Phase conjugation of twisted Gaussian Schell model beams in stimulated down-conversion

Stimulated parametric down-conversion is a nonlinear optical process that can be used for phase conjugation and frequency conversion of an optical field. A precise description of the outgoing stimulated field has been developed for the case where the input pump and seed fields are coherent. However, partially coherent beams can have interesting and important characteristics that are absent in coherent beams. One example is the twist phase, a novel optical phase that can appear in partially coherent Gaussian beams and gives rise to a nonzero orbital angular momentum. Here, we consider stimulated down-conversion for partially coherent input fields. As a case study, we use twisted Gaussian Schell-Model beams as the seed and pump beams in stimulated parametric down-conversion. It is shown both theoretically and experimentally that the stimulated idler beam can be written as a twisted Gaussian Schell-Model beam, where the beam parameters are determined entirely by the seed and pump. When the pump beam is coherent, the twist phase of the idler is the conjugate of that of the seed. These results could be useful for the correction of wavefront distortion such as in atmospheric turbulence in optical communication channels, and synthesis of partially coherent beams.

Independently Controlling Stochastic Field Realization Magnitude and Phase Statistics for the Construction of Novel Partially Coherent Sources

In this paper, we present a method to independently control the field and irradiance statistics of a partially coherent beam. Prior techniques focus on generating optical field realizations whose ensemble-averaged autocorrelation matches a specified second-order field moment known as the cross-spectral density (CSD) function. Since optical field realizations are assumed to obey Gaussian statistics, these methods do not consider the irradiance moments, as they, by the Gaussian moment theorem, are completely determined by the field’s first and second moments. Our work, by including control over the irradiance statistics (in addition to the CSD function), expands existing synthesis approaches and allows for the design, modeling, and simulation of new partially coherent beams, whose underlying field realizations are not Gaussian distributed. We start with our model for a random optical field realization and then derive expressions relating the ensemble moments of our fields to those of the desired partially coherent beam. We describe in detail how to generate random optical field realizations with the proper statistics. We lastly generate two example partially coherent beams using our method and compare the simulated field and irradiance moments theory to validate our technique.