Coherent control of spatial and angular Goos–Hänchen shifts with spontaneously generated coherence and incoherent pumping

We propose an efficient scheme to manipulate the Goos-Hänchen (GH) shift of a reflected beam from a metal-clad waveguide, where a coherent atomic medium with a Λ-type configuration is employed as the substrate. Using experimentally achievable parameters, we identify the conditions under which spontaneously generated coherence (SGC) allows us to enhance the spatial and angular GH shifts of the reflected beam. With the help of SGC, the relative phases of the probe and control fields can alter the absorption gain and refractive index of the atomic medium, thereby manipulating the magnitudes, signs, and positions of the spatial and angular shifts. Furthermore, the spatial and angular GH shifts can be coherently controlled via adjusting the incoherent pumping rate and the intensity of the control field. Our proposal provides an avenue for the manipulation of spatial and angular GH shifts and potential applications in optical switching and optical steering.