Invite paper: Self-imaging in multimode graded-index fibers and its impact on the nonlinear phenomena

The phenomenon of periodic self-imaging of optical beams, occurring inside any graded-index (GRIN) medium, was studied during the decade of the 1970s and was exploited to commercialize the GRIN lens. It has been found in recent years that the periodic self-imaging also affects the nonlinear propagation of optical pulses inside multimode GRIN fibers. In this paper, we first present the theory of self-imaging in linear GRIN fibers using a modal expansion approach. It is shown that the optical field at any point inside the fiber can be written without any reference to the fiber modes as a two-dimensional integration over the input field using a propagation kernel that is similar to that found in diffraction theory. However, this kernel has a specific property that reproduces the input field precisely in a periodic fashion along the length of a GRIN fiber (self-imaging). We apply this kernel to study the propagation of a Gaussian beam and discuss how self-imaging is modified by self-focusing produced by the Kerr nonlinearity. We then consider propagation of the continuous and pulsed Gaussian beams inside a GRIN fiber and discuss how self-imaging affects the modulation instability, leads to the formation of GRIN solitons, and produces novel temporal and spectral features when short optical pulses are launched that are intense enough to form high-order solitons.