Enhancement Factors: A Central Concept during 50 Years of Surface-Enhanced Raman Spectroscopy.

In this Perspective, we provide an overview of the core concepts around surface-enhanced Raman spectroscopy (SERS) enhancement factors (EFs), including both theoretical and experimental considerations: EF definitions, the distinction between maximum and average EFs, EF distribution and hot-spot localization, EF measurement and its order of magnitude. We then highlight some of the current challenges in this field, focusing on a selection of topics that we feel are both topical and important: analyte-capture onto a SERS substrate, surface-enhanced resonant Raman scattering, orientation/tensorial effects, and nonradiative effects. We hope this Perspective can provide a platform to reflect on the past 50 years of SERS and its future.

Generalised coupled-dipole model for core-satellite nanostructures.

Plasmonic core-satellite nanostructures have recently attracted interest in photocatalytic applications. The core plasmonic nanoparticle acts like an antenna, funnelling incident light into the near-field region, where it excites the smaller satellite nanoparticles with resonantly enhanced absorption. Computer simulations of the optical absorption by such structures can prove challenging, even with state-of-the-art numerical methods, due to the large difference in size between core and satellite particles. We present a generalised coupled-dipole model that enables efficient computations of light absorption in such nanostructures, including those with many satellites. The method accurately predicts the local absorption in each satellite despite being two orders of magnitude weaker than the absorption in the core particle. We assess the range of applicability of this model by comparing the results against the superposition T-matrix method, a rigorous solution of Maxwell's equations that is much more resource-intensive and becomes impractical as the number of satellite particles increases.

Long-range atmospheric transport of microplastics across the southern hemisphere.

Airborne microplastics (MPs) can undergo long range transport to remote regions. Yet there is a large knowledge gap regarding the occurrence and burden of MPs in the marine boundary layer, which hampers comprehensive modelling of their global atmospheric transport. In particular, the transport efficiency of MPs with different sizes and morphologies remains uncertain. Here we show a hemispheric-scale analysis of airborne MPs along a cruise path from the mid-Northern Hemisphere to Antarctica. We present the inaugural measurements of MPs concentrations over the Southern Ocean and interior Antarctica and find that MPs fibers are transported more efficiently than MPs fragments along the transect, with the transport dynamics of MPs generally similar to those of non-plastic particles. Morphology is found to be the dominant factor influencing the hemispheric transport of MPs to remote Antarctic regions. This study underlines the importance of long-range atmospheric transport in MPs cycling dynamics in the environment.

Interface-Dependent Selectivity in Plasmon-Driven Chemical Reactions.

Plasmonic nanoparticles can drive chemical reactions powered by sunlight. These processes involve the excitation of surface plasmon resonances (SPR) and the subsequent charge transfer to adsorbed molecular orbitals. Nonetheless, controlling the flow of energy and charge from SPR to adsorbed molecules is still difficult to predict or tune. Here, we show the crucial role of halide ions in modifying the energy landscape of a plasmon-driven chemical reaction by carefully engineering the nanoparticle-molecule interface. By doing so, the selectivity of plasmon-driven chemical reactions can be controlled, either enhancing or inhibiting the metal-molecule charge and energy transfer or by regulating the vibrational pumping rate. These results provide an elegant method for controlling the energy flow from plasmonic nanoparticles to adsorbed molecules, in situ, and selectively targeting chemical bonds by changing the chemical nature of the metal-molecule interface.

Comparison of dynamic corrections to the quasistatic polarizability and optical properties of small spheroidal particles.

The optical properties of small spheroidal metallic nanoparticles can be simply studied within the quasistatic/electrostatic approximation, but this is limited to particles much smaller than the wavelength. A number of approaches have been proposed to extend the range of validity of this simple approximation to a range of sizes more relevant to applications in plasmonics, where resonances play a key role. The most common approach, called the modified long-wavelength approximation, is based on physical considerations of the dynamic depolarization field inside the spheroid, but alternative empirical expressions have also been proposed, presenting better accuracy. Recently, an exact Taylor expansion of the full electromagnetic solution has been derived [Majic et al., Phys. Rev. A 99, 013853 (2019)], which should arguably provide the best approximation for a given order. We here compare the merits of these approximations to predict orientation-averaged extinction/scattering/absorption spectra of metallic spheroidal nanoparticles. The Taylor expansion is shown to provide more accurate predictions over a wider range of parameters (aspect ratio and prolate/oblate shape). It also allows us to consider quadrupole and octupole resonances. This simple approximation can therefore be used for small and intermediate-size nanoparticles in situations where computing the full electromagnetic solution is not practical.

Direct radiative effects of airborne microplastics.

Microplastics are now recognized as widespread contaminants in the atmosphere, where, due to their small size and low density, they can be transported with winds around the Earth1-25. Atmospheric aerosols, such as mineral dust and other types of airborne particulate matter, influence Earth's climate by absorbing and scattering radiation (direct radiative effects) and their impacts are commonly quantified with the effective radiative forcing (ERF) metric26. However, the radiative effects of airborne microplastics and associated implications for global climate are unknown. Here we present calculations of the optical properties and direct radiative effects of airborne microplastics (excluding aerosol-cloud interactions). The ERF of airborne microplastics is computed to be 0.044 ± 0.399 milliwatts per square metre in the present-day atmosphere assuming a uniform surface concentration of 1 microplastic particle per cubic metre and a vertical distribution up to 10 kilometres altitude. However, there are large uncertainties in the geographical and vertical distribution of microplastics. Assuming that they are confined to the boundary layer, shortwave effects dominate and the microplastic ERF is approximately -0.746 ± 0.553 milliwatts per square metre. Compared with the total ERF due to aerosol-radiation interactions27 (-0.71 to -0.14 watts per square metre), the microplastic ERF is small. However, plastic production has increased rapidly over the past 70 years28; without serious attempts to overhaul plastic production and waste-management practices, the abundance and ERF of airborne microplastics will continue to increase.

Quantitative theory of integrating sphere throughput: comparison with experiments.

We present a rigorous approach for measuring the throughput of an integrating sphere, from which the so-called sphere multiplier M can be derived. The critical ingredients of this approach are: (i) the transmitted power is measured at the base of an integrating port to avoid non-ideal port effects associated with reflections on the port wall; (ii) to implement this last point, optical fibers are used for light collection, providing a well-defined collection area and numerical aperture; (iii) the angular-dependent fiber throughput and detector sensitivity are determined experimentally and accounted for. We demonstrate in particular that a more realistic theory, accounting for the propagation of skew rays through the fiber, is needed to quantitatively model the fiber effect on the measured sphere throughput. We show experimentally that failure to fulfill these three points produces erroneous results, by as much as 50%. With an accurate experimentally derived sphere multiplier, agreement with theory is then obtained only if realistic ports (with non-zero reflectivity) are assumed. This provides experimental evidence for recent theoretical predictions of the importance of realistic ports [Tang et al., Appl. Opt.57, 1581 (2018)APOPAI0003-693510.1364/AO.57.001581]. Using the same experimental techniques, we also present clear experimental proof of two other predictions from that study: that the angular distribution exiting the port is strongly altered and that the overall port transmittivity is drastically reduced for high aspect ratio ports. This work will provide a solid basis for future quantitative measurements of absolute throughput and for further developments of the theory of integrating spheres.

Definition and properties of logopoles of all degrees and orders.

Logopoles are a recently proposed class of solutions to Laplace's equation with intriguing links to both solid spheroidal and solid spherical harmonics. They share the same finite-line singularity as the former and provide a generalization of the latter as multipoles of negative order. In a previous paper [Majic and Le Ru, Phys. Rev. Res. 1, 033213 (2019)2643-156410.1103/PhysRevResearch.1.033213], we introduced and discussed the properties and applications of these new functions in the special case of axisymmetric problems (with azimuthal index m=0). This allowed us to focus on the physical properties without the added mathematical complications. Here we expand these concepts to the general case m≠0. The chosen definitions are motivated to conserve some of the most interesting properties of the m=0 case. This requires the inclusion of Legendre functions of the second kind with degree -m≤n

Extinction-to-Absorption Ratio for Sensitive Determination of the Size and Dielectric Function of Gold Nanoparticles.

Gold nanoparticles (AuNPs) have become an essential tool for a variety of fields across the biological, physical, and chemical sciences. The characterization of AuNPs by UV-vis spectroscopy is simple and commonly used but remains prone to error because of size and shape polydispersity and uncertainties in the dielectric function. We here propose and demonstrate a method to significantly improve this routine characterization technique by measuring not only the extinction but also the absorption spectrum. Specifically, we show that by considering the ratio of the extinction to absorption spectra, denoted η, we are able to determine the volume of AuNPs with a significant increase in accuracy compared to the UV-vis extinction method. We also prove an important property of η: it is independent of particle shape within the quasi-static/dipolar approximation, typically for particle sizes up to 100 nm. This shape independence results in very strong constraints for the theoretical predictions to agree with the experiments. We show that the spectral shape of η can therefore be used to discriminate between different proposed data sets for the dielectric function of gold, a long-standing challenge in plasmonics research.

Anion-regulated binding selectivity of Cr(III) in collagen.

We present a mechanism for the selectivity of covalent/electrostatic binding of the Cr(III) ion to collagen, mediated by the kosmotropicity of the anions. Although a change in the long-range ordered structure of collagen is observed after covalent binding (Cr(III)-OOC) in the presence of SO4 2- at pH 4.5, the νsym (COO- ) band remains intense, suggesting a relatively lower propensity for the Cr(III) to bind covalently instead of electrostatically through Cr(H2 O)6 3+ . Replacing SO4 2- with Cl- reduces the kosmotropic effect which further favors the electrostatic binding of Cr(III) to collagen. Our findings allow a greater understanding of mechanism-specific metal binding in the collagen molecule. We also report for the first time, surface-enhanced Raman spectroscopy to analyze binding mechanisms in collagen, suggesting a novel way to study chemical modifications in collagen-based biomaterials.

Numerically stable formulation of Mie theory for an emitter close to a sphere.

Numerical implementations of Mie theory make extensive use of spherical Bessel functions. These functions are, however, known to overflow/underflow (grow too large/small for floating point precision) for orders much larger than the argument. This is not a problem in applications such as plane wave excitation, as the Mie series converge before these numerical problems arise. However, for an emitter close to the surface of a sphere, the scattered field in the vicinity of the sphere is expressed as slowly converging series, with multipoles up to order 1000 required in some cases. These series may be used to calculate experimentally relevant quantities such as the decay rate of an emitter near a sphere. In these cases, overflow/underflow prevents any calculation in double precision using Mie theory, and alternatives are either computationally intensive (e.g., arbitrary precision calculations) or not accurate enough (e.g., the electrostatics approximation). We present here a formulation of Mie theory that overcomes these limitations. Using normalized Bessel functions where the large growth/decay is extracted as a prefactor, we re-express the Mie coefficients for scattering by spheres in a normalized form. These normalized expressions are used to accurately compute the series for the electric field and decay rate of a dipole emitter near a spherical surface, in cases where the Mie coefficients would normally overflow before any degree of accuracy can be obtained.

Present and Future of Surface-Enhanced Raman Scattering.

The discovery of the enhancement of Raman scattering by molecules adsorbed on nanostructured metal surfaces is a landmark in the history of spectroscopic and analytical techniques. Significant experimental and theoretical effort has been directed toward understanding the surface-enhanced Raman scattering (SERS) effect and demonstrating its potential in various types of ultrasensitive sensing applications in a wide variety of fields. In the 45 years since its discovery, SERS has blossomed into a rich area of research and technology, but additional efforts are still needed before it can be routinely used analytically and in commercial products. In this Review, prominent authors from around the world joined together to summarize the state of the art in understanding and using SERS and to predict what can be expected in the near future in terms of research, applications, and technological development. This Review is dedicated to SERS pioneer and our coauthor, the late Prof. Richard Van Duyne, whom we lost during the preparation of this article.

Combined Extinction and Absorption UV-Visible Spectroscopy as a Method for Revealing Shape Imperfections of Metallic Nanoparticles.

Metallic nanoparticle solutions are routinely characterized by measuring their extinction spectrum (with UV-vis spectroscopy). Theoretical predictions such as Mie theory for spheres can then be used to infer important properties, such as particle size and concentration. Here we highlight the benefits of measuring not only the extinction (the sum of absorption and scattering) but also the absorption spectrum (which excludes scattering) for routine characterization of metallic nanoparticles. We use an integrating sphere-based method to measure the combined extinction-absorption spectra of silver nanospheres and nanocubes. Using a suite of electromagnetic modeling tools (Mie theory, T-matrix, surface integral equation methods), we show that the absorption spectrum, in contrast to extinction, is particularly sensitive to shape imperfections such as roughness, faceting, or edge rounding. We study in detail the canonical case of silver nanospheres, where small discrepancies between experimental and calculated extinction spectra are still common and often overlooked. We show that this mismatch between theory and experiment becomes much more important when considering the absorption spectrum and can no longer be dismissed as experimental imperfections. We focus in particular on the quadrupolar localized plasmon resonance of silver nanospheres, which is predicted to be very prominent in the absorption spectrum but is not observed in our experiments. We consider and discuss a number of possible explanations to account for this discrepancy, including changes in the dielectric function of Ag, size polydispersity, and shape imperfections such as elongation, faceting, and roughness. We are able to pinpoint faceting and roughness as the likely causes for the observed discrepancy. A similar analysis is carried out on silver nanocubes to demonstrate the generality of this conclusion. We conclude that the absorption spectrum is in general much more sensitive to the fine details of a nanoparticle geometry, compared to the extinction spectrum. The ratio of extinction to absorption also provides a sensitive indicator of size for many types of nanoparticles, much more reliably than any observed plasmon resonance shifts. Overall, this work demonstrates that combined absorption-extinction measurements provide a much richer characterization tool for metallic nanoparticles.

Electromagnetic interactions of dye molecules surrounding a nanosphere.

Enhanced interaction between light and molecules adsorbed on metallic nanoparticles is a cornerstone of plasmonics and surface-enhanced spectroscopies. Recent experimental access to the electronic absorption spectrum of dye molecules on silver colloids at low molecular coverage has revealed subtle changes in the spectral shape that may be attributed to a combination of factors, from a chemical modification of the molecule in contact with a metal surface to electromagnetic dye-dye and dye-metal interactions. Here we develop an original model to rigorously address the electromagnetic effects. The dye molecules are described as coupled anisotropic polarisable dipoles and their interaction with the core metal particle is described using a generalised Mie theory. The theory is readily amenable to numerical implementation and yields far-field optical cross-sections that can be compared to experimental results. We apply this model to specific adsorption geometries of practical interest to highlight the effect of molecular orientation on predicted spectral shifts and enhancement factors, as a function of surface coverage. These are compared to experimental results and reproduce the measured spectral changes as a function of concentration. These results have direct implications for the interpretation of surface selection rules and enhancement factors in surface-enhanced spectroscopies, and of orientation and coverage effects in molecular/plasmonic resonance coupling experiments.

Realistic ports in integrating spheres: reflectance, transmittance, and angular redirection.

We use Monte Carlo ray-tracing modeling to follow the stochastic trajectories of rays entering a cylindrical port from inside an integrating sphere. This allows us to study and quantify properties of realistic ports of non-negligible length, as opposed to the common thin-port assumption used in most theoretical treatments, where the port is simply considered as a hole in the spherical wall. We show that most practical ports encountered in integrating sphere applications cannot be modeled as thin ports. Indeed, a substantial proportion of rays entering the port can be reflected back into the sphere, with port reflectances as high as 80% demonstrated on realistic examples. This can have significant consequences on estimates of the sphere multiplier and therefore pathlength inside the sphere, a critical parameter in many applications. Moreover, a nonzero port reflectance is inevitably associated with reduced transmittance through the port, with implications in terms of overall throughput. We also discuss angular redistribution effects in a realistic port and the consequences in terms of detected throughput within a fixed numerical aperture. Those results highlight the importance of real port effects for any quantitative predictions of optical systems using integrating spheres. We believe that those effects can be exploited to engineer ports for specific applications and improve the overall sphere performance in terms of pathlength or throughput. This work carries important implications in our theoretical understanding of integrating spheres and on the practical design of optical systems using them.

Spheroidal harmonic expansions for the solution of Laplace's equation for a point source near a sphere.

We propose a powerful approach to solve Laplace's equation for point sources near a spherical object. The central new idea is to use prolate spheroidal solid harmonics, which are separable solutions of Laplace's equation in spheroidal coordinates, instead of the more natural spherical solid harmonics. Using electrostatics as an example, we motivate this choice and show that the resulting series expansions converge much faster. This improvement is discussed in terms of the singularity of the solution and its analytic continuation. The benefits of this approach are further illustrated for a specific example: the calculation of modified decay rates of light emitters close to nanostructures in the quasistatic approximation. We expect the general approach to be applicable with similar benefits to the solution of Laplace's equation for other geometries and to other equations of mathematical physics.

Accurate Modeling of the Polarizability of Dyes for Electromagnetic Calculations.

The wavelength-dependent complex linear polarizability of a dye is a crucial input for the modeling of the optical properties of dye-containing systems. We here propose and discuss methods to obtain an accurate polarizability model by combining absorption spectrum measurements, Kramers-Kronig (KK) tranformations, and density functional theory (DFT) calculations. We focus, in particular, on the real part of the polarizability and its link with static polarizability. In addition, we introduce simple KK-consistent analytic functions based on the theory of critical points as a much more accurate approach to model dye polarizabilities compared with existing models based on Lorentz oscillators. Accurate polarizability models based on critical points and DFT calculations of the static polarizability are derived for five commonly used dyes: Rhodamine 6G, Rhodamine 700, Crystal Violet, Nile Blue A, and Methylene Blue. Finally, we demonstrate explicitly, using examples of Mie Theory calculations of nanoparticle-dye interactions, how an inaccurate polarizability model can result in fundamentally different predictions, further emphasizing the importance of accurate models, such as the one proposed here.

Co-ordinated detection of microparticles using tunable resistive pulse sensing and fluorescence spectroscopy.

Tunable resistive pulse sensing (TRPS) has emerged as a useful tool for particle-by-particle detection and analysis of microparticles and nanoparticles as they pass through a pore in a thin stretchable membrane. We have adapted a TRPS device in order to conduct simultaneous optical measurements of particles passing through the pore. High-resolution fluorescence emission spectra have been recorded for individual 1.9 µm diameter particles at a sampling period of 4.3 ms. These spectra are time-correlated with RPS pulses in a current trace sampled every 20 µs. The flow rate through the pore, controlled by altering the hydrostatic pressure, determines the rate of particle detection. At pressures below 1 kPa, more than 90% of fluorescence and RPS events were matching. At higher pressures, some peaks were missed by the fluorescence technique due to the difference in sampling rates. This technique enhances the particle-by-particle specificity of conventional RPS measurements and could be useful for a range of particle characterization and bioanalysis applications.