Generation of a flexible far-field anomalous hollow beam spot through superposition of two partially coherent sources with different degrees of coherence

Anomalous hollow beams in optical domain were introduced in Cai (2007) and Cai et al. (2008) and as an extension of anomalous hollow electron beams introduced in [Phys. Rev. Lett. 94, 134802 (2005)]. In this paper, for the first time, we demonstrate both theoretically and experimentally that we can obtain a flexible far-field anomalous hollow beam spot of elliptical symmetry with an elliptical solid core through incoherent superposition of two partially coherent sources with different degrees of coherence. The ellipticities and orientation angles of the outer elliptical ring and the inner elliptical solid core are controlled through varying the initial beam parameters. We also demonstrate that incoherent superposition of two partially coherent sources with different degrees of coherence provides a convenient way for constructing various degrees of coherence of the combined source. Our method and results are useful for beam shaping and particle trapping.