Cross-phase modulational instability of circularly polarized helical Bloch modes carrying optical vortices in a chiral three-core photonic crystal fiber.

We report the first, to the best of our knowledge, observation of cross-phase modulational instability (XPMI) of circularly polarized helical Bloch modes carrying optical vortices in a twisted photonic crystal fiber with a three-fold symmetric core, formed by spinning the fiber preform during the draw. When the fiber is pumped by a superposition of left-circular polarization (LCP) and right-circular polarization (RCP) modes, a pair of orthogonal circularly polarized sidebands of opposite topological charge is generated. When, on the other hand, a pure LCP (or RCP) mode is launched, the XPMI gain is zero, and no sidebands are seen. This observation has not been seen before in any system and is unique to chiral structures with -fold rotational symmetry. The polarization state and topological charge of the generated sidebands are measured. By decomposing the helical Bloch modes into their azimuthal harmonics, we are able to deduce the selection rules for the appearance of modulational instability sidebands. We showed that the four waves in the nonlinear mixing process must exhibit the same set of azimuthal harmonic orders.