Optical experiments on second-harmonic generation from split-ring-resonator square arrays show a nonmonotonic dependence of the conversion efficiency on the lattice constant. This finding is interpreted in terms of a competition between dilution effects and linewidth or near-field changes due to interactions among the individual elements in the array.

Plasmonic nanoantennas provide unprecedented opportunities to concentrate light fields in subwavelength-sized volumes. By placing a nonlinear dielectric nanoparticle in such a hot spot, one can hope to take advantage of both the field enhancement provided by nanoantennas and the large, nonlinear optical susceptibility of dielectric nanoparticles. To test this concept, we combine gold gap nanoantennas with second-order, nonlinear zinc sulfide nanoparticles, and perform second harmonic generation (SHG) spectroscopy on the combined hybrid dielectric/plasmonic nanoantennas as well as on the individual constituents. We find that SHG from the bare gold nanoantennas, even though it should be forbidden due to symmetry reasons, is several orders of magnitude larger than that of the bare zinc sulfide nanoparticles. Even stronger second harmonic signals are generated by the hybrid dielectric/plasmonic nanoantennas. Control experiments with nanoantennas containing linear lanthanum fluoride nanoparticles reveal; however, that the increased SHG efficiency of the hybrid dielectric/plasmonic nanoantennas does not depend on the nonlinear optical susceptibility of the dielectric nanoparticles but is an effect of the modification of the dielectric environment. The combination of a hybrid dielectric/plasmonic nanoantenna, which is only resonant for the incoming pump light field, with a second nanoantenna, which is resonant for the generated second harmonic light, allows for a further increase in the efficiency of SHG. As the second nanoantenna mediates the coupling of the second harmonic light to the far field, this double-resonant approach also provides us with control over the polarization of the generated light.

The visible reflectance spectrum of many solar system bodies changes with changing viewing geometry for reasons not fully understood. It is often observed to redden (increasing spectral slope) with increasing solar phase angle, an effect known as phase reddening. Only once, in an observation of the Martian surface by the Viking 1 lander, was reddening observed up to a certain phase angle with bluing beyond, making the reflectance ratio as a function of phase angle shaped like an arch. However, in laboratory experiments this arch-shape is frequently encountered. To investigate this, we measured the bidirectional reflectance of particulate samples of several common rock types in the 400-1000 nm wavelength range and performed ray-tracing simulations. We confirm the occurrence of the arch for surfaces that are forward scattering, i.e. are composed of semi-transparent particles and are smooth on the scale of the particles, and for which the reflectance increases from the lower to the higher wavelength in the reflectance ratio. The arch shape is reproduced by the simulations, which assume a smooth surface. However, surface roughness on the scale of the particles, such as the Hapke and van Horn (1963) fairy castles that can spontaneously form when sprinkling a fine powder, leads to monotonic reddening. A further consequence of this form of microscopic roughness (being indistinct without the use of a microscope) is a flattening of the disk function at visible wavelengths, i.e. Lommel-Seeliger-type scattering. The experiments further reveal monotonic reddening for reflectance ratios at near-IR wavelengths. The simulations fail to reproduce this particular reddening, and we suspect that it results from roughness on the surface of the particles. Given that the regolith of atmosphereless solar system bodies is composed of small particles, our results indicate that the prevalence of monotonic reddening and Lommel-Seeliger-type scattering for these bodies results from microscopic roughness, both in the form of structures * Corresponding author built by the particles and roughness on the surface of the particles themselves. It follows from the singular Viking 1 observation that the surface in front of the lander was composed of semi-transparent particles, and was smooth on the scale of the particle size.

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There are two widely accepted restrictions on the application of the discrete dipole approximation (DDA) in the study of light scattering by particles comparable to the wavelength: (1) when considering dielectric particles, the size of the cells must satisfy the condition kdjmj < 0:5, where k is the wavenumber, d is the size of the cells, and m is the complex refractive index of the constituent material and (2) when considering conductive particles, the size of the cells must be small enough to reproduce sufficiently the evolution of the electromagnetic field in the skin layer. We examine both restrictions when the DDA is applied to irregularly shaped particles and show that its restrictions are not as strong as is widely accepted. For instance, when studying irregularly shaped particles averaged over orientations, even at kdjmj ¼ 1, the DDA provides highly accurate numerical results. Moreover, we show that the impact of using large constituent cells is similar to that produced by surface roughness; therefore, the replacement of the target particle by an array of large constituent cells has the same effect, qualitatively, as incorporating additional small-scale surface roughness on the particle. Such a modification of the target particle can be desirable in many practical applications of DDA when irregularly shaped particles are considered. When applying DDA to conductive, nonspherical particles, the insufficient description of the electromagnetic field in the skin layer does not lead to a violation of the Maxwell equations, although it has a visible but nonmajor influence on the light-scattering properties of the target.

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Abstract.We have analyzed brightness and polarization data of comet 96P/Machholz, obtained with the SOHO-LASCO C3 coronagraph at phase angles up to 167• and 157• , respectively. The polarization data are characteristic of a typical dusty comet. Within error limits the corresponding trigonometric fit describes the new data measured at larger phase angles as well as those of the previously known range. In the phase angle range from 110• to 167• the brightness increases almost linearly by about two orders of magnitude. The gradient is independent of wavelength. From the absence of a diffraction spike we conclude that the grains contributing significantly to the scattered light must have a size parameter x = 2πr/λ ≥ 20, i.e. have a radius larger than 1 µm. Fits of the data with Mie calculations of particles having a power law distribution of power index ≈ 2.5 provide a best fit refractive index m = 1.2 + i0.004. In the framework of effective medium theory and on the assumption of a particle porosity P = 0.5 this leads to a complex refractive index of the porous medium m = 1.43 + i0.009. A higher refractive index is possible for more porous grains with very low absorption. The large particle sizes are in qualitative agreement with findings derived from the analysis of the motion of cometary dust under solar radiation pressure (Fulle and coworkers, see Fulle et al. 2000;Jockers 1997) and with the in-situ measurements of the dust of Halley's comet.

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