Acknowledgements 1. Introduction 2. Electromagnetic wave propagation 3. The absorption of light 4. Specular reflection 5. Single particle scattering: perfect spheres 6. Single particle scattering: irregular particles 7. Propagation in a nonuniform medium: the equation of radiative transfer 8. The bidirectional reflectance of a semi-infinite medium 9. The opposition effect 10. A miscellany of bidirectional reflectances and related quantities 11. Integrated reflectances and planetary photometry 12. Photometric effects of large scale roughness 13. Polarization 14. Reflectance spectroscopy 15. Thermal emission and emittance spectroscopy 16. Simultaneous transport of energy by radiation and conduction Appendix A. A brief review of vector calculus Appendix B. Functions of a complex variable Appendix C. The wave equation in spherical coordinates Appendix D. Fraunhoffer diffraction by a circular hole Appendix E. Table of symbols Bibliography Index.

Theory of Reflectance and Emittance Spectroscopy

The surface plasmon response of metal nanoparticles is studied for different shapes and physical environments. For polyhedral nanoparticles, the surface plasmon resonances are studied as a function of the number of faces and vertices. The modification of these surface plasmons by different surrounding media and the presence of a substrate or other nanoparticles is also discussed. We found that polyhedral nanoparticles composed with less faces show more surface plasmon resonances, and as the nanoparticle becomes more symmetric, the main surface plasmon resonance is blue-shifted. It is also found that the corners induce more surface plasmons in a wider energy range. In the presence of a substrate, multipolar plasmon resonances are induced, and as the nanoparticle approaches the substrate, such resonances are red-shifted. The interaction among nanoparticles also induces multipolar resonances, but they can be red or blue-shifted depending on the polarization of the external field.

Surface Plasmons on Metal Nanoparticles: The Influence of Shape and Physical Environment

Metamaterials enable the tailoring of properties like dielectric permittivity and magnetic permeability. Electromagnetic excitations of metamaterial constituents and their interactions are reviewed, as well as promising future directions. Despite the extraordinary degree of interest in optical metamaterials in recent years, the hoped-for devices and applications have, in large part, yet to emerge. It is becoming clear that the first generation of metamaterial-based devices will most probably arise from their two-dimensional equivalents — metasurfaces. In this Review, we describe recent progress in the area of metasurfaces formed from plasmonic meta-atoms. In particular, we approach the subject from the perspective of the fundamental excitations supported by the meta-atoms and the interactions between them. We also identify some areas ripe for future research and indicate likely avenues for future device development.

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Plasmonic meta-atoms and metasurfaces

Light absorption by aerosols contributes to solar radiative forcing through absorption of solar radiation and heating of the absorbing aerosol layer. Besides the direct radiative effect, the heating can evaporate clouds and change the atmospheric dynamics. Aerosol light absorption in the atmosphere is dominated by black carbon (BC) with additional, significant contributions from the still poorly understood brown carbon and from mineral dust. Sources of these absorbing aerosols include biomass burning and other combustion processes and dust entrainment. For particles much smaller than the wavelength of incident light, absorption is proportional to the particle volume and mass. Absorption can be calculated with Mie theory for spherical particles and with more complicated numerical methods for other particle shapes. The quantitative measurement of aerosol light absorption is still a challenge. Simple, commonly used filter measurements are prone to measurement artifacts due to particle concentration and modification of particle and filter morphology upon particle deposition, optical interaction of deposited particles and filter medium, and poor angular integration of light scattered by deposited particles. In situ methods measure particle absorption with the particles in their natural suspended state and therefore are not prone to effects related to particle deposition and concentration on filters. Photoacoustic and refractive index-based measurements rely on the heating of particles during light absorption, which, for power-modulated light sources, causes an acoustic signal and modulation of the refractive index in the air surrounding the particles that can be quantified with a microphone and an interferometer, respectively. These methods may suffer from some interference due to light-induced particle evaporation. Laser-induced incandescence also monitors particle heating upon absorption, but heats absorbing particles to much higher temperatures to quantify BC mass from the thermal radiation emitted by the heated particles. Extinction-minus-scattering techniques have limited sensitivity for measuring aerosol light absorption unless the very long absorption paths of cavity ring-down techniques are used. Systematic errors can be dominated by truncation errors in the scattering measurement for large particles or by subtraction errors for high single scattering albedo particles. Remote sensing techniques are essential for global monitoring of aerosol light absorption. While local column-integrated measurements of aerosol light absorption with sun and sky radiometers are routinely done, global satellite measurements are so far largely limited to determining a semi-quantitative UV absorption index.

Aerosol light absorption and its measurement: A review

We present a comprehensive solution to the classical problem of electromagnetic scattering by aggregates of an arbitrary number of arbitrarily configured spheres that are isotropic and homogeneous but may be of different size and composition. The profile of incident electromagnetic waves is arbitrary. The analysis is based on the framework of the Mie theory for a single sphere and the existing addition theorems for spherical vector wave functions. The classic Mie theory is generalized. Applying the extended Mie theory to all the spherical constituents in an aggregate simultaneously leads to a set of coupled linear equations in the unknown interactive coefficients. We propose an asymptotic iteration technique to solve for these coefficients. The total scattered field of the entire ensemble is constructed with the interactive scattering coefficients by the use of the translational addition theorem a second time. Rigorous analytical expressions are derived for the cross sections in a general case and for all the elements of the amplitude-scattering matrix in a special case of a plane-incident wave propagating along the z axis. As an illustration, we present some of our preliminary numerical results and compare them with previously published laboratory scattering measurements.

Electromagnetic scattering by an aggregate of spheres

The solution of electromagnetic scattering by a homogeneous prolate (or oblate) spheroidal particle with an arbitrary size and refractive index is obtained for any angle of incidence by solving Maxwell's equations under given boundary conditions. The method used is that of separating the vector wave equations in the spheroidal coordinates and expanding them in terms of the spheroidal wavefunctions. The unknown coefficients for the expansion are determined by a system of equations derived from the boundary conditions regarding the continuity of tangential components of the electric and magnetic vectors across the surface of the spheroid. The solutions both in the prolate and oblate spheroidal coordinate systems result in a same form, and the equations for the oblate spheroidal system can be obtained from those for the prolate one by replacing the prolate spheroidal wavefunctions with the oblate ones and vice versa. For an oblique incidence, the polarized incident wave is resolved into two components, the TM mode for which the magnetic vector vibrates perpendicularly to the incident plane and the TE mode for which the electric vector vibrates perpendicularly to this plane. For the incidence along the rotation axis the resultant equations are given in the form similar to the one for a sphere given by the Mie theory. The physical parameters involved are the following five quantities: the size parameter defined by the product of the semifocal distance of the spheroid and the propagation constant of the incident wave, the eccentricity, the refractive index of the spheroid relative to the surrounding medium, the incident angle between the direction of the incident wave and the rotation axis, and the angles that specify the direction of the scattered wave.

S. Asano

Papers

Light Scattering by a Spheroidal Particle