Local cross-sections and energy efficiencies in the multiple electromagnetic/optical scattering by two perfect electrically-conducting cylindrical particles

Exact mathematical expressions for the intrinsic electromagnetic (EM) cross–sections (i.e. extinction, scattering and absorption) for a pair of perfectly conducting circular cylinders in a homogeneous non–absorptive medium are derived. The multipole expansion method in cylindrical coordinates and the translational addition theorem, applicable to any range of frequencies or particle sizes are used. An effective EM field, incident on the probed cylinder is defined first, which includes the initial and re-scattered field from the second cylinder. It is used jointly with the scattered field to derive the mathematical expressions for the intrinsic/local cross–sections. Numerical computations for the intrinsic extinction (or scattering) energy efficiencies per unit-length for a pair of conducting circular cylinders with different radii in a homogeneous medium are considered. The results computed a priori can be useful in the full characterization of a multiple scattering system of many particles, in conjunction with experimental data for the extrinsic cross–sections.     

Spectral control of an alexandrite laser for an airborne water-vapor differential absorption lidar system

A narrow-linewidth pulsed alexandrite laser has been greatly modified for improved spectral stability in an aircraft environment, and its operation has been evaluated in the laboratory for making water-vapor differential absorption lidar measurements. An alignment technique is described to achieve the optimum free spectral range ratio for the two étalons inserted in the alexandrite laser cavity, and the sensitivity of this ratio is analyzed. This technique drastically decreases the occurrence of mode hopping, which is commonly observed in a tunable, two-intracavity-étalon laser system. High spectral purity (> 99.85%) at 730 nm is demonstrated by the use of a water-vapor absorption line as a notch filter. The effective cross sections of 760-nm oxygen and 730-nm water-vapor absorption lines are measured at different pressures by usingthis laser, which has a finite linewidth of 0.02 cm(-1) (FWHM). It is found that for water-vapor absorption linewidths greater than 0.04 cm(-1) (HWHM), or for altitudes below 10 km, the laser line can be considered monochromatic because the measured effective absorption cross section is within 1% of the calculated monochromatic cross section. An analysis of the environmental sensitivity of the two intracavity étalons is presented, and a closed-loop computer control for active stabilization of the two intracavity étalons in the alexandrite laser is described. Using a water-vapor absorption line as a wavelength reference, we measure a long-term frequency drift (≈ 1.5 h) of less than 0.7 pm in the laboratory.     

Absorption and scattering properties of dense ensembles of nonspherical particles

The purpose of this work is to show that an appropriate multiple T-matrix formalism can be useful in performing qualitative studies of the optical properties of colloidal systems composed of nonspherical objects (despite limitations concerning nonspherical particle packing densities). In this work we have calculated the configuration averages of scattering and absorption cross sections of different clusters of dielectric particles. These clusters are characterized by their refraction index, particle shape, and filling fraction. Computations were performed with the recursive centered T-matrix algorithm (RCTMA), a previously established method for solving the multiple scattering equation of light from finite clusters of isotropic dielectric objects. Comparison of the average optical cross sections between the different systems highlights variations in the scattering and absorption properties due to the electromagnetic interactions, and we demonstrate that the magnitudes of these quantities are clearly modulated by the shape of the primary particles.     

Geometrical-optics code for computing the optical properties of large dielectric spheres

Absorption of electromagnetic radiation by absorptive dielectric spheres such as snow grains in the near-infrared part of the solar spectrum cannot be neglected when radiative properties of snow are computed. Thus a new, to our knowledge, geometrical-optics code is developed to compute scattering and absorption cross sections of large dielectric particles of arbitrary complex refractive index. The number of internal reflections and transmissions are truncated on the basis of the ratio of the irradiance incident at the nth interface to the irradiance incident at the first interface for a specific optical ray. Thus the truncation number is a function of the angle of incidence. Phase functions for both near- and far-field absorption and scattering of electromagnetic radiation are calculated directly at any desired scattering angle by using a hybrid algorithm based on the bisection and Newton-Raphson methods. With these methods a large sphere's absorption and scattering properties of light can be calculated for any wavelength from the ultraviolet to the microwave regions. Assuming that large snow meltclusters (1-cm order), observed ubiquitously in the snow cover during summer, can be characterized as spheres, one may compute absorption and scattering efficiencies and the scattering phase function on the basis of this geometrical-optics method. A geometrical-optics method for sphere (GOMsphere) code is developed and tested against Wiscombe's Mie scattering code (MIE0) and a Monte Carlo code for a range of size parameters. GOMsphere can be combined with MIE0 to calculate the single-scattering properties of dielectric spheres of any size.     

Double-scatter cross sections for two-dimensional random rough surfaces that exhibit backscatter enhancement

Full-wave solutions are given for the single- and double-scatter radar cross sections for two-dimensional random rough surfaces. High-frequency approximations are used for the double-scatter cross sections in order to express them as numerically tractable four-dimensional integrals. The major contributions to the double-scatter cross sections are associated with the quasi-parallel and quasi-antiparallel double-scatter paths. They come from the neighborhoods of specular points. The enhancement of the backscatter cross sections, which is associated with the quasi-antiparallel double-scatter paths, is observed for both the like- and cross-polarized cross sections.     

Isotropic scattering by penetrable cylinders

Isotropic scattering is considered for infinite cylinders thin in the sense that ka < 1, although ?k'a? and cross-sectional shape can be arbitrary within limits (k and k' are, respectively, free-space and interior propagation constants, and a is a characteristic dimension of the cylinder). For circular cylinders, scattering width is found to saturate at its perfectly conducting value, and absorption width is found to peak, when skin depth becomes comparable with cylinder diameter. For a variety of cylinders with and without edges, both scattering and absorption widths are then found to be effectively identical to those of the circular cylinder with equal cross-sectional area. A new analytical formula is obtained for high but not infinite conductivity, and the connection with scattering cross sections of corresponding finite cylinders is discussed.     

Gold Nanocages: Engineering Their Structure for Biomedical Applications

The galvanic replacement reaction between a Ag template and HAuCl₄ in an aqueous solution transforms 30–200 nm Ag nanocubes into Au nanoboxes and nanocages (nanoboxes with porous walls). By controlling the molar ratio of Ag to HAuCl₄, the extinction peak of resultant structures can be continuously tuned from the blue (400 nm) to the near‐infrared (1200 nm) region of the electromagnetic spectrum. These hollow Au nanostructures are characterized by extraordinarily large cross‐sections for both absorption and scattering. Optical coherence tomography measurements indicate that the 36 nm nanocage has a scattering cross‐section of ～ 0.8 × 10^–15 m² and an absorption cross‐section of ～ 7.3 × 10^–15 m². The absorption cross‐section is more than five orders of magnitude larger than those of conventional organic dyes. Exposure of Au nanocages to a camera flash resulted in the melting and conversion of Au nanocages into spherical particles due to photothermal heating. Discrete‐dipole‐approximation calculations suggest that the magnitudes of both scattering and absorption cross‐sections of Au nanocages can be tailored by controlling their dimensions, as well as the thickness and porosity of their walls. This novel class of hollow nanostructures is expected to find use as both a contrast agent for optical imaging in early stage tumor detection and as a therapeutic agent for photothermal cancer treatment.     

Sensitivity studies for imaging a spherical object embedded in a spherically symmetric, two-layer turbid medium with photon-density waves

We present analytic expressions for the amplitude and phase of photon-density waves in strongly scattering, spherically symmetric, two-layer media containing a spherical object. This layered structure is a crude model of multilayered tissues whose absorption and scattering coefficients lie within a range reported in the literature for most tissue types. The embedded object simulates a pathology, such as a tumor. The normal-mode-series method is employed to solve the inhomogeneous Helmholtz equation in spherical coordinates, with suitable boundary conditions. By comparing the total field at points in the outer layer at a fixed distance from the origin when the object is present and when it is absent, we evaluate the potential sensitivity of an optical imaging system to inhomogeneities in absorption and scattering. For four types of background media with different absorption and scattering properties, we determine the modulation frequency that achieves an optimal compromise between signal-detection reliability and sensitivity to the presence of an object, the minimum detectable object radius, and the smallest detectable change in the absorption and scattering coefficients for a fixed object size. Our results indicate that (l) enhanced sensitivity to the object is achieved when the outer layer is more absorbing or scattering than the inner layer; (2) sensitivity to the object increases with the modulation frequency, except when the outer layer is the more absorbing; (3) amplitude measurements are proportionally more sensitive to a change in absorption, phase measurements are proportionally more sensitive to a change in scattering, and phase measurements exhibit a much greater capacity for distinguishing an absorption perturbation from a scattering perturbation.     

Electrostatics analysis of radiative absorption by sphere clusters in the Rayleigh limit: application to soot particles

An analysis of radiative absorption and scattering by clusters of spheres in the Rayleigh limit is developed with an electrostatics analysis. This approach assumes that the largest dimension of the cluster is significantly smaller than the wavelength of the radiation. The electric field that is incident upon and scattered by the cluster can then be represented by the gradient of a potential that in turn satisfies Laplace's equation. An analytical solution for the potential that exactly satisfies the boundary conditions at the surfaces of the spheres is obtained with a coupled spherical harmonics method. The components of the polarizability tensor and the absorption, scattering, and depolarization factors are obtained from the solution. Calculations are performed on fractallike clusters of spheres, with refractive-index values that are characteristic of carbonaceous soot in the visible and the IR wavelengths. Results indicate that the absorption cross sections of fractal soot clusters can be significantly larger in the mid-IR wavelengths than what is predicted for Rayleigh-limit spheres that have the same total volume. The absorption cross section (relative to a sphere of the same volume) is dependent on the number of spheres in the aggregate for aggregates with up to approximately 100 primary spheres, and for larger aggregates the relative absorption becomes constant. The predicted spectral variation of soot absorption in the visible and the mid-IR wavelengths is shown to agree well with experimental measurements.     

Analysis of a simple method for the reduction of phonon peak broadening in surface Brillouin light scattering

We present an investigation of the effect of the collecting lens aperture on the line shape of phonon peaks observed in surface Brillouin light scattering (SBLS) from surfaces of opaque materials and transparent thin films. In general, the broadening that is due to the aperture is asymmetric and can be as large as 60% of the peak frequency shift in the case of a f/1.4 aperture with an angle of incidence theta(i) = 30 degrees . We calculated SBLS spectra accounting for the spread in scattering wave vectors across the collecting lens aperture, the polarization and angular dependence of the scattering, and the spectrometer instrumental function. By performing a detailed comparison between measured and calculated SBLS spectra for Si(001), we identified a set of simple rules for the placement of a rectangular slit in the collecting lens aperture to reduce the effects of aperture broadening. By use of a slit, the peak linewidths can be reduced substantially, without reducing the peak heights significantly, while eliminating false shifts in the measured frequency values.     

Alternative method for concentration retrieval in differential optical absorption spectroscopy atmospheric-gas pollutant measurements

Differential optical absorption spectroscopy is a widely used technique for open-column atmospheric-gas pollution monitoring. The concentration retrieval is based on the fitting of the measured differential absorbance through the Lambert-Beer law. We present an alternative method for calculating the gas concentration on the basis of the proportionality between differential absorbance and differential absorption cross section of the gas under study. The method can be used on its own for single-component analysis or as a complement to the standard technique in multicomponent cases. The performance of the method for the case of cross interference between two gases is analyzed. The procedure can be used with differential absorption cross sections measured in the laboratory or taken from the literature. In addition, the method provides a criterion to discriminate against different species having absorption features in the same wavelength range.     

Multiple-scattering suppression by cross correlation

We describe a new method for characterizing particles in turbid media by cross correlating the scattered intensity fluctuations at two nearby points in the far field. The cross-correlation function selectively emphasizes single scattering over multiple scattering. The usual dynamic light-scattering capability of inferring particle size from decay rate is thus extended to samples that are so turbid as to be visually opaque. The method relies on single-scattering speckle being physically larger than multiple-scattering speckle. With a suitable optical geometry to select nearby points in the far field or equivalently slightly different scattering wave vectors (of the same magnitude), the multiple-scattering contribution to the cross-correlation function may be reduced and in some cases rendered insignificant. Experimental results demonstrating the feasibility of this approach are presented.     

超声造影剂微泡非线性声学特性的数值仿真

以空气泡为例,采用描述气泡半径运动的Rayleigh-Plesset方程,对其在高频声压辐照下的非线性振荡,散射声场和散射截面进行理论和数值研究,为获取更清晰的图像提供理论依据。结果表明:激励声压的频率在微泡的固有谐振频率附近时,可以产生强的二次谐波散射声压。同时,提高入射声强可以增大二次谐波散射截面,但不能改变基波散射截面。     

Spectrally resolved absolute fluorescence cross sections for bacillus spores

Absolute fluorescence cross sections for Bacillus subtilis and B. cereus bacterial spores as both aqueous suspensions and aerosols were measured at a number of excitation wavelengths between 228 and 303 nm. The fluorescence was spectrally resolved at each excitation wavelength. We found that the optimum excitation wavelength for spore fluorescence is between 270 and 280 nm. The fluorescence cross section for aqueous suspensions is four times larger than for dry aerosols when measured under similar conditions. Measurements on wet aerosols showed an increase in fluorescence cross section over dry aerosols, indicating an enhancement of the fluorescence when the bacterial spores are wet. Mie scattering cross sections at 90 degrees to the direction of the incident radiation and extinction cross sections as a function of wavelength for B. subtilis suspensions and fluorescence cross sections for tryptophan are also reported.     

Optical characterization method for black pigments applied to solar-selective absorbing paints

We propose a novel, to our knowledge, method for characterizing the optical properties of pigment particles or powders. Measurements of the diffuse and the total transmittance as well as the diffuse and the total reflectance are used to obtain effective scattering and absorption coefficients per unit length for the particles that are dispersed in a continuous matrix. For dilute dispersions in the single-scattering regime scattering and absorption cross sections of the particles were obtained. The method was applied to two pigments, namely, FeMnCuO(x) and black carbon. The data were obtained by use of pellets consisting of low concentrations of FeMnCuO(x) or black-carbon pigments dispersed in a KBr matrix. The pigment volume concentrations used to evaluate the scattering and the absorption coefficients ranged from 0.053% to 0.530% for FeMnCuO(x) and 0.076% to 0.310% for the black carbon. These ranges were found to exhibit the linear dependence of the coefficients as a function of volume fraction, as given by single-scattering theory.     

Light scattering by a multilayer sphere

The recurrence algorithm for calculating electromagnetic scattering from a multilayer sphere, which was described recently by Wu and Wang [Radio Sci. 26, 1393, (1991)], is derived in a slightly modified form and extended to include a calculation of the internal field and the absorption cross sections of the individual layers. The original algorithm calculates the scattering by a recurrence procedure that propagates the log derivatives of the Debye potentials outward from the core to the outer layer. The extended algorithm then continues the calculation by an inward recurrence procedure that propagates the Debye potentials from the outer layer to the core. Concurrent with the inward propagation, a separate algorithm calculates the absorption cross sections of the imbedded concentric spheres. The results of several example calculations are presented, including the differential cross section and internal electric field of a Luneburg lens.     

声学边界元拟奇异积分计算的自适应方法

提出一种自适应方法计算声学边界元中的拟奇异积分,通过单元分级细分将总积分转移到子单元上以消除拟奇异性。在此方法基础上深入研究拟奇异性,进一步提出接近度的概念,其中临界接近度可作为拟奇异积分计算的理论依据,并可用于预估拟奇异性是否存在。此方法的积分精度可调控,且不受场点位置限制,相比于已有方法更加灵活高效。数值分析表明拟奇异性强弱由场点与单元的相对位置决定,单元上远离场点的区域拟奇异性很弱,无需处理。研究结果为处理边界元法中的拟奇异性问题提供了新的选择和参考。     

Modeling of gas absorption cross sections by use of principal-component-analysis model parameters

Monitoring the amount of gaseous species in the atmosphere and exhaust gases by remote infrared spectroscopic methods calls for the use of a compilation of spectral data, which can be used to match spectra measured in a practical application. Model spectra are based on time-consuming line-by-line calculations of absorption cross sections in databases by use of temperature as input combined with path length and partial and total pressure. It is demonstrated that principal component analysis (PCA) can be used to compress the spectrum of absorption cross sections, which depend strongly on temperature, into a reduced representation of score values and loading vectors. The temperature range from 300 to 1000 K is studied. This range is divided into two subranges (300-650 K and 650-1000K), and separate PCA models are constructed for each. The relationship between the scores and the temperature values is highly nonlinear. It is shown, however, that because the score-temperature relationships are smooth and continuous, they can be modeled by polynomials of varying degrees. The accuracy of the data compression method is validated with line-by-line-calculated absorption data of carbon monoxide and water vapor. Relative deviations between the absorption cross sections reconstructed from the PCA model parameters and the line-by-line-calculated values are found to be smaller than 0.15% for cross sections exceeding 1.27 x 10(-21) cm(-1) atm(-1) (CO) and 0.20% for cross sections exceeding 4.03 x 10(-21) cm(-1) atm(-1) (H2O). The computing time is reduced by a factor of 10(4).     

Generalized Lorenz-Mie theory for an arbitrarily oriented, located, and shaped beam scattered by a homogeneous spheroid

The theory of an arbitrarily oriented, shaped, and located beam scattered by a homogeneous spheroid is developed within the framework of the generalized Lorenz-Mie theory (GLMT). The incident beam is expanded in terms of the spheroidal vector wave functions and described by a set of beam shape coefficients (G(m)(n),(TM),G(m)(n),(TE)). Analytical expressions of the far-field scattering and extinction cross sections are derived. As two special cases, plane wave scattering by a spheroid and shaped beam scattered by a sphere can be recovered from the present theory, which is verified both theoretically and numerically. Calculations of the far-field scattering and cross sections are performed to study the shaped beam scattered by a spheroid, which can be prolate or oblate, transparent or absorbing.