Orientation dependence of optical activity in light scattering by nanoparticle clusters

Abstract

The optical properties of nanoparticle clusters vary with the spatial arrangement of the constituent particles, but also the overall orientation of the cluster with respect to the incident light. This is particularly important in the context of nanoscale chirality and associated chiroptical responses, such as circular dichroism or differential scattering of circularly polarised light in the far-field, or local degree of optical chirality in the near-field. We explore the angular dependence of such quantities for a few archetypal geometries: a dimer of gold nanorods, a helix of gold nanospheres, and a linear chain of silicon particles. The examples serve to illustrate the possible variation of chiroptical responses with the direction of light's incidence, but also, consequently, the importance of a robust orientation-averaging procedure when modelling general clusters of particles in random orientation. Our results are obtained with the rigorous superposition T-matrix method, which provides analytical formulas for exact orientation-averaged properties.

Orientation-averaged light scattering by nanoparticle clusters: far-field and near-field benchmarks of numerical cubature methods

“…In contrast, the cubature methods used in this work have predetermined nodes and weights, regardless of the integrand's angular profile. The advantage is expected to be highest for sharply-defined angular properties, as exhibited by large elongated nanostructures supporting collective modes with well-defined momentum 40 . We tested briefly some adaptive cubature methods 61,62 , and did not observe a better performance on the above examples compared to Levedev, spherical t-design, or Gauß-Legendre cubatures.…”

“…Indeed, averaging the response along x, y, z axes is a commonly-used procedure for orientation-averaging in this regime 10 . Larger particles and/or clusters of particles may however show very directional responses, such as the photonic jet effect in large Mie scatterers 41 , or waveguide modes along chains of particles 40 or dielectric particles with a high aspect ratio 42 .…”

“…Our first illustration considers light scattering by a 'fingers crossed' dimer of gold nanorods 43 , which has attracted considerable interest in recent years as a prototypal structure for chiral plasmonics [44][45][46][47][48][49][50][51] . We recently revisited this geometry with a focus on the angular dependence of the chiroptical far-field properties, namely the circular dichroism in extinction, scattering and absorption 40 . Despite its sim- plicity, involving only two particles, the structure reveals an interesting response arising from the hybridisation of localised plasmon resonances, and a balance between absorption and scattering contributions as the size of the structure is varied 43 .…”

“…For very small dimers this angular response is relatively smooth nonetheless, and as a result the orientation-averaged response may be reasonably approximated by the average over 3 orthogonal incidence directions. As the scale of the dimer increases, however, this is no longer an accurate approximation 40 . We confirm here this observation with a more complete characterisation of numerical angular averaging, using the previouslydefined seven cubature methods (Fig.…”

Multiple scattering of light in nanoparticle assemblies: user guide for the TERMS program

“…• Orientation-averaged far-field properties can be obtained at very little computational cost, with analytical formulae 21,[36][37][38][39] . Orientationaveraged near-field quantities can also be computed 15,22 , albeit with some computational overhead, providing analytical benchmark results 40 .…”