Tunable cratering of lateral Goos–Hänchen shifts in reflection and transmission of structured light in chiral atomic medium

The birefringence cratering of reflection, transmission and corresponding Goos Hänchen (GH) shift are investigated in reflection and transmission beams through four level chiral atomic medium of structured light. The reflection and transmission of left and right circularly polarized light obey normalization condition and strong cratering oscillation functions of positions and azimuthal quantum number \(\ell \) of control field. Crater types reflection and transmission are investigated whose numbers increase with azimuthal quantum numbers having varying in shapes. The GH shifts in reflection and transmission is positive and oscillated with position \(x/\lambda \) and \(y/\lambda \). The numbers of crater in GH shifts depend on the azimuthal quantum number \(\ell \) of control field. The values of both GH shift in reflection and transmission varies in the range of \(6\lambda \le S_R^{(-)}\le 12\lambda \) and \(6\lambda \le S_T^{(-)}\le 12\lambda \) with increasing craters to increase azimuthal quantum number \(\ell \) of control field. The modified results of the GH shifts are useful for biosensor and plasmonster technology.