Phase change of light reflected by a discontinuity in the derivatives of the refractive index

The amplitude and phase representation of classic plane electromagnetic waves is used to model light propagating through transparent stratified media, with a continuous refractive index profile. Numeric solutions for the nonlinear amplitude equation at normal incidence are obtained. Discontinuities of the refractive index derivatives exhibit reflection enhancement. Depending on the order of the discontinuity, the phase change upon reflection obtained from the numerical results can be ±π/2 in addition to the usual 0, or ±π.