Band Structure Of Photonic Crystals Research Articles

A novel eigenvalue method for calculating the band structure of lossy and dispersive photonic crystals

A novel eigenvalue method is proposed to calculate the band structure of lossy and dispersive photonic crystal (PC). Using an idea from quantum transport problem, a standard linear eigenvalue equation rather than a nonlinear eigenvalue equation is obtained by a rigorous and artful transformation. And the physical parameters of lossy and dispersive PC are obtained by solving the linear eigenvalue equation using finite-difference frequency-domain (FDFD) method. Compared with other methods, the proposed method has great features, such as clear concept, simple calculation, less computing time and storage. A dielectric PC is simulated by the proposed method, and the results accord well with those from the traditional FDFD method, which verifies the validity of the proposed method. Moreover, the dispersion relation of the lossy and dispersive PC is calculated by the proposed method, and the surface plasmon frequency is obtained. Furthermore, the influence of loss on the dispersion relation and eigenmode field distribution is studied. The results provide some theoretical guidance for studying the lossy and dispersive PC.

Nanoscale All-Angle Waveguide Based on Plasmon Band Effect in Triangular Array of MWCNTs

In this paper, we present a nanoscale all-angle waveguide based on plasmon band effect in triangular array of multiwall carbon nanotubes (MWCNTs) which propagates the light beam in structure for any incident angle. We analyze photonic characteristics of the proposed MWCNT based nanoscale structure using finite-difference time-domain method. Multi pole Drude-Lorentz model is used for dispersive dielectric function of MWCNTs. Using this model, photonic properties of triangular MWCNT based photonic crystal like band structure, reflection and transmission coefficients are calculated and the effects of different structural parameters are studied for engineering the desired band structure. The MWCNT array with 20 nm lattice constant is designed in Silicon as a host. Considering coupled plasmonic-Bragg guided mode, we create a tunable optical waveguide by inserting engineered line defects of MWCNTs inside the structure.

Polarization characteristics of chiral photonic crystal fibers with an elliptical hollow core

The theoretical study of dielectric-chiral photonic crystal fiber (PCF) with an elliptical hollow core is presented. The band structure of chiral photonic crystal (PhC) is calculated by using a modified plane-wave expansion (PWE) method. By examining the out-of-plane photonic bandgaps (PBGs) of chiral PhC, a kind of chiral PCF with a hollow core is designed and their eigenstates are calculated. The distributions of mode field and polarization state are demonstrated, and how the structural asymmetry of the core together with the chirality in the background affects the modal polarization is discussed. The dependences of birefringence on chirality for different ellipticities of core are investigated.

Abandoned Functionality of Thin‐Film Opal Photonic Crystals

Angle‐resolved polarized transmission spectra of thin‐film opals are studied experimentally and theoretically as a function of the azimuthal rotation of the plane of incidence at different angles of light incidence. In such 3‐dimensional lattices, the refraction acquires the form of diffraction orders, each with a distinct spectrum, that propagate simultaneously along different directions. The corresponding continuous and patchy stop‐bands in the photonic energy band structure of the opal photonic crystal are determined numerically. For diffraction at high Miller index planes, the diffraction pattern is often distorted due to multiple‐wave diffraction. The finite stacking of hexagonally close‐packed layers leads to an intrinsic 3‐fold rotation symmetry of these spectra, which is particularly pronounced in transmission for frequencies that correspond to wave vectors within the 1st Brillouin zone. Despite the cubic symmetry of the opal lattice, cross‐polarization coupling effects occur in the volume of the opal crystal. These effects are associated with the fact that, the opal eigenmodes are Bloch waves whose electromagnetic field distributions and dispersion relations are markedly different from plane waves.

Fluorescent polystyrene photonic crystals self-assembled with water-soluble conjugated polyrotaxanes

We demonstrate control of the photoluminescence spectra and decay rates of water-soluble green-emitting conjugated polyrotaxanes by incorporating them in polystyrene opals with a stop-band spectrally tuned on the rotaxane emission (405–650 nm). We observe a suppression of the luminescence within the photonic stop-band and a corresponding enhancement of the high-energy edge (405–447 nm). Time-resolved measurements reveal a wavelength-dependent modification of the emission lifetime, which is shortened at the high-energy edge (by ∼11%, in the range 405–447 nm), but elongated within the stop-band (by ∼13%, in the range 448–482 nm). We assign both effects to the modification of the density of photonic states induced by the photonic crystal band structure. We propose the growth of fluorescent composite photonic crystals from blends of “solvent-compatible” non-covalently bonded nanosphere-polymer systems as a general method for achieving a uniform distribution of polymeric dopants in three-dimensional self-assembling photonic structures.

STUDY OF BAND STRUCTURE OF TWO-DIMENSIONAL ANISOTROPIC HONEYCOMB PHOTONIC CRYSTALS

Using the plane wave expansion method, we have calculated, for both E and H polarizations, the band structure of 2D anisotropic photonic crystals with honeycomb lattice composed of anisotropic tellurium ( Te ) rods embedded in air background. The two rods in the unit cell are chosen square and circular in shape. Here, from a practical point of view, in order to obtain maximum band gaps, we have also studied the band structure as a function of size of rods.

Finite difference time domain method for calculating the band structure of a 2D photonic crystal and simulating the lensing effect

A finite difference time domain method based on regular Yee's algorithm in an orthogonal coordinate system is utilized to calculate the band structure of a two-dimensional square-lattice photonic crystal comprising dielectric cylinders in air background and to simulate the image formation of mentioned structure incorporating the perfectly matched layer boundary condition. By analyzing the photonic band diagram of this system, we find that the frequency region of effective negative refraction exists in the second band in near-infrared domain. In this case, electromagnetic wave propagates with a negative phase velocity and the evanescent waves can be supported to perform higher image resolution.

Impact of photonic crystal boundary shape on the existence of one-way edge mode

The band structure of a two-dimensional photonic crystal (PhC) formed by a triangular lattice of air columns in a gyromagnetic material is investigated in the case when an external dc magnetic field is applied to it. It is shown that large magnetic-field-induced (MFI) bandgap is obtainable by optimizing the parameters of the PhC. The interface between a PhC with MFI bandgap and air may support unidirectional or bidirectional propagating edge modes, or even no mode, closely depending on the boundary shape of the truncated PhC. The transmission property of one-way mode sustained by the gyromagnetic PhC boundary is discussed through numerical simulation.

Fabrication of Novel Two-Dimensional Nanopatterned Conductive PEDOT:PSS Films for Organic Optoelectronic Applications

This paper presents a novel strategy to fabricate two-dimensional poly(3,4 ethylenedioxythiophene):poly(styrene sulfonate) (PEDOT:PSS) photonic crystals (PCs) combining electron beam lithography (EBL) and plasma etching (PE) processes. The surface morphology of PEDOT:PSS PCs after mild oxygen plasma treatment was investigated by scanning electron microscopy. The effects on light extraction are studied experimentally. Vertical extraction of light was found to be strongly dependent on the geometric parameters of the PCs. By changing the lattice type from triangular to square and the geometrical parameters of the photonic structures, the resonance peak could be tuned from a narrow blue emission at 445 nm up to a green emission at 525 nm with a full width at half-maximum of 20 nm, which is in good agreement with Bragg's diffraction theory and free photon band structure. Both finite-difference time-domain and plane wave expansion methods are used to calculate the resonant frequencies and the photonic band structures in the two-dimensional photonic crystals showing a very good agreement with the experiment results. A 2D nanopatterned transparent anode was also fabricated onto a flexible polyethylene terephthalate (PET) substrate and it was integrated into an organic light-emitting diode (OLED). The obtained results fully confirm the feasibility of the developed process of micro/nano patterning PEDOT:PSS. Engineered polymer electrodes prepared by this unique method are useful in a wide variety of high-performance flexible organic optoelectronics.

Lasing in nanoimprinted two-dimensional photonic crystal band-edge lasers

We demonstrate optically pumped polymer band-edge lasers based on a two-dimensional photonic crystal slab fabricated by nanoimprint lithography (NIL). Lasing was obtained at the photonic band-edge, where the light exhibits a low group velocity at the Γ point of the triangular lattice photonic crystal band structure. The active medium was composed of a dye chromophore-loaded polymer matrix directly patterned in a single step by nanoimprint lithography. Plane-wave and finite difference time domain algorithms were used to predict experimental lasing frequencies and the lasing thresholds obtained at different Γ points. A low laser threshold of 3 μJ/mm2 was achieved in a defect-free photonic crystal thus showing the suitability of nanoimprint lithography to produce cost-efficient optically pumped lasers.

New method for computation of band structures in 1D photonic crystals based on the Fresnel equations

In this paper, we present a new method for calculation of band structure in one-dimensional bilayer photonic crystals, based on the Fresnel equations. We derive a new relation to obtain the band structure without using the Floquet theorem. It is shown that this relation can be simplified under the assumption that the single-path phase-shift acquired through the individual layers of the photonic crystal be equal to. The results obtained by our method are compared with the ones obtained from the transfer matrix method to show that they are exactly identical.

Fabrication of two dimensional high aspect ratio polymer photonic crystal laser

Photonic crystals have attracted much attention from researchers because of the control over the propagation and emission of light and particular optical properties. In this paper, we reported on the design, fabrication and test of a two-dimensional polymer photonic crystal laser. First of all, a two-dimensional polymer photonic crystal laser with a triangle-lattice structure was described. Rhodamine 6G doped in PMMA was chosen as the gain material. Then, plane wave method based on the Maxwell equations was utilized to calculate the distribution of the photonic band gap. We calculated the band structure of a triangle lattice photonic crystal with a low refractive index. High resolution electron beam lithography combined with electroplating was used to fabricate the silicon nitride mask. A high aspect ratio two-dimensional photonic crystal laser was fabricated by X-ray lithography in one-step process to overcome the limitation of the thickness by the conventional methods to realize a real two-dimensional laser. Meanwhile, processes of sample preparations and fabrication were optimized in order to avoid the oxidation of the gain material and reduce the diffraction effect on the structures.

Calculation of the band diagrams of metallic wire photonic crystals

The band structures of three-dimensional metallic photonic crystals in the form of thin wires are calculated using integral equations and periodic Green’s functions with allowance for several tens of current harmonics and several thousands of space harmonics. The convergence of the algorithm, the accuracy of the results, and the dependence of the bandgap width are studied.

Effect of a magnetic field on a two-dimensional metallic photonic crystal

We study the effect of a static magnetic field on the band structure of a two-dimensional metallic photonic crystal (MPC). The band structure of the MPC has been calculated using the transfer matrix method. It is found that the position of the photonic band gap and the band edges of the MPC depends on the polarization of the incident light and intensity of the applied magnetic field. In our calculations we consider linearly polarized light as well as right- and left-circularly polarized light. In the case of right-circularly polarized light it is found that as the intensity of the magnetic field increases the width of the band gap of the crystal decreases. At a certain magnetic field strength the band gap disappears altogether. In other words there is a transition from a metallic photonic band gap material to a transparent dielectric material. This is an interesting effect which is similar to the metal-insulator transition that occurs in semiconductors. On the other hand, for left-circularly and linear polarized light the band edges shift to the higher energy and the band gap increases in the presence of a magnetic field. This implies that the MPC switches from a transparent state to reflecting states due to the application of the magnetic field. This is an interesting effect which might be used to make photonic switches.

Computing Extremal Eigenvalues for Three-Dimensional Photonic Crystals with Wave Vectors Near the Brillouin Zone Center

The band structures of three-dimensional photonic crystals can be determined numerically by solving a sequence of generalized eigenvalue problems. However, not all of the spectral structures of these eigenvalue problems are well-understood, and not all of these eigenvalue problems can be solved efficiently. This article focuses on the eigenvalue problems corresponding to wave vectors that are close to the center of the Brillouin zone of a three dimensional, simple cubic photonic crystal. For these eigenvalue problems, there are (i) many zero eigenvalues, (ii) a couple of near-zero eigenvalues, and (iii) several larger eigenvalues. As the desired eigenvalues are the smallest positive eigenvalues, these particular spectral structures prevent regular eigenvalue solvers from efficiently computing the desired eigenvalues. We study these eigenvalue problems from the perspective of both theory and computation. On the theoretical side, the structures of the null spaces are analyzed to explicitly determine the number of zero eigenvalues of the target eigenvalue problems. On the computational side, the Krylov-Schur and Jacobi-Davidson methods are used to compute the smallest, positive, interior eigenvalues that are of interest. Intensive numerical experiments disclose how the shift values, conditioning numbers, and initial vectors affect the performance of the tested eigenvalue solvers and suggest the most efficient eigenvalue solvers.

The band structures of metallic photonic crystals filled with different mediums

提出了一种利用全反射抑制二维光子晶体表面电磁波泄漏的方法，并计算了不同背景介质下的二维金属Cu光子晶体的带隙结构，得到了带隙结构与填充率间的关系曲线。计算方法采用时域有限差分，金属型光子晶体由Cu柱构成。分别计算了以空气为背景介质和以PMMA为背景介质的正方晶格金属型光子晶体的带隙结构。研究结果表明：以PMMA为背景介质的正方晶格金属型光子晶体与以空气为背景介质相比，第一带隙更窄，第二带隙中心频率更低，且在填充率大于0.70时将会出现第三带隙。这对进一步扩展这种光子晶体的应用具有良好的参考意义。;A method is proposed to inhibit the leakage of electromagnetic waves on the surface of 2D photonic crystals using total internal reflection. The band structures of 2D metallic photonic crystals with different background mediums are analyzed. The band structures as a function of the filling factor are obtained via FDTD method. The metallic photonic crystals are composed of Cu columns. Two kinds of background media, air and PMMA, were selected in this study. The band structures of these two 2D square-lattice metallic photonic crystals were analyzed separately. The results indicate that the metallic photonic crystals filled with PMMA have a narrower first band gap and a lower second band gap than the metallic photonic crystals filled with air. A third band gap appears in the metallic photonic crystals with PMMA as the background medium when the filling factor reaches 0.70. This work provides a good reference value for the application of photonic crystals.

Effects of structure parameters on the bandgap of two dimensional Archimedes A7 photonic crystals

PDF HTML阅读 XML下载 导出引用 引用提醒 结构参数对二维Archimedes A7晶格光子晶体禁带的影响 DOI: 作者: 作者单位: 太原理工大学 物理与光电工程学院,太原理工大学 物理与光电工程学院,太原理工大学 物理与光电工程学院,太原理工大学 材料科学与工程学院,太原理工大学 物理与光电工程学院 作者简介: 通讯作者: 中图分类号: 基金项目: 国家自然科学基金资助项目（项目编号：60927007）与山西省自然科学基金资助项目（项目编号：2011011003-1）资助课题. Effect of structure parameters on the bandgap of two dimensional Archimedes A7 photonic crystals Author: Affiliation: College of Physics and Optoelectronics, Taiyuan University of Technology,College of Physics and Optoelectronics,Taiyuan University of Technology,College of Physics and Optoelectronics, Taiyuan University of Technology,College of Materials Science and Engineering, Taiyuan University of Technology,College of Physics and Optoelectronics, Taiyuan University of Technology Fund Project: 摘要 | 图/表 | 访问统计 | 参考文献 | 相似文献 | 引证文献 | 资源附件 | 文章评论 摘要:利用平面波展开法研究了空气背景中介质圆柱和方柱构造的二维Archimedes A7晶格光子晶体的禁带结构随介质折射率、填充比的变化关系进行了研究,并进一步计算了介质方柱的旋转角度对完全光子禁带宽度的影响。研究发现,介质圆柱构造的Archimedes A7晶格结构在介质柱折射率最低为n=2.40时就出现完全光子禁带，当n=2.60时禁带宽度达到最大值。介质方柱构造的Archimedes A7晶格结构在介质柱折射率n=3.80时完全禁带宽度达到最大值，且随着折射率的增加禁带宽度变化很小；在介质方柱折射率恒定情况下，其最大禁带宽度与旋转角度无关，但旋转后出现完全禁带的填充比范围明显扩大。 Abstract:Plane wave expansion method is introduced to simulate the band structures of two-dimensional photonic crystals made of Archimedes A7 lattice of circular and square dielectric rod in air. The bandgaps of Archimedes A7 lattice with dielectric rods is also discussed as the refractive index, filling fraction and rotation angle change. The results show that the complete bandgap can be obtained when the refractive index is greater than 2.40, the width of complete bandgap reaches the maximum when the dielectric refractive index of the circular rod is equal to 2.60. For the Archimedes A7 lattice of square dielectric rod, the complete bandgap reaches the maximum when the dielectric refractive index equals 3.80.The maximum complete bandgap changes in a narrow range as the refractive index increases. When the rotation angle of the square dielectric rods changes, the maximum bandgaps keeps constant for a fixed refractive index.However after the change of rotation angle, the complete bandgap appears in alarge scale of the filling fraction. 参考文献 相似文献 引证文献

CONVERGENT ADAPTIVE FINITE ELEMENT METHODS FOR PHOTONIC CRYSTAL APPLICATIONS

We prove the convergence of an adaptive finite element method for computing the band structure of two-dimensional periodic photonic crystals with or without compact defects in both the TM and TE polarization cases. These eigenvalue problems involve non-coercive elliptic operators with discontinuous coefficients. The error analysis extends the theory of convergence of adaptive methods for elliptic eigenvalue problems to photonic crystal problems, and in particular deals with various complications which arise essentially from the lack of coercivity of the elliptic operator with discontinuous coefficients. We prove the convergence of the adaptive method in an oscillation-free way and with no extra assumptions on the initial mesh, beside the conformity and shape regularity. Also we present and prove the convergence of an adaptive method to compute efficiently an entire band in the spectrum. This method is guaranteed to converge to the correct global maximum and minimum of the band, which is a very useful piece of information in practice. Our numerical results cover both the cases of periodic structures with and without compact defects.

Band structure of photonic crystal with dispersive and lossy materials using Dirichlet-to-Neumann wave vector eigen equation method

We present the Dirichlet-to-Neumann wave vector eigen equation (DtN-WVEE) method to calculate the band structure of photonic crystal (PhC) with dispersive and lossy materials, and then use finite-difference time-domain method to verify the validity of the results of the DtN-WVEE method. Since the material is lossy with a non-zero imaginary part of epsilon, the wave vector of PhC band structure also has a non-zero imaginary part which results in the reduction of the intensity of the mode. We further present the band structure which gives the relationship among the normalized frequency, the real part of the wave vector, and the imaginary part of the wave vector. To our knowledge, the band structure of lossy PhC has not been well studied yet, and our results can be useful in designing the devices using surface plasmon polariton effect.

Controlling surface plasmon polaritons by a static and/or time-dependent external magnetic field

We have demonstrated numerically by using of Fourier modal method (FMM) that the interface between a metal and a uniformly magnetized two-dimensional photonic crystal fabricated from a transparent dielectric magneto-optical (MO) material possesses a one-way frequency range in which a surface plasmon polariton (SPP) is allowed to propagate only in one direction. The time-reversal symmetry breaking is implied by the MO properties of the photonic crystal material, namely, bismuth iron garnet (BIG), which may be magnetically saturated by fields of the order of tens of milli tesla. The results obtained by FMM have been validated by a theoretical model and a standard plane-wave method that yield separately a nonreciprocal dispersion relation for the SPP and the band structure of the two-dimensional magneto-optical photonic crystal (2D MOPhC), respectively. These spectra represent the key characteristics assuring the functionality of the one-way waveguide associated with the both underlying mechanisms, namely, time-reversal symmetry breaking and a suppression of disorder-induced backscattering. By using a generalized finite-difference time-domain (FDTD) method, which allows studying the propagation of electromagnetic (EM) waves through media with a tensor MO permittivity, we studied transport properties of the one-way waveguide. We examined the influence of specific types of boundary conditions on one-way functionality in the presence of a static external magnetic field and have shown that the SPP can be dynamically controlled by applying a time-dependent magnetic field. By evaluating the Fourier transform of the energy density, we have analyzed the behavior of the field patterns observed in the waveguide in the case of ac magnetic field, and have interpreted new and interesting features associated with the redistribution of the EM field that may offer new mechanisms for dynamical control of SPP flow.