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Lorenz-Mie resonances produced by small spheres are analyzed as a function of their size and optical properties (epsi > or < 0, mu > or < 0). New generalized (mu not equal to 1) approximate and compact expressions of the first four Lorenz-Mie coefficients (a1, b1, a2, and b2) are calculated. With these expressions and for small particles with various values of epsi and mu, the extinction cross section (Q(ext)) is calculated and analyzed, in particular for resonant conditions. The dependence on particle size of the extinction resonance, together with the resonance shape (FWHM), is also analyzed. In addition to the former analysis, a study of the scattering diagrams for some interesting values of epsi and mu is also presented.
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We numerically calculate the light scattering intensity fluctuations and the cross-polarization intensity fluctuations of optically soft spherical particles containing an eccentrically located spherical particle. In all cases the magnitude of the signals tends to increase with particle asymmetry. Such a system approximates a biological cell in solution.
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Illumination intensities that are used to induce scattering and fluorescence in aerosols can be large enough to cause variations in the refractive index. Methods used to calculate the scattering from homogeneous particles may not be valid for these systems. We use the finite-difference time-domain method and an iterative technique to model scattering by microspheres that contain a saturable absorber. We illustrate this technique by calculating the scattering from spheres that contain tryptophan. We show the Mueller scattering matrices along with the internal intensity distributions for different incident intensities. The backscattering increases as the illumination intensity becomes large enough to saturate the absorption in regions of the sphere.
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The scattering of light from spherically shaped particles has been well characterized: it has been derived analytically, modeled computationally and measured experimentally. However, many natural and man-made particle systems are not spherical and these have formed the basis of many recent investigative programs. Modeling the light scattered by non-spherical particle systems using numerical algorithms often is limited by the computational power required to attain a mathematical solution, although increasing capacity and enhanced algorithm sophistication continually extend our capabilities. Experimental measurements can require expensive apparatus and can seldom simultaneously and accurately record all the scattering characteristics. Therefore, computational and experimental approaches often complement one another and enhance our knowledge of the light scattering and the particle systems. Theoreticians and modelers often seek experimental data for verification and to find regions of applicability of their models, and experimentalists may use theoretical results for calibration and performing inversions. Research collaborations between the camps inevitably develop.
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We present modeling results in video format showing the changes that occur in the light scattered by a spherical oleic-acid host droplet containing a spherical water inclusion as the inclusion parameters vary. When the system symmetry is broken, a second set of diffraction rings appears on the side opposite the inclusion. The inclusion also acts as a second coherent source, contributing to an interference structure in the scattering pattern, the spatial frequency of which varies with the position of the inclusion.
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We provide experimental results from the scattering of light by deformed liquid droplets and droplets with inclusions. The characterization of droplet deformation could lead to improved measurement of droplet size as measured by commercial aerodynamic particle-sizing instruments. The characterization of droplets with inclusions can be of importance in some industrial, occupational, and military aerosol monitoring situations. The nozzle assembly from a TSI Aerodynamic Particle Sizer was used to provide the accelerating flow conditions in which experimental data were recorded. A helium-neon laser was employed to generate the light-scattering data, and an externally triggered, pulsed copper vapor laser provided illumination for a droplet imaging system arranged orthogonal to the He-Ne scattering axis. The observed droplet deformation correlates well over a limited acceleration range with theoretical predictions derived from an analytical solution of the Navier-Stokes equation.
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We provide theoretical results from the scattering of light by deformed liquid droplets and droplets with inclusions. With improved instrumentation and computer technologies available, researchers are able to employ two-dimensional angular optical scattering as a tool for analyzing such particle systems and which then could be applied in industrial, occupational, and military aerosol measurement. We present numerically calculated spatial light-scattering data from various droplet morphologies. We describe characteristic features of the theoretical data and compare these with the experimental results.
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Two-dimensional angular optical scattering (TAOS) patterns from clusters of polystyrene latex spheres are measured in the near-forward and near-backward directions. In both cases, the scattering pattern contains a rich and complicated structure that is the result of the interaction and interference of light among the primary particles. Calculations are made for aggregates that are similar to those generated experimentally and also demonstrate the rich structure in the scattering pattern. A comparison of the experimental and theoretical TAOS patterns gives good qualitative agreement.
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We have developed an experimental method based on the visibility factor of light-scattering minima to obtain size-polydispersity information from contaminants upon a flat substrate. We verify the method by using double-interaction-model calculations and use this technique to examine experimentally the radial variation of a micrometer-sized fiber and the size polydispersity of spherical particles upon a substrate.
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We derive and examine the general expression for the scattering asymmetry parameter g. For aggregate particles, the asymmetry parameter is made up of two terms. One term accounts for interference effects of the electromagnetic fields radiating from the individual subsystems. The other term contains the effects of the interaction of the electromagnetic fields between these subsystems. Enhanced backscatter is one phenomenon resulting from these interactions. Numerical results demonstrate that interference effects play a dominant role when the separation distance between two-sphere aggregates is smaller than half the incident wavelength. As the separation distance becomes large, both interference and interaction effects drop off and the asymmetry parameter approaches that of the individual particle constituents.
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We derive a multipole scattering solution for a system resembling a simple cell. In the model, a spherical cytoplasm is surrounded by a concentric cell membrane. Contained within the cytoplasm is a nonconcentric spherical nucleus. Because of the nature of the (multipole expansion) solution, numerical results can be acquired quite rapidly. We show that the resulting scatter is very sensitive to the system geometry and optical properties. Such a solution may also be used to calculate the scatter from fluorescing molecules located within the cell. © 1998 Society of Photo-Optical Instrumentation Engineers.
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A prominent characteristic of the light scattered from a microparticle containing inclusions is a fluctuation in the intensity that is due to the changing positions of the inclusions with respect to each other and the host droplet. We calculate the magnitude of these fluctuations for a host sphere containing a single eccentrically located spherical inclusion and experimentally measure the fluctuation amplitudes for host spheres containing multiple inclusions. We find that, for sufficiently small single inclusions, the amplitude of the scattering fluctuations increases approximately linearly with the area of the inclusion. For multiple inclusions, the fluctuation amplitude increases with concentration with an approximate power-law dependence.
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The scattering phase functions of micrometer-sized glycerol droplets containing spherical latex inclusions undergo random fluctuations with time. We measure scattering intensities in the near-forward and near-backward scattering directions and find them to have strong positive correlations during some time periods and strong negative correlations during other time periods. The characteristic time constants of these correlations are of the order of seconds. We calculate scattering correlations from two types of scattering system. Correlations from a two-sphere system generally are positive, whereas correlations from a sphere containing a single spherical inclusion may be both positive and negative. Calculations of correlations from our experimental data are consistent with diffusion of inclusions within the host droplet, rather than interference effects between the inclusions.
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A quantitative analysis of the fluctuations in the scattering associated with micrometer-size glycerol droplets that contain spherical latex inclusions are performed. Scattering intensities at two angles (the near-forward and the near-backward directions) are measured as functions of time. We analyze these signals using two techniques. We find that calculated autocorrelation time constants associated with these signals are not consistent with current models based on interference of light scattering from latex inclusions that exhibit Stokes-Einstein diffusion. The intensity fluctuations at different scattering angles display extended periods of both positive and negative correlations with characteristic time constants of the order of seconds. The time constants associated with the cross correlations provide information on the physical parameters of the inclusions.
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Effective medium theories are valuable tools that can provide effective refractive indices of composite media whose constituents are much smaller than the wavelength of the illuminating radiation. Extended theories have been developed to remove this limitation on the constituent size. Although these extended theories are not derived without additional limitations, useful regions of applicability do exist. We examine an extended effective-medium approximation and show that its predicted absorption efficiencies obtained agree well with exact theoretical results obtained for a naturally occurring system of interest, water droplets containing carbon inclusions.
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The light-scattering Mueller matrix for an r approximately 2.0 microm radius, rough quartz fiber contains phase information different from that of a perfectly cylindrical fiber of the same optical constants and radius. The rough surface creates higher-frequency, smaller-amplitude oscillations that mask the lowerfrequency oscillations indicative of a perfect cylinder. Roughness also causes scatter outside the plane of incidence.
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The light-scattering Mueller matrix for an r = 0.345-microm-radius quartz fiber, illuminated at lambda = 0.4416 microm, is examined as a function of contamination with MgO crystals. When the MgO contamination is low, the matrix elements resemble those of a fiber of slightly larger radius. The MgO contamination creates higher-frequency, smaller-amplitude oscillations in the matrix elements that mask the lower-frequency oscillations indicative of a perfect cylinder. The contamination also causes scatter outside the plane of incidence.
