Refractive index gradient measurement across the thickness of a dielectric film by the prism coupling method

A method is proposed for measuring the refractive index gradient $n(z)$ in nonuniformly thick dielectric films. The method is based on the excitation of waveguide modes in a film using the prism coupling technique and on the calculation of $n(z)$ and film thickness $H_f$ with the help of the angular positions of the TE or TM modes. The method can be used for an arbitrary shape of the index modulation over the film thickness in the limit of a small gradient $(\Delta n(z)/n(z)\ll 1)$.