Extinction and scattering of light by nonspherical plasmonic particles in absorbing media

Abstract

Electromagnetic scattering by spheres embedded in an absorbing medium has attracted much attention and has been solved recently by an extension of conventional Lorenz-Mie (LM) theory. By contrast, no relevant studies have been published for nonspherical absorbing particles. To the best of our knowledge, we present the first T-matrix method (TMM) formalism and relevant computer simulations for nonspherical particles embedded in an absorbing host. We also derive analytical electrostatic and improved electrostatic approximations (EA and IEA) for small spheroids in an absorbing host. To exemplify the developed theory and computer codes, we consider randomly oriented prolate and oblate Au and Ag nanospheroids, cigar-like nanorods, and nanodisks embedded in a water-like absorbing medium with the complex refractive index 1.33+i(0-0.3), in a lossy poly(3-hexylthiophene) (P3HT) matrix, and the lossless poly(methyl methacrylate) (PMMA). We analyze two far-field optical observables inherent to the particles: the extinction cross section and the normalized 4 × 4 scattering matrix. Specifically, we discuss the spectral extinction, the phase function, and the depolarization ratio, which characterizes the cross-polarized intensity of scattered light. To normalize the phase function, we also calculated the effective far-field scattering cross section. For maximal size parameters less than 1, IEA and TMM cross section spectra agree perfectly, independently on the aspect ratio (1–10) and imaginary part of host absorption (0–0.3). Thus, IEA provides a simple, accurate, and user-friendly alternative to TMM codes when the maximal particle size is less than 200 nm, irrespective of the host absorption. The general effect of increasing host absorption is to decrease and broaden the plasmonic extinction and scattering peaks, independently of the particle shape, material (Au or Ag), and the size correction of optical constants. However, in the lossy P3HT matrix, the dominant plasmonic resonances (PRs) are red-shifted and narrowed compared to the corresponding peaks in PMMA. In particular, the absolute FWHM of 12–20 nm and the relative FWHM/PR values of 1.9–2.5% were found for prolate Au and oblate Ag particles embedded in P3HT. This unusual narrowing is explained by the extreme spectral dependence of P3HT absorption. The phase function of Au and Ag nanorods is symmetrical irrespective of the aspect ratio and the host absorption, but it does not follow the Rayleigh law. The host absorption decreases the spectral maxima of the depolarization ratio and shifts them slightly to the red.