Abstract: Total reflection at the interface between a medium with high refractive index and an ultra-thin material with low refractive index is studied.An ultra-thin material with low refractive index is inserted in the medium with high refractive index.The reflection curve is analyzed by using the transfer matrix method.Numerical simulations show that the reflectivity can not reach 100% although the incident angle is lager than the critical angle of total reflection when the material with low refractive index is thinner than the wavelength.That is,the optical tunneling effect appears.The quantitative analysis is helpful to understand the concepts of evanescent waves and optical tunneling effects.

Key words: transfer matrix, total reflection, ultra-thin material with low refractive index, evanescent wave