Polariton Green’s functions for semi-infinite spatially dispersive media with applications to molecular crystal reflectivity spectra

A complete set of polariton Green’s functions are deduced for the half-space. The symmetry conditions used by Fuchs and Kliewer and Rimbey and Mahan placed on electromagnetic fields in a semi-infinite homogeneous isotropic medium are shown to correspond to external current densities in an infinite anisotropic medium. Solutions to Maxwell’s equations in spatially dispersive media are delineated for arbitrary polarization. Components of the Green’s dyadic are related to the surface Green’s function derived by Garcia-Moliner and Rubio. The normal incidence reflectivity spectra of 1-5 bis(dimethylamino) -pentamethinium perchlorate is calculated near the intense (f∼3.31), 4090 Å molecular transition using the linear response theory of Davydov, and the reflectivity theories of Mahan and Obermair, Rimbey and Mahan, and Fuchs and Kliewer. A one-dimensional interacting exciton–phonon system is used as the model Hamiltonian. The general features of the metallic reflection spectrum, i.e., bandwidth, phonon shoulder, and peak height, are reproduced satisfactorily. The formalisms of Mahan and Obermair and Rimbey and Mahan reproduce the spectrum more accurately than the Fuchs–Kliewer reflectivity indicating the ABC P (0+) =0 is appropriate for this Frenkel exciton system.