Coherence synthesis in nonlinear optics

It is commonly assumed that nonlinear frequency conversion requires lasers with high coherence; however, this assumption has constrained our broader understanding of coherence and overlooked the potential role of incoherence in nonlinear interactions. In this work, we study the synthesis of optical spatial coherence in second harmonic generation using quadratic nonlinear photonic crystals. We demonstrate a method where the second harmonic coherence is customized by employing quantitative phase retrieval and a complex square-root filter sequentially on fundamental frequency speckles. As a proof-of-concept, we experimentally show incoherent imaging of a smiley face transitioning from infrared to visible light. Moreover, we apply this method to produce two representative types of structured light beams in second harmonic generation: incoherent vortex and Airy beams. During the nonlinear synthesis of incoherent vortex beams, we have, for the first time, experimentally verified the conservation of orbital angular momentum in the nonlinear frequency conversion process of a low-coherence source. Furthermore, the generated second-harmonic incoherent Airy beam preserves the self-acceleration characteristics of its fundamental frequency counterpart, remaining unaffected by reductions in coherence. Our results not only deepen the fundamental understanding of optical coherence but also unlock exciting possibilities for applications in infrared imaging and fluorescence microscopy where optical nonlinear interactions play an important role.