Paper detail

Exactly Solvable Dielectrics, Radiation Induced Forces and Causality

We present an exactly solvable model of a classical dielectric medium that gives an unambiguous local decomposition of field and charge motion and their contribution to the conserved quantities. The result is a set of four branches to the dispersion law that gives full independent freedom in the selection of initial data of the fields and charge motion, in contrast with constitutive laws. This is done with special care to the forces that exist at surfaces, coatings and the ends of packets. As a result the utility of a stress-tensor as a function of field strengths and dielectric response for deriving general forces is called into question. The Abraham-Minkowskii paradox is clarified from this point of view and the export of such notions to realistic media and metamaterials are discussed. One result of this model is a mathematically simpler and more intuitive understanding of causality in media than the Brillouin and Sommerfeld theories. Necessary elastic medium response is estimated and some implications of this picture for quantum effects are included based on conservation laws. This model can be extended to manifestly maintain these features as general nonlinear and time and space dependent changes in medium response are introduced. The extent to which this can provide a universal description for all dielectrics is discussed. A microscopic treatment of negative index materials from this point of view is included as an illustration of the extreme economy and simplicity of these methods.