Effective optical constants and effective optical properties of ultrathin trilayer structures

This work presents an extension of the characteristic effective medium approximation (CEMA) to ultrathin trilayer systems. The extension has been carried out analytically and is supported by corresponding calculations of the effective optical constants of Cu-Au-Cu and Ag-SiO-Ag trilayer systems using the CEMA approximation. This work is in essence a generalization of the characteristic effective medium approximation introduced earlier for ultrathin bilayer structures. This method is used to derive the effective optical constants of a trilayer system, consisting of three thin layers with each constituent layer of thickness much less than the wavelength of the incident radiation. Within this regime a trilayer system is viewed as one effective layer referred to as an effective stack (ES) with well defined effective optical constants, which can be used to calculate the optical properties of the trilayer stack within a specified wavelength range. The CEMA based calculations of the effective optical constants are applied to two trilayer systems with a total of five stacks. Three are Cu-Au-Cu and two are Ag-SiO-Ag stacks. The thicknesses of the parent layers in the Cu-Au-Cu stack range from 3 to 30 nm for Cu and 4 to 40 nm for Au; in the Ag-SiO-Ag stack the constituent layers are 6 nm for Ag, but range from 5 to 10 nm for SiO. This study is for normal or near normal incidence spectroscopy in a wavelength range that extends from visible to near infrared. The agreement between CEMA based ES stack results and those of the standard CMT technique is very satisfactory.     

具有非均匀渐变界面DBR的光学特性分析

应用特征矩阵法研究了非均匀渐变界面Al_0.9Ga_0.1As/Al_yGa_1-yAs/GaAs/Al_xGa_1-xAs DBR的光学特性.建立了非均匀渐变界面Al_yGa_1-yAs的折射率模型，并得到了渐变界面特征矩阵的解析解，通过特征矩阵法分别计算了突变GaAs/Al_0.9Ga_0.1As DBR和渐变DBR的反射谱和反射相移，分析了非均匀渐变层对DBR光学特性的影响，对渐变DBR，需要在DBR前面再增加一定厚度的非均匀渐变相位匹配层才能使整个DBR满足中心波长相位匹配条件，并通过光学厚度近似方法求出相位匹配层厚度. 关键词： DBR 反射谱 反射相移 特征矩阵法     

Ellipsometry on magnetooptic thin film multilayer systems

The optical and magnetooptical properties of thin film multilayer systems including a ferromagnetic absorbing layer were measured by ellipsometry. These were compared to calculations, using the ellipsometric data of each individual layer and measuring their thicknesses by FECO to determine the refractive indices and magnetooptical parameters of each layer for the calculation of the whole stack. Agreement between calculated and measured properties of the stack showed to be strongly dependent on the precision in measuring film thickness.     

有效介质近似在Cu-MgF2复合纳米颗粒薄膜光学性质中的适用性研究

采用射频磁控共溅射技术制备了Cu体积分数分别为15%和30%的Cu-MgF2复合纳米颗粒薄膜。透射电镜形貌图像表明,薄膜由不同形状的Cu晶态纳米微粒镶嵌于主要为非晶态的MgF2陶瓷基体中构成。用椭偏光谱技术计算得到Cu-MgF2复合薄膜在270~830 nm波段的光学常数谱。用考虑颗粒形状效应的有效介质近似计算得到Cu-MgF2复合薄膜在相同波段的光学常数谱。把两样品的透射电镜形貌图像与光学常数理论谱、实验谱相结合,分析讨论了Cu-MgF2复合薄膜的光学特性。结果表明:去极化因子取值0.33的麦克斯韦噶尼特(Maxwell-Garnett)模型可以较好地解释Cu体积分数为15%的Cu-MgF2复合薄膜的光学性质,而去极化因子取值0.6的布鲁格曼(Bruggeman)模型可以较好地解释Cu体积分数为30%的Cu-MgF2复合薄膜的光学性质。     

Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack

A theoretical method is described for calculating the bidirectional scattering characteristic for any given thin-film multilayer geometry in which the surfaces and interfaces are assumed to be rough, and where statistical inhomogeneities in the optical permittivities may also exist in each layer. The light energy scattered in any direction depends on geometrical thickness, the permittivities of the ideal layer stack and also on the corresponding auto- and cross-correlation functions. The expressions that are obtained for the scattered field are completely general in the sense of the Born approximation of first order in the imperfections and the exciting fields. The contributions of interface and volume scattering can be assumed arbitrarily because both are derived in a unique way. The main new result consists in the occurrence of four different possibilities of coupling between the scattered and exciting waves due to the standing wave character of both light waves. It is easy to show that the case of a columnar structure reduces the theoretical effort and leads to a similarity of this volume case to that of normal interface scattering. The matrix formalism used in analogy to the normal calculations of reflection and transmission coefficients allows a simple physical interpretation of the light propagation through the layer system and straightforward numerical calculations.     

Theoretical study of optical characteristics of multilayer coatings ZnO/CdS/CdTe using first-principles calculations

A new method for predicting optical characteristics of multilayer coatings based on calculated material properties is presented. This method combines the use of the full potential linear-augmented plane wave method (FP-LAPW) within the framework of the Density Functional Theory (DFT) and the optical matrix approach for modeling the multilayer assembly. The simulation process is applied to thin films of the II–VI semiconductors compounds. The optical constants of each thin film are determined by using the first principle calculations. Each layer is represented by the square Abeles matrix, including all necessary data in the calculation of the optical characteristics (as transmittance, reflectance and absorbance). The simulation of multilayer optical response includes the effect of thickness, light polarization and incident angle. The obtained results are helpful in the design of the multilayer systems with required properties.     

Application of spectroscopic ellipsometry to the investigation of the optical properties of cobalt-nanostructured silica thin layers

Spectroscopic ellipsometry is used to investigate optical properties of cobalt-implanted silica thin films. The films under investigation are 250 nm thick thermal SiO₂ layers on Si substrates implanted with Co⁺ ions at energy of 160 keV and at fluences of 10¹⁷ ions/cm² for different temperatures of substrate during implantation (77 and 295 K). Changes due to Co⁺ implantation are clearly observed in the optical response of the films. Optical behaviours are furthermore different for the three implantation temperatures. To understand the optical responses of these layers, the ellipsometric experimental data are compared to different models including interference effects and metal inclusions effects into the dielectric layer. The simulated ellipsometric data are obtained by calculating the interferences of an inhomogeneous layer on a Si substrate. The material within this layer is considered as an effective medium which dielectric function is calculated using the Maxwell-Garnett effective medium approximation. We show that although the structures of these layers are very complicated because of ion-implantation mechanisms, quite simple models can provide relatively good agreement. The possibilities of ellipsometry for the study of the optical properties of such clusters-embedded films are discussed. We especially provide the evidence that ellipsometry can give interesting information about the optical properties of nanostructured layers. This is of special interest in the field of nanostructured layered systems where ellipsometry appears to be a suitable optical characterization technique.     

Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack

Abstract

A theoretical method is described for calculating the bidirectional scattering characteristic for any given thin-film multilayer geometry in which the surfaces and interfaces are assumed to be rough, and where statistical inhomogeneities in the optical permittivities may also exist in each layer. The light energy scattered in any direction depends on geometrical thickness, the permittivities of the ideal layer stack and also on the corresponding auto- and cross-correlation functions. The expressions that are obtained for the scattered field are completely general in the sense of the Born approximation of first order in the imperfections and the exciting fields. The contributions of interface and volume scattering can be assumed arbitrarily because both are derived in a unique way. The main new result consists in the occurrence of four different possibilities of coupling between the scattered and exciting waves due to the standing wave character of both light waves. It is easy to show that the case of a columnar structure reduces the theoretical effort and leads to a similarity of this volume case to that of normal interface scattering. The matrix formalism used in analogy to the normal calculations of reflection and transmission coefficients allows a simple physical interpretation of the light propagation through the layer system and straightforward numerical calculations.     

First-principles study of the optical properties of PbTiO<Subscript>3</Subscript>

The optical properties of PbTiO₃ were studied from first principles using the density functional theory. The dielectric functions and optical constants are calculated using the full potential–linearized augmented plane wave (FP-LAPW) method with the generalized gradient approximation (GGA). The theoretical calculated optical properties and energy loss (EEL) spectrum yield a static refractive index of 2.83 and a plasmon energy of 23.1 eV for cubic phase. The effective electron number at low energy saturates near 20 eV with the value of 18.1 for the effective electron number. In the tetragonal phase the static refractive index decreases to 2.59 and yields a plasmon energy of 22.7 eV.     

First-principles study of the structural, elastic, electronic, optical, and vibrational properties of intermetallic Pd2Ga

The structural,elastic,electronic,optical,and vibrational properties of the orthorhombic Pd2Ga compound are investigated using the norm-conserving pseudopotentials within the local density approximation in the frame of density functional theory.The calculated lattice parameters have been compared with the experimental values and found to be in good agreement with these results.The second-order elastic constants and the other relevant quantities,such as the Young’s modulus,shear modulus,Poisson’s ratio,anisotropy factor,sound velocity,and Debye temperature,have been calculated.It is shown that this compound is mechanically stable after analysing the calculated elastic constants.Furthermore,the real and imaginary parts of the dielectric function and the optical constants,such as the optical dielectric constant and the effective number of electrons per unit cell,are calculated and presented.The phonon dispersion curves are derived using the direct method.The present results demonstrate that this compound is dynamically stable.     

利用光学薄膜模型研究垂直腔面发射激光器的光学特性

可以把垂直腔面发射激光器看作是多层光学薄膜,应用光学薄膜原理对其光学薄膜的特性进行了研究。计算分析了布拉格反射镜和谐振腔模的反射谱受器件结构变化的影响。通过利用菲涅耳系数矩阵法计算,得到了光在垂直腔面发射激光器器件结构中形成的驻波场分布。结果表明,利用菲涅耳系数矩阵法设计垂直腔面发射激光器的光学薄膜是一种快捷准确的方法。     

First-principles study of the structural, elastic, electronic, optical, and vibrational properties of intermetallic Pd2Ga

The structural, elastic, electronic, optical, and vibrational properties of the orthorhombic Pd₂Ga compound are investigated using the norm-conserving pseudopotentials within the local density approximation in the frame of density functional theory. The calculated lattice parameters have been compared with the experimental values and found to be in good agreement with these results. The second-order elastic constants and the other relevant quantities, such as the Young's modulus, shear modulus, Poisson's ratio, anisotropy factor, sound velocity, and Debye temperature, have been calculated. It is shown that this compound is mechanically stable after analysing the calculated elastic constants. Furthermore, the real and imaginary parts of the dielectric function and the optical constants, such as the optical dielectric constant and the effective number of electrons per unit cell, are calculated and presented. The phonon dispersion curves are derived using the direct method. The present results demonstrate that this compound is dynamically stable.     

Tuning a conventional quantum well laser by nonresonant laser field dressing of the active layer

Tunable semiconductor lasers may be considered as a critical technology for optical communications. We investigate the theoretical feasibility of tuning a conventional GaAs/Al_0.2Ga_0.8As quantum well laser emitting at 825 nm by non-resonant laser-dressing of the active layer. Conduction and valence subbands are sensitive to the intense dressing field and this effect can be used to blueshift the active interband transition. The laser-dressed electron and hole states are calculated in the effective mass approximation by using the finite difference method. Emitted wavelength, threshold current and characteristic temperature are discussed as functions of the dressing laser parameter and cavity length.     

Ab initio calculations of the elastic, electronic, optical, and vibrational properties of PdGa compound under pressure

The structural, elastic, electronic, optical, and vibrational properties of cubic PdGa compound are investigated using the norm-conserving pseudopotentials within the local density approximation (LDA) in the framework of the density functional theory. The calculated lattice constant has been compared with the experimental value and has been found to be in good agreement with experimental data. The obtained electronic band structures show that PdGa compound has no band gap. The second-order elastic constants have been calculated, and the other related quantities such as the Young’s modulus, shear modulus, Poisson’s ratio, anisotropy factor, sound velocities, and Debye temperature have also been estimated. Our calculated results of elastic constants show that this compound is mechanically stable. Furthermore, the real and imaginary parts of the dielectric function and the optical constants such as the electron energy-loss function, the optical dielectric constant and the effective number of electrons per unit cell are calculated and presented in the study. The phonon dispersion curves are also derived using the direct method.     

高压下氧化镉弹性性质、电子结构和光学性质的第一性原理研究

 运用基于密度泛函理论的平面波赝势方法（PWP）,计算研究了氧化镉NaCl结构（B1结构）和CsCl结构（B2结构）在不同压力条件下的几何结构、弹性性质、电子结构和光学性质。交换关联能分别采用广义梯度近似（GGA）和局域密度近似（LDA）。通过比较计算和实验得到的晶格常数和体模量不难发现,LDA的计算结果更符合实验值。在高压的作用下,两种结构的导带能级有向高能级移动的趋势,而价带能级有向低能级移动的趋势,因此直接带隙变大。同时,对照态密度分布图及高压下能级的移动情况,分析了CdO两种结构在高压作用下的光学性质。     

Nonlocal effects in ellipsometry of metallic films on metals

A simple but exact generalization of optical surface response formalism beyond the long wavelength approximation (LWA) is developed and evaluated within the hydrodynamic approximation for a nonlocal three layer model describing a metal film between a dielectric and a metallic substrate. In the LWA an explicit analytical formula for the ellipsometry ratio ρ = r_p/r_s in terms of bulk optical constants of the layer materials is given. Model calculations show that classical optics can reproduce nonlocal results only with a strange effective dielectric function of the film reflecting substrate properties up to large film thickness.     

Prediction study of the structural,elastic, electronic and optical properties of the antiperovskite BiNBa3

We use an ab initio full-potential linear muffin-tin orbital method within the local density approximation (LDA) to study the structural, elastic, electronic and optical properties of the antiperovskite BiNBa₃. The calculated lattice parameter is in good agreement with previous calculations. The elastic constants and their pressure dependence are calculated; we found a linear dependence of elastic stiffness on the pressure. We estimated the Debye temperature of this compound from the average sound velocity. We also present results of the effective masses for the electrons in the conduction band (CB) and the holes in the valence band (VB). To complete the fundamental characteristics of this compound we have analyzed the optical properties.     

A method for calculating the light extinction coefficients of a polymer layer with small nematic liquid-crystal droplets

A method is proposed for analyzing radiation extinction coefficients of polymer films containing small nematic liquid-crystal droplets with cylindrical symmetry. This method is based on the Rayleigh-Gans approximation and the effective scattering matrix. The orientational ordering of both liquid-crystal molecules in droplets and the droplets in a layer is described by multilevel order parameters. The extinction of radiation in polymer films is analyzed for the cases of oblique and normal incidence of light. Simple and convenient expressions are derived for calculating and estimating the extinction coefficients for the case of normal incidence of light on a layer containing spherical droplets. The error of the method is estimated.     

An ab initio study of the structural,elastic, electronic and optical properties of the newly synthesized nitridoaluminate LiCaAlN2

The structural parameters, elastic constants, electronic structure and optical properties of the recently reported monoclinic quaternary nitridoaluminate LiCaAlN₂ are investigated in detail using the ab initio plane-wave pseudopotential method within the generalized gradient approximation. The calculated equilibrium structural parameters are in excellent agreement with the experimental data, which validate the reliability of the applied theoretical method. The chemical and structural stabilities of LiCaAlN₂ are confirmed by calculating the cohesion energy and enthalpy of formation. Chemical band stiffness is calculated to explain the pressure dependence of the lattice parameters. Through the band structure calculation, LiCaAlN₂ is predicted to be an indirect band gap of 2.725 eV. The charge-carrier effective masses are estimated from the band structure dispersions. The frequency-dependent dielectric function, absorption coefficient, refractive index, extinction coefficient, reflectivity coefficient and electron energy loss function spectra are calculated for polarized incident light in a wide energy range. Optical spectra exhibit a noticeable anisotropy. Single-crystal and polycrystalline elastic constants and related properties, including isotropic sound velocities and Debye temperatures, are numerically estimated. The calculated elastic constants and elastic compliances are used to analyse and visualize the elastic anisotropy of LiCaAlN₂. The calculated elastic constants demonstrate the mechanical stability and brittle behaviour of the considered material.     

Optical and microwave analysis of mushroom-type waveguides for traveling wave electroabsorption modulators based on asymmetric intra-step-barrier coupled double strained quantum wells by full-vectorial method

The finite difference method is exploited for a full-vectorial analysis of mushroom-type waveguides for traveling wave electroabsorption modulators (TWEAM) based on asymmetric intra-step-barrier coupled double strained quantum wells (AICD-SQW). In this analysis, the discontinuities of the normal components of the electric field across abrupt dielectric interfaces which are known as the limitations of scalar and semivectorial approximation methods are considered. The optical field distributions in mushroom-type TWEAM based on AICD-SQW and conventional ridge-type TWEAM of the same active region for 1.55 μm operation are presented. The important parameters in the high-frequency TWEAM design such as optical effective index which defines optical velocity and transverse mode confinement factor are calculated. Then, the transmission line microwave properties (microwave index, microwave loss, and characteristic impedance) of TWEAMs are obtained. The modulation response of mushroom-type TWEAM is calculated using circuit model by considering interaction between microwave and optical fields in waveguide and compared with conventional ridge-type TWEAM. It is found that increasing the width of p-cladding layer with the same i-layer to reduce the resistance in p-i-n mushroom-type waveguide of TWEAM based on AICD-SQW can improve the microwave propagation loss and thus the high-speed electro-optical response.