Abstract

From a matrix formulation of the boundary conditions we obtain the fundamental invariant for an interface and a remarkably simple factorization of the interface matrix, which enables us to express the Fresnel coefficients in a new and compact form. This factorization allows us to recast the action of an interface between transparent media as a hyperbolic rotation. By exploiting the local isomorphism between SL(2, C) and the (3+1)-dimensional restricted Lorentz group SO(3, 1), we construct the equivalent Lorentz transformation that describes any interface.

© 2000 Optical Society of America

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