In this paper we consider the use of a one-dimensional fractional Fourier transform for gradient-index optical waveguides. We calculate eigenfunctions of the transform in view of a limited range in the spatial and spectral domain.

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Abstract. This research has simulated the propagation of the light beams through the quadratic index media. Five methods of simulation were considered and the propagating beams corresponding to different input signals such as Airy-Gaussian beams, rectangular function pulses, triangular function pulses, cosine function signals and finite eigenfunctions were demonstrated. Originally, FrFT was used in quantum mechanics; however, recently it has increasingly become a focus of opticists. As a result, extensive research involving its properties, optical realization and potentiality opportunities in optic applications has been performed. Thus, currently FrFT is actively used in optical image processing [3]. Moreover, the fractioning of some transformation provides a new degree of freedom (fraction order) that can be used for a more complete description of the object (signal) or as an additional encoding parameter.FrFT is used in differential equation solving, in quantum mechanics and quantum optics, in optical theory of diffraction, in optical system and optical signal processing