Wave propagation of exciton polaritons by a wave-vector-space method

The constitutive equation for Frenkel exciton polarization in a bounded medium is derived from both macroscopic Lagrangian theory and microscopic coherent-wave theory. The result corresponds to the Hopfield and Thomas model previously thought to apply to the Wannier exciton. We show that the Frenkel exciton must be regarded as a finite-volume object and so the change of the exciton binding energy near a surface must be included in the optics problem of transmission/reflection near its resonance (the so-called additional boundary condition or ABC problem). The combination of the exciton polarization equation and the wave equation is then solved by a new mathematical method in wave-vector space (k space). We show that the truly macroscopic nonlocal susceptibility must contain surface terms that previous macroscopic theories did not include. We obtain a different solution to the problem with this theory that requires no boundary conditions. By transforming to real space, we also derive the ABC needed for a macroscopic real-space approach and point out the important (but often confused) difference between macroscopic and microscopic boundary conditions.