Pure-triplet scattering for radiative transfer in binary discrete random finite media with reflective boundaries and internal source of radiation

The stochastic solution of the monoenergetic radiative transfer equation in a finite slab random medium with pure-triplet anisotropic scattering is considered. The random medium is assumed to consist of two randomly mixed immiscible fluids labelled by 1 and 2. The extinction function, the scattering kernel, and the internal source of radiation are treated as discrete random variables, which obey the same statistics. The theoretical model used here for stochastic media transport assumes Markovian processes and exponential chord length statistics. The boundaries of the medium under consideration are considered to have specular and diffuse reflectivities with an internal source of radiation inside the medium. The ensemble-average partial heat fluxes are obtained in terms of the average albedos of the corresponding source-free problem, whose solution is obtained by using the Pomraning-Eddington approximation. Numerical results are calculated for the average forward and backward partial heat fluxes for different values of the single scattering albedo with variation of the parameters that characterize the random medium. Compared to the results obtained by Adams et al. in the case of isotropic scattering based on the Monte Carlo technique, it can be demonstrated that we have good comparable data.     

Pure-triplet scattering for radiative transfer in binary discrete random finite media with reflective boundaries and internal source of radiation

The stochastic solution of the monoenergetic radiative transfer equation in a finite slab random medium with pure-triplet anisotropic scattering is considered. The random medium is assumed to consist of two randomly mixed immiscible fluids labelled by 1 and 2. The extinction function, the scattering kernel, and the internal source of radiation are treated as discrete random variables, which obey the same statistics. The theoretical model used here for stochastic media transport assumes Markovian processes and exponential chord length statistics. The boundaries of the medium under consideration are considered to have specular and diffuse reflectivities with an internal source of radiation inside the medium. The ensemble-average partial heat fluxes are obtained in terms of the average albedos of the corresponding source-free problem, whose solution is obtained by using the Pomraning–Eddington approximation. Numerical results are calculated for the average forward and backward partial heat fluxes for different values of the single scattering albedo with variation of the parameters that characterize the random medium. Compared to the results obtained by Adams et al. in the case of isotropic scattering based on the Monte Carlo technique, it can be demonstrated that we have good comparable data.     

Radiation transfer in an anisotropically scattering plane-parallel medium with space-dependent albedo ω(x)

A method of analysis is presented for solving radiation-transfer problems involving space-dependent albedo ω(x) for an absorbing, emitting and anisotropically scattering plane-parallel medium with reflecting boundaries. The albedo is represented in terms of Legendre polynomials in the form ω(x) = Σ^R_r=0D_rP_r(x/L), where x is the optical variable, L is the half optical-thickness of the slab, P_r(x/L) are the Legendre polynomials and D_r are known expansion coefficients. The effects of spatial variation of albedo on the reflectivity and transmissivity of a medium having a slab geometry are examined for the cases of both forward and backward anisotropic scattering over a wide range of system variables. The effects of ω(x) on the angular distribution of radiation are also shown for some representative cases.     

The HN method for half-space Albedo and constant source problems for isotropic and anisotropic scattering kernels

The H_N method, which is developed recently, is used to solve the half-space albedo and the half-space constant source problems for both isotropic and extremely anisotropic scattering kernels. It has been shown that the method solves the problems in a concise manner and leads to fast converging numerical results as shown in tables.     

Maximum time-resolved hemispherical reflectance of absorbing and isotropically scattering media

This paper presents a parametric study of the time-resolved hemispherical reflectance of a plane-parallel slab of homogeneous, cold, absorbing, and isotropically scattering medium exposed to a collimated Gaussian pulse. The front surface of the slab is transparent while the back surface is assumed to be cold and black. The 1-D time-dependent radiation transfer equation is solved using the modified method of characteristics. The parameters explored include (1) the optical thickness, (2) the single scattering albedo of the medium, and (3) the incident pulse width. The study pays particular attention to the maximum transient hemispherical reflectance and identifies optically thin and thick regimes. It shows that the maximum reflectance is independent of the optical thickness in the optically thick regime. In the optically thin regime, however, the maximum hemispherical reflectance depends on all three parameters explored. The transition between the optically thick and thin regimes occurs when the optical thickness is approximately equal to the dimensionless pulse width. Finally, correlations relating the maximum of the hemispherical reflectance as a function of the optical thickness, the single scattering albedo of the materials, and the incident pulse width have been developed. These correlations could be used to retrieve radiation characteristics or serve as initial guesses for more complex inversion schemes accounting for anisotropic scattering.     

单轴各向异性手征介质平板的反射和透射特性研究

研究了光轴平行于界面的单轴各向异性手征介质平板对平面电磁波的反射和透射特性, 推导出了反射和透射系数(功率)公式; 按介电常数的正负分4种情形给出了反射和透射功率曲线; 讨论了手征参数对反射和透射特性的影响, 特别是给出了伪布儒斯特角与手征参数的变化关系曲线. 关键词： 单轴各向异性手征介质 手征参数 伪布儒斯特角 反射和透射     

Reflection and transmission of Laguerre Gaussian beam from uniaxial anisotropic multilayered media

Based on angular spectrum expansion and 4 × 4 matrix theory, the reflection and transmission characteristics of a Laguerre Gaussian(LG) beam from uniaxial anisotropic multilayered media are studied. The reflected and transmitted beam fields of an LG beam are derived. In the case where the principal coordinates of the uniaxial anisotropic media coincide with the global coordinates, the reflected and transmitted beam intensities from a uniaxial anisotropic slab and three-layered media are numerically simulated. It is shown that the reflected intensity components of the incident beam, especially the TM polarized incident beam, are smaller than the transmitted intensity components. The distortion of the reflected intensity component is more evident than that of the transmitted intensity component. The distortion of intensity distribution is greatly affected by the dielectric tensor and the thickness of anisotropic media. We finally extend the application of the method to general anisotropic multilayered media.     

一种适于1维磁等离子体电磁波传输特性的FDTD分析

 提出了一个新的分析各向异性磁等离子体中电磁波传输特性的时域有限差分（FDTD）方法。该方法是将电流密度矢量与电场强度矢量之间的本构方程基于拉普拉斯变换原理转到复频域,然后再逆变换到时域得到它们之间显式的方程,最后再结合指数差分,得到离散时域的显式的FDTD迭代方程,解决了本构方程中电流密度矢量的分量相互耦合而不易直接离散的困难。该方法在数学上具有简单明了和易于计算的特点,同时通过该方法计算各向异性等离子体板的电磁波反射和透射系数,与其解析解进行比较,结果表明了该方法的准确性和有效性。     

Interior radiances in optically deep absorbing media—III. Scattering from haze L

The interior radiances are calculated within an optically deep absorbing medium scattering according to the Haze L phase function. The dependence on the solar zenith angle, the single scattering albedo, and the optical depth within the medium is calculated by the matrix operator method. The development of the asymptotic angular distribution of the radiance in the diffusion region is illustrated through a number of examples; it depends only on the single scattering albedo and on the phase function for single scattering. The exact values of the radiance in the diffusion region are compared with values calculated from the approximate equations proposed by Van de Hulst. The variation of the radiance near the lower boundary of an optically thick medium is illustrated with examples. The attenuation length is calculated for various single scattering albedos and compared with the corresponding values for Rayleigh scattering. The ratio of the upward to the downward flux is found to be remarkably constant within the medium. The heating rate is calculated and found to have a maximum value at an optical depth of two within a Haze L layer when the sun is at the zenith. The location of this maximum moves toward the top of the haze layer as the solar zenith angle increases and also as the single scattering albedo decreases. When the single scattering albedo is less than 0·8, the downward flux is so small within the diffusion region that experimental measurements are probably not possible.     

Surface polaritons and transmission in multi-layer structures containing anisotropic left-handed materials

We study the surface polaritons and optical transmission in multi-layer structures containing alternate anisotropic left-handed materials and isotropic right-handed materials. By means of the transfer matrix method, the dispersive relations of the surface polaritons are derived. In contrast to the single left-handed slab, the multi-layer structure is capable of supporting more surface polaritons due to the existence of more interfaces between the left-handed and right-handed layers. We further make detailed investigations of the optical transmission associated with the surface polaritons. Numerical results show that the variance of the thickness of each layer will obviously affect the positions of the transmission peaks, corresponding to the surface polariton branches. Moreover, the presence of the absorption in the anisotropic left-handed materials plays a crucial role in the optical transmission spectra. PACS 41.20.Jb; 73.20.Mf; 78.20.Bh; 42.70.Qs     

Linear periodic and quasiperiodic anisotropic layered media with arbitrary orientation of optic axis—A numerical study

We study numerically the linear properties of periodic and quasiperiodic anisotropic layered media. Each anisotropic slab can have arbitrary orientation of optic axis. We apply the general numerical code to recover the known results for solc filters. We propose novel periodic structures where the location and width of the gaps can be controlled easily. We also study the transmission properties of a Fibonacci sequence of anisotropic layers and show the interesting features like self-similarity and scaling.     

任意入射辐射条件下介质特性对瞬态辐射传递的影响

用基于Monte Carlo法的DRESOR法在平行平板系统内具有吸收、无发射介质中研究不同波形入射、壁面反射、介质散射率、光学厚度、各向异性散射等条件对瞬态辐射传递的影响.任意连续波形入射辐射是目前大多数数值方法很难处理的瞬态辐射问题,而DRESOR法通过在系统内计算一单位入射辐射能对介质的DRESOR数分布,就能计算任意连续波形入射辐射条件下高方向分辨率的瞬态辐射强度结果.DRESOR法和Monte Carlo法计算的结果进行了比较验证,两者吻合较好,证明了DRESOR法处理瞬态入射辐射问题的正确性和有效性.     

一种高效计算各向异性磁化等离子体的时域有限差分算法

利用电流密度和电场强度的卷积关系,引入电流密度和电场强度分段线性近似,导出一种适合各向异性磁化等离子体介质的FDTD算法的计算公式.计算各向异性碰撞磁化等离子体平板对平行于磁场传播的电磁波的反射和透射系数,与解析结果比较,验证该算法的高效性和高精度,与电流密度卷积(JEC)算法和分段线性电流密度卷积(PLCDRC)算法相比,计算精度及计算效率显著提高.此外,用该算法验证了法拉第旋转效应.     

Temperature response in participating media with anisotropic scattering caused by pulsed lasers

It is not by isotropic scattering but by anisotropic scattering that radiant energy is redistributed in some materials containing real particles, fibers, or impurities. In some instances, great difference can be caused in transient thermal behavior between isotropic scattering and anisotropic scattering media. Ray tracing method combined with Hottel's zonal method is introduced to deduce thermal radiative source term for various optical boundary conditions induced by collimated incidence passing through translucent boundary. Temperature response caused by laser pulse at non-incident side of participating and anisotropic scattering media is examined. We investigate effects of scattering albedo, scattering phase function, initial temperature of media and thickness of media on temperature response. Results obtained for anisotropic scattering media are compared with those for isotropic scattering one and show that anisotropic scattering must be considered in the simulating measurement of thermophysical properties by the laser flash method for some materials with big scattering albedo which behave anisotropically, or big error will be introduced; forward scattering can increase excess temperature and backward scattering can decrease it at non-incident side of the considered sample irradiated by laser pulse.     

各向异性蜂窝夹芯材料的电磁传输性能分析算法研究

蜂窝夹芯结构作为天线罩最常用的透波材料, 其电各向异性特征对电磁传输性能具有不可忽略的影响. 本文基于各向异性蜂窝夹芯材料对电磁波水平极化和垂直极化分量的有效介电常数, 建立了多层蜂窝夹芯材料的等效传输线网络传输方程, 并给出了其传输系数的计算公式.该计算公式由于考虑了材料的三维各向异性特征, 不仅理论上可以计算多层各向异性介质板对任意方向入射电磁波的传输系数, 而且能够揭示出材料方向角对传输性能的影响规律.同时, 通过传输线网络等效, 其计算效率远高于有限元等方法.数值算例表明, 本方法能够有效地揭示蜂窝夹芯材料的各向异性对其传输性能的影响, 计算结果在入射角为0°–80° 时与有限元法符合很好. 关键词： 电磁传输性能 电各向异性介质 蜂窝夹芯材料     

The DRESOR method for radiative heat transfer in a one-dimensional medium with variable refractive index

This paper extends the DRESOR (Distribution of Ratios of Energy Scattered by the medium Or Reflected by the boundary surface) method to radiative transfer in a variable refractive index medium. In this method, the intensity is obtained from the source term along the curved integration paths determined only by the variable refractive index, and the DRESOR values are calculated by the Monte Carlo method in which the propagation of the energy bundles are affected by Snell's law. With given temperatures on the black boundaries of a one-dimensional medium, the temperature distribution inside the medium with a variable scattering property is calculated under the condition of radiative equilibrium. It is shown that the DRESOR method has a good accuracy in the cases studied. For an isotropic-scattering medium with the same optical thickness, the scattering albedo has no effect on the temperature distribution, which can be obtained from the general equations and can be seen as an extension of what exists for a constant refractive index; however, the different refractive index causes obvious changes in the temperatures inside the medium. The effect of anisotropic scattering on the temperature distribution cannot be ignored, although it is still weaker than the effect caused by variation in the refractive index.     

各向异性超常材料平板透镜的聚焦特性分析

运用矢量角谱理论研究各向异性超常材料平板透镜的聚焦特性,得到了光束在平板透镜内外各区域的矢量场分布,揭示了超常材料平板透镜的聚焦特性跟材料的各向异性参数之间的定量关系,发现聚焦场的偏振态因平板透镜的各向异性特性而发生改变.作为矢量理论的具体应用,分析了光轴方向磁导率为-1,其他各向异性参数均为1的超常材料平板透镜的聚焦特性,发现此类透镜对初始沿某一横向方向偏振的光束能实现部分聚焦,并发生偏振旋转现象.     

二维八重准晶有机光子晶体平板的光学传播特性

采用时域有限差分法研究了二维八重准晶有机光子晶体的光传输特性,重点分析了光束在聚苯乙烯空气柱平板结构和聚苯乙烯介质柱结构中的透射特性与光局域特性。研究结果表明,即使在低折射率对比度的情况下,两种完整八重准晶平板结构中均出现了可见光波段的光子带隙和本征模,且光子带隙中心位置随着平板厚度的增大而红移。当在两种准晶结构中引入缺陷微腔时,带隙内的缺陷模产生位置和波长红移特性随着微腔结构的变化规律明显不同,这种差异性是由两种物理机制(即光子晶体缺陷能级变化与微腔所支持的驻波条件)共同作用的结果。这一研究结果将为实验制备有机准晶发光器件提供一定的理论基础。     

Interior radiances in optically deep absorbing media—I Exact solutions for one-dimensional model

The exact solutions are obtained for a one-dimensional model of a scattering and absorbing medium. The results are given for both the reflected and transmitted radiance for any arbitrary surface albedo as well as for the interior radiance. These same quantities are calculated by the matrix operator method. The relative error of the solutions is obtained by comparison with the exact solutions as well as by an error analysis of the equations. The importance of an accurate starting value for the reflection and transmission operators is shown. A fourth-order Runge-Kutta method can be used to solve the differential equations satisfied by these operators in order to obtain such accurate starting values. Except for extremely large values of the optical thickness of a layer, the reflection and transmission operators calculated from accurate starting values obtained by the Runge-Kutta method are orders of magnitude (a factor of 10¹¹ better in a typical case at unit optical depth) more accurate than those obtained by the use of the single scattering approximation for an optically thin layer. The relative error in the reflection and transmission operators is less than 10^-12 and 10^-8 respectively up to an optical thickness of 32,768 when calculated by this procedure, while the relative error in the interior radiance is less than 10^-8 at all points within a layer of optical thickness 32,768. It is shown that flux conservation is a poor test of the accuracy of a numerical method, since flux is conserved to all orders for a conservative medium when the doubling method is used, no matter how inaccurate the starting values may be.     

Influence of the divergence of a light beam on the characteristics of collinear diffraction

Two types of anisotropic collinear diffractions of light on a diffraction grating are theoretically investigated, including that where the light is scattered forward in the direction of the incident radiation and that where the light is scattered backward in the direction toward the incident radiation. For both types, two-dimensional transfer functions are calculated, and the character of their transformation upon variation of the light wavelength and the period of the diffraction grating is analyzed. The dependence of the integrated diffraction efficiency and transmission band of diffraction filters on the divergence angle of the light beam is studied.