Heterochromatic nonlinear optical responses in upconversion nanoparticles for point spread function engineering

Point spread function (PSF) engineering of the emitter can code higher spatial frequency information of an image to break diffraction limit but suffer from the complexed optical systems. Here we present a robust strategy to simultaneously achieve diverse PSFs from upconversion nanoparticles under a single doughnut-shape scanning beam. By saturating the four-photon state, the high-frequency information can be extracted through the doughnut emission PSF. In contrast, the complementary lower frequency information can be carried out by the Gaussian-like emission PSF, as a result of over-saturated at the two-photon state. With the Fourier domain heterochromatic fusion, we verify the capability of the synthesised PSF to cover both low and high-frequency information, yielding the overall enhanced image quality. We show a spatial resolution of 40 nm, 1/24th of the excitation wavelength. This work suggests a new scope for developing nonlinear multi-colour emitting probes to improve image quality and noise control in nanoscopy.