Recently, it has been suggested that chemical reactions can be facilitated by using mm-scale composites of plasmonic metal nanoparticles on porous oxides. This effect was shown recently to be predominantly associated with the heating induced by illumination. In this study, we study the sensitivity of the temperature rise to various parameters. We show that, the temperature rise in photocatalysts is typically weakly-dependent on the illumination wavelength, pulse duration, particle shape, size and density but is strongly sensitive to the beam size and the host thermal conductivity. Our results indicate that although plasmonic nanoparticles are thought of as nanoscale heat sources, the heat generation from which does not differ so much from macroscopic heat sources. On a more general level, this work is instrumental in uprooting some common misconceptions associated with the role of thermal effects in applications that rely on heat generation from a large number of particles.
Over the last few decades, extensive previous studies of the nonlinear response of metal nanoparticles report a wide variation of nonlinear coefficients, thus, revealing a highly confused picture of the underlying physics. Here, we provide a systematic study of the nonlinear response of metal spheres under continuous-wave illumination within a purely thermal model. The improved modeling allows us to demonstrate a much better match to experimental measurements of the scattering from single metal nanoparticles compared to previous attempts. We then use these results to study the thermo-optical nonlinearity of many-nanoparticle composites. We show that the thermo-optical nonlinearity of the composite is strongly sensitive to the host thermal conductivity only. Our results can be used to interpret correctly the differences in chemical reaction enhancements originating from the thermo-optical nonlinearity at different illumination intensities.
In this work, quite different from many previous studies in the ultrafast region, we study the thermo-optical nonlinearity of a single metal nanoparticle and many-nanoparticle composite under continuous-wave illumination. For single metal nanoparticle system, we show that the thermal effect is able to qualitatively explain the experimental results of the strong nonlinear scattering from sufficiently small Au nanoparticle. To characterize the thermo-optical nonlinearity of single nanoparticle of finite size, we use the best experimentally measured data of the temperature dependent permittivities of bulk gold and calculate the temperature and scattering cross-section of the nanoparticle. We show that, quite counterintuitively, the particle temperature changes with its size non-monotonically. Furthermore, our numerical model shows much better agreement with the nonlinear scattering measurement results than the previous studies. The results of the single nanoparticle system are then used to study the thermo-optical nonlinearity of many-nanoparticle composites. Specifically, the temperature distribution of the many-nanoparticle composite is calculated by properly summing the heat generated by all nanoparticles in the composite as well as modeling by simulation. We show that, in contrast to the case of a single nanoparticle, the temperature distribution and thus the thermo-optical nonlinearity of the composite are weakly dependent on the illumination wavelength, nanoparticle size, and density, but is strongly sensitive to the beam size and the thermal conductivity of the host material. These results are critical for the optimization of the photo-thermal effect in many applications. More importantly, since photo-thermal effects were shown to be responsible for observations of faster chemical reactions, our results can be used to interpret correctly the differences in chemical reaction enhancements originating from the thermo-optical nonlinearity at different illumination intensities.
Modal expansion techniques have long been used as an efﬁcient way to calculate radiation of sources in closed cavities. With one set of cavity modes, calculated once and for all, the solution for any arbitrary conﬁgu-ration of sources can be generated almost instantaneously, providing clear physical insight into the spatial variation of Greens function and thus the local density of states. Nanophotonics research has recently generated an explo-sion of interest in generalizing modal expansion methods to open systems, for example using quasinormal mode / resonant state expansion . Yet one major practical obstacle remains: numerical generation of resonator modes is slow and unreliable, often requiring considerable skill and hand guiding.
Here, we present a practical numerical method for generating suitable modes, possessing the trifecta of traits: speed, accuracy, and reliability. Our method is capable of handling arbitrarily-shaped lossy resonators in open systems. It extends existing methods that expand modes of the target struc-ture using modes of a simpler analytically solvable geometry as a basis . This process is guaranteed to succeed due to completeness, but is ordinarily inefﬁcient because optical structures are usually piecewise uniform, so the resulting ﬁeld discontinuities cripple convergence rates. Our key innovation is use of a new minimal set of basis modes that are inherently discontinuous, yet remarkably simple. We choose to implement our method for the General-ized Normal Mode Expansion (GENOME)  which unlike its alternatives , is valid for any source conﬁguration, including the important case of sources exterior to the scatterer. We achieve rapid exponential convergence, with 4 accurate digits after only 16 basis modes, far more than is necessary. This also means lightning-speed simulation results, faster by 2-3 orders of mag-nitude compared to mode generation using COMSOL. Finally, our method is extremely reliable, as it culminates in a small dense linear eigensystem. No modes go missing, nor are there spurious modes that need to be manually discarded, which is critical to the success of modal expansion methods.
 M. B. Doost et al., Phys. Rev. A 90, 013834 (2014), C. Sauvan et al.,
Phys. Rev. Lett., 110 237401, (2013)
 P. Chen, D. Bergman and Y. Sivan, Phys. Rev. Appl., accepted (2018).
We obtain an eigenmode expansion of the electromagnetic Green’s tensor G(r,r') for lossy resonators in open
systems, which is simple yet complete. This enables rapid simulations by providing the spatial variation of G0(r,r') over both r and r' in one simulation. Few eigenmodes are often necessary for nanostructures, facilitating
both analytic calculations and unified insight into computationally intensive phenomena such as Purcell
enhancement, radiative heat transfer, van der Waals forces, and Förster resonance energy transfer. We bypass
all implementation and completeness issues associated with the alternative quasinormal eigenmode methods, by
defining modes with permittivity rather than frequency as the eigenvalue. Thus, modes decay rather than diverge
at infinity, and are defined by a linear eigenvalue problem, readily implemented using any numerical method.
We demonstrate its general implementation in COMSOL Multiphysics, using the default in-built tools.
Metamaterials consisting of long, circular, cylinders are very popular. It is a fundamental challenge to characterize the effective electromagnetic response of such composites. In this framework, the radius of cylinder is assumed to be considerably smaller than the external wave length, thus the dominant scattered EM fields can be approximately replaced by dipole fields. Previous works dealt mainly with two dimensional (2D) scenarios, i.e., characterizing the effective electromagnetic response for light propagation perpendicular to the cylinder axis. In this work, we generalize this treatment to three dimensions (3D), i.e., we characterize the effective electromagnetic response for light propagation at any angle, and find that the resulting electromagnetic response is non-local, i.e., it depends on the wavevector component parallel to the cylinder axis. We retrieve analytically, the full polarizability tensor and show that it has different contributions for different polarized incoming EM waves (transverse electric and transverse magnetic with respect to the cylindrical axis). It is also diagonal, i.e., it contains no magneto-electric coupling, showing that claims in previous studies were incorrect. Having closed form expressions for polarizability allows us to use effective medium approximation methods, and tailor the spectral response for both electric and magnetic dipolar contributions. It is important to emphasize that for the first time, this gives a fully systematic way to characterize the magnetism. Our analysis holds for additional structures based on cylindrical geometry, such as hole arrays, all-dielectric metamaterials, and multi-layer cylinders. It can be used to explain the electromagnetic response of wire media attributed with a negative refractive index, effective magnetism and hyperbolic dispersion relations. In addition, this approach can be applied to more complex unit cells e.g., consisting of clusters of parallel cylinders.
We show that metal nanoparticles can be used to improve the performance of super-resolution fluorescence nanoscopes based on stimulated-emission-depletion (STED). Compared with a standard STED nanoscope, we show theoretically a resolution improvement by more than an order of magnitude, or equivalently, depletion intensity reductions by more than 2 orders of magnitude and an even stronger photostabilization. Moreover, we present experimental evidence that an optimum resolution, limited by the sizes of the particles used, can be reached for the hybrid NPs for a power of the STED beam one order of magnitude smaller than for the bare cores.