Controllable large positive and negative Goos–Hänchen shifts with a double-Lambda atomic system

We study the Goos–Hänchen shift (GHS) of a reflected light beam from a cavity containing a double-[Formula: see text] atomic medium that is bounded by two glass slabs. Applying both coherent and incoherent fields to the atomic medium leads to positive and negative controllability of GHS. For some specific values of the parameters of the system, the amplitude of the GHS becomes large, namely, in the order of [Formula: see text] times the wavelength of the incident light beam. These large shifts are found at more than one angle of incidence with a wide range of parameters of the atomic medium.