Scattering solution to the problem of additional boundary conditions

Maxwell's boundary conditions (MBCs) were long known to be insufficient to determine the optical responses of spatially dispersive medium. Supplementing MBCs with additional boundary conditions (ABCs) has become a normal yet controversial practice. Here, the problem of ABCs is solved by analyzing some subtle aspects of a physical surface. A generic theory is presented for handling the interaction of light with the surfaces of an arbitrary medium and applied to study the traditional problem of exciton polaritons. We show that ABCs can always be adjusted to fit the theory in the examples studied here but they can by no means be construed as intrinsic surface characteristics, which are instead captured by a surface scattering amplitude. Methods for experimentally extracting the spatial profile of this quantity are proposed.