Two-dimensional photonic crystals with a lattice defect: Spectrum of defect modes, localization of light, and formation of evanescent waves

Properties of an electromagnetic field localized in the defect modes of two-dimensional photonic crystals are studied. The defect-mode spectrum of these structures is calculated, electromagnetic field localization and channeling effects are analyzed, and the properties of the field inside and beyond a photonic crystal with a lattice defect are also studied. The calculations show that the electromagnetic field is localized in the defect mode of a photonic crystal in a region smaller than the wavelength. The dependence of the defect-mode spectrum on the parameters of the photonic crystal is investigated and possibilities for controlling the spectrum of defect modes are indicated. It is shown that the optical field leaving a photonic crystal possesses the properties of a evanescent wave, which means that spatial resolution substantially greater than the wavelength of the radiation can be achieved in the near field and opens up possibilities for using photonic crystals with a lattice defect in near-field optical microscopy. The possibility of externally controlling an optical field localized in the defect modes of a photonic crystals is demonstrated.     

二维点缺陷正方光子晶体的微腔结构

通过平面波展开法对由Al₂O₃介质棒在空气背景介质中构成含有点缺陷的二维正方光子晶体微腔结构进行研究,计算得出缺陷态能带以及缺陷态模场分布。缺陷模对应的电磁波波长为470~476nm。对该微腔结构的品质因数的求解,得出缺陷态光谱曲线。在光谱曲线中,随着传输波长的增大,将产生几个峰值,并且在475nm处的波动最为明显,反映出在475nm附近的电磁波段在缺陷处的光强较大。进一步利用全矢量等效折射率法研究该结构缺陷模频率的稳定性,得出等效折射率的变化曲线。从等效折射率变化曲线可以看出,当传输波长达到475nm时,该结构已经达到稳定传输的区域。含缺陷模的二维光子晶体微腔结构在光子晶体发光二极管以及高阈值半导体激光器等方面有着重要的应用价值。     

矩形掺杂光子晶体中电磁波的模式和缺陷模

利用一维矩形掺杂光子晶体中电磁波横向受限的条件,推导出电磁波在其中各个模式满足的关系式,利用它研究了电磁波各模式的特性.利用特征法研究了电磁波的缺陷模随模式量子数和矩形边长的变化规律,得出了一维矩形掺杂光子晶体缺陷模的新结构. 关键词： 矩形光子晶体 受限 模式 缺陷模     

矩形掺杂光子晶体中电磁波的模式和缺陷模

利用一维矩形掺杂光子晶体中电磁波横向受限的条件,推导出电磁波在其中各个模式满足的关系式,利用它研究了电磁波各模式的特性.利用特征法研究了电磁波的缺陷模随模式量子数和矩形边长的变化规律,得出了一维矩形掺杂光子晶体缺陷模的新结构.     

Propagation characteristics of two-dimensional photonic crystals in the terahertz range

Based on the plane wave expansion method, the complete band gaps of two-dimensional terahertz photonic crystals with typical structures are optimized through varying structural parameters. During our calculation, two kinds of lattice structures that are very promising for the materials of terahertz components are found and some interesting phenomena that were not reported in the former papers are also presented. Using the finite difference time domain method, we simulated the electromagnetic field distribution of THz waves in a PC splitter. And by the plane wave expansion method, we achieved the dispersion relation and defect modes in a rotated PC waveguide. These results provide a useful guide and a theoretical basis for the developments of THz functional components. PACS 42.72.Ai; 42.70.Qs     

Optical isolator based on nonreciprocal coupling of two Tamm plasmon polaritons

In this paper, we have studied the one-dimensional photonic crystal (PC) including a magneto-optical metal defect using the developed transfer matrix method for magnetic materials. Around the two interfaces between metal and one-dimensional PC, two nonsymmetric Tamm magneto-plasmon polaritons may be excited and coupled. The coupled states take on a clear nonreciprocal behavior and result in nonreciprocal transmission. The results are demonstrated through electromagnetic field distribution simulations based on finite element software. It provides a useful reference to realize optical isolator design.     

Localization and channeling of light in defect modes of two-dimensional photonic crystals

The spatial distribution of the electromagnetic field in a two-dimensional photonic crystal with a lattice defect is investigated. It is shown that in such a structure the field can be localized in a region smaller than one wavelength in size. The dependence of the spectrum of defect modes on the parameters of a two-dimensional photonic crystal is investigated. The light field at the exit of the photonic crystal possesses properties of a nonradiative mode, making it possible to achieve spatial resolution in the near-field much higher than the radiation wavelength. The possibilities of using this phenomenon in optical near-field microscopy to produce optical memory devices and to increase the efficiency of nonlinear optical interactions are discussed. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 5, 323–328 (10 September 1999)     

缺陷态对4340钢-环氧树脂二维声子晶体带隙的影响

采用平面波展开法及平面波超元胞法研究缺陷态对4340钢-环氧树脂二维声子晶体带隙的影响. 以环氧树脂作为基底,把正方形结构排列的4340钢均匀的插入基底中,计算完整晶体、45°线缺陷态晶体、90°线缺陷态晶体、135°线缺陷态晶体、180°线缺陷态晶体的带隙. 结果表明,缺陷态的带隙宽度与完整晶体的带隙宽度相比最大可增大约31倍;对于不同的缺陷结构在F=0.1-0.9的范围内均有带隙出现且随着缺陷态角度的增大. 同时讨论带隙数目N,最低带隙相对宽度Δω/ω_g与填充率F之间的关系. 关键词： 缺陷态 带隙宽度 带隙数目     

The beam splitting in the photonic crystal at a degenerate state

In this paper, using the plane-wave expansion and finite difference time-domain methods, the photons behavior in the photonic crystal is investigated. Theoretically, when a polarized wave is incident from the background medium to the photonic crystal, the beam propagation directions in the photonic crystal determined by two methods are approximately same. But in this paper, the results exhibit that there is an additional direction obtained by the finite difference time-domain method compared with the plane-wave expansion. Considering basic physical mechanism of the photon behavior, the present work circumvents the electromagnetic field distribution in the photonic crystal at a degenerate state, which can reasonably explain the phenomenon. Finally, it shows that a photonic crystal can be properly designed to achieve double refraction simultaneously at one frequency, which can also offer new thoughts and foundation for the novel beam splitter that applied to many optical systems.     

斜入射角对二维正方形光子晶体带隙的影响

利用平面波法导出了光子晶体本征方程的矩阵形式,以此为基础计算了二维空气孔型正方形光子晶体在正入射时及斜入射时的带结构,并将带结构中混杂在一起的TE波和TM波的模式分离开来以分析斜入射角对带结构的影响.计算结果显示用电场E表示和用磁场H表示计算出来的结果完全一样,与电磁场是相互统一的结论完全吻合.研究还发现,TE波和TM波的第一带隙是完全分开的.随着波矢k的倾斜角度的增大,TE波的第一带隙逐渐减小并在波矢在（－1,0,1）平面内时完全消失.而TM波的带结构则随着波矢k的倾斜角的增大而变得平坦,带隙也是先随之增大,后又逐渐变小直至消失.     

带缺陷二维光子晶体的透射谱研究

在一维线缺陷的研究基础上进一步应用转移矩阵方法数值研究带其它缺陷的二维正方晶格圆柱光子晶体的透射谱,缺陷的引入使得原来不透电磁波的禁带中,出现了缺陷模,即某一波长的电磁波可以透过,计算结果表明禁带位置、宽度,缺陷模的位置与透过率随着缺陷的种类、介质、程度有关,特别是都受到波源的入射角调制.     

Localized electromagnetic modes and the transmission spectrum of a one-dimensional photonic crystal with lattice defects

The properties of localized electromagnetic modes in a one-dimensional photonic crystal with a structural defect layer were studied. The role of the defect was played by an anisotropic nematic liquid crystal layer. The frequency and the damping factor of defect modes were shown to substantially depend on the defect layer thickness and the orientation of the optical axis of the nematic. The transmission spectra of photonic crystals with one and two lattice defects were studied. Taking into account the special feature of nematic liquid crystals distinguishing them from usual crystals, namely, large permittivity anisotropy, it was shown that the transmission spectrum of the photonic crystal could be controlled by varying the orientation of the optical axis of the nematic, for instance, under the action of an external electric field.     

Torque on birefringence in one-dimensional finite photonic band-gap structure with defects

We theoretically study the optical torque on the layers in one-dimensional finite photonic crystal with birefringent defect layers. The fields in each layer are deduced by Berreman's 4 × 4-matrix method. We found out that the strong electromagnetic fields enhance both torque and force on the layers at defect mode. These investigations suggest an efficient method to construct the micro-motor driven by electromagnetic wave.     

Ewald's dynamical theory of diffraction for a defect crystal

The paper is based on the Ewald's approach to the problem of interaction of an electromagnetic wave with a coulomb crystal lattice. Born's formalism of the crystal dynamics is used. Defects of the lattice modify the dynamical matrix of the crystal which can be simply inverted in a case of a small defect density. The final formula describes the distribution of the scattered intensity of the incident light wave as a function of the defect configuration. The possibility of the extension of the method to the Laue theory is briefly discussed.     

时变磁化等离子体光子晶体光子局域态分析

采用磁化等离子体的分段线形电流密度卷积(Piecewise Linear Current Density Recursive Convolution,PLCDRC)时域有限差分(Finite-Different Time-Domain,FDTD)算法研究了具有单一缺陷层一维时变磁化等离子体光子晶体的光子局域态特性。以高斯脉冲为激励源,用算法公式所得的电磁波透射系数来讨论了等离子体上升时间对其缺陷模的影响。结果表明,改变等离子体上升时间和密度可以获得不同的缺陷模。     

带有KTP缺陷的2维光子晶体设计与能带特性

 设计了一种通过改变缺陷介质折射率实现能带特性改变的可调谐2维光子晶体激光器微腔,在光子晶体中引入点缺陷磷酸氧钛钾(KTP),在KTP两端施加交流电场控制KTP晶体折射率变化。实验过程中观察到了正方排列的光子晶体随着KTP 晶体折射率逐渐增大,晶体禁带数量减少,且向归一化频率小的方向移动,禁带宽度基本不变;而三角排列的晶格能带随着KTP折射率增大,禁带逐渐变窄,且有向低频方向移动的趋势。用平面波展开法分析了晶体的能带结构,得到理上的描述。     

Design of a novel wideband single-mode waveguide in a photonic crystal slab structure

We propose a novel photonic crystal slab waveguide that provides a single-mode band with large bandwidth. The proposed waveguide is obtained by introducing a line defect in a triangular lattice of air holes in a dielectric slab. This line defect consists of holes which are not located in the original lattice points. The plane wave expansion (PWE) method is used to extract the band diagram of guiding modes and based on the results, photonic crystal holes in the defect row and its adjacent rows are modified to maximize the waveguide bandwidth. We show that using the proposed structure, a single-mode bandwidth of 17% can be achieved.     

二维非晶光子材料的缺陷态

应用多重散射方法计算了二维介质柱构成的非晶光子材料的缺陷态。在非晶光子材料中抽掉不同位置的圆柱会产生频率不同的缺陷模，但缺陷模的能量都是非常局域的，能量基本上集中在以缺陷波长1／3为半径的圆内。这表明非晶光子材料中形成的缺陷模不仅具有周期性光子晶体的缺陷模的强局域化特征，同时缺陷模更富于变化。     

On transmittance and localization of the electromagnetic wave in two-dimensional graphene-based photonic crystals

Two-dimensional graphene-based photonic crystal (GPC) formed by a periodic array of the homogeneous dielectric cylinders etched in the alternating graphene and dielectric layers and its inverse counterpart are considered. The transmittance of the photonic crystal is obtained. The waveguide due to the localization of the electromagnetic wave on the lattice defect that breaks the translational symmetry of the GPC of two different topologies is studied. The different topologies of GPC are characterized by different photonic band structures with different widths of photonic band gaps (PBG) and provide different frequencies for the localized electromagnetic wave due to the defect. The frequencies of the localized mode for both type of the GPC, located inside the lowest PBG, are in the range of THz or tens of THz depending on the topology of the GPC. It is shown that the photonic band gap always can be tuned by changing the chemical potential of graphene to provide formation of the localized photonic mode due to the defect. The technological advantages of the GPC, as well as the opportunity to tune the PBG and the frequency of the localized electromagnetic wave in the terahertz region of spectrum for the GPC are discussed.     

Point defect states of a hollow cylinder in two-dimensional phononic crystal

Point defect states in two-dimensional phononic crystal of a hollow mercury cylinder in a water host are studied.An improved plane expansion method combined with the supercell technique is used to calculate the band gaps and the pressure distribution at the defect position.The sonic pressure of defect modes shows that the waves are localized at or near the defect.As the filing fraction increases,more defect modes appear in the band gaps.