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.
Monzon
JJ
Departamento de Optica, Facultad de Ciencias Fisicas, Universidad Complutense, Madrid, Spain.
Sanchez-Soto
LL