Label-free super-resolution with coherent nonlinear structured-illumination microscopy

Structured-illumination microscopy enables up to a two-fold lateral resolution improvement by spatially modulating the intensity profile of the illumination beam. We propose a novel way to generalize the concept of structured illumination to nonlinear widefield modalities by spatially modulating, instead of field intensities, the phase of the incident field while interferometrically measuring the complex-valued scattered field. We numerically demonstrate that for second-order and third-order processes an almost four-and six-fold increase in lateral resolution is achievable, respectively. This procedure overcomes the conventional Abbe diffraction limit and provides new possibilities for label-free super-resolution microscopy.