Graphite格子光子晶体带隙的数值模拟

采用平面波展开法模拟计算了由锗圆柱构成的Graphite格子二维光子晶体的带隙结构,发现由空气背景中的介质柱构成的二维Graphite格子结构的光子晶体具有完全光子带隙,并得到了使完全带隙最大化的结构参数。数值计算结果表明,Graphite结构二维光子晶体在填充比从f=0.058到f=0.605连续变化的很大范围内都有完全带隙出现,在低能区出现了Δ=0.053(ωa/2πc)的较大带隙。     

二维正方格子磁性光子晶体的带隙结构

采用平面波展开的方法计算了正方格子二维磁性光子晶体(MPC)的光子带隙结构.散射子的形状分别为：长方形，正方形，六角形和圆形.通过调节磁导率，填充率和散射子的旋转角度，找到了MPC各种结构的最大的绝对带隙宽高比ω_R.研究发现：随着磁导率的增加，MPC绝对带隙中心频率ω_g单调减小，绝对带隙宽度Δω和其宽高比ω_R可能不同时达到最大值.而随着填充率或者散射子旋转角的增加，基本不改变ω_g的大小，各种结构的Δω和ω_R同时达到最大值. 关键词： 磁性光子晶体 光子带隙结构     

Optimize design super collimation in square lattice two-dimensional photonic crystals

The plane wave expansion (PWE) method was used to get the three-dimensional band diagram and equifrequency surface (EFS). From the EFS the maximum flatness half width (MFHW) and its position were got. The relation between MFHW and filling fraction P_f, dielectric ratio ε_b/ε_a were given in order to get the optimal structure we employ in this paper. Then the maximum super collimation was given by beam propagation method (BPM).     

Dual-negative-refraction and imaging effects in normal two-dimensional photonic crystals with hexagonal lattices

A novel dual-negative-refraction (DNR) effect is studied in two types of normal two-dimensional photonic crystals (2DPCs) with hexagonal lattices. Systematical analyses of the band structures and equifrequency surfaces indicate that the DNR may be realized when the overlapping second and third bands with relatively flat shapes and only a slight separation are available at some frequencies close to the band's peak of 2DPCs. Further simulations have not only confirmed the DNR and corresponding dual-imaging effects in normal 2DPCs with hexagonal lattices but also revealed some relative rules to the dual images. In particular, the thickness as well the cutoff value at terminations of PCs can strongly influence the performance of dual images and even determine whether the dual images would appear. Moreover, a relatively low working frequency is recommended to minimize the distortion degree of dual images.     

Band gap properties of two-dimensional photonic crystals with rhombic lattice

A new structure of two-dimensional photonic crystals (PCs) with rhombic lattice is proposed in this paper. It provides more flexibility in the design of photonic crystal devices and makes the designer be able to choose a more suitable lattice angle to satisfy different demands. The first Brillouin zone (1st BZ) of this structure is discussed and the general wave vectors are derived. The plane wave expansion (PWE) method is used to analyze the band gap properties. The impact of different lattice angels on the band gaps is analyzed, and the band gap map is also given.     

The properties of two-dimensional photonic crystals bandgap structure with rhombus lattice

The relative bandgap ω_R of photonic crystals structure with rhombus lattice for both TE and TM modes is studied by the plane wave expansion method. Based on the analysis, a bending waveguide of U type can be easily obtained. The steady-state distribution of the electric field with ω = 0.4765(a/λ) of TM mode is given by FDTD method and the transmission is obtained by FFT of the time domain field. All of the sufficient analysis shows the conceptual framework of the proposed rhombus lattice PCs and its great potential application in photonic integration circuit.     

Magneto-optical defects in two-dimensional photonic crystals

We analyze the properties of magneto-optical defect states in two-dimensional photonic crystals. With out-of-plane magnetization, the magneto-optical coupling splits doubly-degenerate TE states into two counter-rotating modes at different frequencies. The strength of magneto-optical coupling strongly depends on the spatial overlap of the cavity domain structures and the cross product of the modal fields. The transport property of the resultant nonreciprocal states is demonstrated in a junction circulator structure with a magneto-optical cavity coupled to three waveguides. By a proper matching of the magneto-optical frequency splitting with the cavity decay rate into the waveguide, ideal three-port circulator characteristics with complete isolation and transmission can be achieved, with an operational bandwidth proportional to the magneto-optical constant. The proposed optical circulator in a bismuth-iron-garnet/air photonic crystal is demonstrated with finite-difference time-domain calculations and is compared to an alternative implementation of silicon/air crystal infiltrated with a single bismuth-iron-garnet domain.     

Diffraction inhibition in two-dimensional photonic crystals

We show the existence of flat equal-frequency contour across the entire first Brillouin zone in two-dimensional photonic crystals. Under this condition, light diffraction can be inhibited. Moreover, the beam can be highly localized between two neighboring rows of the defect-free photonic crystal. Such a finding may have novel applications in light beam manipulations and on-chip integrated photonic devices.     

Band structure of two-dimensional square lattice photonic crystals of circular dispersive metamaterial rods

By virtue of the efficiency of the Dirichlet-to-Neumann map method, the details of the band structure of a two-dimensional square lattice photonic crystal composed of dispersive metamaterial circular rods in air background has been studied. We show that there are two flat bands at the band structure of the system for both H-polarization and E-polarization. These flat bands are created around the magnetic resonance frequency, surface plasmon frequency and magnetic surface plasmon frequency. We realized that the modes with frequencies lying above the resonance frequency behave like resonant cavity modes created in a single metallic cylindrical waveguide. While, due to the relatively large and imaginary refractive index of the metamaterial rods at the frequencies lying below the resonance frequency, the modes are localized modes with negligible penetration into the rods. Moreover, the modes are localized at the interface of the cylindrical metamaterial rods and the air background for the frequencies around the surface plasmon frequency and the magnetic surface plasmon frequency.     

Negative refraction in two-dimensional photonic crystals

We present some of our recent results for negative refraction in photonic crystals. The concept of negative refraction in photonic crystals is firstly introduced. Then, the propagation of electromagnetic waves in photonic crystals is systematically studied. By the layer Korringa–Kohn–Rostoker method, the coupling efficiency between external plane waves and the Bloch waves in photonic crystals is investigated. It is found that the coupling coefficient is highly angular dependent even for an interface between air with n=1 and a photonic crystal with effective index n_eff=-1. It is also shown that, for point imaging by a photonic crystal slab, owing to the negative refraction, the influence of the surface termination on the transmission and the imaging quality is significant. Finally, we present results experimentally demonstrating negative refraction in a two-dimensional photonic crystal at optical communication wavelengths. PACS 42.70.Qs; 41.85.Ct; 42.30.Va     

Band gap extension in honeycomb lattice two-dimensional plasma photonic crystals in the presence of dissipation

We investigate two types of honeycomb lattice two-dimensional plasma photonic crystals that possess large photonic band gaps in the presence of dissipation. We obtain a clear insight into the band structures and find imaginary parts of the eigenvalue band structure at the symmetry points display discontinuous behaviour when the filling factor of plasma in type-1 structure is low. Further more, we show how the photonic band gaps are affected by the normalized plasma frequency, radius of cylinder, dielectric constant and collision frequency. Our results demonstrate the band gap extension by increasing normalized plasma frequency in both type structures and radius of plasma cylinders in type-1 structure. The width of band gaps could also be enlarged by decreasing dielectric cylinder's radius. The bands shift toward lower frequencies when relative dielectric constant increases in both two types. These results may provide theoretical instructions to design new optoelectronic devices.     

A two—dimensional photonic crystal with six large bandgaps formed by a hexagonal lattice of anisotropic cylinders

The plane-wave expansion method is used to calculate the band structure of a two-dimensional photonic crystal formed by a hexagonal structure of anisotropic cylinders. Two cylindrical inclusions in the unit cell have two different radii, R₁ and R₂ (R₁2). By reducing the symmetry of the structure and choosing appropriately parameters R₂ and s=R₁/R₂ (s<1), we obtain six large complete bandgaps, among which three are over 0.05 ω_e (where ω_e=\frac{2πc}{a}) in the high region of the normalized frequency (however, one of these over 0.065 ω_e is not stable). There are two other stable complete bandgaps in the low-frequency region.     

Dust lattice wave dispersion relations in two-dimensional hexagonal crystals including the effect of dust charge polarization

A dusty plasma crystalline configuration with equal charge dust grains and mass is considered. Both charge and mass of each dust species are taken to be constant. Two differential equations for a two-dimensional hexagonal crystal on the basis of a Yukawa-type potential energy and a “dressed” potential energy, accounting for dust charge polarization, are derived and compared. The dispersion relation for both longitudinal and transverse wave propagation in an arbitrary direction is derived. A comparison to analytical and experimental results reported previously is carried out.     

Engineering absolute band gap in anisotropic hexagonal photonic crystals

We analyze the band gap spectra of two-dimensional anisotropic photonic crystals created by a hexagonal lattice of rods covered by an interfacial layer (e.g. tellurium tubes). Using the plane-wave numerical expansion method, we study the modification of the band gap spectrum when the rods are infiltrated with other material, and discuss the optimization strategies leading to the maximum value of the absolute band gap.     

Superbending effect in two-dimensional graded photonic crystals

We study the superbending effect in a two-dimensional graded photonic crystal (GPC) for both TE and TM modes. We show that the lateral beam shift is extremely sensitive to the wavelength for the TM mode but not TE mode, indicating the potential in designing some special superbending devices, for example, TE/TM splitter and polarization-indifference waveguide at prescribed wavelengths.     

Optical circulators in two-dimensional magneto-optical photonic crystals

We propose an optical circulator formed of a magneto-optical cavity in a 2D photonic crystal. With spatially engineered magnetic domain structures, the cavity can be designed to support a pair of counterrotating states at different frequencies. By coupling the cavity to three waveguides, and by proper matching of the frequency split of the cavity modes with the coupling strength between the cavity and the waveguide, ideal three-port circulators with complete isolation and transmission can be created. We present a guideline for domain design needed to maximize the modal coupling and the operational bandwidth for any given magneto-optical constant.     

Band-edge-induced Bragg diffraction in two-dimensional photonic crystals

Two-dimensional photonic crystals composed of two orthogonal volume diffraction gratings have been photogenerated in photopolymers. When the read beam is set at the Bragg angle, the diffraction efficiency of the transmission grating is strongly enhanced at the band edge of the reflection grating recorded in the material. Such a device provides Bragg operation and enhancement of the diffraction efficiency of the thin diffraction grating together with good wavelength selectivity. Such advantages could be interesting for optical signal processing.     

Refraction of light in two-dimensional photonic crystals

Refraction of light at an interface between a homogeneous dielectric and a two-dimensional photonic crystal is studied. Using the isofrequency method, various cases of refraction, including a change in the magnitude and direction of the wave vector of the incident wave, in the refractive indices of the media, and in the mutual orientation of the interface and the translation vectors of the photonic crystal, are investigated. Different types of refraction and the possibilities for realizing negative and multiwave refraction are considered.     

Wave-vector diagrams for two-dimensional photonic crystals

Photonic crystals exhibit band gaps, meaning that electromagnetic fields cannot propagate in them for specific ranges of wavelengths and directions. The calculation of band structure diagrams has been intensively studied and is now well understood. In contrast to that, so-called wave-vector diagrams (i.e. dispersion surfaces, depicting the loci of all relevant wave vectors at a fixed wavelength) are less known and used. In principle, they show how the effective index of the structure depends on the direction of propagation. A method to calculate explicitly wave-vector diagrams for two-dimensional photonic crystals is derived which leads finally to quadratic eigenvalue problems. Results for square and triangular lattices are presented and some applications are discussed.