Metal nanospheres under intense continuous-wave illumination: A unique case of nonperturbative nonlinear nanophotonics

Abstract

We show that the standard perturbative (i.e., cubic) description of the thermal nonlinear response of a single metal nanosphere to intense continuous-wave (CW) illumination is sufficient only for a temperature rise of up to 100 degrees above room temperature. Beyond this regime, the slowing down of the temperature rise requires a nonperturbative description of the nonlinear response, even though the permittivity is linearly dependent on the temperature and despite the deep subwavelength effective propagation distances involved. Using experimental data, we show that, generically, the increase of the imaginary part of the metal permittivity dominates the increase of the host permittivity as well as the resonance shift due to the joint changes to the real parts of the metal and host. Thus, the main nonlinear effect is a decrease of the quality factor of the resonance. We further analyze the relative importance of the various contributions to the temperature rise and thermal nonlinearity, compare the nonlinearity of Au and Ag, demonstrate the potential effect of the nanoparticle morphology, and show that although the thermo-optical nonlinearity of the host typically plays a minor role, its thermal conductivity and its temperature dependence is important. Finally, we discuss the differences between CW and ultrafast thermal nonlinearities.

Size-dependence of the photothermal response of a single metal nanosphere

“…(2) shows that the variation of the temperature inside the NP is at the order of ∼ κ h /κ m which is small for common gas and liquid host but can be substantial for dielectric solid host, e.g., for semiconductors [40]. As shown in ous studies of the nonlinear thermo-optic response that relied on the uniform temperature assumption [33,34].…”

“…Therefore, the present study highlights the importance of the size-dependent particle temperature to identifying the optimal conditions for heat generation. In order to avoid additional complexity due to nonlinear effect [33], i.e., the temperature-dependence of the optical and thermal properties of the materials, we limit the illumination intensity such that the particle temperature rise is lower than 100 K such that the material parameters can be assumed to be temperature-independent, as suggested in [34]. We focus on modeling the heat generation from a single metal NP.…”

Thermal effects – an alternative mechanism for plasmon-assisted photocatalysis

“…For a thorough discussion of these effects, see Refs. [21,22] as well as the necessary temperature-dependent permittivity data presented in Refs. [23][24][25][26] and references therein.…”

“…the thermo-optic nonlinearity of the metal (and potentially of the host) causes the temperature to be much lower than the linear prediction [21,22]. As to the question of melting, for small nanoparticles this is not a trivial issue.…”

Eppur Si Riscalda - and yet, It (Just) Heats Up: Further Comments on “Quantifying Hot Carrier and Thermal Contributions in Plasmonic Photocatalysis”

“…In this context, the linear model works perfectly well for most of the data presented in [5] (as well as for all the data of several other papers we criticize in [2], see discussion in [16, p. 270-271] to quote. Either way, these claims were raised in [17,18] in the quite different context of a single illuminated NP configuration, where temperature-induced changes to the metal permittivity are dominant. As shown below, in the current context of a mm-scale composite that contains a very large number of sparsely dispersed NPs, the nonlinear thermo-optic response originates from the host (as it occupies the vast majority of the sample volume), see also [19].…”