基于组合拟合法的冰晶粒子的光散射计算

利用组合拟合法计算了冰晶粒子的单次散射特性。给出了消光效率因子、单次散射反照度及非对称因子的拟合公式,利用拟合公式对有效粒子尺度为20μm和120μm的六种冰晶粒子的消光效率因子、单次散射反照度及非对称因子进行了计算。结果表明,粒子的消光效率因子、单次散射反照率和非对称因子随着入射波长的增加有着较大的起伏,后两者随着波长的增加而变化趋势基本一致;对于单次散射反照率来说,在可见光波段,反照率非常接近于1;在短波段,粒子的非对称因子变化较小,并且随着波长的增加,非对称因子会逐渐增大。     

Photon tunneling contributions to extinction for laboratory grown hexagonal columns

A new treatment predicting the extinction and absorption properties of ice particles is evaluated in this study using laboratory measurements of the extinction efficiency, Q_ext. In this treatment, the degree of ‘photon tunneling’ for ice crystals is unspecified, and laboratory measurements of Q_ext were used in conjunction with this scheme to quantify the significance of this process by determining a tunneling factor, denoted t_f. The term tunneling here refers to the interaction of a particle with radiation outside its area cross-section. A t_f of 1.0 corresponds to tunneling exhibited by ice spheres as predicted by Mie theory, while a t_f of 0 indicates no tunneling.

The laboratory work entailed Fourier transform infrared spectroscopy (FTIR) for optical depth measurements in an ice cloud grown in a chamber, over a wavelength range of 2–18 μm. From these measurements, the extinction efficiency Q_ext as a function of wavelength was determined. Ice particle size spectra were measured in the cloud chamber, and were used to predict Q_ext using the radiation scheme noted above and also using a new implementation of T-matrix, which is based on the exact geometry of a ‘pristine’ hexagonal ice crystal, without approximating the crystal as a spheroid.

Results show that t_f values determined from the laboratory measurements and the new radiation scheme are qualitatively in agreement with t_f values based on fundamental theory. Mean Q_ext errors (relative to measured Q_ext) over all wavelengths sampled were 3.0% when using a constant optimized t_f in the radiation scheme, and 2.3% when using a t_f scheme based on complex angular momentum theory. Moreover, Q_ext as predicted from T-matrix over the wavelength interval 8–12 μm is also in excellent agreement with the measured Q_ext. A single wavelength calculation at 14 μm was performed using the finite difference time domain (FDTD) and T-matrix methods, both of which agreed precisely with the measured Q_ext value. This validates the integrity of T-matrix, FDTD, the new radiation scheme, and the laboratory measurements for the corresponding range of wavelengths and size parameters. Collectively, these results indicate the tunneling contributions predicted for solid hexagonal columns are realistic.     

A study of the absorption and extinction properties of hexagonal ice columns and plates in random and preferred orientation, using exact T-matrix theory and aircraft observations of cirrus

Absorption and extinction properties of the finite hexagonal ice column and hexagonal ice plate in random and preferred orientation are studied at the wavelength of 80 μm using a new implementation of exact T-matrix theory. For the case of random orientation at size parameters around two, it is shown that the hexagonal ice column and hexagonal ice plate absorption resonances are diminished relative to Mie theory, and the same behaviour is also noted for an aggregate particle consisting of eight hexagonal elements. The absorption properties of the aggregate particle have been calculated using the finite-difference time-domain method. It is also shown that extinction and absorption solutions for the hexagonal ice column and hexagonal ice plate can differ significantly if incidence occurs perpendicular or parallel to the cylindrical axis of the hexagon. For the case of perpendicular incidence on the edge of the hexagon, absorption solutions can exceed those of Mie theory, and for the case of parallel incidence, behaviour of the extinction solutions for hexagonal ice columns and hexagonal ice plates is shown to be similar to previously published work based on the prolate and oblate spheroid. Interference structure, associated with surface waves, is resolved on the hexagonal column extinction solution and the hexagonal plate absorption solution, thereby demonstrating that surface waves can exist on a non-axisymmetric geometry. The usefulness of assuming the hexagonal ice column in retrieval of ice crystal effective size is also investigated using aircraft based radiometric observations of semi-transparent cirrus at the wavelengths of 8.5 and 11 μm.     

Modeling of radiation transport in coupled atmosphere-snow-ice-ocean systems

A radiative transfer model for coupled atmosphere-snow-ice-ocean systems (CASIO-DISORT) is used to develop accurate and efficient tools for computing the bidirectional reflectance distribution function (BRDF) of sea ice for a wide range of situations occurring in nature. These tools include a method to generate sea ice inherent optical properties (IOPs: single-scattering albedo, extinction optical depth, and scattering asymmetry parameter) for any wavelength between 300 and 4000 nm as a function of sea ice physical parameters including real and imaginary parts of the sea ice refractive index, brine pocket concentration and effective brine pocket size, air bubble concentration and effective air bubble size, volume fraction of ice impurities and impurity absorption coefficient, and sea ice thickness. The CASIO-DISORT code was used to compute look-up tables (LUTs) of the Fourier expansion coefficients of the BRDF as a function of angles of illumination and observation, sea ice IOPs, and ocean albedo. By interpolation in the LUTs one efficiently obtains accurate BRDF values. To include snow on the ice we modified DISORT2 to accept Fourier expansion coefficients for the BDRF as input instead of the BRDF itself, thereby reducing the computation time by a factor of about 60. The BRDF computed by CASIO-DISORT or retrieved from the LUTs applies to diffuse light only. To remedy this shortcoming we added a specular Gaussian beam component to the new BRDF tool and verified that it works well for BRDFs for bare and snow-covered sea ice.     

Light absorption and scattering by aggregates: Application to black carbon and snow grains

A geometric-optics surface-wave approach has been developed for the computation of light absorption and scattering by nonspherical particles for application to aggregates and snow grains with external and internal mixing structures. Aggregates with closed- (internal mixing) and open-cell configurations are constructed by means of stochastic procedures using homogeneous and core-shell spheres with smooth or rough surfaces as building blocks. The complex aggregate shape and composition can be accounted for by using the hit-and-miss Monte Carlo geometric photon tracing method. We develop an integral expression for diffraction by randomly oriented aggregates based on Babinet's principle and a photon-number weighted geometric cross section. With reference to surface-wave contributions originally developed for spheres, we introduce a nonspherical correction factor using a non-dimensional volume parameter such that it is 1 for spheres and 0 for elongated particles. The extinction efficiency, single-scattering albedo, and asymmetry factor results for randomly oriented columns and plates compare reasonably well with those determined from the finite-difference time domain (FDTD) and the discrete dipole approximation (DDA) computer codes for size parameters up to about 20. The present theoretical approach covers all size ranges and is particularly attractive from the perspective of efficient light absorption and scattering calculations for complex particle shape and inhomogeneous composition.We show that under the condition of equal volume and mass, the closed-cell configuration has larger absorption than its open-cell counterpart for both ballistic and diffusion-limited aggregates. Because of stronger absorption in the closed-cell case, most of the scattered energy is confined to forward directions, leading to a larger asymmetry factor than the open-cell case. Additionally, light absorption for randomly oriented snowflakes is similar to that of their spherical counterparts under the condition of equal geometrical cross section area for both external and internal mixing states; however, nonspherical snowflakes scatter less light in forward directions than spheres, resulting in a substantial reduction of the asymmetry factor. We further demonstrate that small soot particles on the order of 1 μm internally mixed with snow grains could effectively reduce snow albedo by as much as 5-10%. Indeed, the depositions of black carbon would substantially reduce mountain-snow albedo, which would lead to surface warming and snowmelt, critical to regional climatic surface temperature amplification and feedback.     

On the impact of non-sphericity and small-scale surface roughness on the optical properties of hematite aerosols

We perform a comparative modelling study to investigate how different morphological features influence the optical properties of hematite aerosols. We consider high-order Chebyshev particles as a proxy for aerosol with a small-scale surface roughness, and spheroids as a model for nonspherical aerosols with a smooth boundary surface. The modelling results are compared to those obtained for homogeneous spherical particles. It is found that for hematite particles with an absorption efficiency of order unity the difference in optical properties between spheres and spheroids disappears. For optically softer particles, such as ice particles at far-infrared wavelengths, this effect can be observed for absorption efficiencies lower than unity. The convergence of the optical properties of spheres and spheroids is caused by absorption and quenching of internal resonances inside the particles, which depend both on the imaginary part of the refractive index and on the size parameter, and to some extent on the real part of the refractive index. By contrast, small-scale surface roughness becomes the dominant morphological feature for large particles. This effect is likely to depend on the amplitude of the surface roughness, the relative significance of internal resonances, and possibly on the real part of the refractive index. The extinction cross section is rather insensitive to surface roughness, while the single-scattering albedo, asymmetry parameter, and the Mueller matrix are strongly influenced. Small-scale surface roughness reduces the backscattering cross section by up to a factor of 2-3 as compared to size-equivalent particles with a smooth boundary surface. This can have important implications for the interpretation of lidar backscattering observations.     

Scattering phase functions of horizontally oriented hexagonal ice crystals

Finite-difference time domain (FDTD) solutions are first compared with the corresponding T-matrix results for light scattering by circular cylinders with specific orientations. The FDTD method is then utilized to study the scattering properties of horizontally oriented hexagonal ice plates at two wavelengths, 0.55 and 12 μm. The phase functions of horizontally oriented ice plates deviate substantially from their counterparts obtained for randomly oriented particles. Furthermore, we compute the phase functions of horizontally oriented ice crystal columns by using the FDTD method along with two schemes for averaging over the particle orientations. It is shown that the phase functions of hexagonal ice columns with horizontal orientations are not sensitive to the rotation about the principal axes of the particles. Moreover, hexagonal ice crystals and circular cylindrical ice particles have similar optical properties, particularly, at a strongly absorbing wavelength, if the two particle geometries have the same length and aspect ratio defined as the ratio of the radius or semi-width of the cross section of a particle to its length. The phase functions for the two particle geometries are slightly different in the case of weakly absorbing plates with large aspect ratios. However, the solutions for circular cylinders agree well with their counterparts for hexagonal columns.     

随机取向非球形沙尘气溶胶粒子的光学特性

利用离散偶极子近似法分析了一种随机取向旋转椭球体沙尘气溶胶粒子模型在尺度参数变化范围为0.1~23时(波长0.55!m对应有效半径为0.01~2!m)的光学特性,研究了沙尘粒子非球形性程度对其光学特性的影响,并考察了非球形粒子的随机取向能否用等体积球体来代替。就随机取向单分散和多分散旋转椭球体沙尘气溶胶而言,粒子非球形特征越明显,消光效率因子、不对称因子和单次散射反照率基本上偏离其等体积球体越大;对于相同的非球形,不对称因子偏离其等体积球体的相对偏差要比消光效率因子和单次散射反照率要大。非球形粒子的随机取向并不能使其光学特性严格等效为其等体积球体的光学特性。如果粒子形状偏离球体较小,则非球形粒子的随机取向的平均效果能使其消光效率因子、不对称因子和单次散射反照率近似用等体积球体的对应光学参量来等效;而如果粒子形状偏离球形较大,仅有单次散射反照率可以近似用等体积球体的单次散射反照率来等效,例如,轴半径比为16的旋转椭球体沙尘粒子的单次散射反照率偏离其等体积球体仅在3%以内。     

基于不规则衍射理论的冰晶粒子的光散射研究(英文)

在不规则衍射理论的基础上,分析了从可见光到近红外波段冰晶粒子的光散射特性。计算了粒子尺度为20μm,50μm,80μm的五种典型冰晶粒子的消光效率因子和吸收效率因子。最后,为了评估不规则衍射理论的精确性,与有限时域差分法和几何光学法进行了比较。     

On geometric optics and surface waves for light scattering by spheres

A geometric optics approach including surface wave contributions has been developed for homogeneous and concentrically coated spheres. In this approach, a ray-by-ray tracing program was used for efficient computation of the extinction and absorption cross sections. The present geometric-optics surface-wave (GOS) theory for light scattering by spheres considers the surface wave contribution along the edge of a particle as a perturbation term to the geometric-optics core that includes Fresnel reflection–refraction and Fraunhofer diffraction. Accuracies of the GOS approach for spheres have been assessed through comparison with the results determined from the exact Lorenz–Mie (LM) theory in terms of the extinction efficiency, single-scattering albedo, and asymmetry factor in the size–wavelength ratio domain. In this quest, we have selected a range of real and imaginary refractive indices representative of water/ice and aerosol species and demonstrated close agreement between the results computed by GOS and LM. This provides the foundation to conduct physically reliable light absorption and scattering computations based on the GOS approach for aerosol aggregates associated with internal and external mixing states employing spheres as building blocks.     

Statistical approach of the effects of roughness on the polarization of light scattered by dust grains

In order to study the effect of shape on the optical properties of dust grains, we statistically analyze the linear polarized scattered light. We start by examining a homogeneous spherical grain using the discrete dipole approximation (DDA) Draine (Astrophys J 1988;333:848). Using a uniform law we remove elements of matter on the surface of the grain to describe a random roughness. Then, for various scattering angles, the linear polarization P_l is calculated. We successively repeat the simulation in order to obtain a sample of random variables constituting the values P_l of the linear polarization. The analysis of the results is then achieved through a Gaussian kernel method which provides the probability density function of P_l for each scattering angle. We present the results for a typical interstellar grain of water–ice with radius a comparable to the incident wavelength λ so that the parameter size x≡2πa/λ1. We apply this method for two wavelengths in the near IR, when water–ice is transparent at 1.9 μm, and, when water–ice is absorbing at 3.1 μm. We find that the shape of the density function of the linear polarization is asymmetric to the mean value of the density function and non-unimodal for several scattering angles. This allows us to separate the effects of roughness from those of volume. When water–ice is absorbing, we also observe a significant shift of the polarization peak toward greater scattering angles.     

Modeling single-scattering properties of small cirrus particles by use of a size-shape distribution of ice spheroids and cylinders

In this study, we model single-scattering properties of small cirrus crystals using mixtures of polydisperse, randomly oriented spheroids and cylinders with varying aspect ratios and with a refractive index representative of water ice at a wavelength of 1.88 μm. The Stokes scattering matrix elements averaged over wide shape distributions of spheroids and cylinders are compared with those computed for polydisperse surface-equivalent spheres. The shape-averaged phase function for a mixture of oblate and prolate spheroids is smooth, featureless, and nearly flat at side-scattering angles and closely resembles those typically measured for cirrus. Compared with the ensemble-averaged phase function for spheroids, that for a shape distribution of cylinders shows a relatively deeper minimum at side-scattering angles. This may indicate that light scattering from realistic cirrus crystals can be better represented by a shape mixture of ice spheroids. Interestingly, the single-scattering properties of shape-averaged oblate and prolate cylinders are very similar to those of compact cylinders with a diameter-to-length ratio of unity. The differences in the optical cross sections, single-scattering albedo, and asymmetry parameter between the spherical and the nonspherical particles studied appear to be relatively small. This may suggest that for a given optical thickness, the influence of particle shape on the radiative forcing caused by a cloud composed of small ice crystals can be negligible.     

Scattering and absorption of light by ice particles: Solution by a new physical-geometric optics hybrid method

A new physical-geometric optics hybrid (PGOH) method is developed to compute the scattering and absorption properties of ice particles. This method is suitable for studying the optical properties of ice particles with arbitrary orientations, complex refractive indices (i.e., particles with significant absorption), and size parameters (proportional to the ratio of particle size to incident wavelength) larger than ∼20, and includes consideration of the edge effects necessary for accurate determination of the extinction and absorption efficiencies. Light beams with polygon-shaped cross sections propagate within a particle and are traced by using a beam-splitting technique. The electric field associated with a beam is calculated using a beam-tracing process in which the amplitude and phase variations over the wavefront of the localized wave associated with the beam are considered analytically. The geometric-optics near field for each ray is obtained, and the single-scattering properties of particles are calculated from electromagnetic integral equations. The present method does not assume additional physical simplifications and approximations, except for geometric optics principles, and may be regarded as a “benchmark” within the framework of the geometric optics approach. The computational time is on the order of seconds for a single-orientation simulation and is essentially independent of the size parameter. The single-scattering properties of oriented hexagonal ice particles (ice plates and hexagons) are presented. The numerical results are compared with those computed from the discrete-dipole-approximation (DDA) method.     

Application of the pseudo-spectral time domain method to compute particle single-scattering properties for size parameters up to 200

The applicability, efficiency, and accuracy of the pseudo-spectral time domain (PSTD) method are investigated with specific emphasis on the computation of the single-scattering properties of homogeneous dielectric particles. By truncating the high spectral terms, the Gibbs phenomenon is eliminated, and, consequently, the applicability of the PSTD is enhanced. The PSTD simulations for ice spheres, with moderate refractive indices and size parameters up to 200, are compared with the exact Lorenz–Mie solutions at three wavelengths. In addition, the comparison is extended to a case with an extremely large refractive index (7.150+i2.914) and size parameters up to 40. Furthermore, the single-scattering properties of randomly oriented spheroids and circular cylinders for size parameters up to 150 and 75, respectively, are calculated with the PSTD in comparison with those computed from the T-matrix method. The aspect ratio of the spheroid and the diameter-to-length ratio of the circular cylinder are 0.5 and 1, respectively. The relative errors, given by the PSTD for these randomly oriented non-spherical particles, are smaller than 2% for the extinction efficiencies and asymmetry factors and less than 30% for the phase function. The PSTD is also employed to compute the phase matrices of randomly oriented hexagonal columns with size parameters of 50 and 100. The simulations show the PSTD to be a robust method for simulating the single-scattering properties of particles with small-to-medium size parameters and for a wide range of refractive indices.     

Design, analysis and optimization of silicon-on-insulator photonic crystal dual band wavelength demultiplexer

A highly efficient photonic crystal dual band wavelength demultiplexer (DBWD) using silicon-on-insulator (SOI) substrates is proposed for demultiplexing two optical communication wavelengths, 1.31 μm and 1.55 μm. Demultiplexing of two wavelength channels is obtained by modifying the propagation properties of guided modes in two arms of Y type photonic crystal structure. Propagation characteristics of proposed DBWD are analyzed utilizing 3D finite difference time domain (FDTD) method. Enhancement in spectral response is further obtained by optimizing the Y junction of demultiplexer giving rise to high transmission and extinction ratio for the wavelengths, 1.31 μm and 1.55 μm. Hence it validates the efficiency of proposed optimized DBWD design for separating two optical communication wavelengths, 1.31 μm and 1.55 μm. Tolerance analysis was also performed to check the effect of variation of air hole radius, etch depth and refractive index on the transmission characteristics of the proposed design of SOI based photonic crystal DBWD.     

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基于Mie散射理论和方法,研究了航天器尾喷焰等离子体中Al2O3粒子的光学散射特性,分析了复折射率对单个Al2O3粒子消光效率因子、散射效率因子、吸收效率因子、散射相函数以及单次反照率的影响。同时,基于多分散系粒子尺度单峰分布,分析了Al2O3粒子按粒径分布后散射场的有关效应因子及散射相函数的变化,并进行了相应的数值模拟。理论和数值模拟研究表明,航天器尾喷焰等离子体Al2O3粒子复折射率的虚部和实部、粒径的大小与分布对其散射相函数、消光和散射效率因子以及单次反照率均有明显的影响。     

Optical properties of ice particles in young contrails

The single-scattering properties of four types of ice crystals (pure ice crystals, ice crystals with an internal mixture of ice and black carbon, ice crystals coated with black carbon, and soot coated with ice) in young contrails are investigated at wavelengths 0.65 and 2.13 μm using Mie codes for coated spheres. The four types of ice crystals show differences in their single-scattering properties because of the embedded black carbon whose volume ratio is assumed to be 5%. The bulk-scattering properties of young contrails consisting of the four types of ice crystals are further investigated by averaging their single-scattering properties over a typical ice particle size distribution found in young contrails. The effect of the radiative properties of the four types of ice particles on the Stokes parameters I, Q, U, and V is also investigated for different viewing zenith angles and relative azimuth angles with a solar zenith angle of 30° using a vector radiative transfer model based on the adding-doubling technique. The Stokes parameters at a wavelength of 0.65 μm show pronounced differences for the four types of ice crystals, whereas the counterparts at a wavelength of 2.13 μm show similar variations with the viewing zenith angle and relative azimuth angle. However, the values of the results for the two wavelengths are noticeably different.     

Retrieval of cirrus particle sizes using a split-window technique: a sensitivity study

This paper examines the sensitivity of retrieved ice particle sizes using split-window method to the light scattering program for the single scattering calculation. We find that for randomly oriented hexagonal ice particles the retrieval algorithm using the anomalous diffraction theory (ADT) significantly overestimates the mean effective ice particle sizes, D_ge. The retrieved D_ge based on the geometric optics method (GOM) and Mie theory agrees with reference results within 20% when D_ge<30 μm. Based on the speculation that there is no “tunneling” for complex particles, some recent studies suggest that the ADT is an appropriate method to simulate the absorption coefficient for irregularly shaped particles in the infrared. In this study, however, we find that the overestimation of D_ge due to the ADT is largely caused by the neglect of refraction and reflection processes, instead of by the neglect of “tunneling” in the absorption calculations. By considering complex particle shapes such as aggregates with surface roughness, we further find that the retrieved D_ge based on the GOM is not sensitive to the particle shapes. Note that both ADT and GOM do not consider the “tunneling”, but the retrieved D_ge based on the ADT is about two times larger than those based on the GOM. “Tunneling” plays a significant role in the retrieved D_ge only when the D_ge is larger than 30–35 μm. In this study, we also examine the sensitivities of retrieved D_ge to the ice particle size distributions assumed in the retrieval algorithm and to the errors in the emissivities. It is found that when the D_ge is larger than 30–40 μm, the retrieved D_ge becomes very sensitive to the uncertainties related to the ice particle size distributions and to the errors in cirrus emissivities derived from measurements.     

Design of a Photonic Crystal Fiber with Zero Dispersion Wavelength Near 0.65 μm

The zero dispersion point of an index-guided photonic crystal fiber with triangular lattice of air holes has been shifted to 0.65 μm by varying the diameter of air hole of different rings. Using FDTD method, we have estimated group velocity dispersion, effective refractive index, the fiber parameter, and the mode field of the fundamental mode. It has been realized that the value of zero dispersion point is mainly decided by the air holes of the first ring. This fiber can be used for biomedical application, spectroscopy, and supercontinuum generation.     

Multi-order diffractive optical elements for achromatic interconnections at 1.30 μm and 1.55 μm

We propose a class of diffractive components allowing free-space optical systems to operate at the two telecommunication wavelengths simultaneously. These are fifth order diffractive components working at the sixth order at 1.30 μm and at the fifth order at 1.55 μm. Simulation results showing the link efficiency between two single-mode fibres as a function of the wavelength are presented. The width of the two transmission windows depends on the architecture of the whole system, which must be designed in accordance with technological realizability.