Non-linear optics in liquid-crystalline phases A 4 × 4 matrix formalism

Abstract

The 4 × 4 matrix formalism of Berreman has been extended to include nonlinear optical terms. A non-linear source has to be added to the original homogeneous differential equation, giving an inhomogeneous equation that can be solved by standard procedures. The final expression can be given in a compact form by applying the Hamilton-Cayley theorem. The formalism is illustrated in the treatment of three-wave mixing in cholesteric phases.