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As vector wavefunctions are available to represent incident and scattered fields in an isotropic dielectric-magnetic medium endowed with magnetoelectric gyrotropy, a transition matrix can be conceptualized to relate the scattered field coefficients to the incident field coefficients for scattering by an arbitrary scatterer composed of a linear medium. The elements of the transition matrix must satisfy certain conditions for zero backscattering. For a scatterer composed of a uniaxial dielectric-magnetic medium endowed with magnetoelectric gyrotropy, the extended boundary condition method (EBCM) can be formulated to determine the transition matrix. The numerical results obtained thereby lead to the formulation of a sufficient set of three zero-backscattering conditions: (i) the scatterer is a body of revolution with the incident plane wave propagating along the axis of revolution; (ii) the impedances of both mediums are identical; and (iii) the magnetoelectric-gyrotropy vectors of both mediums are aligned along the axis of revolution, whether or not both magnetoelectric-gyrotropy vectors are co-parallel.

Some objects feel colder to the touch than others at the same (room) temperature. But explaining why by linear, single-factor reasoning is inadequate because the time-dependent thermal energy transfer at solid interfaces initially at different temperatures is determined by the thermal inertia kρc, a function of three thermophysical properties: thermal conductivity k, density ρ, and specific heat capacity per unit mass c. In time-dependent problems 1/kρc plays the role of a resistance. As an example, although the thermal conductivity of aluminum is 16 times that of stainless steel, this does not translate into a 16-fold difference in interfacial thermal energy flux densities. Nor does it result in a markedly greater perceived coldness of aluminum; the difference is barely perceptible. Similarly, despite the 600-fold difference in the thermal conductivity of iron relative to that of wood, the ratio of thermal energy flux densities is only about 4.6.

In his interesting and informative book Is That a Fact?, Joe Schwarcz avers that pigs do not sweat and the saying “sweating like a pig” originates in iron smelting. Oblong pieces of hot iron, with a fancied resemblance to a sow with piglets, cool in sand to the dew point of the surrounding air, and hence water condenses on the “pig.” But this explanation, which I have seen on the Internet, lacks a few caveats. It implies that molten iron, solidifying and cooling, anywhere, anytime, accretes liquid water, as if this were a special property of cooling iron. Set aside that real pigs sweat perceptibly from their snouts; kiss a pig and verify for yourself. Pigs also sweat imperceptibly. Imperceptible (insensible) perspiration is water vapor from the skin and lungs exuded without sensible condensation. That from humans is about 1 liter/day. Sweat is 99% liquid water, NaCl the dominant solute, secreted quickly, sometimes profusely, by subcutaneous sweat glands in response to thermal stress, in contrast to the slow, continuous diffusion of water vapor through skin.

Effective-medium theories for electromagnetic constitutive parameters of particulate composite materials are theories of averages. Standard deviations are absent because of the lack of rigorous theories. But ensemble averages and standard deviations can be calculated from a rigorous theory of reflection by planar multilayers. Average reflectivities at all angles of incidence and two orthogonal polarization states for a multilayer composed of two kinds of electrically thin layers agree well with reflectivities for a single layer with the same overall thickness and a volume-weighted average of the relative permittivities of these two components. But the relative standard deviation can be appreciable depending on the angle of incidence and the polarization state of the incident illumination, and increases with increasing difference between the constitutive parameters of the two layers. This suggests that average constitutive parameters obtained from effective-medium theories do not have uniform validity for all calculations in which they might be used., 12 pages (accepted for publication in Journal of Modern Optics)

An Internet search for why objects, especially humans, cool more rapidly in water than in air, both at the same temperature, and by how much, yields off-the-cuff answers unsupported by experiment or analysis. To answer these questions in depth requires a smattering of engineering heat transfer, including radiative transfer, and the different thermophysical properties of the two fluids. The correct ratio for humans is closer to 2 than to 10, and if this were not so, swimming in cool water could be fatal.

The extended boundary condition method can be used to study plane-wave scattering by an ellipsoid composed of an orthorhombic dielectric-magnetic material whose relative permittivity dyadic is a scalar multiple of its relative permeability dyadic. The scattered and internal field phasors can be expanded in terms of appropriate vector spherical wavefunctions with unknown expansion coefficients, whereas the incident-field phasors can be similarly expanded but with known expansion coefficients. The scattered-field coefficients are related to the incident-field coefficients through a matrix. The scattering, absorption, and extinction efficiencies were calculated thereby in relation to the propagation direction and the polarization state of the incident plane wave, the constitutive-anisotropy parameters, and the nonsphericity parameters of the ellipsoid, when the eigenvectors of the real permittivity dyadic are aligned along the three semi-axes of the ellipsoid. As the electrical size of the ellipsoid increases, multiple lobes appear in the scattering pattern. The total scattering efficiency can be smaller than the absorption efficiency for some configurations of the incident plane wave but not necessarily for others. The nonsphericity of the object has a stronger influence on the total scattering efficiency than on the absorption efficiency. The forward-scattering efficiency increases monotonically with the electrical size for all configurations of the incident plane wave, and so does the backscattering efficiency for some configurations. For other configurations, the backscattering efficiency has an undulating behavior with increase in electrical size and is highly affected by the shape and the constitutive anisotropy of the ellipsoid. Even though the ellipsoid is not necessarily a body of revolution, it is anisotropic, and it is not impedance matched to free space, the backscattering efficiency can be minuscule but the forward-scattering efficiency is not. This feature can be useful for harvesting electromagnetic energy.

Green thunderstorms have been observed from time to time in association with deep convection or severe weather events. Often the green coloration has been attributed to hail or to reflections of light from green foliage on the ground. Some skeptics who have not personally observed a green thunderstorm do not believe that green thunderstorms exist. They suggest that the green storms may be fabrications by excited observers. The authors have demonstrated the existence of green thunderstorms objectively using a spectrophotometer. During the spring and summer of 1995 the authors observed numerous storms and recorded hundreds of spectra of the light emanating corn these storms. It was found that the subjective judgment of colors can vary somewhat between observers, but the variation is usually in the shade of green. The authors recorded spectra of green and nongreen thunderstorms and recorded spectral measurements as a storm changed its appearance from dark blue to a bluish green. The change in color ...

Scattering by a uniformly translating sphere of a pulse that modulates the amplitude of a linearly polarized plane wave was formulated using the frame-hopping method involving a laboratory inertial reference frame and the sphere's comoving inertial reference frame. The incident signal was defined in the laboratory frame and transformed to the comoving frame with the Lorentz transformation, thereby altering the incident signal's spectrum, direction of propagation of the carrier plane wave, and the direction of the incident electric field, depending on the sphere's velocity. In the comoving frame, the incident signal was Fourier-transformed to the frequency domain, and the scattered field phasors were computed in all directions using the constitutive parameters of the material of the sphere at rest. The scattered signal in the comoving frame was obtained using the inverse Fourier transform. Finally, the scattered signal in the laboratory frame was obtained by inverting the original Lorentz transformation. The backscattered signal was found to depend strongly on the sphere's velocity, when the sphere's speed is an appreciable fraction of the speed of light in free space. The change in the backscattered signal compared with the backscattered signal from a stationary sphere is the greatest when the sphere's velocity is either parallel or antiparallel to the direction of propagation of the incident signal. The backscattered signal is also affected by motion transverse to the incident signal's direction of propagation; then, the backscattered signal depends on whether or not the motion is aligned with the direction of the incident electric field.

Materials that are effectively chiral at microwave frequencies can be fabricated by embedding identical, randomly oriented chiral inclusions, often metal helices, in a continuous matrix. We show that the chirality parameter can be calculated in the dilute limit using single scattering theory. The required tumble-averaged forward scattering by an individual inclusion is determined by the method of moments. Values of the effective chirality parameter are determined directly from the constitutive parameters of the matrix and the geometry and concentration of the inclusions. Comparisons are made with measurements previously reported in the literature. In addition, a chiral composite material was fabricated specifically to validate the calculations over frequencies including resonance. The measurements agree well with the calculations, providing quantitative values of the chirality parameter over a wide frequency band. It appears that the chirality parameter is appreciable only near the resonant frequencies of the inclusion. Finally, it is clear that an oscillator model can be used to describe the frequency dependence of the complex chirality parameter, and that therefore our results are consistent with the Kramers-Kronig relation. >

Given the paucity of optical methods for sizing nanoparticles (those between 1 and 100 nm), more methods are needed if, as has been predicted, such particles have a bright future. Linearly polarized light is transformed into elliptically polarized light upon scattering by small spheres at 90°. The resulting circular polarization increases as the fifth power of particle diameter and the shift of the azimuth of the vibration ellipse from the vertical increases as the square if the particles are negligibly absorbing. Titanium dioxide spheres (in air) with diameters between 20 and 120 nm give circular polarizations between about 10−5 and 10−1 for incident light of wavelength 450 nm. The corresponding azimuth shifts (in radians) lie between about 10−2 and 1. These values are within reach of experimental techniques based on polarization modulation. Metallic spheres yield much larger circular polarizations and azimuth shifts (with signs opposite those for negligibly absorbing spheres), both of which increase approximately as the square of particle diameter.

In a previous article1 I analyzed in detail the physical factors resulting in greater cooling rates of objects in still water than in still air, emphasizing cooling of the human body. By cooling rate I mean the rate of decrease of core temperature uncompensated by metabolism. I concluded that the “correct ratio for humans is closer to 2 than to 10.” To support this assertion I subsequently did experiments, which I report following a digression on hypothermia.

The optical properties of a snowpack are calculated, giving relations between the asymptotic flux extinction coefficient and albedo under diffuse illumination on the one hand and the density, grain size, and wavelength, on the other. A geometrical optics calculation of the properties of a single grain is used with approximate solutions of the radiative transfer problem. Most of the scattering is the result of change in direction of the light beam upon transmission through the grain, rather than reflection. The asymptotic flux extinction coefficient is directly proportional to the snowpack density and inversely proportional to the square root of the grain size. The albedo under diffuse illumination is independent of density and proportional to the square root of the grain size. The derived relations agree with experimental data to within 20% for the flux extinction coefficient and to better than 2% for the albedo without using adjustable parameters. Higher values of the flux extinction coefficient will be measured if the snow is confined within a finite cylinder with absorbing sides. An analysis of this effect is given.

The scattering of electromagnetic waves by a spherical shell with intrinsic optical activity is calculated exactly from electromagnetic theory using the constitutive relations for an optically active, isotropic medium. The solution so obtained reduces to the standard solution in the limit of equal refractive indices for left− and right−circularly polarized waves. Expressions are given for single−particle cross sections and scattering matrix elements as well as circular dichroism and optical rotation for an aggregate of shells. These expressions are potentially applicable to the calculation of scattering contributions to optical rotatory dispersion and circular dichroism spectra for those particles of biological origin which can be modeled by an optically active shell.

Shape can strongly affect scattering by particles at wavelengths near bulk absorption bands. An example is scattering by many components of the atmospheric aerosol at wavelengths in the transmission window centered around 10 μm. An exact solution to the problem of scattering by an irregular particle, even if it were available, would yield more detail than necessary. An alternative approach is to formulate the irregular particle scattering problem in terms of the kinds of averages inherent in the optical properties of an ensemble of particles. Such a statistical method has been applied to an ensemble of small irregular particles by averaging over a range of electromagnetic microstates, in this instance randomly oriented anisotropic oscillators (i.e., Rayleigh ellipsoids). Infrared backscattering spectra calculated by this method agree better with laboratory-measured spectra for ammonium sulfate particles than those calculated using Mie theory.

(1983). Reply to “A note on the orientation and size of noctilucent cloud particles”. Tellus B: Chemical and Physical Meteorology: Vol. 35, No. 1, pp. 76-76.

Discussion sur la relation entre le spectre de dimension des gouttelettes de nuage, le contenu en eau et l'epaisseur optique du nuage