Linear and nonlinear dielectric theory for a slab: The connections between the phenomenological coefficients and the...

The response of dielectric media to electromagnetic fields can be described by using either the response to a Maxwell field E or to an externally produced field E. The former response is measured by phenomenological (dielectric) coefficients and the latter by susceptibilities. With the purpose of clarifying some recent proposals, the connections between the linear (two-point) and first non-vanishing nonlinear (four-point) dielectric coefficients and the susceptibilities for media confined to a slab are examined using a general procedure developed sometime ago. Unlike the relations found for correlations between a local polarization density and the integrated polarization densities (total polarizations), the point-point connections give rise to non-vanishing cross correlations between polarization densities which are parallel and perpendicular to the slab surfaces. The cross correlations in the two-point connections vanish when one polarization density is integrated to form the correlations between a local polarization density and the total polarization thereby losing angular information. The integrated parallel and perpendicular correlations remain different. When the four-point connections are similarly integrated most, but not all, cross correlations vanish. The angular correlations induced by the slab surfaces render the use of point-point correlations that are valid for isotropic media invalid for use in the integrated slab densities. In addition, the nonlinear fluctuations in the perpendicular components are drastically reduced relative to those in the parallel components or in isotropic media.