Flexible scattering order formulation of the discrete dipole approximation.

The discrete dipole approximation (DDA) is a well-known method for computation of the scattering of light from nonspherical particles. Here, we present a new scattering order formulation (SOF) of the DDA that allows the user to represent the scattering particle with higher flexibility than in conventional DDAs, while the computer memory required always scales as O(N). In our new SOF, the user can locate each dipole independently, or off-grid, in space, assign each dipole a unique size and a unique dipole shape as appropriate, and assign each dipole a unique magnetoelectric polarizability with no constraints. The cost of this flexibility is that the computation time is increased from O(N l o g N) to O(N 2). To compensate, our model allows the user to vary the range of dipole interaction in a unique manner. We find that, in cases in which the scatterer has at least one dimension that is sufficiently small compared with the wavelength, a relatively small number of iterations is required for convergence of the simulation, and in addition, a small dipole interaction range can be invoked to reduce the computation time to O(N) while still producing results that are sufficiently accurate.

The SSSS scheme: a method for calculating multiple scattering of electromagnetic radiation by a collection of sparsely spaced spherical scatterers of Mie-scattering size based on first principles.

We present a method for calculating multiple scattering of electromagnetic radiation by a collection of sparsely spaced spherical scatterers (SSSS) of Mie-scattering size based on first principles rather than radiative transfer theory. In this respect, our methodology is conceptually similar to the superposition T-matrix method. However, our implementation, which we call the SSSS scheme, differs in a number of respects. Overall, the SSSS scheme is simpler, it is better suited numerically to sparse spacing, and the computer memory required is only linearly dependent on the total number of scatterers. We suggest that the SSSS scheme would be particularly useful for examining the effects of different spatial configurations of drops within water clouds in Earth's atmosphere and would also be useful in other fields of research in which the exact configuration of a collection of sparsely spaced Mie-sized scatterers is important.

Considerations concerning backscattering in the scattering order formulation of the discrete dipole approximation as applied to non-absorbing scatterers.

The progression of secondary waves emanating from scattering centers within a non-absorbing material in the visible part of the electromagnetic spectrum (wavelength 0.500 µm) is traced using two modeling schemes: the scattering order formulation (SOF) of the discrete dipole approximation (the original SOF) and the SOF with the Twersky approximation, according to which the path of the secondary waves in a successive scattering chain does not loop through the same scattering center more than once (the SOF-Twersky). It is shown that for smaller submicron-sized scatterers (radius 0.100-0.200 µm), the scattering phase function in the backscattering hemisphere converges after a small number of orders of scattering, as does the scattering phase function in the forward scattering hemisphere. For larger submicron-sized to micron-sized scatterers (radius 0.300-0.500 µm), however, the scattering phase function in the backscattering hemisphere deviates significantly from the correct scattering phase function for a small number of orders of scattering, even as the scattering phase function in the forward scattering hemisphere remains at reasonable values. These results point to the particular importance of higher orders of scattering in reducing backscattering by particles composed of non-absorbing materials. Likewise, the results imply that a possible source for the lack of convergence in the original SOF lies in a certain lack of destructive interference of secondary waves propagating in particular into the backscattering hemisphere. The extent to which "downward recursion" can ameliorate this lack of destructive interference of secondary waves propagating into the backscattering hemisphere within the SOF is also examined. In the SOF with downward recursion, looping of secondary scattered waves is allowed, unlike the other versions of the SOF; however, the scattering centers situated the largest distance from one another within a given scatterer interact with one another first, and the interactions proceed to smaller and smaller scattering center separations.

Direct comparison between single-scattering properties of ordered and disordered aggregates of nano-sized scattering centers.

In this study, we examine the single-scattering properties of aggregates of nano-sized spherical scattering centers (spherules) of different sizes and refractive indices, with an emphasis on contrasting the single-scattering properties of ordered and disordered aggregates, holding all other parameters constant. The ordered aggregates are constructed by arranging the spherules in a simple cubic configuration, while the disordered aggregates are constructed using an ideal amorphous solid algorithm. The single-scattering properties of both kinds of aggregates are computed using the superposition T-matrix method. We find that, in most cases, the scattering and absorption and hence extinction of radiation by ordered aggregates is stronger than for disordered aggregates: for the cases we examine, the average percent difference in scattering efficiency is 14%, and the maximum percent difference in scattering efficiency is 44%; the average percent difference in absorption efficiency is 5.3%, and the maximum percent difference in absorption efficiency is 18%; the average percent difference in extinction efficiency is 12%, and the maximum percent difference in extinction efficiency is 40%. These differences have implications regarding radiative transfer in systems of amorphous particles in general.

Predicting the refractive index of amorphous materials using the Bruggeman effective medium approximation.

Previous studies have shown that the Lorentz-Lorenz relationship, or molar refractivity/specific refractivity effective medium approximation, enables a reasonable prediction of the refractive index of amorphous water ice, given the refractive index of crystalline water ice. In the current study, we show that the Bruggeman effective medium approximation provides an even closer match to measurements of the refractive index of several amorphous materials, given the refractive index of their crystalline phase. We show that the Bruggeman effective medium approximation provides a good match to measurements of the refractive index of amorphous ice as well. Thus, assuming that the volume fraction of the scattering centers is a constant for a given amorphous material (with respect to a given range of wavelengths) seems to be a more robust assumption than assuming that the molar mass and molar refractivity or specific refractivity are preserved in going from the crystalline state to the amorphous state of the same material. Our results have implications for astrophysics applications, as well as for the optics of non-crystalline materials in general.

Sensitivity study on the contribution of scattering by randomly oriented nonspherical hydrosols to linear polarization in clear to semi-turbid shallow waters.

The influence of hydrosol nonsphericity on the polarization characteristics of light under water is investigated by combining accurate single-scattering models for randomly oriented spheroidal scatterers with a radiative transfer model that employs Stokes formalism and considers refraction of direct unpolarized solar radiation and 100% linearly polarized radiation at the air-water interface followed by single scattering. Variations in what we call the "linear polarization phase function" (the degree of linear polarization as a function of scattering angle and the angle of linear polarization as a function of scattering angle) are examined for a wide range of spheroid aspect ratios and complex refractive indices of hydrosols. Implications for polarization-sensitive marine organisms and for remote sensing of the marine environment are discussed.

Sensitivity study on the effect of the optical and physical properties of coated spherical particles on linear polarization in clear to semi-turbid waters.

The influence of internal inhomogeneities within hydrosol particles on the polarization characteristics of light is investigated by combining an accurate coated sphere (core-shell) single-scattering model with a radiative transfer model that employs Stokes formalism and considers refraction of direct solar radiation at the air-water interface followed by single scattering. A Junge particle size distribution is assumed. Variations in what we call the "linear polarization phase function" (the degree of linear polarization as a function of scattering angle and the E-vector orientation as a function of scattering angle) are examined as a function of variations in the characteristics of the hydrosol particles. An extensive sensitivity study on the influence of variations in the real and imaginary parts of the refractive index of both the core and shell of the hydrosol particles and on the influences of variations in the ratio between the core radius and shell radius is conducted, varying the values of these parameters over the entire parameter space documented in the literature for actual hydrosol particles. In addition, calculations are conducted for specific parameter combinations in order to demonstrate the influence of some of the most important groups of hydrosols, namely, phytoplankton, gas bubbles, carbonaceous hydrosols, and mineral hydrosols, on the polarization field under water. Variations as a function of solar zenith angle are also investigated. Due to the assumption of single scattering, the results presented are relevant to conditions of low wind speed and a low scattering optical depth and/or low single-scattering albedo within the water body (clear to semi-turbid waters at shallow geometric depths and/or moderate to strong absorption within the water body) outside of Snell's window. Possible implications for aquatic animal polarization vision, for light polarization pollution, and for remote sensing are discussed.

Sensitivity tests on the convergence tendency of the scattering order formulation of the discrete dipole approximation.

In this study, we performed a series of sensitivity tests in order to elucidate the convergence tendency of the scattering order formulation (SOF) of the discrete dipole approximation (DDA). Using both the original formulation of the SOF and a new marching SOF, the progression of orders of scattering marches, along with the propagation of the incident plane wave through the scatterer, allow dipoles that come into steady-state oscillation with the incident wave earlier to more quickly advance to the next order of scattering that is local to them. Using the original SOF, we found that for cases in which the simulations converge (rods and very small spheres), there are a number of different possible convergence tendencies, among them convergence behavior that resembles the decaying oscillations of a damped harmonic oscillator. For the cases in which the original SOF does not converge, we did not find an indication that the lack of convergence is due to a numerical issue, such as round-off error, or that the divergence could be alleviated by increasing the dipole resolution or by decreasing the size of the marching step in the marching SOF. For cases in which the original SOF does not converge, with both the original SOF and the marching SOF, we found that the calculated extinction cross section exhibits oscillations about the correct value, but with increasing amplitude rather than with decreasing amplitude.

The spectral and spatial distribution of light pollution in the waters of the northern Gulf of Aqaba (Eilat).

The urbanization of the shores of the Gulf of Aqaba has exposed the marine environment there, including unique fringing coral reefs, to strong anthropogenic light sources. Here we present the first in situ measurements of artificial nighttime light under water in such an ecosystem, with irradiance measured in 12 wavelength bands, at 19 measurement stations spread over 44 square km, and at 30 depths down to 30-m depth. At 1-m depth, we find downwelling irradiance values that vary from 4.6 × 10-4 µW cm-2 nm-1 500 m from the city to 1 × 10-6 µW cm-2 nm-1 in the center of the gulf (9.5 km from the city) in the yellow channel (589-nm wavelength) and from 1.3 × 10-4 µW cm-2 nm-1 to 4.3 × 10-5 µW cm-2 nm-1 in the blue channel (443-nm wavelength). Down to 10-m depth, we find downwelling irradiance values that vary from 1 × 10-6 µW cm-2 nm-1 to 4.6 × 10-4 µW cm-2 nm-1 in the yellow channel and from 2.6 × 10-5 µW cm-2 nm-1 to 1.3 × 10-4 µW cm-2 nm-1 in the blue channel, and we even detected a signal at 30-m depth. This irradiance could influence such biological processes as the tuning of circadian clocks, the synchronization of coral spawning, recruitment and competition, vertical migration of demersal plankton, feeding patterns, and prey/predator visual interactions.

Formation of highly porous aerosol particles by atmospheric freeze-drying in ice clouds.

The cycling of atmospheric aerosols through clouds can change their chemical and physical properties and thus modify how aerosols affect cloud microphysics and, subsequently, precipitation and climate. Current knowledge about aerosol processing by clouds is rather limited to chemical reactions within water droplets in warm low-altitude clouds. However, in cold high-altitude cirrus clouds and anvils of high convective clouds in the tropics and midlatitudes, humidified aerosols freeze to form ice, which upon exposure to subsaturation conditions with respect to ice can sublimate, leaving behind residual modified aerosols. This freeze-drying process can occur in various types of clouds. Here we simulate an atmospheric freeze-drying cycle of aerosols in laboratory experiments using proxies for atmospheric aerosols. We find that aerosols that contain organic material that undergo such a process can form highly porous aerosol particles with a larger diameter and a lower density than the initial homogeneous aerosol. We attribute this morphology change to phase separation upon freezing followed by a glass transition of the organic material that can preserve a porous structure after ice sublimation. A porous structure may explain the previously observed enhancement in ice nucleation efficiency of glassy organic particles. We find that highly porous aerosol particles scatter solar light less efficiently than nonporous aerosol particles. Using a combination of satellite and radiosonde data, we show that highly porous aerosol formation can readily occur in highly convective clouds, which are widespread in the tropics and midlatitudes. These observations may have implications for subsequent cloud formation cycles and aerosol albedo near cloud edges.

Sensitivity study on the effects of hydrosol size and composition on linear polarization in absorbing and nonabsorbing clear and semi-turbid waters.

A full Mie scattering subroutine is employed to calculate what we call the linear polarization phase function (LPPF; percent polarization and e-vector orientation of radiation as a function of scattering angle) that results from refraction of the direct solar beam from air into water followed by single scattering by spherical hydrosols. The separate effects of refraction at the air-water interface, hydrosol size, the real and imaginary parts of the hydrosol refractive index, and absorption by the surrounding medium (water) on the LPPF are investigated. All of the above factors are found to alter the LPPF, changing the value of the maximum percent polarization (P(max)), the location of P(max), the number of fluctuations in the LPPF, or the location of the neutral points (points of 0 percent polarization), though absorption by the surrounding medium is found to have only a minimal effect. The character and extent of the influence on the LPPF is found to depend on the scattering regime (Rayleigh, Mie, or geometric optics). We conclude that in calculating underwater polarization, it is important to take into consideration Mie scattering even in relatively clear waters. We also find a coupling between the partial polarization and the e-vector orientation, which suggests that for some polarization-based visual tasks, only one of these would suffice. Other implications for aquatic animal polarization vision are discussed.