Fresnel formulas as Lorentz transformations
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.
Departamento de Optica, Facultad de Ciencias Fisicas, Universidad Complutense, Madrid, Spain.
JJ
Monzon
LL
Sanchez-Soto