Cut-off frequency variation in optical waveguides due to photon tunnelling

We show that the cut-off frequency (low corner frequency) for an undersized waveguide can change due to the photon tunnelling phenomenon. The Helmholtz wave equation will be used to calculate the tunnelling time of a photon through a refraction index barrier. We report an analytical expression for the transit time of the photon in a refraction index barrier as well as the transmission coefficient. It is predicted that the tunnelling time depends on the refraction index, the thickness of the barrier and also on the incident wave frequency. We will exploit this idea to obtain light coupling to a classically forbidden region, hence describing the cut-off frequency variation. A comparison with the experimental data is also reported.