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

The spectral properties of a one-dimensional photonic crystal with a structure defect—anisotropic nanocomposite layer incorporated between two multilayer dielectric mirrors—have been theoretically investigated. Some specific features are revealed in the transmission spectrum of a photonic crystal. They are primarily due to the resonant behavior of the effective permittivity of nanocomposite and the strong dependence of this parameter on the volume fraction of nanoparticles in the composite.     

Tetragonal photonic woodpile structures

The photonic properties of dielectric woodpile structures with face-centered-tetragonal (fct) and body-centered-tetragonal (bct) lattice symmetries are theoretically studied. Computational calculation of the photonic band structure reveals a photonic band gap between the second and third photonic band in both symmetries. A complete photonic band gap is not found in the bct structure due to a band gap shift with variable direction of lightflow. When the degree of layer disorder in fct woodpiles is increased, the stop bands slightly narrow and the attenuation of the optical transmission is reduced. Even so, layer-to-layer misalignment in dielectric woodpile structures may be tolerable up to 20–30% in most applications. The complete photonic band gap in fct woodpiles remains open with planar layer-to-layer disorder up to 60–70%.     

一维函数光子晶体的研究

本文提出一种新型函数光子晶体, 其折射率是空间位置函数. 由费马原理, 我们给出光在一维、 二维和三维函数光子晶体中的运动方程, 以及一维函数光子晶体的色散关系、 带隙结构和透射率, 再利用传输矩阵理论研究函数光子晶体周期数、 入射角和介质层的厚度等对透射率和禁带结构的影响, 计算发现通过选择不同的折射率空间分布函数, 可以得到比传统光子晶体更宽或更窄的禁带结构. 这样为我们设计不同带隙结构的光子晶体提供理论依据.     

Optical bistability in one-dimensional photonic band gap structures with coupled nonlinear defects

Using the transfer matrix method, we study the transmission property of one-dimensional photonic band gap structure with two coupled nonlinear defects separated by a linear middle layer and find that such composite structure exhibits a bistability that’s strongly dependent of the linear middle layer. The switching threshold values can be greatly reduced just by choosing the proper parameters of the linear middle layer.     

Optical properties of chiral photonic crystals with graded modulation parameters

The oblique transmission of light through a layer of a chiral photonic crystal with graded modulated parameters is considered. The problem is solved by the Ambartsumian’s layer addition method. Dependences of amplitude characteristics on the wavelength at different incident angels are presented for two cases: namely, for the case of a chiral photonic crystal with a linearly varied spatial period of modulation and in the case of a chiral photonic crystal with a linearly varied spatial depth of modulation. The case of a minimal influence of dielectric boundaries is considered. It is shown that in both cases a broadening of the photonic forbidden band gap takes place.     

Large photonic band gap's in one-dimensional multilayer structures

A one-dimensional photonic lattice constructed from a material possessing a higher value of dielectric constant has been studied under the consideration of photonic band gap, filling fraction, and the competition of different transmission mechanism of the incoming electromagnetic waves. A special attention has been paid to the localized state introduced by the introduction of defect in our multilayer structure.     

Anisotropy of nonlinear optical transmission at the edge of the photonic band gap of an apodized layered medium

The effect of Kerr nonlinearity on the transmission of laser radiation in a one-dimensional photonic crystal has been investigated by the transfer-matrix method, modified to describe nonlinear effects. The crystal under study is a thin-film multilayer structure with a spatial distribution of the refractive index, which makes it possible to eliminate side bands in the transmission spectrum at each side of the photonic band gap and significantly increase the slope of the transmission curve. The transmission spectrum of such a photonic crystal structure has been studied for two opposite directions of laser radiation propagation. The anisotropy of nonlinear transmission is most pronounced near the edge of the photonic crystal band gap, which lies in the near-IR region. The proposed structure, having strong transmission anisotropy and sufficiently low reflection in the forward direction, can operate as an optical diode (analog of an electron diode).     

利用基于自动复形技术的二维光子晶体模型设计宽角度宽波长偏振分束器

基于自动复形技术，在148—152μm的近红外波段设计了可以实现全角度偏振分束（TM模透过，TE模反射）的波状膜层二维光子晶体结构.从能带角度解释了全角度偏振分束的原理.波状膜层倾角θ和a-Si单层膜厚T分别可以在38°—49°和014—015μm的范围内变动，不影响全角度的偏振特性.对波状膜层进行了变形，针对波长128—1 31μm设计了宽角度偏振分束的箭羽型二维光子晶体结构.对比两种结构的能带，阐明了二 维光子晶体偏振分束器光线入射角范围的拓宽与能带结构变化的关系.能带计算全部采用平 面波展开算法. 关键词： 偏振分束 平面波展开 完全禁带     

Transmission properties of one-dimensional graded photonic crystals and enlargement of omnidirectional negligible transmission gap

We investigate numerically the transmission properties of one-dimensional (1D) graded photonic crystals (PCs) in detail. Under the condition of linearly graded structures, the gap broadening of three cases is calculated: the case when the thickness of low index layer is increased, the case when the thickness of high index layer is increased and the case when the thickness values of both layers are increased simultaneously. Then the gap broadening of another graded case with the thickness exponentially increased is presented. At last the enlargement of omnidirectional negligible transmission band gap is obtained.     

Optical properties of a periodic one-dimensional semiconductor-organic photonic crystal in UV region

Optical properties of a one-dimensional semiconductor-organic photonic crystal with periodic AlN/3-octylthiophenes (P3OT) multilayer structure are exhibited and confirmed by a calculation of the transfer matrix method (TMM). An AlN/P3OT multilayer structure displays incomplete photonic band gap behavior in the UV region. The AlN/P3OT multilayers with four pairs of 35-nm-AlN and 35-nm-P3OT layers exhibit a high reflectivity of 89% and less absorption of 10% at a wavelength of about 300 nm. These results demonstrate the AlN/P3OT multilayer structure could be a good candidate for absolute inhibition of reflection in the ultraviolet region for a given orientation.     

Study of s-polarized photonic bandgap structure in three component optical fibonacci multilayers composed of nanoscale materials

In this communication dispersion relation, reflection and transmission coefficient for quasiperiodic optical multilayers arranged according to the three-component Fibonacci rule is derived using transfer matrix method. In this work Fibonacci multilayers using three different photonic band gap (PBG) materials is designed and its photonic band gap structure is presented. Also, a detailed calculation for allowed and forbidden frequency bands for s-polarized radiation of light incident on these structures at various angles is presented. It is demonstrated that in case of s-polarized mode of radiation, widening in the band gap and frequency shifts occur as one moves towards the higher frequency region, which shows that such a multilayer can be used as an efficient polarizer. The effect of an imaginary value for the propagation vector Q on the existence of forbidden photonic bands in these lattices is also studied.     

Resonant three-dimensional photonic crystals

The theory of the exciton-polariton band structure of a resonant three-dimensional photonic crystal is developed for an arbitrary dielectric contrast and an arbitrary effective mass of an exciton excited in a composite material. The calculation is performed for a periodic array of semiconductor balls embedded in a dielectric matrix. The position of the lower polariton dispersion branches is shown to depend monotonically on the exciton effective mass and to be governed by the interaction of light with the first several states of a mechanical exciton quantum-confined within each ball. The effect of excitonic states on the band gap of a photonic crystal in the [001] direction is considered analytically in terms of a two-wave approximation.     

Zero permittivity band characteristics in one-dimensional plasma dielectric photonic crystal

We consider the oblique propagation of electromagnetic waves in one-dimensional plasma dielectric photonic crystals, the superlattice structure consisting of alternating plasma and dielectric materials using transfer matrix method. Our results show that photonic band gaps for all polarizations can be obtained in one-dimensional plasma dielectric photonic crystals. These structures can exhibit a new type of band or gap, for the incidence angles other than normal incidence, near frequencies where the electric permittivity of the plasma layer changes sign. This new band or gap arises, from the dispersive properties of the plasma layer, only for TM polarized waves and its width increases with the increasing angle of incidence. This differential behaviour under polarization can be utilized in the design of an efficient polarization splitter. The band characteristic is affected by the plasma width, the plasma density, dielectric width, the dielectric constant of the dielectric medium and angle of incidence.     

Polaritonic and photonic gap interactions in a two-dimensional photonic crystal

If an ionic material is used in a photonic crystal, the lattice resonance creates a polaritonic gap in the infrared range. The interaction between a polaritonic gap and the structure gap in a 2D square photonic crystal is studied by transfer matrix photonic band structure calculations. The polaritonic gap appears for a surprisingly low volume density of the ionic material. The TM gaps are larger than the TE gaps, as in the dielectric case. By varying the lattice constant, the structure gaps can be shifted across the polaritonic gap, and the effects of merging the two gaps can be studied.     

一维光子晶体光学特性的复平面波展开法研究

应用复平面波展开法对一维光子晶体的光子带隙, 透射特性进行了分析. 通过对色散关系和透射系数的数值计算发现一维光子晶体周期结构个数以及折射率分布对光学晶体透射系数以及光子带隙的影响. 对于含有整数个周期结构的光子晶体有共振点出现在光子帯隙外的频率范围内, 共振点的个数比周期结构个数少1. 带隙倾斜斜率等于折射率的比值. 折射率比值越大, 带隙的范围越大.     

Band structure of a two-dimensional resonant photonic crystal

The band structure of two-dimensional resonant photonic crystals of two types has been calculated using the expansion of eigenfunctions in plane waves. Crystals of one type consist of infinite dielectric cylinders forming a square lattice filled with a resonant gas, and crystals of the other type consist of infinite cylindrical holes filled with a resonant gas and forming a square lattice in a dielectric matrix. It has been shown that, in both cases, the dispersion of a resonant gas in combination with the dispersion of a two-dimensional structure with a photonic band gap leads to the appearance of an additional narrow transmission band near the edge of the band gap or an additional band gap in the continuous spectrum of the photonic crystal. The calculations performed have demonstrated that new dispersion properties substantially depend on the density of the resonant gas, the position of the resonant frequency with respect to the edge of the band gap, and the direction of propagation of electromagnetic waves.     

含特异材料一维超导光子晶体的带隙特性研究

利用传输矩阵法研究了含特异材料的一维超导光子晶体的带隙特性. 研究表明, 这类超导光子晶体同样具有由传统的电介质材料构成的超导光子晶体一样的低频带隙, 且在一定的参数下该低频带隙可以相当宽. 但在一定的结构参数下, 这类超导光子晶体同完全由传统的电介质构成的光子晶体一样不存在低频带隙. 还就超导光子晶体的偏振特性、光子晶体结构参数及环境温度的变化对光子带隙结构的影响进行了研究. 关键词： 超导光子晶体 传输矩阵法 特异材料 光子带隙     

二维光子晶体禁带特性研究

采用平面波展开法对二维光子晶体分别在E和H极化下的带隙进行了计算. 考虑了填充比、晶格结构、介电常数对最大绝对帯隙的影响. 结果表明,不论是正方晶格还是三角晶格,TM模在介质柱型光子晶体中更容易形成带隙;TE模在空气孔型光子晶体中更容易形成带隙. 填充比一定,最大绝对帯隙宽度并非随着介电常数增大总是增大,而是存在一个峰值. 相对介电常数一定,最大绝对帯隙宽度随填充比的变化也存在一个峰值. 不论空气孔型还是介质柱型结构,三角晶格比正方晶格更容易形成帯隙. 关键词： 平面波展开法 TE模 TM模 最大绝对帯隙     

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.     

Photonic band gaps structure properties of two-dimensional function photonic crystals

The tunable two-dimensional photonic crystals band gap, absolute photonic band gap and semi-Dirac point are beneficial to designing the novel optical devices. In this paper, tunable photonic band gaps structure was realized by a new type two-dimensional function photonic crystals, which dielectric constants of medium columns are functions of space coordinates. However for the two-dimensional conventional photonic crystals the dielectric constant does not change with space coordinates. As the parameter adjustment, we found that the photonic band gaps structures are dielectric constant function coefficient, medium columns radius, dielectric constant function form period number and pump light intensity dependent, namely, the photonic band gaps position and width can be tuned. we also obtained absolute photonic band gaps and semi-Dirac point in the photonic band gaps structures of two-dimensional function photonic crystals. These results provide an important theoretical foundation for design novel optical devices.