Phase structuring of 2D complex coherence states

It was shown in a recent publication [Opt. Lett.43, 4727 (2018)OPLEDP0146-959210.1364/OL.43.004727] that structuring the phase of 1D-sourced complex coherence states results in breaking the Cartesian symmetry for the far-field spectral density, leading to its one-sided radial acceleration, asymmetric splitting, and other effects. We extend this result from 1D to 2D (scalar) optical beams and consider examples of novel 2D sources with separable (in Cartesian coordinates) and nonseparable phase distributions of the complex coherence states, illustrating the possibilities in asymmetric manipulation of the 2D far-fields.