  We report on highly nonlinear luminescence being observed from individual
spherical gold nanoparticles immobilized on a glass surface and illuminated by
continuous-wave (CW) lasers with relatively low power. The nonlinear
luminescence shows optical super-resolution beyond the diffraction limit in
three dimensions compared to the scatting of the excitation laser light. The
luminescence intensity from most nanoparticles is proportional to the 5th--7th
power of the excitation laser power and has wide excitation and emission
spectra across the visible wavelength range. Strong nonlinear luminescence is
only observed near the glass surface. High optical nonlinearity excited by low
CW laser power is related to a long-lived dark state of the gold nanoparticles,
where the excitation light is strongly absorbed. This phenomenon has potential
biological applications in super-resolution and deep tissue imaging.
