Goos-Hanchen shift description in planar optical waveguides

In this paper, using the Helmholtz wave equation and the tunneling time of a photon through an index of refraction barrier, the reflection delay time and reflection coefficient calculated and analytical expression for these quantities are introduced. It predicts that, the reflection delay time and coefficients depends on the refraction index, the thickness of barrier, the incident angle, and the incident wave frequency. Using these relations, we obtain the light penetration depths as well as horizontal shifts for reflection component of incident light to interface of two media. Our results completely describe the nature of Goos-Hanchen shifts in planar optical slab waveguides as a common device in optical integrated circuits (OIC). Also, the experimental data and our prediction completely close together.