Large and negative Goos–Hänchen shift near the Brewster dip on reflection from weakly absorbing media

Applying Artmann's formula to a light beam in the TM state of wave polarization, we show analytically the existence of a large and negative Goos-Hänchen shift near the angle of the Brewster dip on reflection from a weakly absorbing semi-infinite medium. The shift is opposite that in the case of total internal reflection, and it can be an order of magnitude larger than a wavelength if the absorption of the reflecting medium is sufficiently weak. Examples are given, and the detectibility of the shift is discussed.