Topological localized region of Goos-Hänchen shifts in reflection and transmission

In this manuscript, the Goos-Hänchen shift of the transmitted and reflected probe beam is controlled and modified. Topologically localized regions are reported in the G-H shift by introducing the position and orbital angular momentum dependency in the Rabi frequencies of the control fields. The system parameters along with the azimuthal quantum number are used to control and modify G-H shift as well as the topological regions. Crater and peak type topological regions are reported in the G-H shift of the reflected as well as transmitted beam. The number of localized regions are reported to strictly follow the general formula 2l2. The maximum shift in the reflected spectrum is reported to be Sr/λ=−140, where as in the transmitted spectrum it is only St/λ=−15. The modified results might have significant applications in optical waveguide switches and sensors