The frequency crossover for the Goos-Hanchen shift

For total reflection, the Goos-Hanchen (GH) shift is proportional to the wavelength of the laser beam. At critical angles, such a shift is instead proportional to the square root of the product of the beam waist and wavelength. By using the stationary phase method (SPM) and, when necessary, numerical calculations, we present a detailed analysis of the frequency crossover for the GH shift. The study, done in different incidence regions, sheds new light on the validity of the analytic formulas found in literature.