The Lorenz Number and the Lorenz Gauge—Known Concepts,Unknown Physicist

Ludvig Lorenz was Denmark's first theoretical physicist of international recognition. Despite his important contributions to a broad range of experimental and theoretical physics, he generally appears as a somewhat peripheral figure in histories of late‐nineteenth‐century physics and is completely overshadowed by his near‐namesake H. A. Lorentz. Herein, a selected number of Lorenz's works is introduced with an eye on those which are still of relevance to modern physics and today eponymously associated with his name. These contributions are known as the Lorenz number, the Lorenz gauge, the Lorenz–Lorentz law or formula, and the Lorenz–Mie scattering theory.     

Debye Series Formulation for Generalized Lorenz‐Mie Theory with the Bromwich Method

The formulation of the Debye series ready for implementation in generalized Lorenz‐Mie theory (theory of interaction between an arbitrary shaped beam and a homogeneous sphere) is presented in the framework of the Bromwich method.     

Particle Sizing in a Flow Environment Using Light Scattering Patterns

This study introduces measurements of light scattering intensities individually produced from polystyrene micro‐spheres illuminated by focused Gaussian beams in a flow environment. These light scattering signatures are correlated to the particle size. The Fourier domain information of the light scattering signatures are interpreted and translated to recover the dimension of each particle. A hardware‐software interface is designed to capture, analyze and interpret the collection of various scattering light intensities. A major contribution of this study is in consolidating the implementation of the Lorenz‐Mie theory with the experimental results of collected light scatterings for the purpose of particle sizing through novel pattern analysis techniques. In so doing, a synergetic approach is considered in bringing together the hardware design with the software implementations for an integrated hardware‐software interface.     

Numerical analysis on the optical force calculation in the Rayleigh scattering regime

Optical Review - The radiation force calculated in the Rayleigh regime is investigated by comparison with the generalized Lorenz Mie Theory (GLMT). The basic concepts behind the Rayleigh regime and...     

On the structures of some light scattering theories depending on whether or not the Bromwich formulation may be used,e.g. spherical versus spheroidal coordinates

The generalized Lorenz–Mie theories for a homogeneous sphere (interaction between an electromagnetic arbitrary shaped beam and a sphere defined by its diameter and its complex refractive index), and for other particles as well (such as cylindrical particles, with circular or elliptical cross-sections) have been developed by using the Bromwich method. Conversely, this method cannot be used for spheroidal particles. Whether it is possible or not to use the Bromwich method implies a certain number of consequences concerning (i) the definition of TM- and TE-waves, (ii) the definition of genuine beam shape coefficients to describe the beam, (iii) the possibility of developing a localized beam model to describe the illuminating beam. These three issues may be enlightened by referring to the properties of the Bromwich method.     

Scattering of Gaussian beam by a spheroidal particle with a spherical inclusion at the center

An analytic solution to electromagnetic scattering by a spheroidal particle having a spherical inclusion at the center, for oblique incidence of a Gaussian beam, is obtained within the framework of the generalized Lorenz–Mie theory (GLMT). By virtue of a transformation between the spheroidal and spherical vector wave functions, a theoretical procedure is developed to deal with the boundary conditions. Numerical results of the normalized differential scattering cross section are evaluated.     

Whispering gallery modes and effect of coating on Raman spectra of single microspheres

Raman spectra and fluorescence of BaTiO₃ and silica microspheres of different sizes have been studied. The observed whispering gallery modes (WGMs) have been assigned using theoretical simulations based on the Lorenz–Mie theory. The WGMs are found to have selective enhancements in the Raman spectra. The variations in the Raman spectra with the radial position of the excitation spot and excitation wavelength have been correlated with the morphology‐dependent internal field distributions of the microspheres. The effect of a thin dye coating on the fluorescence and Raman spectra was studied, and a coating thickness of ∼200 nm was estimated from the theoretical simulation of experimentally observed data based on the Aden and Kerker theory. Copyright © 2011 John Wiley & Sons, Ltd.     

Absorption coefficient measurements of particle-laden filters using laser heating: Validation with nigrosin

A laser-heating technique, referred as the laser-driven thermal reactor, was used in conjunction with laser transmissivity measurements to determine the absorption coefficient of particle-laden substrates (e.g., quartz-fiber filters). The novelty of this approach is that it analyzes a wide variety of specific samples (not just filtered samples) and overcomes measurement issues (e.g., absorption enhancement) associated with other filter-based particle absorption techniques. The absorption coefficient was determined for nigrosin-laden, quartz-fiber filters and the effect of the filter on the absorption measurements was estimated when compared to the isolated nigrosin results. The isolated nigrosin absorption coefficient compared favorably with Lorenz–Mie calculations for an idealized polydispersion of spherical particles (based on a measured nigronsin/de-ionized water suspension size distribution) dispersed throughout a volume equivalent to that of the nigrosin-laden filter. To validate the approach, the absorption coefficient of a nigrosin/de-ionized water suspension was in good agreement with results obtained from an ultraviolet/visible spectrometer. In addition, the estimated imaginary part of the refractive index from the Lorenz–Mie calculations compared well with literature values and was used to estimate the absorption coefficient of optically opaque packed nigrosin.     

相对折射率趋近于1的颗粒Mie散射与反常衍射的分析比较

利用Ｍｉｅ散射与反常衍射理论的数值计算，对球形颗粒Ｍｉｅ散射和反常衍射作了大量详细的计算和分析比较，提出了相对折射率趋近于１的颗粒的反常衍射近似替代Ｍｉｅ散射的判据。     

Interferometric Sizing of Single‐Axis Birefringent Glass Fibers

This paper deals with the on‐line sizing of small diameter glass fibers (i.e. d<30 μm) produced for textiles and reinforcement applications. Two models based on the Lorenz‐Mie Theory are introduced to predict the basic light scattering properties and the response of a phase Doppler interferometer (PDI) to the sizing of infinite glass fibers. Among other parameters, these models take into account particular effects such as the fiber's single‐axis birefringence and the fiber's refractive index dependence on its cooling rate (i.e. diameter). Both effects have a weak influence on the mean response of the PDI but a strong influence on the resonance structures of its phase‐diameter relationship. Two optical set‐ups were selected from a numerical optimization procedure and tested experimentally. Experimental results are presented demonstrating the validity of the models and the ability of the developed PDI set‐ups to study some features of the fiber drawing‐process: fluctuations of the fiber diameter when the nozzle is submitted to a convective perturbation and, when the fiber take‐up velocity is modulated, the detection of hollow fibers.     

Scattering by a spheroidal particle illuminated with a couple of on-axis Gaussian beams

An on-axis Gaussian beam for any angle of incidence is expanded in terms of the spheroidal vector wave functions. With such an expansion, the problem of interaction between a couple of on-axis Gaussian beams and a spheroidal particle is studied in the framework of the generalized Lorenz–Mie theory (GLMT). The scattering characteristics are described in detail, and numerical results of the normalized differential scattering cross section are presented.     

Gaussian beam scattering by a chiral sphere

Based on the generalized Lorenz–Mie theory that provides the general framework, an analytic solution to Gaussian beam scattering by a chiral sphere is constructed, by expanding the incident Gaussian beam, scattered fields and internal fields in terms of spherical vector wave functions. The unknown expansion coefficients are determined by a system of equations derived from the boundary conditions. For a localized beam model, numerical results of the normalized differential scattering cross section are presented.     

On-axis Gaussian beam scattering by an eccentrically coated conducting cylinder

Based on the generalized Lorenz–Mie theory (GLMT) framework, an exact analytic solution to electromagnetic scattering by an eccentrically coated conducting cylinder is constructed, for oblique incidence of an on-axis Gaussian beam described by a localized beam model. The solution is found by the classical separation of variables technique and the translational addition theorem. For a tightly focused Gaussian beam propagating perpendicularly to the cylinder axis, numerical results of the normalized differential scattering cross section are presented, and the scattering characteristics are discussed concisely.     

Generalized Lorenz‐Mie Theory for a Sphere with an Eccentrically Located Inclusion,and Optical Chaos

This paper deals with the case when a homogeneous spherical particle (called the inclusion) is embedded at an arbitrary location inside a sphere (called the main or host sphere). Similarly as for previous Generalized Lorenz‐Mie Theories, many applications are expected from this theory, in particular in the field of optical particle characterization. Another interesting prospect concerns the behavior of morphology‐dependent resonances (MDRs). From an electromagnetic point of view, these MDRs correspond to solutions of characteristic equations associated with boundary conditions and lead to internal fields which are concentrated near the rim of the scatterer. It is also shown that this geometrical optics approximation (expressed in terms of rays) is equivalent to a mechanical problem (expressed in terms of trajectories). This mechanical problem leads to chaotic behavior corresponding to optical chaos phenomena in the optical language. We therefore exhibit a class of particles (i) for which the electromagnetic problem is exactly solvable in the framework of a GLMT and (ii) which exhibits chaotic signatures. It is expected that these chaotic signatures would be revealed in salient features of the scattering diagrams, opening the way to refined optical particle characterization in the presence of inhomogeneities.     

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.     

Refractive index of liquids at high pressures

In this age of laser technology, the importance of studies on piezo– and elasto‐optic properties of liquids cannot be over-emphasized. In many applications such as acousto‐optic modulators, acoustic probes, high speed optical scanners and deflectors, etc., in the field of communications, a precise knowledge of the elasto‐optic coefficient of the liquids would be of immense help in the proper choice of the suitable acousto‐opticmaterials, as well as in the various design considerations. Besides being of immediate use in the various applications mentioned above, precise determinations of the piezo‐optic and elasto‐optic coefficients for liquids have a special importance in relation to the theory of optics. It is well known that the Lorentz‐Lorenz refraction formula does not accurately give the refractive index of a liquid in terms of the index for the vapor; the deviations from the formula are even more striking when we consider the changes in the refractive index of a liquid produced by changes of temperature or pressure. The explanation of these failures is a matter of considerable interest, and various attempts have been made to formulate theories giving better results. It is obvious that reliable experimental data regarding variations of refractive index under precisely defined physical conditions would be of value in testing such theories, and especially in determining the extent to which the refractivity of a dense fluid is a function of temperature independently of any changes in volume. Furthermore, it appears that these measurements can also be used to critically evaluate the various equations of state for liquids.     

瞬态积分浓度场的测量研究

根据污染扩散烟雾粒子的成像理论、粒子光散射原理和数字图像技术,建立了烟雾粒子非定常瞬态积分浓度与 其散射图像强度之间的数学关系,通过烟雾粒子散射图像强度的数字化分析和处理来定量测量非定常瞬态污染扩散相对 瞬态积分浓度场。并利用该方法对烟雾扩散的非定常瞬态积分浓度场进行了实际测量。     

Size Measurement of Very Small Spherical Particles by Mie Scattering Imaging (MSI)

The Mie Scattering Imaging method (MSI) gathers out‐of‐focus images of dispersed spherical particles present in a laser light sheet and extracts the individual particle diameter from these images. The general idea of the method has been around for more than a decade and a number of papers has dealt with it over recent years. Our work focuses on small particle sizes from 20 μm down to 2 μm, a range which has not been tackled so far although it is of great importance in particle systems. We present an optical set‐up with a special arrangement of camera lenses that allows to work in this range. An evaluation algorithm based on correlation of the experimental optical information with theoretical Mie scattering was found to give the most accurate results for particle sizing. Besides accuracy measurements on solid spheres the versatility of the method is demonstrated by an example of transient droplet growth between 2–7 μm.     

Non-monotonic thermoelectric behavior of lead telluride in quantum‐well‐like structures

Transport coefficients of quantum‐well‐like structures may in special circumstances show several interesting features. We have obtained theoretical expressions for transport coefficients including Lorenz factor and Seebeck coefficient in well-like structures taking into account the contributions from various sub-bands. Calculations based on the model have been presented for lead telluride quantum wells of varying well width (a). The results indicate a significant deviation in the transport behaviour as compared to the bulk particularly for a<100 nm. Unlike in the bulk material changes in Lorenz factors are rather less pronounced and at a=10 nm it is virtually a constant at 2.0. The Seebeck coefficient on the other hand shows a sharp rise below 100 nm. This region may be of particular interest in thermoelectric device applications. The results show an unusual behaviour of the Lorenz factor and Seebeck coefficient below a 100 nm well width. Moreover, contributions from quantized sub‐bands occupied up to the Fermi level may under certain conditions lead to a non-monotonic behavior which is also reported in some recent experimental measurements on particular PbTe quantum well structures.