Extinction by a homogeneous spherical particle in an absorbing medium

Light absorption by a planar array of spherical particles and a matrix in which they are embedded: statistical approach

The fractions of light energy absorbed by a 2D array of spherical particles and the matrix in which they are embedded are determined. The solution is based on a volume integral equation and a statistical approach. The absorption coefficient of the array is found via the internal fields of the particles. The absorption coefficient of a matrix is found as the difference between the absorption coefficients of the composite structure and the particles. Numerical results are presented for arrays of metal, semiconductor, and dielectric nano- and microparticles of short-range order and imperfect long-range order in the absorbing media at normal and oblique incidence of a plane wave.

Extinction and attenuation by voids in absorbing host media

Extinction and attenuation by particles in an absorbing host have suffered a long-lasting controversy, which has impeded the physical insights on the radiative transfer in the voids dispersed composite. In this paper, we outline the existing extinction definitions, including an equivalence theorem neglecting the host absorption, the near-field analytical definition neglecting the far-field effects, and the operational way which simulates the actual detector readings. It is shown that, under the independent scattering approximation, the generalized operational definition is equivalent to a recent effective medium method according to the rigorous theory of multiple scattering. Using this generalized extinction, we show the important influences of the host absorption on the void extinction. Specifically, at the void resonance, the extinction cross sections of the small voids can be positive, zero, and even negative, which is regulated quantitively by host absorption. Considering the voids in SiC or Ag, the intriguing properties are verified through the attenuation coefficient calculated by the Maxwell-Garnett effective medium theory. In contrast, the equivalent theorem cannot describe any void resonance structures in the absorbing media. Also, the near-field definition fails to generate negative extinction and cannot thus describe the diminished total absorption by the voids. Our results might provide a better understanding of complex scattering theory in absorbing media.

Polarized radiative transfer in seawater-in-oil emulsions floated on seawater considering the impact of oil absorption on seawater droplet scattering

Among various remote sensing approaches, optical polarization remote sensing shows great advantages in identifying oil-water emulsions in seawater and has become one of the most promising detection technologies. Herein, we focus on exploring the sensitivity of polarized radiative transfer properties for oil emulsion polarization detection to the influence factors of viewing angle, droplet volume fraction and radius, incident wavelength, and emulsion thickness. The radiative properties of seawater droplets dispersed in crude oil are calculated using the improved Lorenz-Mie theory considering the absorption of crude oil as the host medium, after which the reflected Stokes vector and the degree of linear polarization (DOLP) of seawater-in-oil emulsions floating on seawater are obtained using the spectral element method. By analyzing the calculation results of a 0° viewing azimuth angle, the detection wavelength and viewing zenith angles corresponding to the highest sensitivity of the DOLP to the above factors are significantly different; thus, quantitative remote sensing detection of the droplet volume fraction, droplet diameter, and emulsion thickness is possible. Exploring the sensitivity of polarized remote sensing signals for oil emulsion polarization detection to the above factors is a prerequisite for quantitative polarization detection of oil emulsions.

Optical characteristics of a monolayer of identical spherical particles in an absorbing host medium

The problem of light interaction with a 2D ensemble of homogeneous spherical particles embedded into an unbounded homogeneous absorbing host medium is considered. Based on the statistical approach, the equations are derived to characterize optical response of such a system with taking into account multiple scattering of light. Numerical data are presented for the spectral behavior of coherent transmission and reflection, incoherent scattering, and absorption coefficients of thin dielectric, semiconductor, and metal films containing a monolayer of particles with various spatial organization. The results are compared with the characteristics of the inverse structure: particles consist of the host medium material and vice versa. Data for the redshift of the surface plasmon resonance of the monolayer of gold (Au) nanoparticles in the fullerene (C ₆₀) matrix are presented as a function of the monolayer filling factor. They are in qualitative agreement with the known experimental results. The findings have potential applications in the development of new electro-optical and photonic devices.

Extinction by plasmonic nanoparticles in dispersive and dissipative media

Extinction of small metallic spheres has been well understood through the classical Mie theory when the host medium is dispersive and transparent. However, the role of host dissipation on the particulate extinction remains a competition between the enhancing and reducing effects on the localized surface plasmonic resonance (LSPR). Here, using a generalized Mie theory, we elaborate on the specific influence mechanisms of host dissipation on the extinction efficiency factors of a plasmonic nanosphere. To this end, we isolate the dissipative effects by comparing the dispersive and dissipative host with its dissipationless counterpart. As a result, we identify the damping effects of host dissipation on the LSPR including the resonance widening and amplitude reducing. The resonance positions are shifted by host dissipation, which cannot be predicted by the classical Fröhlich condition. Finally, we demonstrate that a wideband extinction enhancement due to host dissipation can be realized away from the positions of the LSPR.

Extinction, absorption, and scattering of light by plasmonic spheres embedded in an absorbing host medium

Although the general Lorenz-Mie formalism for spheres in an absorbing host has been developed, no correct analytical expressions in the small-particle limit have been published so far. Here, we derive two sets of analytical expressions for the extinction, absorption, and far- and near-field scattering cross sections of small particles embedded in an absorbing host. One set is a modification of the electrostatic approximation (EA) for an absorbing host, whereas the other represents an improved electrostatic approximation (IEA) based on the generalized Lorenz-Mie theory and a new form of Mie coefficients for the internal field expansion. To illustrate the accuracy of the derived approximations, we consider Au and Ag nanospheres embedded in model hosts (real part of the refractive index, 1.33; imaginary part, 0-0.3), in a lossless poly(methyl methacrylate) (PMMA), and a lossy poly(3-hexylthiophene) (P3HT) matrix. In general, the IEA cross sections agree with those calculated using Lorenz-Mie theory if the particle diameter is not greater than 50 nm. Two small-particle limits are found for the near-field scattering cross sections. When host absorption is negligible, the scattering efficiency scales as the fourth power of the size parameter. In contrast, for nonzero absorption, the scattering efficiency scales as the first power of the size parameter. For a spectrally independent host, an increase in host absorption broadens and suppresses plasmonic peaks. We found an exception to this general tendency for near-field scattering by small (10-50 nm) particles; for these, an increase in host absorption increases the scattering peak. This surprising behavior is explained analytically. For 10-30 nm Au particles in the PMMA and P3HT matrixes, the EA and IEA data perfectly agree with the exact Lorenz-Mie simulations, in contrast to the previously reported conclusions. In particular, replacing PMMA with P3HT shifts the plasmonic peaks of the 10 nm particles from 540 nm to 650 nm and strongly enhances near- and far-field scattering. However, far-field scattering does not contribute to the extinction derived from the generalized optical theorem.

Optical theorems and physical bounds on absorption in lossy media

Two different versions of an optical theorem for a scattering body embedded inside a lossy background medium are derived in this paper. The corresponding fundamental upper bounds on absorption are then obtained in closed form by elementary optimization techniques. The first version is formulated in terms of polarization currents (or equivalent currents) inside the scatterer and generalizes previous results given for a lossless medium. The corresponding bound is referred to here as a variational bound and is valid for an arbitrary geometry with a given material property. The second version is formulated in terms of the T-matrix parameters of an arbitrary linear scatterer circumscribed by a spherical volume and gives a new fundamental upper bound on the total absorption of an inclusion with an arbitrary material property (including general bianisotropic materials). The two bounds are fundamentally different as they are based on different assumptions regarding the structure and the material property. Numerical examples including homogeneous and layered (core-shell) spheres are given to demonstrate that the two bounds provide complimentary information in a given scattering problem.

Effect of host medium absorption on polarized radiative transfer in dispersed media

This paper focuses on polarized radiative transfer in a thin layer composed of titanium dioxide particles while considering the effect of host medium absorption on particle scattering. The single-scattering properties of particles in an absorbing medium are calculated using the modified Lorenz-Mie program recently developed based on the first-principles theory of electromagnetic scattering, and the vector radiative transfer equation is solved by using the spectral element method. The relative errors of Stokes parameters caused by using the conventional Lorenz-Mie theory are systemically investigated. The results show that neglecting the effect of host medium absorption on particle scattering has a more significant impact on the radiation intensity than the polarization components in most cases. Meanwhile, the relative errors of Stokes parameters induced by using the conventional Lorenz-Mie theory obviously increase with the increase of the host medium absorption index and particle size parameter. Due to the larger scattering coefficients and scattering albedos (i.e., for the case of particle size parameter x=10.0 in this study), the relative errors of Stokes parameters of monodisperse particles are obviously larger than those of polydisperse particles. Moreover, it is found that the relative errors of the Stokes parameters change nonlinearly with the particle volume fraction, especially for large size particles.

Scattering of a damped inhomogeneous plane wave by a particle in a weakly absorbing medium

We use the volume integral equation formulation to consider frequency-domain electromagnetic scattering of a damped inhomogeneous plane wave by a particle immersed in an absorbing medium. We show that if absorption in the host medium is sufficiently weak and the particle size parameter is sufficiently small, then (i) the resulting formalism (including the far-field and radiative-transfer regimes) is largely the same as in the case of a nonabsorbing host medium, and (ii) one can bypass explicit use of sophisticated general solvers of the Maxwell equations applicable to inhomogeneous-wave illumination. These results offer dramatic simplifications for solving the scattering problem in a wide range of practical applications involving absorbing host media.

Multiple scattering of polarized light by particles in an absorbing medium

We study multiple scattering of light by particles embedded in an absorbing host medium using a recently developed single-scattering and vector radiative-transfer methodology directly based on the Maxwell equations. The first-principles results are compared with those rendered by the conventional heuristic approach according to which the single-scattering properties of particles can be computed by assuming that the host medium is nonabsorbing. Our analysis shows that the conventional approach yields very accurate results in the case of aerosol and cloud particles suspended in an absorbing gaseous atmosphere. In the case of air bubbles in water, the traditional approach can cause large relative errors in reflectance, but only when strong absorption in the host medium makes the resulting reflectance very small. The corresponding polarization errors are substantially smaller.

Far-field Lorenz-Mie scattering in an absorbing host medium. II: Improved stability of the numerical algorithm

A recently developed FORTRAN program computing far-field optical observables for spherical particles in an absorbing medium has exhibited numerical instability arising when the product of the particle vacuum size parameter and the imaginary part of the refractive index of the host becomes sufficiently large. We offer a simple analytical explanation of this instability and propose a compact numerical algorithm for the stable computation of Lorenz-Mie coefficients based on an upward recursion formula for spherical Hankel functions of a complex argument. Extensive tests confirm an excellent accuracy of this algorithm approaching machine precision. The improved public-domain FORTRAN program is available at https://www.giss.nasa.gov/staff/mmishchenko/Lorenz-Mie.html.