PARTIALLY COHERENT SOURCES WITH HELICOIDAL MODES

On the basis of the modal theory of coherence, we study partially cohe rent sources whose modes belong to the class of Laguerre-Gauss functio ns for which the Laguerre polynomial has zero order. These modes prese nt a phase profile with a helicoidal structure, which is responsible f or notable phenomena, such as the propagation of optical vortices, bea m twisting, and the presence of dislocations in interference patterns. By suitably choosing the eigenvalues associated with such modes, diff erent partially coherent sources are obtained: sources with a flattene d Gaussian profile, twisted Gaussian Schell-model sources with a satur ated twist, and a new class of sources having an annular profile. Owin g to the shape-invariance property of the underlying modes, the fields radiated by these sources do not change their transverse profile thro ugh propagation, except for scale and phase factors. We also prove tha t, if any such source is covered by a circularly symmetric filter, the new modal structure can be found in a straightforward manner.