  The fractional Fourier transform (FRFT) naturally exists in the strongly
nonlocal nonlinear (SNN) media and the propagation of optical beams in SNN
media can be simply regarded as a self-induced FRFT. Through FRFT technic the
evolution of fields in SNN media can be conveniently dealt with and an
arbitrary square-integrable input field presents generally as a revivable
higher order spatial soliton which reconstructs its profile periodically after
every 4 times of Fourier transforms. The self-induced FRFT would illuminate the
prospect of the SNN media in new applications such as continuously tunable
nonlinearity-induced FRFT devices.
