Understanding the interplay between illumination and the electron distribution in metallic nanostructures is a crucial step towards developing applications such as plasmonic photocatalysis for green fuels, nanoscale photodetection and more. Elucidating this interplay is challenging, as it requires taking into account all channels of energy flow in the electronic system. Here, we develop such a theory, which is based on a coupled Boltzmann-heat equations and requires only energy conservation and basic thermodynamics, where the electron distribution, and the electron and phonon (lattice) temperatures are determined uniquely. Applying this theory to realistic illuminated nanoparticle systems, we find that the electron and phonon temperatures are similar, thus justifying the (classical) single-temperature models. We show that while the fraction of high-energy “hot” carriers compared to thermalized carriers grows substantially with illumination intensity, it remains extremely small (on the order of 10−8). Importantly, most of the absorbed illumination power goes into heating rather than generating hot carriers, thus rendering plasmonic hot carrier generation extremely inefficient. Our formulation allows for the first time a unique quantitative comparison of theory and measurements of steady-state electron distributions in metallic nanostructures.

No abstract

Recent experiments claimed that the enhancement of catalytic reaction rates occurs via the reduction of activation barriers driven by non-equilibrium ("hot") electrons in plasmonic metal nanoparticles. These experiments place plasmonic photo-catalysis as a promising path for enhancing the efficiency of various chemical reactions. Here, we argue that what appears to be photo-catalysis is in fact thermo-catalysis, driven by the well-known plasmon-enhanced ability of illuminated metallic nanoparticles to serve as heat sources. Specifically, we point to some of the most important papers in the field, and show that a simple theory of illumination-induced heating can explain the extracted experimental data to remarkable agreement, with minimal to no fit parameters. We further show that any small temperature difference between the photocatalysis experiment and a control experiment performed under uniform external heating is effectively amplified by the exponential sensitivity of the reaction, and very likely to be interpreted incorrectly as "hot" electron effects.

The ultrafast response of metals to light is governed by intriguing nonequilibrium dynamics involving the interplay of excited electrons and phonons. The coupling between them leads to nonlinear diffusion behavior on ultrashort time scales. Here, we use scanning ultrafast thermomodulation microscopy to image the spatiotemporal hot-electron diffusion in thin gold films. By tracking local transient reflectivity with 20-nm spatial precision and 0.25-ps temporal resolution, we reveal two distinct diffusion regimes: an initial rapid diffusion during the first few picoseconds, followed by about 100-fold slower diffusion at longer times. We find a slower initial diffusion than previously predicted for purely electronic diffusion. We develop a comprehensive three-dimensional model based on a two-temperature model and evaluation of the thermo-optical response, taking into account the delaying effect of electron-phonon coupling. Our simulations describe well the observed diffusion dynamics and let us identify the two diffusion regimes as hot-electron and phonon-limited thermal diffusion, respectively.

Zhou et al. (Reports, 5 October 2018, p. 69) claim to have proven dominance of “hot” electrons over thermal effects in plasmonic photocatalysis. We identify experimental flaws that caused overestimation of the hot carrier contribution. As an alternative interpretation, we fully reproduce their data using a purely thermal Arrhenius law with a fixed activation energy and intensity-dependent heating.

The nonlinear Schrödinger equation i (partial differential)(z)A(z,x,t)+(inverted Delta)(2)(x,t)A+[1+m(kappax)]|A|2A=0 models the propagation of ultrashort laser pulses in a planar waveguide for which the Kerr nonlinearity varies along the transverse coordinate x, and also the evolution of 2D Bose-Einstein condensates in which the scattering length varies in one dimension. Stability of bound states depends on the value of kappa=beamwidth/lattice period. Wide (kappa>>1) and kappa=O(1) bound states centered at a maximum of m(x) are unstable, as they violate the slope condition. Bound states centered at a minimum of m(x) violate the spectral condition, resulting in a drift instability. Thus, a nonlinear lattice can only stabilize narrow bound states centered at a maximum of m(x). Even in that case, the stability region is so small that these bound states are "mathematically stable" but "physically unstable."

We present a unified approach for qualitative and quantitative analysis of stability and instability dynamics of positive bright solitons in multi-dimensional focusing nonlinear media with a potential (lattice), which can be periodic, periodic with defects, quasiperiodic, single waveguide, etc. We show that when the soliton is unstable, the type of instability dynamic that develops depends on which of two stability conditions is violated. Specifically, violation of the slope condition leads to a focusing instability, whereas violation of the spectral condition leads to a drift instability. We also present a quantitative approach that allows to predict the stability and instability strength.

Abstract:We solve the Maxwell and heat equations selfconsistently for metal nanoparticles under intense continuous wave (CW) illumination. Unlike previous studies, we rely on experimentally-measured data for metal permittivity for increasing temperature and for the visible spectral range. We show that the thermal nonlinearity of the metal can lead to substantial deviations from the predictions of the linear model for the temperature and field distribution and, thus, can explain qualitatively the strong nonlinear scattering from such configurations observed experimentally. We also show that the incompleteness of existing data of the temperature dependence of the thermal properties of the system prevents reaching a quantitative agreement between the measured and calculated scattering data. This modeling approach is essential for the identification of the underlying physical mechanism responsible for the thermo-optical nonlinearity of the metal and should be adopted in all applications of hightemperature nonlinear plasmonics, especially for refractory metals, for both CW and pulsed illumination.