Multi-wave mixing dependence Goos–Hänchen shift of structured light in atomic medium

The reflection, transmission, and related Goos–Hänchen (GH) shifts of structured light are investigated by multi-wave mixing conditions in this paper. The terms absorption, dispersion, group index, and photon drag rotation of structured light are also studied by multi-wave mixing. The maximum values of group index of [Formula: see text] and rotary photon drag of [Formula: see text] micro-radian are reported in this work. Significant modifications of GH shift in reflection and transmission modes are investigated with azimuthal quantum number of structured light along with multi-wave mixing. Various crater shapes are reported in reflection and transmission modes and with their corresponding GH shifts in reflection and transmission modes. The reflection and transmission GH shifts exhibit a correlation where [Formula: see text]ve reflection GH shift regions correspond to −ve transmitted GH shift regions, and vice versa. The maximum of [Formula: see text]ve and −ve GH shift in reflection and transmission modes is investigated up to [Formula: see text]. The modified GH shifts in reflection and transmission modes have significant applications in high-resolution imaging, sensing, and optical signal processing.