown that, in addition to geometric symmetry, appropriate constituent material combination is essential to obtain flat EFCs at the band edge. A highly directional and enhanced elastic transverse wave source with a half power angular width of only 5.6° and an enhancement factor of 530 is realized simply by utilizing a finite-size 2D solid PC structure.     

Improvement of photovoltaic efficiency using 3D photonic-crystal enhanced light trapping and absorption

The potential of using three-dimensional photonic crystals (PCs) for achieving highly absorptive photovoltaic devices is presented in this study. The diffractive effects of PCs, used as an intermediate layer in the optical collector, on the optical absorption of the photovoltaic structure are theoretically investigated . Different PC configurations implemented in the photovoltaic collectors are modeled, and their absorption enhancements are compared. Longer matter-radiation interaction time for the photovoltaic devices with a PC-based collector results in higher absorption enhancement when compared to the devices using a slab of equivalent volume without a PC structure. The results show that employing simple-cubic (SC) PCs of inverted opal structure facilitates a much stronger enhancement of the absorption efficiency in photovoltaic devices than using the other kinds of PCs. By coupling a SC PC to the intermediate layer of the collector, the enhancement factor across the spectral range (480–1127 nm) could be created by about 2, relative to an ordinary layer of equivalent volume.     

The superprism effect in lithium niobate photonic crystals for ultra-fast, ultra-compact electro-optical switching

We numerically analyze ultra-refraction and slow-light in lithium niobate photonic crystals in order to investigate and then optimize the efficiency of a tunable photonic crystal superprism. In contrast to a passive superprism 1-to-N demultiplexer, we describe a tunable bandpass filter with only three output ports. The electro-optic effect in lithium niobate is used to achieve tunability, with the filter bandwidth shifting in wavelength as the refractive index of the superprism is modified by an externally applied electric field. Such a device could be used to realize a compact and fast wavelength multiplexer/demultiplexer for telecommunications or optical interconnect applications. We calculate constant frequency dispersion contours (plane-wave expansion) to identify initial configurations that show significant ultra-refraction, and verify the expected behavior of light propagation inside the structure using 2D FDTD (finite difference time domain) simulations. We show that the voltage requirements of such an electro-optically tunable superprism could potentially be relaxed by exploiting the enhancement of the electro-optic effect recently discovered by our group [M. Roussey, M.-P. Bernal, N. Courjal, D. Van Labeke, F.I. Baida, Electro-optic effect exaltation on lithium niobate photonic crystals due to slow photons. Appl. Phys. Lett. 89 (24) (2006) 241110], which we believe to be due to the presence of slow-light in the nanostructure. We present a methodology that readily identifies superprism design points showing both strong ultra-refraction as well as low group velocity. However, we find that this improved voltage efficiency comes at the cost of reduced operating bandwidth and increased insertion losses due to proximity to the band-edge.     

Reflection spectra of 1D photonic crystals based on aluminum oxide

Optical properties (transmission and reflection) of 1D photonic crystals (PCs) based on mesoporous anodic aluminum oxide with the lattice periods of 188 and 194nm are investigated. The experimentally measured reflection spectrum is compared in its first bandgap region with the theoretical dependence obtained from the dispersion relation for the 1D PC. Angular dependence is established for spectral positions of bandgaps in the 1D PC. A possibility of using mesoporous aluminum-oxide-based 1D PCs as narrow-band filters, narrow-band mirrors, and refractive sensors of molecular compounds is analyzed.     

k=0处的类狄拉克锥

狄拉克锥在电子和经典波体系中分别被发现, 由于其线性能带关系, 伴随着很多独特的现象. 除了一般存在于布里渊区边界处的狄拉克锥, k=0处也存在包含线性能带关系的类狄拉克锥. 这个类狄拉克锥可以由单极子和偶极子的偶然简并而形成. k=0处的类狄拉克锥可以通过两维电介质光子晶体来实现, 利用等效媒质理论, 此时的光子晶体在类狄拉克点频率可以等效为介电常数和磁导率都为零的材料. 电介质双零折射率材料既可以避免阻抗的不匹配, 也可以避免体系推广到高频所引起的强烈损耗. 此外, k=0处的类狄拉克锥与双零折射率的概念可以从两维体系拓展到三维体系, 而且还可以从电磁波体系推广到声波和弹性波体系. 利用具有类狄拉克点的两维光子晶体, 在材料参数都偏离类狄拉克点条件的两个半无限大光子晶体所构成的界面中, 一定存在界面态. 这些界面态的存在可以通过层状多重散射理论得到的表面阻抗以及体能带的几何相位来彻底解释.     

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.     

类石墨烯复杂晶胞光子晶体中的确定性界面态

拓扑绝缘体是当前凝聚态物理领域研究的热点问题.利用石墨烯材料的特殊能带特性来实现拓扑输运特性在设计下一代电子和能谷电子器件方面具有较广泛的应用前景.基于光子与电子的类比,利用光子拓扑材料实现了确定性界面态;构建了具有C_(6v)。对称性的类似石墨烯结构的的光子晶体复杂晶格;通过多种方式降低晶格对称性来获得具有C_(3v),C_3,C_(2v)和C_2对称的晶体,从而打破能谷简并实现全光子带隙结构;将体拓扑性质不同的两种光子晶体摆放在一起,在此具有反转体能带性质的界面上,实现了具有单向传输特性的拓扑确定性界面态的传输.利用光子晶体结构的容易加工性,可以简便地调控拓扑界面态控制光的传播,可为未来光拓扑绝缘体的研究提供良好的平台.     

轴向填充率渐变型二维光子晶体

提出了一种轴向填充率渐变型二维三角晶格方空气孔光子晶体,由锥形孔周期性排布而成,在第三维也就是沿空气孔的轴向,空气孔的尺寸连续改变,实现了填充率渐变,填充率f范围为0.700～0.866。经过模拟,在归一化波长(λ/a)的1.43～2.71和3.41～4.00波段,轴向填充率渐变型光子晶体可以将光向填充率小的方向偏折,具有选光功能。采用电化学腐蚀与MEMS工艺相结合的方式,在p型(100)硅基底上制作了轴向填充率渐变型二维三角晶格方孔光子晶体,整个孔的填充率f在0.800～0.866范围内。     

Study on the anisotropic photonic band gaps in three-dimensional tunable photonic crystals containing the epsilon-negative materials and uniaxial materials

In this paper, the properties of anisotropic photonic band gaps (PBGs) for three-dimensional (3D) photonic crystals (PCs) composed of the anisotropic positive-index materials (the uniaxial materials) and the epsilon-negative (ENG) materials with body-centered-cubic (bcc) lattices are theoretically studied by a modified plane wave expansion (PWE) method, which are the uniaxial materials spheres inserted in the epsilon-negative materials background. The anisotropic photonic band gaps (PBGs) and one flatbands region can be achieved in first irreducible Brillouin zone. The influences of the ordinary-refractive index, extraordinary-refractive index, filling factor, the electronic plasma frequency, the dielectric constant of ENG materials and the damping factor on the properties of anisotropic PBGs for such 3D PCs are studied in detail, respectively, and some corresponding physical explanations are also given. The numerical results show that the anisotropy can open partial band gaps in such 3D PCs with bcc lattices composed of the ENG materials and uniaxial materials, and the complete PBGs can be obtained compared to the conventional 3D PCs containing the isotropic materials. The calculated results also show that the anisotropic PBGs can be manipulated by the parameters as mentioned above except for the damping factor. Introducing the uniaxial materials into 3D PCs containing the ENG materials can obtain the larger complete PBGs as such 3D PCs with high symmetry, and also provides a way to design the tunable devices.     

Band gaps of two-dimensional photonic crystal structure using conjugated polymer (3-octylthiophenes)

The possibility of using conjugated polymer (3-octylthiophenes, P3OT) as two-dimensional (2D) photonic band gap crystals was investigated. The different aspects were examined of the absolute photonic band gap (PBG) formation for 2D photonic crystals (PCs) consisting of P3OT pillars in air. The formation of PBG was exhibited and confirmed by a calculation of transfer matrix method (TMM). It was found that P3OT triangular structure could be good candidate for absolute inhibition of reflection in ultraviolet frequency region for given orientation.     

Study on complete band gap of two-dimensional photonic crystal with quadrangular rods

The plane wave expansion method (PWM) was employed to study the relation between the photonic band gap (PBG) of 2D triangular lattice photonic crystal (PC) and the shapes of rods and dielectric constant. It is shown that the PBG of PC with quadrangular rods is the widest one, compared with the other case with cross section shapes of triangular, circular and hexagon under the same filling ratio, and a peak value appears when the side length ratio of l_x/l_y is equal to 1.21 approximately to any filling ratio. In the aspect of the effects of dielectric constant, the PBG width does not increase monotonically with the increase permittivity ?₂ of the background material to certain permittivity ?₁ of the quadrangular rods, but has a peak value instead. However, the larger the permittivity ?₁ is, the narrower the band width is and the lower the central frequency is, and the dispersion Δ? = ?₂ − ?₁ is larger also.