Band gap studies of 2D photonic crystals with hybrid scatterers

Two-dimensional (2D) photonic crystals (PCs) of a square lattice with dielectric hybrid rods in air are proposed; these PCs consist of a square rod at the center of the unit cell and additional circular rods with their outermost edges against the middle of each side of the lattice unit cell. The band gap structures of PCs can be tailored and optimized by rotating the square rods and adding circular rods to the lattice unit cell. The variation of bands near the complete photonic band gap boundaries, due to some specific modes, is sensitive to certain structural parameters of the system. The results can be understood by analyzing the spatial energy distribution of the electromagnetic fields. Based on such a field analysis, a novel interpretative model is proposed. The PC can be fabricated easily and operated in the microwave region and, hence, should be suitable for applications in new microwave devices.     

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用时域有限差分法研究了电磁波在等离子体光子晶体中的传播特性。数值模拟中使用完全匹配层吸收边界条件,计算了电磁波通过等离子体光子晶体的反射和透射系数。讨论了等离子体密度、等离子体温度、介电常数比和引入缺陷层对等离子体光子晶体光子带隙的影响。     

Photonic band gap failure in photonic crystal devices

The photonic crystal is an artificial material with periodic dielectric constant and the key factor to preserve their band features is its periodicity. When the number of periods of photonic crystal is decreased the photonic band gap cannot prevent the light of the corresponding frequencies from propagating in photonic crystal, in another word, photonic band gap will be failure. The minimum periods of photonic crystal device which can keep photonic band gap effective in miniaturization process is analyzed, the transmittance spectrum is calculated by the Finite-difference time-domain algorithm (FDTD) [1], the minimum periods is got in the simulation and the reason which affects the minimum periods is analyzed in this paper.     

Novel optical modulator using silicon photonic crystals

We propose a novel compact and integrated optical modulator, which consists of p–i–n silicon photonic crystals with triangular lattice and a line defect waveguide. The device operation is based on a dynamic shift of the photonic band gap (PBG), which induced change in the silicon refractive index by the free carrier injection. We have numerically analyzed and investigated its light modulation performance by using plane wave expansion (PWE) method and finite-difference time-domain method. With small size, rapid response time and high extinct ratio, the designed optical modulator can be used in photonic integrated circuits.     

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.     

一维等离子体光子晶体的带隙研究

采用时域有限差分方法(FDTD),结合等离子体计算中的分段线性电流密度卷积技术(PLJERC)对一维等离子体光子晶体(1D-PPC)进行了数值模拟,给出了微分高斯脉冲在一维等离子体光子晶体中的传播过程。计算得到的带隙结构与K-P模型方法的结果一致。计算并分析了等离子体频率、介质介电常数、等离子体-介质层的厚度比以及周期厚度对一维等离子体光子晶体带隙结构的影响。     

Two-dimensional function photonic crystals

In this paper, we have studied two-dimensional function photonic crystals, in which the dielectric constants of medium columns are the functions of space coordinates , that can become true easily by electro-optical effect and optical kerr effect. We calculated the band gap structures of TE and TM waves, and found the TE (TM) wave band gaps of function photonic crystals are wider (narrower) than the conventional photonic crystals. For the two-dimensional function photonic crystals, when the dielectric constant functions change, the band gaps numbers, width and position should be changed, and the band gap structures of two-dimensional function photonic crystals can be adjusted flexibly, the needed band gap structures can be designed by the two-dimensional function photonic crystals, and it can be of help to design optical devices.     

Theoretical study on the photonic band gap in one-dimensional photonic crystals with graded multilayer structure

We theoretically investigate the photonic band gap in one-dimensional photonic crystals with a graded multilayer structure. The proposed structure constitutes an alternating composite layer (metallic nanoparticles embedded in TiO2 film) and an air layer. Regarding the multilayer as a series of capacitance, effective optical properties are derived. The dispersion relation is obtained with the solution of the transfer matrix equation. With a graded structure in the composite layer, numerical results show that the position and width of the photonic band gap can be effectively modulated by varying the number of the graded composite layers, the volume fraction of nanoparticles and the external stimuli.     

Scaling properties of a tetragonal photonic crystal design having a large complete bandgap

Photonic crystal structures (PCs) of tetragonal lattice type are introduced and studied. They feature complete three-dimensional (3D) photonic bandgaps (PBGs). The PC design is based on two systems of ordered, parallel pores being perpendicular to each other. For increasing pore radii, the pore systems interpenetrate and an inverted woodpile geometry arises. The size of the 3D bandgaps depends on the ratio of the cell parameters L_x, L_y, and L_z, the pore radii and the refractive index of the dielectric material. If realized as a silicon/air structure, the maximum 3D gap is larger than 25%. A possible fabrication route for the near-infrared is based on 2D macroporous silicon where perpendicular pores are drilled, e.g., by focused-ion-beam etching. The dispersion behaviour of the PCs is theoretically analysed (band structures, density-of-states), systematically varying all relevant parameters. The optimization of the PBG sizes as well as a possible tunability of the PBG energies are discussed.     

Design of photonic bands for opal-based photonic crystals

To make a device from an opal—or otherwise—the photonic bands and the optical properties derived from them are needed. Knowing the effects of different parameters defining the opal geometry and different possible modifications of its structure are needed, too. An accurate definition of the device will be required to obtain a good performance. With this aim, the optics of light with a wavevector in the vicinity of the L point in the Brillouin zone and its coupling to bare opals band structure are presented. An important aspect is the transition from finite to infinite crystal and the study of size effects on the bands. It is possible to substantially alter the photonic band structure of an opal-based system, while maintaining the lattice structure, simply by growing layers of other materials with an appropriate refractive index. Here, it is shown how, by the growth of accurately controlled thin layers of silicon and germanium, and further processing, one can induce the opening of two complete photonic band gaps (PBGs) in an opal structure. Finally, the possibility to fabricate a simple device consisting in a planar waveguide will be shown. By means of a very simple and inexpensive procedure, engineered planar defects acting as microcavities have been realized. These can be viewed as a particular case of a much more general class of heterostructures that can be grown by combining opal vertical deposition and chemical vapour deposition of oxides. A further step is made by applying electron beam lithography to provide lateral definition and facilitate three-dimensional structuring.     

三角晶格有耗色散光子晶体的能带结构分析

为探讨有耗色散媒质光子晶体的特性,引入一种计算有耗色散光子晶体能带结构的方法,基于有限元法将能带结构的计算简化为求解关于Block波矢的二次特征值问题,可以有效地得到色散材料光子晶体的能带结构和特征模.分析了三角晶格介质光子晶体能带结构并与现有方法对比,结果表明两种方法在TM模和TE模下得到的能带结构完全相同,验证了该方法的有效性.分析了无耗及有耗色散光子晶体的能带结构,发现无耗光子晶体场强集中于色散媒质与空气的接触面,并呈现出明显的表面等离激元特性,具有对称性,而有耗光子晶体场强减小,表面等离激元变弱,对称性被破坏.相关结果可为有耗色散光子晶体以及表面等离激元的研究提供参考.     

Anomalous dispersion in one-dimensional plasma photonic crystals

The anomalous dispersion in one-dimensional plasma photonic crystals (1-DPPCs) is studied. The width of band pass and band gap are compressed, the phase velocity decreases and the cup-off frequency comes close to the frequency of plasma when EM wave oblique incidence on 1-DPPCs. The band gaps are affected by the thickness of plasma, the dielectric constant of the dielectric material, the plasma density and the angle of incidence. Superluminal negative group velocity is discovered in this study. This character is interesting for scientists and may have a potential application.     

Properties of omnidirectional photonic band gap in one-dimensional staggered plasma photonic crystals

In this paper, the properties of the omnidirectional photonic band gap (OBG) realized by one-dimensional (1D) photonic crystals (PCs) with a staggered structure which is composed of plasma and isotropic dielectric layer have been theoretically studied by the transfer matrix method (TMM). From the numerical results, it has been shown that such OBG is insensitive to the incident angle and the polarization of electromagnetic wave (EM wave), and the frequency range and central frequency of OBG can be effectively controlled by adjusting the plasma frequency, the average thickness of plasma layer, the average thickness of dielectric layer and staggered parameters, respectively. The frequency range of OBG can be notably enlarged with increasing the plasma frequency, average thickness of plasma layer, respectively. Moreover, the bandwidth of OBG can be narrowed with increasing the average thickness of dielectric layer. Changing staggered parameters of dielectric and plasma layer means that the OBG can be tuned. It is shown that 1D plasma dielectric photonic crystals (PPCs) with such staggered structure have a superior feature in the enhancement of frequency range of OBG compared with the conventional 1D binary PPCs. This kind of OBG has potential applications in filters, microcavities, and fibers, etc.     

Control of photonic band gaps in one-dimensional photonic crystals

The photonic band gaps in one-dimensional photonic crystals (PCs) are theoretically investigated. A new method to broaden the photonic band gaps is introduced. Based on the similar method, a kind of photonic crystals is constructed to generate photonic band gaps with proportioned central frequencies. This technology can be used for designing nonlinear PCs for harmonic generation.     

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应用多光子非线性Compton散射模型和时域有限差分法,对Compton散射对时变非磁化等离子体光子晶体禁带的影响进行了研究,提出了将多光子非线性Compton散射电磁波和入射电磁波作为等离子体光子晶体产生光子禁带的新机制,给出了电磁场的Maxwell方程组和叠代方程的修正方程,并进行了数值模拟。结果表明,Compton散射使等离子体禁带宽随等离子体上升时间的增大比散射前有明显减小而最后趋于定值,均匀等离子体透射率峰值比线性等离子体增大得更多,利用Compton散射可实现对光子禁带的控制。     

Photonic band gap engineering in 2D photonic crystals

The polarization-dependent photonic band gaps (TM and TE polarizations) in two-dimensional photonic crystals with square lattices composed of air holes in dielectric and vice versa i.e., dielectric rods in air, using the plane-wave expansion method are investigated. We then study, how the photonic band gap size is affected by the changing ellipticity of the constituent air holes/dielectric rods. It is observed that the size of the photonic band gap changes with changing ellipticity of the constituent air holes/dielectric rods. Further, it is reported, how the photonic band gap size is affected by the change in the orientation of the constituent elliptical air holes/dielectric rods in 2D photonic crystals.     

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.     

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.     

Enhanced complete photonic band gap in the optimized planar diamond structure

The diamond photonic crystal with dielectric rods has been modified to enlarge the fundamental band gap. By planarizing the diamond structure and reducing the thickness of the hexagonal meshes, the band gap can be increased substantially. The band gap is 29% for a refractive index contrast of 3.6. The modified structure is amenable to fabrication at optical and infrared wavelengths using state-of-the-art silicon-processing methods. Transfer matrix calculations demonstrate a large attenuation within the band gap.     

Enlargement of absolute photonic band gap in modified 2D anisotropic annular photonic crystals

We analyze the absolute photonic band gap in two dimensional (2D) square, triangular and honeycomb lattices composed of air holes or rings with different geometrical shapes and orientations in anisotropic tellurium background. Using the numerical plane wave expansion method, we engineer the absolute photonic band gap in modified lattices, achieved by addition of circular, elliptical, rectangular, square and hexagonal air hole or ring into the center of each lattice unit cell. We discuss the maximization of absolute photonic band gap width as a function of main and additional air hole or ring parameters with different shapes and orientation.