On the Generation of Topological Optical Solitons

We’ve discovered that the second harmonic intensity profiles generated by Bessel like beams are solitary waves of various geometries knotted together by concentric rings. One of which, is two central spots of similar radius knotted by ellipsoidal concentric rings. We show that the spatial profile is invariant against propagation. We observe that their behavior is similar to that of screw dislocation in wave trains: they collide and rebound as they propagate. Their intensity distribution have characteristics of energy density of iso–surfaces that illustrate the right-angle scattering of two Dirac monopoles: the outgoing monopoles are moving along a line at right angles to the line of the incoming monopoles. This right–angle scattering of monopoles, is a direct consequence of the geometry of the Atiyah-Hitchin manifold.

In combining wavefront shaping methods and and ultrafast nonlinear optics, we've developed novel methods of production, study, and control of topological

quantum light for computation. We use higher order Bessel like beams in simple configurations of nonlinear light–matter interactions, to show how these can lead to optical excitations in atomic media of comparable or considerably more complex topologies.