Anomalous behavior of group velocity and index of refraction in a defect photonic band gap structure

In the present paper, we have made an analysis to observe the effect of introduction of defect on dispersion relation, group velocity, and effective group index in a conventional photonic band gap (PBG) structure. The study shows that inside the PBG materials group velocity and effective group index becomes negative in both types (conventional as well as defect PBG structure) of structure at a certain range of frequencies. Also, near the edges of the bands it attains very high values of index of refraction. A defect PBG structure gives a very unique feature that group velocity becomes exactly zero at a particular value of frequency and also becomes several hundred times greater than the velocity of light which is not attainable with the conventional PBG structure. Defect PBG structures with such peculiar characteristics are seen in lasing without inversion, in construction of perfect lens, in trapping of photon and other optical devices.     

Defect modes properties in periodic lossy multilayer containing negative index materials with symmetric and asymmetric geometric structures

In this paper, the characteristic matrix method is used to study the propagation of electromagnetic waves through one-dimensional lossy photonic crystals composed of negative and positive refractive index material layers with symmetric and asymmetric geometric structures with a defect layer at the center of the structure. First, the positive index material defect layer is considered, and the effects of the polarization and the angle of incidence on the defect mode in the transmission spectra of the both structures are investigated. The results show that the number of the defect modes in the transmission spectra depends on the geometry (symmetric or asymmetric) of the structure. In addition, it is shown that the defect mode frequency increases as the angle of incidence increases. This property is independent of the geometry of the structure. Then, for normal incidence, the negative index material defect layer is considered, and the properties of defect modes for both structures are investigated. The results can lead to designing new types of transmission narrow filters.     

One dimensional photonic band gap material as an omnidirectional reflector

In this article, the reflection properties in one-dimensional dielectric-dielectric photonic band gap (PBG) structure have been studied. We have used SiO₂ as material of low refractive index and Te as a high refractive index material. Reflectivity of proposed PBG structure is plotted as a function of wavelength and angle of incidence and omni-directional PBGs are computed theoretically. To obtain reflectance, we used transfer matrix method for solving Maxwell’s equations for electromagnetic wave in PBG structures. For a large range of frequency, the PBG structure is found to exhibit omni-directional reflection which can be exploited in devices such as optical resonators, mirrors, etc.     

Photonic band gap and defect mode from a layered periodic structure with anisotropic nonmagnetic right-handed and left-handed metamaterials

We demonstrate a photonic band gap (PBG) from a layered periodic structure containing anisotropic nonmagnetic right-handed and left-handed metamaterials whose permittivity elements are partially negative. A set of criteria imposed on materials and structures to realize a PBG is derived, and the transmission spectra are also discussed. When a defect layer is introduced, some unusual properties are found in contrast to that of a defect mode in ordinary PBG structures.     

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。     

Modal propagation characteristics of EM waves in ternary one-dimensional plasma photonic crystals

We have theoretically studied the modal dispersion characteristics, group velocity, and effective group as well as phase index of refraction of ternary one-dimensional (1D) plasma photonic band gap (PBG) structure having periodic multilayers of three different materials in one unit cell. The dispersion characteristics related for such structure is derived by solving Maxwell wave equation based on principle of Kronig-Penny model. From the computed results we observe that the dispersion characteristics of such structure also show the frequency gap and cutoffs as found in (binary) one-dimensional plasma photonic crystal. The frequency gap is shown to become larger with the increase of plasma frequency as well as plasma width. It is seen that such structure provide additional degree of freedom to control dispersion characteristic, group velocity and effective index of refraction compared to conventional one-dimensional plasma photonic crystal.     

Properties of Defect Modes in Periodic Lossy Multilayer with Negative-Index-Materials

Employing the characteristic matrix method, this study investigates transmission properties of onedimensional defective lossy photonic crystals composed of negative and positive refractive index layers with one lossless defect layer at the center of the crystal. The results of the study show that as the refractive index and thickness of the defect layer increase, the frequency of the defect mode decreases. In addition, the study shows that the frequency of the defect mode is sensitive to the incidence angle, polarization, and physical properties of the defect layer, but it is insensitive to the small lattice loss factor. The peak of the defect mode is very sensitive to the loss factor, incidence angle, polarization, refractive index, and thickness of the defect layer. This study also shows that the peak and the width of the defect mode are affected by the numbers of the lattice period and the loss factor. The results can lead to designing new types of narrow filter structures and other optical devices.     

非线性一维光子晶体特性的动态调制

对含有非线性材料的一维光子晶体带隙结构进行了数值计算.在外部入射光强调制下,非线性缺陷层折射率的改变会引起禁带内缺陷模的移动,而光子晶体禁带位置与宽度基本保持不变;若基本周期层取非线性材料,随入射光强的改变,禁带内部缺陷模发生相同的移动,同时,禁带位置和禁带宽度也会发生移动.利用这一性质可以对光子晶体进行动态外部调制,在此基础上对非线性一维光子晶体动态滤波选频进行了实验设计.     

混合准周期异质结构的带隙补偿与展宽

基于一维光子晶体异质结构的多帯隙交叠补偿思想,提出了一种新颖的混合准周期级联结构,用于扩大全方位光子带隙.该全方位反射器结构由Fibonacci准周期结构和Thue-Morse准周期结构级联构成,研究表明,相比单种准周期结构,其全方位光子带隙宽度有显著提高.系统研究了结构参数(如周期数、阶数、介质折射率和厚度)对该结构光子带隙的影响,通过与周期结构带隙特性的比较,分析了准周期结构易于实现多带隙交叠的原因,为更复杂带隙结构的补偿和展宽奠定了设计基础.     

Near-field optics with photonic crystals

Finite-difference time-domain (FDTD) analysis of light propagation in a defect mode of a two-dimensional photonic band-gap (PBG) structure demonstrates that the light field is localized in such a structure within areas with subwavelength (λ/10) sizes. FDTD simulations reveal efficient formation of an evanescent wave at the output of such a PBG structure, permitting the subwavelength resolution to be achieved in the near field. A probe object with a size less than the wavelength of incident light is shown to perturb the near-field distribution behind the PBG structure and to change the signal detected in the far-field zone. The field intensity distribution inside a PBG structure is also sensitive to the presence of a probe object, offering a way to control the light field localized in defect modes of PBG structures. Received: 9 August 1999 / Accepted: 18 October 1999 / Published online: 10 November 1999     

Complete photonic band gaps in one-dimensional ternary photonic crystals containing single negative materials

Complete photonic band gaps (PBGs) are found in one-dimensional ternary photonic crystals (1D TPCs) composed of an ordinary dielectric and single negative metamaterials. The proposed TPC gives omni directional PBG completely independent of polarizations dependent weekly on angle of incidence. Here the choice of different parameters of TPC is done in such a way so that it eliminates the Brewster's-angle transmission resonance, thus allowing a complete 3D PBG. It exhibits a photonic band or gap near frequencies where either the magnetic permeability or the electric permittivity of the metamaterial changes sign, whose width increases with the increasing angle of incidence. These result from the dispersive properties of the metamaterials and disappear for the particular case of propagation along the stratification direction. The results are discussed in terms of incident angle, layer thickness, dielectric constant of the dielectric material for TE and TM polarizations.     

二维三角柱光子晶体的传输特性

利用时域有限差分方法对二维三角介质柱光子晶体的传输特性进行了研究,计算了不同晶格、同一晶格柱体截面面积不同、放置方位角不同、入射波入射方向不同时光子晶体的传输特性。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,三角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在一定范围内对光子禁带有重要影响;对不同入射方向时光子晶体的传输特性的研究结果表明,在低频范围内,入射角对禁带宽度和中心频率没有任何影响,在高频段,透射率随入射角变大而降低。研究结果为实验上制作三角柱光子晶体器件提供了重要的理论依据。     

Helical modes in low- and high-swirl jets measured by tomographic PIV

We report on a parallel study on properties of large-scale vortical structures in low- and high-swirl turbulent jets by means of the time-resolved tomographic particle image velocimetry technique. The high-swirl jet flow is featured by a well-established bubble-type vortex breakdown with a central recirculation zone. In the low-swirl flow, the mean axial velocity, while intermittently acquiring negative values, remains positive in the mean but with a local velocity defect immediately downstream from the nozzle exit, followed by a spiralling vortex core system and its eventual breakdown. Measurements of the 3D velocity fields allowed direct analysis of the azimuthal/helical modes via Fourier transform over the azimuthal angle and proper orthogonal decomposition (POD) analysis in the Fourier space. A precessing vortex core is detected for both swirl cases, whereas the POD analysis showed that the one originating in the bubble-type vortex breakdown is much more energetic and easier to detect.     

Defect mode properties in a one-dimensional photonic crystal

Based on the transfer matrix method (TMM), the interaction of electromagnetic waves with one-dimensional (1D) defective photonic crystal in ultraviolet (UV) frequency region had been studied. With the calculated transmittance characteristics in the wavelength domain, it can be found that the defect mode can be generated within the photonic band gap (PBG) at the central wavelength. Also the effects of many parameters such as the angle of incidence, the state of polarization and the defect layer thickness have been taken in account. A significant effect in generating multiple defect peaks within the PBG has been illustrated.     

Approximate analysis of planar photonic bandgap waveguides: a simple semi-analytical method

A semi-analytical approximate method, Vopt, is applied to a planar photonic bandgap (PBG) waveguide and a coupler configuration. The variational process of the Vopt method presents simple effective index analysis of the complex two dimensional (2-D) structures. The Vopt method expresses the refractive index profile of the 2-D structure as two 1-D refractive index profiles and obtains the optimized indices for the two structures iteratively. The Vopt method separates the planar PBG waveguide into an effective multilayer waveguide confining optical field in the lateral direction and a 1-D Bragg reflector that gives characteristic reflection/transmission spectra. The results obtained by the Vopt method show good agreement with the numerical results of the finite difference time domain analysis. The present analysis is helpful in understanding the optical properties of such complex waveguides and can be used as starting approximation for optimizing the structures for various applications.     

One-dimensional photonic crystals with a planar oriented nematic layer: Temperature and angular dependence of the spectra of defect modes

Transmission spectra of a one-dimensional photonic crystal (PC) formed by two multilayer dielectric mirrors and a planar oriented layer of 5CB nematic liquid crystal (LC) that is sandwiched between these mirrors and serves as a structure defect are investigated experimentally. Specific features of the behavior of the spectrum of defect modes as a function of the angle of incidence of light on the crystal are studied for two polarizations: parallel and perpendicular to the director of the LC; the director either lies in the plane of incidence or is perpendicular to it. It is shown that, for the configurations considered, the maxima of the defect modes shift toward the short-wavelength region as the tilt angle of incidence radiation increases; this tendency is more manifest for the parallel-polarized component, when the director lies in the plane of incidence. In the latter case, the width of the photonic band gap (PBG) appreciably decreases. The temperature dependence of the polarization components of the transmission spectra of a PC is investigated in the case of normal incidence of light. The spectral shift of defect modes due to the variation of the refractive index of the LC at the nematic-isotropic liquid phase transition point is measured. It is shown that, in real PCs, the amplitude of defect modes decreases when approaching the center of the band gap, as well as when the number of layers in the dielectric mirrors increases. Theoretical transmission spectra of the PCs calculated by the method of recurrence relations with regard to the decay of defect modes are in good agreement with experimental data.     

含复合缺陷层的光子晶体的光学特性

运用传输矩阵法研究了在一维光子晶体中插入缺陷层的透光特性。在无缺陷层的一维光子晶体中能产生467~510 nm、1 279~1 715 nm两处明显的光子带隙。重点研究了插入缺陷层后,在1 279~1 715 nm的光子带隙中缺陷层厚度和入射角度大小分别与透射光谱变化的关系。研究发现：缺陷模的位置对入射角变化很敏感;出现缺陷模的数量和插入缺陷层的数量相同;一维光子晶体厚度的增大不会改变缺陷模的数量和位置,只改变透射峰的宽度和透射率。     

Spectral properties of a one-dimensional photonic crystal with a resonant defect nanocomposite layer

The spectral properties of a one-dimensional photonic crystal with a defect nanocomposite layer that consists of metallic nanoballs distributed in a transparent matrix and is characterized by an effective resonance permittivity are studied. The problem of calculating the transmission, reflection, and absorption spectra of p-polarized waves in such structures is solved for oblique incidence of light, and the spectral manifestation of defect-mode splitting as a function of the volume fraction of nanoballs and the structural parameters is studied. The splitting is found to depend substantially on the nanoball concentration in the defect, the defect layer thickness, and the angle of incidence. The angle of incidence is found at which the resonance frequency of the nanocomposite is located near the edge of the bandgap or falls in the frequency region of a continuous spectrum. The resonance situation appearing in this case results in an additional transmission band or an additional bandgap in the transmission spectrum.     

大带隙二维光子晶体结构的研究

针对三种常见的介质柱横截面分别为正六边形,正方形和圆形的二维光子晶体,提出了一种增大光子带隙的方法.直角坐标系下,使X方向长度增大p倍,并以原点为中心旋转角度φ,通过调整p和φ来降低结构对称性,使用平面波展开法,对其进行了大量的仿真分析.结果表明,结构改变后的光子晶体具有较大的带隙率.对于三种介质柱的三角晶格结构的光子晶体,最大带隙率能达到12％以上,尤其对于正方柱三角晶格光子晶体,最大带隙率达到15.1％.     

Colour characterization of a Morpho butterfly wing-scale using a high accuracy nonstandard finite-difference time-domain method

In certain species of moths and butterflies iridescent colours arise from subwavelength diffractive structures. The optical properties of such a structure depend strongly on wavelength, incidence angle and state of polarization of illuminating radiation and on the viewing angle. Such structures can be analyzed only by solving Maxwell's equations, but since analytical solutions exist for only a few simple, highly symmetric structures numerical methods must be employed. We investigated the optical properties of butterfly wings in two dimensions by simulating a scale structure using a high accuracy version of nonstandard finite-difference time-domain algorithm. The simulated structure is a computer-generated model of a certain quasi-periodic arrangement of tree-like structures observed in the transmission electron micrograph (TEM) image of a transverse cross-section of a single scale from Morpho butterfly wings. We assumed that the structure is made of a slightly lossy dielectric material. We checked the accuracy and validity of our approach, by computing scattered field intensities due to an infinite cylinder and compared the results with analytical calculations using Mie theory. Next we deduced the wavelength dependence of a real refractive index and an absorption coefficient for the ground scales on the wings of Morpho sulkowskyi butterfly by computing the reflectivity and transmissivity spectrum of a scale at normal incidence, and comparing with experimental measurements. Finally, we calculated the tristimulus values and corresponding colour coordinates for various viewing directions from the scale's far-field reflectivity and transmissivity spectra to characterize its colour rendering abilities.