Fig. 1: The setup used for the realization of the fractional Schrödinger equation.
From: Experimental realisations of the fractional Schrödinger equation in the temporal domain
a In the initial section, the hologram is installed to shape the input pulse. In the propagation section, the hologram inducing the spectral phase shift, which represents the effect of the fractional GVD, is used to emulate the propagation through the optical Lévy waveguide (for clarity’s sake, this hologram is drawn in the rotated form, facing the figure’s plane). For the measurements, the single-shot spatial-spectrum interferometry technique is used to measure the pulse’s amplitude and phase. The temporal profile of the input, and the evolution of the structure of the propagating beam in the case of Q3, as defined in (b), are schematically shown at the top of the figure. b Four different quadrants, Q1 to Q4, in the parameter plane of (LGVD, α). Quadrants Q1 and Q2 correspond to the cases with LGVD > 0 and 1 ≤ α ≤ 2 and 0 ≤ α ≤ 1, respectively. Q3 and Q4 are defined similarly but with LGVD < 0. Areas B1 and B2 in (b) designate two extreme cases with α close to 0 and 2, respectively.
