Anomalous diffraction approximation method for retrieval of spherical and spheroidal particle size distributions in total light scattering

Using total light scattering technique to measure the particle size distribution has advantages of simplicity in measurement principle and convenience in the optical arrangement. However, the calculation of extinction efficiency based on Mie theory for a spherical particle is expensive in both time and resources. Thus, a simple but accurate approximation formula for the exact extinction efficiency may be very desirable. The accuracy and limitations of using the anomalous diffraction approximation (ADA) method for calculating the extinction efficiency of a spherical particle are investigated. Meanwhile, the monomodal and bimodal particle size distributions of spherical particles are retrieved using the genetic algorithm in the dependent model. Furthermore, the spheroidal model in the retrieval of non-spherical particle size distribution is also discussed, which verifies the non-sphericity has a significant effect on the retrieval of particle size distribution compared with the assumed homogeneous isotropic sphere. Both numerical computer simulations and experimental results illustrate that the ADA can be successfully applied to retrieve the particle size distributions for spherical and spheroidal particles with high stability even in the presence of random noise. The method has advantages of simplicity, rapidity, and suitability for in-line particle size measurement.     

薛定谔猫态光场与二能级原子相互作用系统的量子特性

在非旋波近似下,通过采用相干态正交化展开的方法,研究了薛定谔猫态光场与二能级原子相互作用系统中,原子的布局数和光场的反聚束效应,并与旋波近似下的结果进行了对比.在旋波近似与非旋波近似下,讨论了初始光场强度、相干态间的相位角以及失谐量对原子布局数和光场反聚束效应的影响;在非旋波近似下,讨论了强弱耦合情况下光场的反聚束效应.研究结果表明:旋波近似与非旋波近似下,原子的布局数随着初始光场强度的不同,表现出不同的特性;当初始光场强度较小时,旋波近似与非旋波近似下,原子的布局数表现出相同的特性;随着初始光场强度的增大,旋波近似下,原子的布局数将表现出坍塌现象.耦合强度较大时,光场的聚束与反聚束效应在非旋波近似与旋波近似下有较大的区别;非旋波近似下,随着初始光场强度的增大,光场一直处于聚束效应状态;而旋波近似下,光场的聚束效应与反聚束效应交替出现.     

微小颗粒的光散射数值模拟

简单介绍了以经典Mie理论为基础的光散射测量技术在颗粒直径和颗粒浓度测量中广泛的应用。分别以Mie理论和离散偶极子近似理论(DDA)为基础, 用数值计算方法分析了球型颗粒的光散射特性，给出了微小颗粒对平行入射光散射的强度函数和散射偏振度的数值计算方法。得到了强度函数和偏振度随相关物理参量变化的三维图，为微小颗粒散射研究提供了一种三维视图。计算结果表明：当尺度参量x＜4时，2种方法所得结果差异不大；随尺度参量增大，2种方法所得结果出现较大差异。与经典Mie理论相比，由于离散偶极子近似理论可以解决各种形状的颗粒散射问题，其应用前景更广泛。     

Rabi-oscillations without rotating-wave approximation

We consider the interaction of an ensemble of two level atoms with linearly polarized light. This problem is solved in terms of the well-known Bloch equations for various amplitudes of the incident light field without rotating-wave approximation (RWA). Closed-form solutions are obtained for small and very high electric field amplitudes. In the latter case severe deviations from the results obtained with RWA are observed.     

Acceleration of the iterative solver in the discrete dipole approximation: Application to the orientation variation of irregularly shaped particles

We have applied a method of reducing the number of iterations required to solve a system of linear equations in the discrete dipole approximation. This method obtains an initial guess of dipole polarization from those with similar particle characteristics (e.g., the size parameter and refractive index) calculated a priori. If the initial guess is closer to the solution, the number of iterations of the linear equation solution becomes smaller than that calculated with an arbitrary initial value.

This method was applied to various particle orientations using spline interpolation of the initial guess of dipole polarization from orientations calculated a priori.

We studied three types of particle model: an aggregate, a deformed sphere with moderate surface roughness, and a particle with a large number of edges. For the particle with a large number of edges, we propose a new model called the overlapping mixture of multiple tetrahedra (OMMT).

The proposed method is most advantageous for particles with moderate surface roughness (e.g., a deformed sphere), for which the calculation time was reduced to 20–40% of the original calculation time. For OMMT and an aggregate, the computation time was reduced to 30–60% and 40–90%, respectively. The differences in the scattering coefficient, absorption coefficient, intensity and polarization introduced by our method were less than 0.008%, 0.03%, 0.1%, and 0.08%, respectively.

If the light scattering properties vary slowly with the orientation variation, interpolation of the results is more efficient than the proposed method and produces only a small difference in the results. However, the interpolation of the results fails for particles such as BCCA64, for which our proposed method produces more accurate results.     

Evaluation of Influence of Multiple Scattering Effect in Light-Scattering-Based Applications

The extinction cross sections of a system containing two particles are calculated by the T-matrix method, and the results are compared with those of two single particles with single-scattering approximation. The necessity of the correction of the refractive indices of water and polystyrene for different incident wavelengths is particularly addressed in the calculation. By this means, the volume fractions allowed for certain accuracy requirements of single-scattering approximation in the light scattering experiment can be evaluated. The volume fractions calculated with corrected refractive indices are compared with those obtained with fixed refractive indices which have been rather commonly used, showing that fixed refractive indices may cause significant error in evaluating multiple scattering effect. The results also give a simple criterion for selecting the incident wavelength and particle size to avoid the ＇blind zone＇ in the turbidity measurement, where the turbidity change is insensitive to aggregation of two particles.     

THE TWO-PHOTON DEGENERATE JAYNES－CUMMINGS MODEL WITH AND WITHOUT ROTATING-WAVE APPROXIMATION

We take into account the two-photon process and generalize the Jaynes－Cummings (JC) model to the case of atomic level degenerate in the projections of the angular momenta, and we establish two-photon degenerate JC models with and without the rotating-wave approximation (RWA) quantum theory. Comparing the atom population inversion of the generalized JC model with that of the original JC model, we found that the revival period of the degenerate JC model becomes longer and the maximum amplitude of atomic inversion decreases with RWA. Without RWA, the quantum chaos of the generalized JC model is much weaker than that of the original JC model.     

Exact eigenstates of the two-photon Jaynes-Cummings model with the counter-rotating term

We have investigated the eigenenergy spectrum of the two-photon Jaynes-Cummings (JC) model with and without the rotating-wave approximation (RWA). Our analysis has indicated that the counter-rotating term dramatically changes the nature of the RWA energy spectrum and that the non-RWA spectrum can be approximated by the RWA spectrum only in the range of a sufficiently small coupling constant. Furthermore, unlike the one-photon counterpart, the two-photon JC model without the RWA is well defined only if the coupling parameter is below a certain critical value. As a result, the dynamics of the two-photon JC model without the RWA is significantly different from its RWA counterpart. For instance, the counter-rotating term can dramatically enhance the field squeezing effect. Besides, we would expect that the quantum dynamics of the two-photon JC model without the RWA is qualitatively different from that of the usual one-photon case.     

Ground State of Jaynes-Cummings Model: Comparison of Solutions with and without the Rotating-Wave Approximation

The eigenenergy spectrum of the Jaynes-Cummings （JC） model with and without the rotating-wave approx- imation （RWA） is investigated. The numerical analysis indicates that the non-RWA spectrum can only be approximated by the RWA in the range of sufficiently small coupling constant and detuning. In other region, the counter-rotating terms remarkably change the nature of the RWA energy spectrum. A simple expression with high accuracy for ground eigenenergy and eigenvector non-RWA shows that the ground state is not a dark state state. for non-RWA is available. The ground eigenvector for and very different from that of RWA which is a dark state.     

Geometric curvature and phase of the Rabi model

We study the geometric curvature and phase of the Rabi model. Under the rotating-wave approximation (RWA), we apply the gauge independent Berry curvature over a surface integral to calculate the Berry phase of the eigenstates for both single and two-qubit systems, which is found to be identical with the system of spin-1/2 particle in a magnetic field. We extend the idea to define a vacuum-induced geometric curvature when the system starts from an initial state with pure vacuum bosonic field. The induced geometric phase is related to the average photon number in a period which is possible to measure in the qubit–cavity system. We also calculate the geometric phase beyond the RWA and find an anomalous sudden change, which implies the breakdown of the adiabatic theorem and the Berry phases in an adiabatic cyclic evolution are ill-defined near the anti-crossing point in the spectrum.     

Laser acceleration of light impurity from an ultrathin foil of complex ionic composition

The model of acceleration of light impurity particles from a planar ultrathin foil of complex ionic composition under an ultrashort high-power high-contrast laser pulse is proposed. Both the mode of pure Coulomb acceleration of ions, characteristic of extremely high electron energies, and acceleration under conditions of spatial charge separation controlled by a finite characteristic electron temperature are studied. Accurate and approximate analytical approaches for describing impurity particle acceleration are formulated. Spatial and spectral characteristics of accelerated particles are determined. Particle dynamics is studied in both the approximation of test impurity particles and taking into account their intrinsic electrostatic field, depending on the relative charge density of light particles.     

随机取向烟幕凝聚粒子的消光特性

采用蒙特卡罗方法根据团簇-团簇凝聚(CCA)模型对由球形原始微粒凝聚而成的烟幕凝聚粒子进行模拟,用离散偶极子近似(DDA)方法研究随机取向烟幕凝聚粒子的消光特性.结果表明,凝聚粒子的消光特性受到原始微粒数量以及粒径的影响,粒子的凝聚将减弱烟幕的消光性能;当凝聚结构中原始微粒的数目一定时,存在使烟幕消光性能达到最大的原始微粒粒径.     

光散射聚集速率测定中T矩阵方法的应用

聚集速率是评估胶体体系特性及稳定性的关键参数, 静态光散射和动态光散射则是测量聚集速率的两个重要方法. 然而, 用静态光散射和动态光散射测量聚集速率时, 需要知道有关单粒子和双粒子聚集体光散射特性的数据. 为此, 通常需要把动、静两种方法结合, 才能消去这个数据. 以前各种近似理论曾用来解决这个问题, 但因粒子尺寸和形状的限制, 结果并不理想. 而T矩阵方法可以不受粒子大小和形状的限制计算其光散射特性. 本工作用T矩阵方法直接计算静态光散射和动态光散射所必须的粒子散射特性, 并将该法得到的聚集速率与动静态光散射结合法得到的聚集速率进行了比较, 两者结果很接近. 本工作为简化静态光散射和动态光散射测量聚集速率, 扩展其应用范围开辟了新途径. 关键词： T矩阵')" href="#">T矩阵 光散射法 聚集速率     

Numerical simulation of multiple light scattering in layers consisting of opaque particles with a dull surface (geometrical optics approximation)

A numerical model is presented which allows one, in the geometrical optics approximation, to calculate scattering contributions of specified multiplicity in layers comprised of opaque particles with dull surfaces. For definiteness, the particles are assumed to be spherical with the Lambertian law of light scattering by the particle surface. The greatest scattering multiplicity is restricted, in this model, only by computer capacity. In this paper, the scattering multiplicities up to the sixth order inclusively are studied. Layers of moderate optical thickness, as well as the case of a semi-infinite medium with different particle packing densities, are analyzed for different geometries of illumination and observation. It is shown that for conservative scattering by the particle surface, the contribution of higher-order scattering decreases with increasing order number, which is related to the shadow-hiding effect. The scattering indicatrices of higher orders approach the isotropic case. The even and odd scattering orders show a systematic difference between themselves.     

光全散射法测量微粒尺寸分布的研究

本文从光全散射法的基本原理出发,提出了测量微粒尺寸分布的独立道模式光全散射测量法和非独立模式光全散射测量法,解决了以往光全散射法只能测量微粒的平均直径,不能给出尺寸分布,并且测量范围小,测量结果有多值性的缺陷,独立模式光全散射测量法还能用于测量多峰分布微粒的尺寸分布,数值计算和实验研究表明用本文方法,测量结果准确,可靠。     

Emission spectrum of a qubit in Rabi model in strong coupling regime

The analytical eigenenergies and eigenstates of the Rabi model are obtained approximately based on a unitary transformation and a generalized rotating-wave approximation (GRWA). Using these analytical expressions without the rotating wave approximation (RWA), we generalize the definition of the physical emission spectrum valid with the RWA in order to meet without the RWA with some modifications. Taking into account the counter-rotating wave terms and the intercrossing of energy level in the strong coupling regime, the physical emission spectrum of qubit is investigated. Different from the case with RWA, the multi-peak vacuum Rabi splitting, even when the qubit initially in its ground state and the bosonic field initially in vacuum, can emerge. These new features of physical emission spectrum originate from the effect of counter-rotating wave terms. Moreover, the intercrossing of energy level can also be observed in the strong coupling regime.     

Light scattering by particles of toroidal shape in the Rayleigh-Gans-Debye approximation

Expressions for the calculation of the amplitude and indicatrix of light scattering by optically soft toroidal and tubular particles are obtained in the Rayleigh-Gans-Debye (RGD) approximation. Light scattering cross sections of toroidal particles in the RGD approximation and cross sections obtained by the method of discrete dipoles are numerically compared.     

Geometrical optics approximation for light scattering by absorbing spherical particles

By means of geometrical optics, an approximation method is presented to compute the light scattering intensity of absorbing spherical particles illuminated by a plane wave. For absorbing particles, the effective refractive index and the effective refractive angle are related to the complex refractive index and incident angle. The formulas for calculation of the break of phases of reflection and refraction, which are different from the case of transparent particles, are exactly derived. Verification of the geometrical optics approximation (GOA) was performed by case studies and comparison of the present results with the Mie scattering. It is found that agreement between the GOA and the Mie theory is excellent in forward directions for weakly/moderately absorbing particles. Differently, for strongly absorbing particles, good agreement between the calculation methods is in the forward directions and large scattering angles. The agreement between the GOA and the Mie theory is better for larger particles.     

Light attenuation by disperse layers with a high concentration of oriented anisotropic spherical particles

An analysis is made of the applicability of Beer’s law to the calculation of coefficients of directed (coherent) transmittance of light-scattering media formed by oriented anisotropic spherical liquid-crystal droplets. It is shown on the basis of comparison with experimental data that the application of Beer’s law to a layer with a high concentration of anisotropic particles leads to large errors in the calculation of transmittance. The interference approximation, taking into account the interference of waves scattered by separate particles, leads to better agreement with the experiment than Beer’s law, which assumes a linear relation between the attenuation factor of a disperse medium and the particle concentration.     

Dipole squeezing in the multi-photon Jaynes-Cummings model with and without the rotating-wave approximation

By virtue of the numerical method of Graham and Höhnerbach [12], we have investigated the quantum fluctuations of the atomic dipole variables in the multiphoton Jaynes-Cummings model with and without the rotating wave approximation (RWA) when it is restricted to the following initial condition: the atom in its superposition state and the field in the vacuum state. We found that even under the conditions in which the RWA is considered to be valid there are significant effects of virtual-photon field on dipole squeezing predicted in the RWA, and dipole squeezing turns to disappear for sufficiently strong coupling.