Fresnel formulas as Lorentz transformations

From a matrix formulation of the boundary conditions we obtain the fundamen tal 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 o f an interface between transparent media as a hyperbolic rotation. By explo iting the local isomorphism between SL(2, C) and the (3 + 1)-dimensional re stricted Lorentz group SO(3, 1), we construct the equivalent Lorentz transf ormation that describes any interface. (C) 2000 Optical Society of America [S0140-3232(00)01208-4].