Modal decomposition with difference frequency generation

Modal decomposition enables structured light to be unraveled into a spatial mode basis, revealing key field properties. Typically, this is done using a linear projective system in measurement mode. Here, we demonstrate a nonlinear optical approach to modal decomposition, where an unknown infrared beam is spatially overlapped with a sequentially encoded modal set on a visible beam. We validate this method with structured light examples, including orbital angular momentum and Hermite-Gaussian beams. This nonlinear approach expands modal analysis to inconvenient wavelengths, extending the role of nonlinear optics beyond frequency conversion to modal detection.