Electromagnetic response of a dipole-coupled ellipsoidal bilayer

We derive an expression for the polarizability of an ellipsoidally shaped cell-like structure at field frequencies where membrane molecular resonances (vibrational and electronic) are important. We first present analytical results for the dielectric function of a flat, dipole coupled, bilayer consisting of molecules with one prominent resonance frequency. Due to the nature of the dipole coupling the dielectric function is different for the field being parallel or perpendicular to the bilayer normal with two new resonance frequencies omega=omega;(0 parallel) and omega=omega;(0 perpendicular ). We then combine this anisotropic bilayer dielectric function with the analytical solution of Gauss equation for an ellipsoid with an anisotropic coating (the coating dielectric function being different parallel and perpendicular to the coating normal) in order to find the polarizability of an ellipsoidal bilayer membrane. In particular, we find that for a thin-walled (compared to the size of the cell) membrane the resonance frequencies of the polarizability are the same as for a flat bilayer (independent of the cell shape). However, our analytic result for the geometric weights for the oscillator strengths is sensitive to the shape; the geometric weight for the omega=omega;(0 perpendicular ) (omega=omega;(0 parallel)) peak is largest when the external field is along the largest (smallest) axis. The geometric weights are shown to be constrained by three sum rules.