We show analytically that bright and dark spatial self-similar waves can propagate in graded-index amplifiers exhibiting self-focusing or self-defocusing Kerr nonlinearities. The intensity profiles of the novel waves are identical with those of fundamental bright or dark spatial solitons supported by homogeneous passive waveguides with the same type of nonlinearity. Thus, we reveal a previously unnoticed connection between spatial solitons and self-similar waves. We also suggest that the discovered self-similar waves can be used in a promising scheme for the amplification and focusing of spatial solitons in future all-optical networks.
We discover analytically an extensive family of optical similaritons, propagating inside graded-index nonlinear waveguide amplifiers. We show that there exists a one-to-one correspondence between these novel similaritons and standard solitons of the homogeneous nonlinear Schrödinger equation. We demonstrate that for certain inhomogeneity and gain profiles, the newly discovered similaritons turn into solitons over sufficiently long propagation distances.
A new class of partially coherent beams with a separable phase, which carry optical vortices, is introduced. It is shown that any member of the class can be represented as an incoherent superposition of fully coherent Laguerre-Gauss modes of arbitrary order, with the same azimuthal mode index. The free-space propagation properties of such partially coherent beams are studied analytically, and their M2 quality factor is investigated numerically.
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