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We show that the standard perturbative (i.e., cubic) description of thethermal nonlinear response of small metal nanospheres to intense continuouswave illumination is insufficient already beyond temperature rises of a fewtens of degrees. In some cases, a cubic-quintic nonlinear response issufficient to describe accurately the intensity dependence of the temperature,permittivity and field, while in other cases, a full non-perturbativedescription is required. We further analyze the relative importance of thevarious contributions to the thermal nonlinearity, identify a qualitativedifference between Au and Ag, and show that the thermo-optical nonlinearity ofthe host typically plays a minor role, but its thermal conductivity isimportant.

Metal nanospheres under intense continuous wave illumination - a unique case of non-perturbative nonlinear nanophotonics