Reflection of a TE-polarised Gaussian beam from a layered structure under conditions of resonance excitation of waveguide modes

The problem of reflection of a TE-polarised Gaussian light beam from a layered structure under conditions of resonance excitation of waveguide modes using a total internal reflection prism is considered. Using the spectral approach we have derived the analytic expressions for the mode propagation lengths, widths and depths of m-lines (sharp and narrow dips in the angular dependence of the specular reflection coefficient), depending on the structure parameters. It is shown that in the case of weak coupling, when the propagation lengths l_m of the waveguide modes are mainly determined by the extinction coefficient in the film, the depth of m-lines grows with the mode number m. In the case of strong coupling, when l_m is determined mainly by the radiation of modes into the prism, the depth of m-lines decreases with increasing m. The change in the TE-polarised Gaussian beam shape after its reflection from the layered structure is studied, which is determined by the energy transfer from the incident beam into waveguide modes that propagate along the structure by the distance l_m, are radiated in the direction of specular reflection and interfere with a part of the beam reflected from the working face of the prism. It is shown that this interference can lead to the field intensity oscillations near m-lines. The analysis of different methods for determining the parameters of thin-film structures is presented, including the measurement of mode angles θ_m and the reflected beam shape. The methods are based on simultaneous excitation of a few waveguide modes in the film with a strongly focused monochromatic Gaussian beam, the waist width of which is much smaller than the propagation length of the modes. As an example of using these methods, the refractive index and the thickness of silicon monoxide film on silica substrate at the wavelength 633 nm are determined.