Accurate calculation of Goos-Hänchen shift at critical angle for complex laser beam profiles using beam propagation method

Abstract

The characteristics of an incident Gaussian monochromatic light beam at sharp critical angle are investigated and analyzed. The numerical results are obtained using fast Fourier transform based beam propagation method (FFT-BPM). In this study, we adapt the FFT-BPM propagator to evaluate the reflected and refracted fields at a step discontinuity in the transverse electric (TE) polarizations. The field properties in the denser and rare medium are carefully examined. Further, the Goos-Hänchen (GH) shift is calculated based on the lateral field using the FFT-BPM at sharp critical angle which cannot be obtained by other analytical methods. Moreover, the effects of the wavelength and denser medium refractive index on the GH shift are also investigated. The calculated results are in good agreement with that introduced in the literature. Moreover, the suggested analysis could shed light on more accurate modeling techniques for the GH shift calculation and its impact on the relevant photonic applications. In this regard, the calculated GH shifts at sharp critical angle are used for monitoring glucose concentration variations in biomedical applications with high sensitivity. Additionally, we presented for the first time to the authors’ knowledge- the effect of the incident field pattern such as: Lorentz-Gauss, Super-Gaussian, Super-Lorentzian, and super-Lorentz-Gauss on the GH calculations.