Weak measurement of the Goos–Hänchen shift for a Hermite–Gaussian laser beam

We report on an experimental investigation of the Goos–Hänchen (GH) optical beam shift in the vicinity of the critical angle of incidence at an air–glass interface using a weak value amplification (WVA) technique for two mutually orthogonal first order Hermite–Gaussian (HG) modes (HG₁₀ and HG₀₁) of a light beam at 633 nm generated by a phase-only reflective spatial light modulator. We have developed a mathematical approach to visualize the beam shaping due to the WVA scheme of beam shifts for the HG modes. The study reveals the angle of incidence dependency of the GH shift in the total internal reflection condition. For both modes, a detailed study of the horizontal and transverse beam shift values with varied post-selection angles is also reported. In addition, a comparison of the beam shift values for both of the selected modes with the fundamental mode (HG₀₀) has been demonstrated. We found a significant enhancement (about two to three times) in the beam shifts for the first order HG₁₀ and HG₀₁ modes compared to the fundamental mode (HG₀₀). Our results clearly demonstrate the advantages of the HG modes of the light beam-exploiting WVA technique and thus may contribute significantly to this field and open up important applications in photonic manipulation and future technologies.