Optical Properties of Helical Cylindrical Molecular Aggregates: The Homogeneous Limit

Using a Frenkel exciton model, we study the optical absorption spectrum and linear and circular dichroism (CD) spectra of cylindrical molecular aggregates. We demonstrate that such aggregates can always be described as a stack of molecular rings with nearest-neighbor rings rotated relative to each other by a helical angle γ. For homogeneous aggregates, the cylindrical symmetry allows for a decomposition of the Hamiltonian into a set of effective one-dimensional Hamiltonians, which are characterized by a transverse wavenumber k2. The helical nature of the cylinder renders these Hamiltonians complex and noninversion symmetrical in general. Only the bands with k2 = 0 and k2 = ±1 are dipole-allowed and yield contributions to the various linear spectra studied. The k2 decomposition also allows for a convenient separation of the CD into ring and helical contributions, which in turn allows us to explain the strong sensitivity of this spectrum to various system parameters, such as the molecular orientations and the ratio of cylinder length and circumference. The latter is explicitly demonstrated by numerically studying the size dependence of the spectra for chlorosomes of green bacteria. The results suggest that the strong variation of the CD as reported experimentally may result from size variations. We also present analytical results valid for long cylinders. In this case, we find three superradiant states to be responsible for the complete linear optical response: one at total wave vector k = 0 and the other two (degenerate) at wave vectors determined by the circumference and the helical angle γ