Spectroscopic signature of fractal excitons

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Abstract
The dependence of the optical or infrared spectra of an object on its shape, size and dimensionality is considered for objects that are aggregates of molecules whose transition dipoles are coupled. The exciton model is used in our analysis. First we review the spectroscopy and density of states of one, two and three dimensional aggregates. We show how the spectroscopic signature depends on the shape, size and dimensionality of these Euclidian structures. Next we explore, through a variety of computer experiments, some properties of non-Euclidian aggregates, i.e. fractals. These fractals are grown by diffusion-limited aggregation (DLA) in a plane and have a Hausdorff dimensionality of ca. 1.7. For fractal aggregates containing from 100 to 1000 monomers (e.g. molecules) and grown under a variety of conditions we find that the density of states distributions are essentially invariant. The shape of these distributions for fractals is also distinct from the density of states of the Euclidian structures. Likewise the spectra of the fractals we have studied show a regularity in optical cross-section vs. energy (or wavelength). The spectra of fractals appear then to have a characteristic signature. To our knowledge there have been no assignments of fractal exciton spectra. However, our analysis provides a qualitative description of these spectra.

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