Temperature field of radiative equilibrium in a two-dimensional graded index medium with gray boundaries

In this paper, a numerical method is presented for the study of the radiative transfer in a two-dimensional graded index semitransparent medium with diffuse gray boundaries. The numerical method is a combination of the linear refractive index bar model, the discrete curved ray-tracing technique and the pseudo source adding method (LRIB-CRTP). In the traditional ray-tracing technique, it is difficult to deal with the diffuse gray boundary while solving the radiative transfer. Using the pseudo source adding method, the diffuse gray boundary of the medium can be treated as a black boundary. We have also studied the radiative equilibrium temperature field of the medium and analyzed the influence of some parameters involved. The results show that the directional discrete number is important for the medium having a large absorption coefficient. The results also show that the refractive index distribution greatly influences the temperature field, whereas the linear absorption coefficient distribution has little influence on the temperature field.     

Thermal emission and volumetric absorption of a graded index semitransparent medium layer

Both thermal emission and volumetric absorption characteristics of a graded index semitransparent medium layer are investigated numerically. The semitransparent and specular emerging surface of the medium layer is parallel to an opaque and diffuse substrate wall. Monochromatic spectrum or gray medium is considered in the analysis. A pseudo-source adding method is combined with a ray-splitting and -tracing technique to solve the radiative transfer in the medium. As examples, constant and linear refractive index distributions are examined for an isothermal layer and the medium layer with a linear temperature distribution. Directional and hemispherical thermal emissions from the emerging surface as well as the volumetric absorption to the diffuse and parallel incidence of radiation are investigated, respectively. The results show that the refractive index distribution has significant influences on thermal emission and volumetric absorption of a semitransparent medium layer. The optical thickness, temperature distribution and the reflectivity of substrate wall react in combination with the refractive index distribution.     

Inhomogeneous Vacuum: An Alternative Interpretation of Curved Spacetime

The strong similarities between the light propagation in a curved spacetime and that in a medium with graded refractive index are found. It is pointed out that a curved spacetime is equivalent to an inhomogeneous vacuum for light propagation. The corresponding graded refractive index of the vacuum in a static spherically symmetrical gravitational field is derived. This result provides a simple and convenient way to analyse the gravitational lensing in astrophysics.     

结合计算层析与光学相干层析测量折射率分布

通过将计算层析技术与光学相干层析技术相结合,测量散射介质非均匀折射率分布。该方法测量散射样品折射率分布时,通过光学相干层析技术测量散射样品折射率分布在多个方向上的投影,采用计算层析技术实现对样品折射率分布的层析重建,克服了传统折射率光学测量方法如单纯的基于光学相干层析原理的焦点追迹法和光程匹配法,不能测量散射介质非均匀折射率分布的缺点。采用该方法在实验中对梯度折射率棒的径向相对折射率分布进行层析重建,取得了较好的实验结果。     

Curved ray tracing method for one-dimensional radiative transfer in the linear-anisotropic scattering medium with graded index

The curved ray tracing method (CRT) is extended to radiative transfer in the linear-anisotropic scattering medium with graded index from non-scattering medium. In this paper, the CRT is presented to solve one-dimensional radiative transfer in the linear-anisotropic scattering gray medium with a linear refractive index and two black boundaries. The predicted temperature distributions and radiative heat flux at radiative equilibrium are determined by the proposed method, and numerical results are compared with the data in references. The results show that the CRT has a good accuracy for radiative transfer in the linear-anisotropic scattering medium with graded index and the dimensionless emissive power and dimensionless radiative heat flux depend on the dimensionless refractive index gradient. It can also be seen that the dimensionless refractive index gradient has important effects on the temperature discontinuity at the boundaries.     

A method for measuring two-dimensional refractive index distribution with the total internal reflection of p-polarized light and the phase-shifting interferometry

Based on the total internal reflection of p-polarized light and the phase-shifting interferometry, an alternative method for measuring the two-dimensional refractive index distribution of a material is presented. The p-polarized light is incident on the boundary between a right-angle prism and a tested material. When the total internal reflection occurs at the boundary, and the p-polarized light has a phase variation. It depends on the refractive index of the tested material. Firstly, the two-dimensional phase variation distribution of the p-polarized light at the boundary is measured by the four-step phase shifting interferometric technique. Then, substituting the data into the special equations derived from Fresnel equations, the two-dimensional refractive index distribution of the tested material can be obtained.     

吸收-透射界面下正弦折射率介质内辐射换热

对具有吸收-透射性边界面的梯度折射率半透明介质层,建立了介质内热辐射传递与边界面辐射换热的数理模型,并采用数值弯曲光线跟踪法求解介质内的热辐射传递。通过数值模拟,分析了正弦折射率下,边界面的反射特性、吸收率以及介质层光学厚度对介质内热辐射平衡温度场及热流分布的影响。结果表明,边界面的反射特性与吸收率对介质内辐射换热均有重要影响,吸收率的影响与边界面反射特性、介质层光学厚度及环境条件相关,呈现特征不同的作用。     

Inverse radiation problem of temperature distribution in one-dimensional isotropically scattering participating slab with variable refractive index

In this paper, an inverse analysis is performed for estimation of source term distribution from the measured exit radiation intensities at the boundary surfaces in a one-dimensional absorbing, emitting and isotropically scattering medium between two parallel plates with variable refractive index. The variation of refractive index is assumed to be linear. The radiative transfer equation is solved by the constant quadrature discrete ordinate method. The inverse problem is formulated as an optimization problem for minimizing an objective function which is expressed as the sum of square deviations between measured and estimated exit radiation intensities at boundary surfaces. The conjugate gradient method is used to solve the inverse problem through an iterative procedure. The effects of various variables on source estimation are investigated such as type of source function, errors in the measured data and system parameters, gradient of refractive index across the medium, optical thickness, single scattering albedo and boundary emissivities. The results show that in the case of noisy input data, variation of system parameters may affect the inverse solution, especially at high error values in the measured data. The error in measured data plays more important role than the error in radiative system parameters except the refractive index distribution; however the accuracy of source estimation is very sensitive toward error in refractive index distribution. Therefore, refractive index distribution and measured exit intensities should be measured accurately with a limited error bound, in order to have an accurate estimation of source term in a graded index medium.     

变折射率介质中光线追迹通用算法的研究

基于几何光学的光线折射和反射原理提出了变折射率介质中的光线追迹算法,给出了在光线追迹过程中进行递推的反射光线和折射光线的方向余弦方程;解决了空间中法线的确定和光线回转等问题。最后通过对多种不同的存在解析解的特殊折射率分布的数值解值和解析解值的比较,验证了算法的正确性,并且讨论了应用算法时应该注意的问题和算法中还有待解决的问题。该算法不但具有广泛的适用性,基本不受折射率分布的制约,而且其数值解精度达10^-5。该算法在变折射率介质的光学设计和空间成像补偿等方面有着广阔的应用前景。     

Radiative intensity solution and thermal emission analysis of a semitransparent medium layer with a sinusoidal refractive index

The radiative intensity in a sinusoidal refractive index semitransparent medium layer is solved by the curved ray-tracing method in combination with the pseudo-source adding method. One boundary of the medium layer is an opaque diffuse substrate wall. The other boundary is a semitransparent specular or diffuse surface, from which the medium thermal emission emerges. With considering a linear temperature distribution, the radiative intensity formulae are, respectively, deduced under the two boundary conditions. On the basis of the radiative intensity solutions, the directional and hemispherical emission of the medium layer with a specular surface as well as the hemispherical emission of that with a diffuse surface are calculated. The influences of the optical thickness, sinusoidal refractive index distribution and linear temperature distribution on the thermal emission are investigated. The results show that the effects of refractive index and temperature distribution are significant and are different under the two reflecting modes of the surface.     

色散、群速与群折射率

本文讨论了群折射率存在的物理意义,指出群折射率不仅包含了折射率概念而且还体现了折射率的色散性质,同样能作为材料本身的光学性质参量.接着指出在折射率的白光干涉法测量中存在着忽视色散作用而导致的将群折射率误认为折射率的情况.将群折射率与折射率区别开来,不仅可以消除折射率测量中所存在的错误,而且可以突出色散现象在光传播时间特性上的意义.为此建立了折射率与群折射率的相互变换关系,通过对于典型物质的折射率与群折射率变换关系的计算,说明二者在数值上的差别甚至对于气体介质来说也是不能忽略的.     

一种新型光谱表面等离子体共振二维探测方法在DNA微阵列中的应用

在此前曾提出过一种新型二维折射率探测方法——并行扫描光谱表面等离子体共振(surface plasmon resonance, SPR)成像方法。在这种方法中,使用线形光照明,CCD得到的图像包含SPR光谱信息和一维空间信息,进而通过计算可得到折射率的一维分布信息。通过一维扫描,就能够得到整个被扫描区域内的折射率二维分布信息。该方法具有高灵敏、高通量的优点,适合微阵列(microarray)的检测, 并完善了这种方法的数据处理过程,使用空气折射率作为参考,消除了无法精确控制入射角的难题。使用该方法对手工点制的军团菌mip DNA探针微阵列进行了检测,证明了这种方法高灵敏无标记地探测微阵列的可行性。我们得到的军团菌mip DNA探针制备浓度与其等效折射率的关系,这对基于SPR的微阵列技术的发展有着重要的参考意义。     

Finite element method for modeling radiative transfer in semitransparent graded index cylindrical medium

Both Galerkin finite element method (GFEM) and least squares finite element method (LSFEM) are developed and their performances are compared for solving the radiative transfer equation of graded index medium in cylindrical coordinate system (RTEGC). The angular redistribution term of the RTEGC is discretized by finite difference approach and after angular discretization the RTEGC is formulated into a discrete-ordinates form, which is then discretized based on Galerkin or least squares finite element approach. To overcome the RTEGC-led numerical singularity at the origin of cylindrical coordinate system, a pole condition is proposed as a special mathematical boundary condition. Compared with the GFEM, the LSFEM has very good numerical properties and can effectively mitigate the nonphysical oscillation appeared in the GFEM solutions. Various problems of both axisymmetry and nonaxisymmetry, and with medium of uniform refractive index distribution or graded refractive index distribution are tested. The results show that both the finite element approaches have good accuracy to predict the radiative heat transfer in semitransparent graded index cylindrical medium, while the LSFEM has better numerical stability.     

蔗糖溶液折射率与浓度关系的理论和实验探究

光在介质中的传播遵循费马原理.在均匀介质中光沿直线传播,非均匀介质中,光的传播轨迹比较复杂.本文以蔗糖溶液为研究对象,设计了光在非均匀介质中传播实验,建立了相关模型,理论分析了溶液折射率随深度(浓度)变化的关系.进行了数据拟合,得出溶液折射率随液体深度变化的表达式.     

渐变折射率薄膜的分层评价探讨

首先阐述了将渐变折射率薄膜细分为多层均匀薄膜的分层介质理论,接着给出了一种获得最佳分层数目的分层评价方法,最后以线性变化渐变折射率薄膜为例说明了如何优化获得渐变折射率薄膜的分层数目.研究发现：渐变折射率薄膜的分层数目与薄膜的厚度和薄膜的折射率变化快慢有关,在一定的折射率变化范围内,渐变折射率薄膜的分层数目随着薄膜厚度的增加先减小后增大. 关键词： 渐变折射率 分层介质理论 分层评价     

On the derivation of vector radiative transfer equation for polarized radiative transport in graded index media

Light transport in graded index media follows a curved trajectory determined by Fermat's principle. Besides the effect of variation of the refractive index on the transport of radiative intensity, the curved ray trajectory will induce geometrical effects on the transport of polarization ellipse. This paper presents a complete derivation of vector radiative transfer equation for polarized radiation transport in absorption, emission and scattering graded index media. The derivation is based on the analysis of the conserved quantities for polarized light transport along curved trajectory and a novel approach. The obtained transfer equation can be considered as a generalization of the classic vector radiative transfer equation that is only valid for uniform refractive index media. Several variant forms of the transport equation are also presented, which include the form for Stokes parameters defined with a fixed reference and the Eulerian forms in the ray coordinate and in several common orthogonal coordinate systems.     

Nonlinear interaction and reflection of incoherent light beams

The interaction dynamics between two incoherent light beams in a medium with thermal nonlin-earity is studied both experimentally and theoretically. It is shown that in the mode of a nonlinear reflection the transformation of a spatial structure of a weak signal beam can be theoretically described in the framework of a spatially distributed model for a nonlinear change in the refractive index of the medium.     

玻璃基板中热光效应折射率分布的研究和测定

几乎所有的光学材料都具有热致折射率变化的特性,当光束经过局域热源作用下折射率呈梯度分布的介质时会发生偏向,利用这种特性可做成各种热光器件.本文在玻璃基板表面上制备了条形Ti薄膜热源,通过测定出射光束的偏向角,利用解折方法,得出基极截面的折射率分布.根据能量守恒,得到该材料的折射率温度系数,与公布值比较,验证了本方法的正确性.本文对研究和分析热光材料和器件提供了一种有益的方法.     

Control of the distribution of surface plasmon local field by altering the surrounding material

The field distribution of the surface plasmon (SP) around a silver nanowire greatly influences its applications for both spectrum enhancement and nano-waveguide. This paper demonstrates the change of the SP local field distribution of a silver nanowire on glass substrate with the refractive index of the covering medium by numerical simulation. The hot energy site is observed focusing on the interface between the nanowire and the surround material of larger refractive index. Moreover, we also find that the surface plasmon field becomes more confined as the refractive index between the substrate and medium has a larger gap, while a homogeneous distribution of the surrounding dielectric material around the nanowire shows a uniform local field distribution with a larger surface plasmon propagation length. The change of related parameters, such as effective index, mode area, and propagation length are also comprehensively investigated against the refractive index for nanowires with 100, 200, 300 nm diameter. Considering the wide use of polymethyl methacrylate (PMMA) material, the field distribution of silver nanowire partially imbedded in PMMA against the PMMA thickness is also studied.     

多维梯度折射率介质内辐射传递的扩散近似

推导多维梯度折射率介质内稳态辐射传递的扩散近似方程.使用有限元法对扩散近似进行离散和求解,利用两个二维半透明介质的稳态辐射传递问题验证该扩散近似的精度及适用性.算例考虑介质为均匀折射率及梯度折射率两种情况.利用扩散近似分别求解辐射平衡时的边界热流、介质内温度场分布,并与辐射传递方程的求解结果进行对比分析.结果表明:介质折射率变化、散射特性、光学厚度及散射反照率均直接影响扩散近似的精度;在光学厚及强散射条件下,该扩散近似可以作为一种快速算法应用于梯度折射率介质稳态辐射传递的求解.