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Assuming a non-paraxial propagation operator, we study the propagation of anelectromagnetic field with an arbitrary initial condition in a quadratic GRINmedium. We show that at certain specific periodic distances, the propagatedfield is given by the fractional Fourier transform of a superposition of theinitial field and of a reflected version of it. We also prove that forparticular wavelengths, there is a revival and a splitting of the initialfield. We apply this results, first to an initial field given by a Besselfunction and show that it splits into two generalized Bessel functions, andsecond, to an Airy function. In both cases our results are compared with theexact numerical ones.

Generalized revival and splitting of an arbitrary optical field in GRIN media