Optical Absorption of Dye Molecules in a Spherical Shell Geometry

Abstract

Dipole−dipole interactions between neighboring dye molecules can cause substantial spectral changes in optical absorption, with a strong dependence on nearneighbors' relative distances and orientations. Such effects have been previously investigated in dimers, as well as planar arrangements of dipoles, but not to our knowledge in a threedimensional spherical configuration. This work provides a comprehensive exploration of the effect of dipolar interactions in such a geometry, varying the dye concentration, orientations, and uniformity in coverage. We also contrast this coupled-dipole model to a simpler but often-used homogeneous effective-medium approximation, which ignores effects of orientation and nonuniformity. The results provide a first step toward the full description of light scattering in a complex anisotropic core−shell geometry, which is of strong relevance in surface-enhanced spectroscopy applications, as well as in the strong coupling between molecular emitters and optical nanoresonators.

Electromagnetic interactions of dye molecules surrounding a nanosphere

“…The dotted black line, identical in all panels, shows the single isolated dye's lorentzian lineshape for reference. Without the sphere, we confirm the well-characterised red-shift and blue-shift of the absorption peak as the separation between dipole decreases 17 , corresponding to J-aggregate and H-aggregate configurations (head-to-tail vs side-by-side induced dipoles, respectively) 55 .…”

“…Panels (a)-(c) consider the dipole-dipole interactions in the spherical shell geometry without any core particle. The results for a shell of isotropic dipoles (a) closely resembles the predictions of a simple effectivemedium approximation, namely the splitting of the main absorption line with increasing dye concentration into a main redshifted peak, associated with head-to-tail interactions between neighbouring induced dipoles, and a weaker blue-shifted band associated with side-by-side interactions 17 . This interpretation is supported by the simpler spectral response exhibited by uniaxial dipoles: the radially-oriented dipoles are locally almost parallel (panel (b)), and show only a blue shift as the surface concentration increases; similarly, the tangentially-oriented dipoles favour a head-to-tail interaction between near neighbours (panel (c)).…”

“…The presence of a core sphere adds considerable complexity to the already-rich optical response of interacting dye molecules in arbitrary 3D configurations, which we recently investigated 17 . The core particle, especially when metallic or of high refractive index, can substantially modify the intensity and polarisation of the local field exciting the dipoles, and also their coupling.…”

“…Although dimers with specific relative orientations can capture the essential physics and predict red or blue shifts depending on the electromagnetic interaction between induced dipoles, a quantitative description of a large collection of dye molecules with specific relative positions and orientations requires an explicit account of all their pair-wise interactions. In a recent study 17 we highlighted the importance of collective effects in a complex 3-dimensional geometry such as a spherical arrangement of anisotropic dipoles. This situation carries, with additional complexity, to the case of core-shell structures where the core particle can strongly influence the local field intensity, polarisation, as well as self-reaction and dipole-dipole coupling.…”

“…The bottom panels (d)-(f) introduce a 14 nm radius silver sphere at the centre of the shell of dipoles. The core-shell separation is d = 1 nm, chosen for consistency with previous work 11,17 . Qualitatively, the coverage-dependent spectral shifts follow the same trends as in the void-core situation except for the predicted intensities.…”