An Approach to the Nonlinear Selvedge Response in Nonlocal Metal Optics within the Framework of the Ewald-Oseen Extinction Theorem

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Abstract
The aim of this paper is to present the theoretical foundation for parametric second-harmonic generation in metals in context with a generalized Ewald-Oseen extinction theorem. On the basis of a dyadic sharp-boundary Green's function satisfying a nonlocal propagator equation, the framework of the study is established. Generalized extinction theorems valid in the regime of nonlocal nonlinear optics enable one to consider the selvedge response and the coupling between the selvedge and the bulk in a physically appealing way. With the driven second-harmonic current density acting as an ‘external’ source within the sharp-boundary metal volume, an integral equation appropriate for studies of the nonlinear selvedge scattering problem is given.