Holographic design of hexagonal photonic crystals of irregular columns with large full band gap

The shape and size of the dielectric columns or particles (“atoms”) of photonic crystals (PhCs) formed by holographic lithography are determined by the isointensity surfaces of the interference field; consequently the PhCs’ photonic band gap (PBG) properties are closely related to their fabrication design. Here we have proposed a new structure of two-dimensional (2-D) hexagonal lattice with irregular columns, which can yield a 2-D complete relative band gap of 24.0% in case of the dielectric columns of ε = 13.6 in air, about 27% increase compared with that of the same lattice with regular triangular columns. This band gap size is among the largest for all the possible 2-D PhCs reported until now. The relationship between band gap properties of resultant structure and the specific fabrication conditions such as structure design and the choice of optimum intensity threshold and filling ratio are systematically discussed. The optical design for making this structure by two exposures is explained. This work may demonstrate the unique feature and advantages of photonic crystals made by holographic method and provide a guideline for their design and experimental fabrication.     

Intersecting veins effects of a two-dimensional photonic crystal with a large two-dimensional complete bandgap

Optimal design of a two-dimensional photonic crystal with a square lattice of dielectric rods with intersecting veins in GaAs is investigated numerically using plane wave expansion method. It is shown how a maximum complete two-dimensional bandgap is obtained by optimally connecting the dielectric rods with intersecting veins. The complete two-dimensional photonic bandgap (PBG) of our optimal design reaches Δω = 0.10664(2πc/a) (where a is the lattice constant and c is the speed of light in vacuum) when the radius of dielectric rod is 280.1 nm and the half-vein width is 60 nm. Our result shows 40% the width of PBG higher than that obtained from Ref. [M. Qiu, S. He, J. Opt. Soc. Am. B 17 (2000) 1027] (Δω = 0.0762(2πc/a)). In addition, we found that the complete bandgap can be obtained in a large range of radius R of dielectric rod when the half width of intersecting veins d is larger than 65 nm.     

大带隙二维三角格子光子晶体结构参数的优化设计

光子晶体结构设计优化是理论研究的一个重要内容.运用平面波展开法对圆柱、方柱及正六边柱构造的二维三角格子光子晶体的禁带进行仿真计算,讨论了介质材料分别为GaAs、Si和Ge情况下,柱子形状、旋转角度、填充比的变化对完全光子禁带的影响.发现:对于二维三角格子光子晶体,相对于介质柱,空气柱更易获得完全光子禁带;而相对于圆柱及...     

A novel design of a photonic crystal sensor with improved sensitivity

Biosensors, based on photonic crystal (PC), are emergent subject. The use of PCs in this area brought solutions to both miniaturization and integration challenges that have been facing research groups for long time. We are only recently, by engineering such defects, able to propagate light in complex structures containing molecules of different sizes and shapes. We propose a novel structure containing defects with various sizes. The PC is formed by a dielectric cylinders with permittivity 8.9 (alumina Al₂O₃) and a radius r = 0.2a (a is the square lattice constant), arranged in a square lattice. We use the finite difference time domain to investigate the sensitivity of the proposed sensor to water. The defect based sensing element is introduced in two directions 〈0 1〉 and 〈1 0〉. These simulations show a better sensitivity to water than other analytes. It appears in the transmission curves where the peak shifts to high frequency when the refractive index is changed.     

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).     

Study on maximum band gap of two-dimensional photonic crystal with elliptical holes

In this paper, the maximum photonic band gap (PBG) of two-dimensional (2D) photonic crystal (PC) with elliptical air holes was studied by the finite-difference time-domain (FDTD) method based on changing the ratio (semi-major axis length of elliptical hole to the filling ratio) and azimuth angle of elliptical holes, respectively. It is shown that the PBG exhibits a peak value when the ratio of semi-major axis length to the filling ratio is equal to 0.86 approximately by increasing the filling ratio, and central frequency and the low boundary frequency of PBG decrease linearly with the increasing of semi-major axis length. In the aspect of the influence of azimuth angle from 0 to 90°, the PBG presents a minimum value, and central frequency and the low boundary frequency of PBG become high non-linearly by the increasing of azimuth angle to any filling ratio.     

Defect and dope selective of transmission properties of 2D photonic crystal

The effects of the defect and doping on the transmission properties are investigated in two-dimensional photonic crystal (PC) with triangular rods using the finite difference time domain (FDTD) method. The results show that the width and the central position of the photonic band gap (PBG) depend on the thickness of rods with defect or composite-defect, and the refractive index of doped dielectric rods. The transmission properties of composite-defect combined with doping are further investigated. The thinner the nested concentric triangular rod and the smaller the refractive index is, the wider the band gaps is.     

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.     

Negative refraction in one-dimensional plasma photonic crystals

We have theoretically explored the negative refraction (NR) in one-dimensional plasma photonic crystals (PCs) consisting of plasma and dielectric materials. By using the transfer matrix method and Bloch theorem, we have studied the group velocity and we have obtained the NR in plasma PCs with the help of the group velocity. The results show that plasma PCs can also exhibit the NR although they have a periodically modulated positive permittivity ? and permeability μ. It is also shown that the NR in plasma PCs exhibits difference behaviour in different frequency regions, ω < ω_p and ω > ω_p, respectively. The parameter dependence of the effects is also examined and discussed.     

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.     

Optical properties of one-dimensional photonic crystals containing graded materials

The optical properties of an one-dimensional photonic crystal containing graded materials are studied theoretically. The graded layers have space dispersive permittivity and magnetic permeability which vary along the direction perpendicular to the surface of the layer. The gradation profiles of permittivity are studied in detail. We show that the structure possesses forbidden band gaps in its transmission spectra and the gradation profiles of permittivity affect the band gaps significantly. For the exponential gradation profile ε₁(x) = α e^βx, the number of the band gaps increases and the total frequency region corresponding to the gaps becomes large with increasing parameter β. On the other hand, the position of band gaps can be changed by the adjustment of the gradation profiles even if possessing same volume-average permittivity in the graded layers. Therefore, we can achieve suitable photonic band gaps by choosing gradation profiles of permittivity.     

Electronic and hole minibands in quantum wire arrays of different crystallographic structure

We consider semiconductor heterostructures consisting of GaAs rods embedded in Al_xGa_1 − xAs and disposed in sites of a square or triangular lattice. The electronic and hole spectra around the conduction band bottom and the valence band top are examined for electrons and holes propagating in plane of periodicity, versus geometry of the lattice formed by the rods, concentration of Al in the matrix material, and structural parameters including the filling fraction and the lattice constant. Our calculations use the envelope function and are based on the effective-mass approximation. We show that the electronic and hole spectra resulting from the periodicity of the heterostructure, depend on the factors considered and that the effect of lattice geometry varies substantially with lattice constant. For low lattice constant values the minigaps are significantly wider in the case of triangular lattice, while for high lattice constant values only slightly thiner minigaps occur in the square lattice-based arrays. We discuss the consequences of our findings for the efficiency of solar cells.     

Percolation phenomenon in barium samarium titanate-silver composite

Ba₄Sm_9.33Ti₁₈O₅₄-Ag (BST-Ag) composites were prepared by a solid-state ceramic route and its dielectric properties were investigated in the vicinity of percolation threshold. The structure and microstructure of the composites were analyzed by X-ray diffraction along with optical and scanning electron microscopy observations. The effects of silver content and frequency on the dielectric properties of BST-Ag composites were studied using a LCR meter. The relative permittivity (ε_r) of the composite increases with silver content below the percolation limit and is in agreement with power law. A 0.14 volume fraction of silver loading increases the relative permittivity of the composite from 50 to 450 at 10 kHz. Addition of 0.15 volume fraction of silver increases the relative permittivity of the composite in the order of 10⁵. It is found that the giant relative permittivity is almost constant for frequencies from 1 kHz to 1 MHz. This high ε_r composite offers the perspectives for application in electromechanical devices.     

Metallic nonlinear magnetooptical nonreciprocal isolator

In advanced optical fiber communication systems where reflection light might cause degradation of the signal quality, optical waveguide isolators play an important role. The effect of a metal layer with negative permittivity on the behavior of nonlinear-magnetooptic isolator is studied. The isolator consists of metal film, nonlinear cladding, and magnetooptic substrate. It is found that difference between forward and backward propagation for TM₀ mode increases with increasing the absolute value of the tuning parameter which is the permittivity of the metal film, ?_f. It is also found that the maximum cut-off thickness of the isolator occurs in self-defocusing case around η = 0.65 and at the highest assumed value of ?_f = −8. These results are helpful in fabricating an isolator with high performance.     

具有光子晶体带隙结构的返波振荡器的初步研究

 提出了一种新型的具有光子晶体带隙（PBG）结构的返波振荡器（BWO），利用PBG禁带对BWO工作及输出微波模式进行调制，抑制低次模式，工作在高次模式。通过数值模拟给出了介质柱PBG结构的能带图、禁带限制模式电场分布和周期慢波结构的色散关系曲线，选择晶格常数为0.31 cm，介质柱半径为0.12 cm，介电常数为4.0的三角格子PBG结构可以实现在Ka波段的单一类TM03模式工作，在36～40 GHz的频率范围内，器件可以工作在返波状态，周期长度为0.4 cm。     

Dielectric photonic crystal as medium with negative electric permittivity and magnetic permeability

We show that the two-dimensional photonic crystal (PC) made from a non-magnetic dielectric is a left-handed material in the sense defined by Veselago. Namely, it has negative values for both the electric permittivity ? and the magnetic permeability μ in some frequency range. This follows from a recently proven general theorem. The negative values of ? and μ are found by a numerical simulation. Using values |?| and |μ| for the medium surrounding the PC slab we simulate the Veselago lens, a unique optical device predicted by Veselago. An approximate analytical theory is proposed to calculate the values of ? and μ from the PC band structure. It gives the results that are close to those obtained by the numerical simulation. The theory explains how a non-zero magnetization arises in a non-magnetic PC.     

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     

Relaxor behavior of (Ba,Sr)(Zr,Ti)O3 ferroelectric ceramics

We examine the ferroelectric-relaxor behavior of (Ba_0.65Sr_0.35)(Zr_0.35Ti_0.65)O₃ (BSZT) ceramics in the temperature range from 80 to 380 K. A broad dielectric maximum, which shifts to higher temperature with increasing frequency, signifies the relaxor-type behavior of these ceramics. The value of the relaxation parameter γ∼2 estimated from the linear fit of the modified Curie-Weiss law, indicates the relaxor nature of the BSZT ceramics. The dielectric relaxation rate follows the Vogel-Fulcher relation with T_VF=107 K, E_a=0.121 eV, and ν₀=6.83×10¹⁴ Hz, further supports such relaxor nature. The slim P-E hysteresis loop and ‘butterfly’ shape dc bias field dependence of permittivity at T>T_m (T_m, the temperature of permittivity maximum) clearly signifies the occurrence of nanopolar clusters, which is the typical characteristic of ferroelectric relaxor. At 300 K and 10 kHz, the dielectric constant and loss tan δ are ∼1100 and 0.0015, respectively. The high tunability (∼25%) and figure of merit (∼130) at room temperature show that the BSZT ceramics could be a promising candidate for tunable capacitor applications.     

Dielectric relaxation in single crystal NH4H2PO4 in the high-temperature regime

The dispersion curves of the dielectric response in single crystal NH₄H₂PO₄ were obtained in the radio frequency range and below the high-temperature transition at T_p−160 °C. The results reveal dielectric relaxation at low frequency, which is about 10⁵ Hz at 70 °C, and it shifts to higher frequencies (∼3×10⁶ Hz) as the temperature increases. The relaxation frequency was determined from the peak obtained in the imaginary part of the permittivity as well as from the derivative of the real part of the permittivity. The activation energy E_a=0.55 eV, obtained from the relaxation frequency is very close to that derived from the dc conductivity. We suggest that this dielectric relaxation could be due to the proton jump and phosphate reorientation that cause distortion and change the local lattice polarizability inducing dipoles like      

Absolute photonic band gaps in a two-dimensional photonic crystal with hollow anisotropic rods

The plane-wave expansion method is used to calculate photonic band gaps for two structures with hollow anisotropic tellurium (Te) rods. Both structures are found to have absolute band gaps at the low- and high-frequency regions. Compared with the photonic crystal with solid Te rods, the photonic crystal with hollow Te rods has a large absolute band gap at the high-frequency region: for the triangular lattice of oval hollow Te rods, there is an absolute band gap of 0.058w_e (w_e=2πc/a), and for the square lattice of square hollow Te rods, there is an absolute band gap of 0.056w_e.