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In this work, the one-dimensional finite fractional Fourier transform has been considered in application to gradient optical waveguides. The eigenfunctions of it has been discussed. The relation between obtained functions, Hermite-Gaussian modes and spheroidal functions has been shown. The dependence of input domain width and number of nonzero eigenfunctions of transformation has been demonstrated. The functions which recover its form at given distance from the front plane have been calculated.

Calculation of eigenfunctions of bounded waveguide with quadratic refractive index