  Achieving localization with molecular precision has been of great interest
for extending fluorescence microscopy to nanoscopy. MINFLUX pioneers this
transition through point spread function (PSF) engineering, yet its performance
is primarily limited by the signal-to-background ratio. Here we demonstrate
that applying two-photon excitation to MINFLUX would double its localization
precision through PSF engineering by nonlinear effect. Cram\'er-Rao Bound (CRB)
is studied as the maximum localization precision, and CRB of two-photon MINFLUX
is halved compared to single-photon MINFLUX in all three dimensions. Meanwhile,
in order to achieve same localization precision with single-photon MINFLUX,
two-photon MINFLUX requires only 1/4 of fluorescence photons, contributing to a
possible 4-fold temporal resolution. Benefitted from two-photon excitation,
registration-free multicolor nanoscopy and ultrafast color tracking can be
achieved. Localization precision of MINFLUX can also be doubled using
excitation with second-order Laguerre-Gaussian beams but would suffer from high
fluorescence background compared to single-photon and two-photon first-order
MINFLUX.
