Index profiles of planar optical waveguides determined from the angular dependence of reflectivity

Abstract

The relation between the refractive index distribution and the angular dependence of reflectivity is investigated for planar optical waveguides. Index distributions with rapid variations of the profile function can be determined from the angular dependence of the difference in reflectivity <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\DeltaR</tex> between the waveguide and the substrate by means of numerical parameter optimization. <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\DeltaR</tex> is measured with high precision using a simple lock-in technique. This nondestructive method for profile evaluation is appropriate in particular for monomode waveguides where other methods fall to apply. It is tested with He+-implanted fused silica and results obtained for several ion energies and doses demonstrate the practical use of this method.