Evanescent fields of surface plasmon polaritons (SPP) above metal surfaces can reach 1-2 orders of magnitude higher, nearly atomic field strengths in comparison to the relatively weak exciting laser fields of a femtosecond Ti:sapphire laser oscillator. We used these high plasmonic fields to study the characteristic SPP phenomena of intense field optics experimentally. It was found that both the intensity and the angular distribution of SPP emitted light depend nonlinearly on the exciting laser intensity in the higher-intensity, non-perturbative range of the interactions. These results are supported by our theory. At these strong excitations, an additional, depolarized, diffuse spectrum also appeared which can be attributed either to the fluorescence of Au, or to the non-equlibrium Planck radiation, originating from the fast cooling of the conduction electron cloud of Au excited by the femtosecond laser pulse.