Partially coherent sources generated from the incoherent sum of fields containing random-width Bessel functions

Using the criterion for a genuine cross-spectral density function, we demonstrate the realization of an Im-Bessel correlated source, which has only recently been achieved using the source's coherent-mode representation. In addition, with just a simple change, we create a whole new class of partially coherent sources that have not been realized. We simulate the generation of these sources and compare the results to theoretical predictions to validate our analysis. The partially coherent sources described herein can easily be synthesized using spatial light modulators, and the approach presented in this Letter can be used to design sources for optical trapping, optical tweezers, and other related applications.