Absolute photonic band gaps of two-dimensional square-lattice photonic crystals with Taiji-shaped dielectric rods

A novel structure of two-dimensional (2D) square-lattice photonic crystal (SLPC) composed of Taiji-shaped dielectric rods imbedded in air is constructed and the properties of absolute photonic band gap (PBG) are theoretically analyzed in both the number and width by Plane Wave Expansion Method (PWM). By comparing the absolute PBGs in 2D SLPCs consisting of four shapes of rods with different symmetries (circle, button, semicircle and Taiji) at the same filling ratio, we find that both the number and width of absolute PBG significantly increase with the breaking of scatterer's symmetry, and the Taiji-shaped rods with the poorest symmetry can attain both the most number and the largest width of absolute PBGs. Additionally, we also study the influence of dielectric constant ε and three geometric parameters of Taiji-shaped scatterer on the absolute PBG and discover that the SLPC with Taiji-shaped rods can generate at most nine absolute PBGs and the largest absolute PBG with the width 0.0485 (ωa/2πc).     

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     

空气环型二维光子晶体完全带隙特性研究

采用平面波展开法, 系统研究了空气环型二维光子晶体的完全光子带隙随结构参数变化而改变的规律, 并将其与普通的空气孔型和介质柱型二维光子晶体的完全带隙进行了比较. 研究表明: 空气环型二维光子晶体不仅可以获得更宽的完全带隙, 而且, 当介质折射率较低时, 其可以获得普通空气孔型和介质柱型二维光子晶体在低折射率条件下所无法获得的完全带隙. 关键词： 空气环型二维光子晶体 完全带隙 平面波展开法     

Investigation of photonic band gap in a one-dimensional lossy DNG/DPS photonic crystal

The effects of losses on the photonic band gap (PBG) in a one-dimensional lossy double-negative (DNG)/double-positive (DPS) photonic crystal are theoretically investigated. Using the Lorentz expressions for the permittivity and permeability for the dispersive and lossy DNG material, it is found that the magnetic loss, in comparison with the electric loss, has a more salient influence on the PBG. The magnetic loss is shown to play a vitally important role in the analysis of PBG for this DNG/DPS photonic crystal.     

基于太极形介质柱六角光子晶体禁带特性研究

提出了一种新型的非对称性散射体的二维六角晶格光子晶体结构–-太极形介质柱光子晶体. 利用平面波展开法从理论研究这种光子晶体结构的能带特性以及结构参数对完全禁带的影响. 研究表明:散射体对称性的打破, TE模和TM模能带宽度和数目都会有所增加, 有益于获得更宽的完全禁带以及更多条完全禁带.通过参数优化, 发现在ε = 17, R=0.38 μm, r=0.36R, θ = 0° 时, 获得最大完全带隙宽度0.0541(ωa/2πc); 在ε = 16, R=0.44, r=0.2R, θ = 0°时, 光子晶体完全带隙数目最多达到8条. 关键词： 光子晶体 禁带 平面波展开     

Magnetic surface plasmon-induced tunable photonic bandgaps in two-dimensional magnetic photonic crystals

We experimentally studied magnetically controllable photonic band gaps (PBGs) in two-dimensional magnetic photonic crystals consisting of ferrite rods. Besides the conventional PBG that relates to Bragg scattering, two other types of PBG, resulting from magnetic surface plasmon (MSP) resonance and spin-wave resonance, respectively, are observed. The PBG due to MSP resonance is particularly interesting because of its analogy to surface plasmon in metal; furthermore, it is shown to be completely tunable by an external static magnetic field from both an experimental and a theoretical point of view.     

Theoretical predictions of photonic properties of nanoporous copolymer films as photonic band gap materials using FDTD

Block copolymers (BCPs), which self-organize into ordered 1-, 2- and 3-dimensional periodic equilibrium structures, can exhibit photonic band gaps (PBGs). In this paper, cylinder microdomain nanoporous films are proposed to be treated as a new kind of 2-dimensional BCP based photonic crystal. The minor component of the nanoporous films has been removed chemically with only pores left in order to enhance their dielectric constant contrast, which provides a new solution to achieve necessary PBG properties with BCPs. The finite-difference time-domain (FDTD) method is used to investigate band features of this kind of photonic crystal theoretically. It is noted that the complete band gaps for the H polarization are obtained, although for the E polarization only the incomplete gaps exist. In addition, the gap map of the PBG materials is presented and its characteristics are analyzed. PACS 42.70.Qs; 42.70.Jk; 42.25.Bs     

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.     

The effect of etching interfacial layers on the absolute photonic band gap in two-dimensional photonic crystals

The photonic band structures of two-dimensional (2D) photonic crystals with etched interfacial layers between air rods and the background dielectric is studied theoretically. The effect of etching interfacial layers on absolute photonic band gap (PBG) is analyzed quantitatively. Numerical calculations are carried out based on Maxwell's equations and the plane-wave expansion method. It is shown that the physical property of interfacial layers influence the absolute PBG, and the existence of interfacial layers cannot enlarge the largest absolute PBG of an ideal case without interfacial layers.     

基于空气环结构的大带隙二维光子晶体的设计

用平面波展开法研究了内介质柱截面为长方形的三角晶格空气环型光子晶体的完全带隙特性。通过调节内介质柱的大小、介电常数、旋转角度以及空气环外半径对完全带隙的影响,找到了一组可以获得大带隙二维光子晶体结构的最佳参数。经优化后得到禁带宽度Δω=0.082(2πca-1)(其中a为晶格常数,c为光速),中心频率ω0=0.401(2πca-1),完全带隙宽度与中心频率的比值达到了20.4%,该结果比圆形内介质柱截面空气环结构的完全带隙大,比普通的空气孔结构的完全带隙增大了37%。     

Photonic amorphous diamond structure with a 3D photonic band gap

We report that a full three-dimensional (3D) photonic band gap (PBG) is formed in a photonic amorphous structure in spite of complete lack of lattice periodicity. It is numerically shown that the structure "photonic amorphous diamond" possesses a sizable 3D PBG (18% of the center frequency for Si-air dielectric contrast) and that it can confine light at a defect as strongly as conventional photonic crystals can. These findings present important new insight into the origin of 3D PBG formation and open new possibilities in developing 3D PBG materials.     

Theoretical study on photonic devices based on a commensurate two-pattern photonic crystal

In two-dimensional optical chip applications, the optical wave is classified to two modes according to its polarization: TE and TM. It is desirable to integrate multiple optical wave control devices for different polarizations onto the same plane at the scale of the wavelength. Here we demonstrate a periodic two-pattern photonic crystal with a large, complete photonic bandgap (PBG). It comes from the superposition of two substructures: one contributes the TM PBG and the other contributes the TE PBG. By purposely introducing defects into the substructures, photonic devices for different polarizations can be integrated to bend, split, and resonate TM/TE waves simultaneously on the same plane.     

二维单斜点阵光子晶体的第一布里渊区及带隙计算

二维单斜点阵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，详细讨论了二维单斜点阵光子晶体的第一布里渊区及带隙计算，并与常规方法计算得出的二维正三角形晶格光子晶体的带隙结构进行了比较.最后讨论了临界条件下二维单斜点阵光子晶体的带隙结构，证明了本方法的有效性.     

Analysis of photonic band gaps in a two-dimensional photonic crystal with centrifugal core-shell rods

The absolute photonic band gap (PBG) in two-dimensional (2D) photonic crystal with excentric core-shell rods is studied in this paper. The core rod shifts away from the core-shell rod center, and its position is decided by two new introduced parameters — the shift angle θ and the offset ρ. We use the FDTD algorithm to calculate the photonic bands of the photonic crystal, and analyze how the offset and shift angle affect the photonic bang gap of excentric core-shell photonic crystal for different core rod size. It has been shown that the variation of the photonic band gap is quite peculiar.     

Microwave photonic crystal multiplexer and its applications

The application of photonic band gap (PBG) structures to a microwave switch is studied. For this purpose, a frequency selective multiplexer is implemented combining one-dimensional PBG structures. The tunability of microwave photonic crystals (PCs) with ferrites and/or ferroelectric materials is then considered. A theoretical calculation performed on a two-dimensional hexagonal lattice of air rods embedded in a rectangular ferrite slab shows that the PBG is well tunable with external magnetic field parallel to the air rod. We have also discussed the implementation of microwave switch combining the tunability of PBG structures of ferrite and/or ferroelectric materials and the frequency selective nature of PBG multiplexer.     

Abnormal behaviour of one-dimensional photonic crystal with defect

The effect of introduction a defect in a conventional one-dimensional photonic band gap (PBG) structure in respect of the dispersion relation, reflectivity, group velocity and effective group index of such a structure has been studied. In particular, the dependence of various properties of such a structure on the angle of incidence of the electromagnetic waves has been given more importance in the present study. The study shows that inside the conventional PBG structure as well as defect PBG structure, the group velocity and effective group index become negative for certain ranges of normalized frequency. In a defect PBG structure, it is possible to achieve desired values (negative or positive) of group velocity and effective group index by choosing appropriate angle of incidence, whereas in conventional PBG structures, the maximum (negative and positive) values of group velocities and effective group index are found to be almost independent of the angle of incidence. This is a unique property of defect PBG structure which is different from the properties of conventional PBG structures. Because of this unique property, defect PBG structure may be widely used for construction super lenses, lasing without inversion and other optical systems in photonics.     

外磁场与温度对低温超导光子晶体低频禁带特性的影响

文中用传输矩阵法(TMM)分析了TM波垂直入时,超导光子晶体的低频禁带特性,并讨论了外磁场与温度对禁带的影响.分析结果表明:超导光子晶体存在频率从0开始的低频禁带;当没有外磁场作用时,由于超导中正常态电子的影响,低频禁带的截止频率与温度无关;有外磁场作用时,温度才对截止频率具有可调性.外加恒定磁场时,低频禁带的截止频率随温度升高而减小;而在正常态电子的作用下,温度对处在超导态超导光子晶体禁带截止频率的调节范围相对忽略正常态电子情况下减小.恒温下,通过调节外磁场来控制带隙时,正常态电子的贡献很小可忽略不计;外磁场强度增大禁带截止频率减小.当超导体完全处于正常态时,低频禁带消失.     

Improved air-silica photonic crystal with a triangular airhole arrangement for hollow-core photonic bandgap fiber design

We propose an improved photonic crystal (PC) cladding design for existing air-guiding photonic bandgap (PBG) fibers whose cladding airholes are arranged in a triangular lattice pattern. By increasing the sizes of concentrated silica regions in the cladding PC, we can have a larger degree of freedom in controlling the cladding bandgap regions. We predict that a fiber made from this type of cladding would perform better in terms of the PBG-guiding wavelength range, radiation loss owing to finite cladding size, and the ability to avoid surface mode problems.     

PBG光子晶体光纤的色散特性研究

光子晶体光纤(PCF)是一种具有特殊包层结构的光纤,它是利用光子禁带效应(PBG)来导光的。利用时域有限差分法(FDTD)来分析光波在PCF中传输的色散特性,结果表明,PBG光子晶体光纤的色散值和色散斜率比常规的通信光纤要小。     

Arbitrary-lattice photonic crystals created by multiphoton microfabrication

We used voxels of an intensely modified refractive index generated by multiphoton absorption at the focus of femtosecond laser pulses in Ge-doped silica as photonic atoms to build photonic lattices. The voxels were spatially organized in the same way as atoms arrayed in actual crystals, and a Bragg-like diffraction from the photonic atoms was evidenced by a photonic bandgap (PBG) effect. Postfabrication annealing was found to be essential for reducing random scattering and therefore enhancing PBG. This technique has an intrinsic capability of individually addressing single atoms. Therefore the introduction of defect structures was much facilitated, making the technique quite appealing for photonic research and applications.