_{3}Thin Film Waveguides Using M-line Spectroscopy Results]]>

_{2}O

_{3}thin film by solving the conventional prism waveguide coupler mode dispersion equations. These equations were solved using graphical and numerical methods. The numerical method is based on the Newton-Raphson algorithm. The solution to one mode of propagation was obtained by solving the zero order transverse electric (TE

_{0}) mode and transverse magnetic (TM

_{0}) mode. The values of 1.61±0.02 and 253.00±0.05 nm were obtained for the refractive index and thickness respectively from the graphical solution while the Newton-Raphson algorithm gave 1.6200±0.0007 for the refractive index and 240.1100±0.0005 nm for the film thickness. For two modes of propagation, two TE and two TM modes were considered. The graphical solution for the two TE modes gives a refractive index of 1.5995±0.0002 and a thickness of 772.526±0.001 nm with the Newton-Raphson algorithm giving 1.5995±0.0003 for the refractive index and 767.850±0.005 nm as film thickness. The two modes of propagation for the TM modes gives the graphical results for the refractive index and thickness as 1.6010±0.0002 and 774.671±0.004 nm respectively while the result of the Newton-Raphson algorithm is 1.6010±0.0002 and 773.336±0.003 nm respectively. In comparison with the experimental values obtained, the percentage uncertainty is less than ±5% for both parameters. The results generally, showed a higher uncertainty in determining the film thickness than the refractive index for both TE and TM polarization.]]>