Can the Light Scattering Depolarization Ratio of Small Particles Be Greater Than 1/3?

Abstract

According to the theory of light scattering by small randomly oriented particles, the depolarized ratio of the scattered intensities, I(vh)/I(vv), cannot exceed 1/3. Here we show that this conclusion does not hold for nonspherical plasmon resonant metal particles. Our analysis is based on the Rayleigh approximation and the exact T-matrix method as applied to spheroids and circular cylinders with semispherical ends. For small particles, the condition I(vh)/I(vv) >1/3 can be satisfied within the upper left quadrant of the complex relative dielectric permeability Real(eps) < -2 (rods) and within the upper unit semicircle centered at Real(eps) = -1 (disks). For gold nanorods with the axis ratio exceeding 2, the maximal theoretical values I(vh)/I(vv) lie between 1/3 and 3/4 at wavelengths of 550-650 nm. The extinction and static light scattering spectra (450-850 nm, at 90 degrees degrees) as well as the depolarized ratio of He-Ne laser light scattering were measured with gold nanospheres (the average diameters of 21, 29, and 46 nm) and nanorods (the longitudinal plasmon resonance peak positions at 655, 692, and 900 nm). The measured depolarization ratios of nanospheres (0.07-0.16) and nanorods (0.3-0.48) are in good agreement with theoretical calculations based on estimations of the average particle size and shape.