Lorenz-Mie Theory for Spheres Immersed in an absorbing host medium

Light scattering by particles is often used to determine velocities or concentrations of particles in gaseous or liquid streams. Within the Lorenz-Mie theory, light scattering is well understood both for a single compact spherical particle and a single multilayered particle in a non-absorbing surrounding medium. However, in some cases of practical importance the Lorenz-Mie theory in its present form may fail to describe the scattering because the host medium is absorbing (e.g. water droplets in oil). In this case, a new treatment of the scattering theory is required. In previous work, solutions were obtained in the far-field of the scattering sphere. In this paper, a rigorous solution is derived from the calculation of the total absorption rate of the particle in the host medium, which is valid for all distances from the surface of the encapsulated particle. It is shown that it is necessary to consider finite sizes R of the integrating sphere when dealing with absorbing host media. Cross-sections are defined which are characteristic quantities not only for the particle, depending on the size of a conceptual sphere around the scatterer and the imaginary part of the refractive index of the host medium. The results obtained are discussed for the case of non-absorbing host media and in the far-field approximation. Some numerical examples are given which are also related to experimental results.     

吸收性海水中气泡光散射特性的理论研究

 给出了一种适合于吸收性介质内粒子散射的Mie级数新的表示形式。利用Mie理论研究了吸收性海水中气泡的单散射特性和气泡群的相位函数。与非吸收性海水中气泡的光散射特性相比，分析了海水折射率虚部对气泡光散射的影响。结果表明：180°后向散射的增强是气泡固有的光学性质，与所处介质无关，可以利用后向散射的增强来探测气泡。     

Aggregation and composition effects on absorption and scattering properties of dye-sensitized anatase TiO2 particle clusters

A transition matrix approach is used to compute the scattering and absorption cross sections, as well as phase functions, asymmetry factors and forward scattering ratios, of clusters of spherical particles. In order to approach the local structure and composition of the nanosized active layer of photoelectrochemical solar cells, some clusters consist of homogeneous non-absorbing anatase spherical pigments, others have anatase particles coated with a monolayer of absorbing dye molecules, and others can consist of both uncoated and dye-coated anatase particles. Orientation average values of the volumetric scattering and absorption cross sections are computed in terms of the size of the spherical particles in the clusters and their number. The degree of scattering and absorption when considering dye-coated anatase particles in the clusters is characterized. The effect of dependent scattering on the average angular distribution of the scattered radiation is also considered.     

Radiative properties of densely packed spheres in semitransparent media: A new geometric optics approach

This contribution presents a new Ray-tracing method for calculating effective radiative properties of densely packed spheres in non-absorbing or semitransparent host medium. The method is restricted to the geometric optic objects and neglects the wave effects. The effective radiative properties such as the absorption and scattering coefficients, and phase function are retrieved from the calculation of mean-free paths of scattering and absorption, and the angular scattering probability of radiation propagating in the dispersed medium. The model accounts for the two geometric effects called here as non-point scattering and ray transportation effects. The successful comparison of the current model with data of radiative properties and transmittances of particle beds in a non-absorbing medium reported in the literature confirm its suitability. It is shown that: (i) for opaque or absorbing particles (not systematically opaque), the non-point scattering is the dominant geometric effects whereas both non-point scattering and ray transportation effects occur for weakly absorbing and transparent particles. In the later cases, these two geometric effects oppose and may cancel out. This may explain why the Independent scattering theory works well for packed of quasi-transparent particles; (ii) the non-point scattering and ray transportation effects can be captured through the scattering and absorption coefficients while using the classical form of phase function. This enables using the standard radiative transfer equation (RTE); (iii) the surrounding medium absorption can be accounted for without any homogenization rule. It contributes to increasing the effective absorption coefficient of the composite medium as expected but, at the same time, it reduces the particle extinction; and (iv) the current transfer calculation predicts remarkably the results of direct Monte Carlo (MC) simulation. This study tends therefore to confirm that the RTE can be applied to densely packed media by using effective radiative properties.     

A Review of Elastic Light Scattering Theories

Mie scattering is an important tool for diagnosing microparticles or aerosol particles in technical or natural environments. Mie theory is restricted to spherical, homogeneous, isotropic and non-magnetic particles in a non-absorbing medium. However, as microparticles are hardly ever spherical or homogeneous, there is much interest in more advanced scattering theories. During recent decades, scattering methods for non-spherical and non-homogeneous particles have been developed and even some computer codes are readily available. Extension of Mie theory covers coated spheres, stratified spheres and clustered spheres. For homogeneous non-spherical particles such as spheroids, ellipsoids and finite cylinders, surface discretization methods have been developed. Scattering by inhomogeneous particles may be computed by volume discretization methods.     

Composites of resonant dielectric rods: A test of their behavior as metamaterial refractive elements

We report numerical experiments of optical wave propagation in composites of high refractive index dielectric rods at frequencies where their first electric and magnetic Mie resonances are excited. The arrays of these particles have been extensively studied and proposed as non-absorbing and isotropic metamaterials. We show that negative refraction, observed in such ordered particle arrays, is due to diffraction and that an effective medium theory (EMT) yields constitutive parameters that do not reproduce the observations in these composites, whose transmission also depends on the sample shape. This is further confirmed by disordering the arrays, a case in which large transmission losses appear due to extinction by resonant scattering from the particles. Therefore, these composites, although having little absorption, give rise to large extinction due to scattering and do not constitute an improvement, as low loss refractive elements, upon all previously designed highly absorbing metamaterials.     

Optical and optoacoustic measurements of the absorption properties of spherical gold nanoparticles within a highly scattering medium

In the present paper the requirements for optical parameter characterization of absorbing materials located within a highly scattering medium has been addressed. The measurement scheme incorporates the optoacoustic technique where a single acoustic transducer is used to detect ultrasonic transients generated from laser irradiation. The absorbing medium is based on different concentrations of spherical gold nanoparticles (SGNP’s), these are currently being considered as non-toxic targeted optical contrast agents for both medical imaging and cancer therapeutics. In this paper we present results which demonstrate the two main advantages the optoacoustic technique has over other measurement schemes. These are the possibility to obtain information on the position and dimensions of absorbing bodies using a time of flight analysis (TOF) and secondly, the higher sensitivity of the optoacoustics compared to optical transmission techniques. The former advantage is of particular interest for imaging applications and the latter for detection and characterization of absorbing materials surrounded by high levels of high scattering mediums. We present for the first time the characterization of SGNP within a highly scattering medium. To further demonstrate the feasibility of the optoacoustic technique, the scattering coefficient of the surrounding medium has also been characterized.     

Resonance scattering of canonical elastic shells in absorbing fluid medium

Resonance scattering of elastic spherical shell and cylindrical shell while the surrounding fluid medium has absorption is studied. The normal mode solution derived using exact elastic theory and the separation of variables is still applicable. However, the scattering form function has to be modified for the absorbing medium, otherwise the unreasonable result would be obtained. The backscattering form function in the absorbing medium is redefined, and the form function of elastic spherical and cylindrical shell with vacuum or solid matter filled is calculated in various absorption conditions. The results show that the absorption of surrounding fluid leads to notable attenuation of the coincidence resonances in the mid-frequency, but it has a little influence on the low-frequency resonance scattering induced by the filler inside the shell.     

Radiative properties of scattering and absorbing dense media: theory and experimental study

We investigate the validity of the radiative transfer equation to model transmission of light through an absorbing and scattering medium. Assuming that radiative transfer equation is valid, the inverse scattering problem for non-polarized radiative transfer in one-dimensional absorbing and scattering media is solved using a parameter identification method. We discuss how to identify the albedo, phase function and extinction coefficient of the medium. We present experimental data that confirm that this approach is robust and can be used to make reliable predictions of the behavior of scattering absorbing systems.     

吸收媒质反射束Goos-Hnchen位移的直接计算公式

本文导出了从吸收媒质上反射的s和p两种偏振的Goos-Hnchen位移的一般表达式。若令消光系数等于零,它们就简化成McGuilk和Carniglia给出的仅用于非吸收媒质的公式。吸收媒质的位移,在任何不为零的入射角度时都有。在镓的表面上,位移有几个波长。     

Apparent optical properties of spherical particles in absorbing medium

An apparent absorption efficiency for spherical particles in absorbing medium is introduced to take into account the non-exponential absorption of the near-field scattered radiation in the absorbing medium. The apparent extinction, which is the summation of the apparent scattering efficiency following previous studies and the apparent absorption efficiency, is the same as the actual extinction. These apparent optical properties are suited to radiative transfer equations.     

Scattering of electromagnetic waves by ensembles of particles and discrete random media

Current problems of the theory of multiple scattering of electromagnetic waves by discrete random media are reviewed, with an emphasis on densely packed media. All equations presented are based on the rigorous theory of electromagnetic scattering by an arbitrary system of non-spherical particles. The main relations are derived in the circular-polarization basis. By applying methods of statistical electromagnetics to a discrete random medium in the form of a plane-parallel layer, we transform these relations into equations describing the average (coherent) field and equations for the sums of ladder and cyclical diagrams in the framework of the quasi-crystalline approximation. The equation for the average field yields analytical expressions for the generalized Lorentz-Lorenz law and the generalized Ewald-Oseen extinction theorem, which are traditionally used for the calculation of the effective refractive index. By assuming that the particles are in the far-field zones of each other, we transform all equations asymptotically into the well-known equations for sparse media. Specifically, the equation for the sum of the ladder diagrams is reduced to the classical vector radiative transfer equation. We present a simple approximate solution of the equation describing the weak localization (WL) effect (i.e., the sum of cyclical diagrams) and validate it by using experimental and numerically exact theoretical data. Examples of the characteristics of WL as functions of the physical properties of a particulate medium are given. The applicability of the interference concept of WL to densely packed media is discussed using results of numerically exact computer solutions of the macroscopic Maxwell equations for large ensembles of spherical particles. These results show that theoretical predictions for spare media composed of non-absorbing or weakly absorbing particles are reasonably accurate if the particle packing density is less than ∼30%. However, a further increase of the packing density and/or absorption may cause optical effects not predicted by the low-density theory and caused by near-field effects. The origin of the near-filed effects is discussed in detail.     

Light scattering from mesoscopic objects in diffusive media

No direct imaging is possible in turbid media, where light propagates diffusively over length scales larger than the mean free path .The diffuse intensity is, however, sensitive to the presence of any kind of object embedded in the medium, e.g. obstacles or defects. The long-ranged effects of isolated objects in an otherwise homogeneous, non-absorbing medium can be described by a stationary diffusion equation. In analogy with electrostatics, the influence of a single embedded object on the intensity field is parametrized in terms of a multipole expansion. An absorbing object is chiefly characterized by a negative charge, while the leading effect of a non-absorbing object is due to its dipole moment. The associated intrinsic characteristics of the object are its capacitance Q or its effective radius ,and its polarizability P. These quantities can be evaluated within the diffusion approximation for large enough objects. The situation of mesoscopic objects, with a size comparable to the mean free path, requires a more careful treatment, for which the appropriate framework is provided by radiative transfer theory. This formalism is worked out in detail, in the case of spherical and cylindrical objects of radius R, of the following kinds: (i) totally absorbing (black), (ii) transparent, (iii) totally reflecting. The capacitance, effective radius, and polarizability of these objects differ from the predictions of the diffusion approximation by a size factor, which only depends on the ratio .The analytic form of the size factors is derived for small and large objects, while accurate numerical results are obtained for objects of intermediate size .For cases (i) and (ii) the size factor is smaller than one and monotonically increasing with ,while for case (iii) it is larger than one and decreasing with . Received: 7 August 1998 / Accepted: 3 September 1998     

Transient,combined conduction and radiation in an absorbing,emitting, and isotropically scattering solid sphere

Transient, combined conduction and radiation is solved in an absorbing, emitting, and isotropically scattering solid sphere with a black boundary initially at a uniform temperature and for times t > 0 subjected to a constant temperature at the spherical surface. The collocation method is used to solve the radiation part of this problem and the implicit finite difference scheme is used to solve the conduction part. The effects of the conduction-to-radiation parameter, the single scattering albedo, the optical thickness of the medium on the temperature distribution and the heat flux in the medium are examined.     

Photoacoustic cavitation in spherical and cylindrical absorbers

Photomechanical damage in absorbing regions or particles surrounded by a non-absorbing medium is investigated experimentally and theoretically. The damage mechanism is based on the generation of thermoelastic pressure by absorption of pulsed laser radiation under conditions of stress confinement. Principles of photoacoustic sound generation predict that the acoustic wave generated in a finite-size absorbing region must contain both compressive and tensile stresses. Time-resolved imaging experiments were performed to examine whether the tensile stress causes cavitation in absorbers of spherical or cylindrical shape. The samples were absorbing water droplets and gelatin cylinders suspended in oil. They were irradiated with 6-ns-long pulses from an optical parametric oscillator. Photoacoustic cavitation was observed near the center of the absorbers, even if the estimated temperature caused by absorption of the laser pulse did not exceed the boiling point. The experimental findings are supported by theoretical simulations that reveal strong tensile stress in the interior of the absorbers, near the center of symmetry. Tensile stress amplitudes depend on the shape of the absorber, the laser pulse duration, and the ratio of absorber size to optical absorption length. The photoacoustic damage mechanism has implications for the interaction of ns and sub-nslaser pulses with pigmented structures in biological tissue. Received: 9 October 1998 / Accepted: 5 January 1999 / Published online: 31 March 1999     

Light-induced orientation of the molecules of nematic liquid crystals doped with comb-shaped polymers with different spatial distributions of chromophores

The orienting effect of light on nematic liquid crystals (NLCs) doped with comb-shaped polymers with different spatial distributions of side absorbing azobenzene fragments, i.e., a homopolymer (containing only azofragments), a block copolymer (containing additionally a block of non-absorbing fragments), and a statistical copolymer (containing randomly arranged absorbing and non-absorbing fragments) is experimentally studied. The light-induced Freedericksz transition threshold for the block copolymer is two times lower than that for the homopolymer. For NLC with statistical copolymer dopant, the first-order orientation transition with an extremely wide optical bistability region is observed.     

Calculation of the scattering amplitude from discrete eigenvalues

We show that the scattering amplitude for a target with spherical symmetry can be directly calculated from the discrete eigenvalues of the corresponding stationary wave equation solved under an absorbing boundary condition, and thus uncover a direct connection between the scattering amplitude and the wave number spectrum. As an illustration, we apply this approach to the scattering of an electromagnetic wave by an array of dielectric slabs and find the transmission coefficient of the array to be completely determined by the spacing between adjacent eigenvalues.     

Comparison of radiative transfer approximations for a highly forward scattering planar medium

We examine critically the accuracy of the two-flux, spherical harmonics and discrete ordinates methods for predicting radiative transfer in a planar, highly-forward scattering and absorbing medium. Numerical results for the radiative fluxes show that the two-flux and P₃-approximations yield accurate results compared to solutions based on the F_N-method. Indeed, these approximate methods are relatively simple and have potential for generalization to predict radiative transfer in multidimensional systems, as long as an appropriate simplification of the phase function is utilized.     

Some calculations of temperature profiles in thin films with laser heating

We present some calculations of heat flow in an absorbing film deposited on a non-absorbing substrate. The energy source is a Gaussian laser beam. We analyse the effects of film thickness, thermal conductivity, spot radius and forced cooling on the temperature profile and, in a special case, the time evolution of that profile. The emphasis is on applications in optical bistability.     

Radiation transport and internal reflection in a two region, turbid sphere

We construct an integral equation for the flux intensity in a scattering and absorbing two-region turbid spherical medium using the integro-differential form of the radiative transfer equation. The sphere is uniformly irradiated by an external source of arbitrary angular distribution and contains a distributed volume source. Anisotropic scattering is accounted for by the transport approximation. The Fresnel boundary conditions, which incorporate reflection and refraction, are used at the outer surface and at the interface between the two regions. In this respect, some new interfacial boundary conditions are introduced. For the special case of a non-scattering medium, we obtain exact solutions for specular reflection. Some numerical examples are given which show qualitative agreement with some recent work of other authors. Of particular interest are the emergent angular distribution and the albedo of the surface as a function of the refractive index and the radii of the two regions. We also draw attention to the fact that the boundary conditions at the interface differ according to the relative values of the refractive indices in the two regions. The interfacial boundary conditions for use in diffusion theory are derived and compared with those of Aronson [Boundary conditions for diffusion of light. J opt Soc Am 1995;12:2532]. In appendix B, we show how diffusion theory may be used to include scattering into the problem in a simple way.