Mind the gap: testing the Rayleigh hypothesis in T-matrix calculations with adjacent spheroids.

The T-matrix framework offers accurate and efficient modelling of electromagnetic scattering by nonspherical particles in a wide variety of applications ranging from nano-optics to atmospheric science. Its analytical setting, in contrast to purely numerical methods, also provides a fertile ground for further theoretical developments. Perhaps the main purported limitation of the method, when extended to systems of multiple particles, is the often-stated requirement that the smallest circumscribed spheres of neighbouring scatterers not overlap. We consider here such a scenario with two adjacent spheroids whose aspect ratio we vary to control the overlap of the smallest circumscribed spheres, and compute far-field cross-sections and near-field intensities using the superposition T-matrix method. The results correctly converge far beyond the no-overlap condition, and although numerical instabilities appear for the most extreme cases of overlap, requiring high multipole orders, convergence can still be obtained by switching to quadruple precision. Local fields converge wherever the Rayleigh hypothesis is valid for each single scatterer and, remarkably, even in parts of the overlap region. Our results are validated against finite-element calculations, and the agreement demonstrates that the superposition T-matrix method is more robust and broadly applicable than generally assumed.

Influence of photostability on single-molecule surface enhanced Raman scattering enhancement factors.

Experimental determinations of enhancement factors in Surface Enhanced Raman Scattering (SERS) are intimately intertwined with the photostability of the probes. We study the effect of the limited photostability in single-molecule SERS (SM-SERS) events and show explicitly how this may result in a large under-estimation of the SERS enhancement factors (EFs) obtained experimentally. To this end, we use the bianalyte technique with isotopically edited probes to provide the best-case scenario for the isolation of single molecule events, and study the statistics of EFs at different incident laser powers. When photobleaching stops playing an important role within the integration time used to capture the spectra, SM-SERS EFs approach an upper bound, which is in agreement with estimations of the EFs within the electromagnetic theory of SERS enhancements. Our results reinforce, in addition, the fact that the highest SM-SERS EFs observed experimentally are typically of the order of approximately 10(10).

Phenomenological local field enhancement factor distributions around electromagnetic hot spots.

We propose a general phenomenological description of the enhancement factor distribution for surface-enhanced Raman scattering (SERS) and other related phenomena exploiting large local field enhancements at hot spots. This description extends naturally the particular case of a single (fixed) hot spot, and it is expected to be "universal" for many classes of common SERS substrates containing a collection of electromagnetic hot spots with varying geometrical parameters. We further justify it from calculations with generalized Mie theory. The description studied here provides a useful starting point for a qualitative (and semiquantitative) understanding of experimental data and, in particular, the analysis of the statistics of single-molecule SERS events.

Self-limiting aggregation leads to long-lived metastable clusters in colloidal solutions.

The existence of a metastable state with limited Coulomb-blocked aggregation at the onset of instability in a colloidal solution is proposed and demonstrated both experimentally and theoretically (through Monte Carlo simulations). Such a stable state of small clusters of metallic colloids happens to be extremely important for techniques such as surface-enhanced Raman scattering (SERS), which profits explicitly from collective plasmon resonances in these clusters to boost Raman signals of specific analytes. In fact, SERS provides a unique tool to understand, monitor, and study the onset of aggregation in colloidal silver/gold and to prove the existence of the proposed state at the boundary of colloid coalescence.

Proof of single-molecule sensitivity in surface enhanced Raman scattering (SERS) by means of a two-analyte technique.

A method is proposed to pin down unambiguous proof for single-molecule sensitivity in surface enhanced Raman spectroscopy (SERS). The simultaneous use of two analyte molecules enables a clear confirmation of the single (or few)-molecule nature of the signals. This method eliminates most of the uncertainties associated with low dye concentrations in previous experiments. It further shows that single- or few-molecule signals are very common in SERS, both in liquids and on dry substrates.

A conclusive demonstration of vibrational pumping under surface enhanced Raman scattering conditions.

We provide a conclusive demonstration of vibrational pumping under Surface Enhanced Raman Scattering (SERS) conditions by performing anti-Stokes/Stokes ratio measurements over a large spatial area and low power density, down to 10 K with dried silver colloids, the dye rhodamine 6G, and 676 nm laser excitation. The method we propose allows for the measurement of the cross sections for different modes and also provides the determination of the asymmetry between the anti-Stokes and Stokes SERS cross sections for each mode.

Temperature-dependent anti-stokes/stokes ratios under surface-enhanced Raman scattering conditions.

We make systematic measurements of Raman anti-Stokes/Stokes (aS/S) ratios using two different laser excitations (514 and 633 nm) of rhodamine 6G (RH6G) on dried Ag colloids over a wide range of temperatures (100 to 350 K). We show that a temperature scan allows the separation of the contributions to the aS/S ratios from resonance effects and heating/pumping, thus decoupling the two main aspects of the problem. The temperature rise is found to be larger when employing the 633 nm laser. In addition, we find evidence for mode specific vibrational pumping at higher laser power densities. We analyze our results in the framework of ongoing discussion on laser heating/pumping under surface-enhanced Raman scattering (SERS) conditions.

On the experimental estimation of surface enhanced raman scattering (SERS) cross sections by vibrational pumping.

We present an in-depth analysis of the experimental estimation of cross-sections in surface enhanced raman scattering (SERS) by vibrational pumping. The paper highlights the advantages and disadvantages of the technique, pinpoints the main aspects and limitations, and provides the underlying physical concepts to interpret the experimental results. Examples for several commonly used SERS probes are given, and a discussion on future possible developments is also presented. Obtaining good estimates of SERS cross-sections is, in general, an extremely hard problem and has been a longstanding ambition of the SERS community for reasons that go from the purely applied (quantification of signals) to the more fundamental (comparisons of theoretical electromagnetic enhancement factors with experiment). Any method that can produce a standard protocol for the estimation of cross-sections is, accordingly, of great interest and an effort to understand its principles and limitations is required.

Experimental demonstration of surface selection rules for SERS on flat metallic surfaces.

We have measured the polarization and incident angle dependence of the Surface-Enhanced Raman Scattering (SERS) signal of a nile blue monolayer adsorbed on a flat gold surface. Comparisons with predictions of electromagnetic (EM) theory indicate that the molecules are predominantly adsorbed flat on the surface. These results provide the most direct demonstration of the concept of surface selection rules in SERS, and further confirm the validity of the SERS-EM model beyond the |E|(4)-approximation.

An iterative algorithm for background removal in spectroscopy by wavelet transforms.

Wavelet transforms are an extremely powerful tool when it comes to processing signals that have very "low frequency" components or non-periodic events. Our particular interest here is in the ability of wavelet transforms to remove backgrounds of spectroscopic signals. We will discuss the case of surface-enhanced Raman spectroscopy (SERS) for illustration, but the situation it depicts is widespread throughout a myriad of different types of spectroscopies (IR, NMR, etc.). We outline a purpose-built algorithm that we have developed to perform an iterative wavelet transform. In this algorithm, the effect of the signal peaks above the background is reduced after each iteration until the fit converges close to the real background. Experimental examples of two different SERS applications are given: one involving broad backgrounds (that do not vary much among spectra), and another that involves single molecule SERS (SM-SERS) measurements with narrower (and varying) backgrounds. In both cases, we will show that wavelet transforms can be used to fit the background with a great deal of accuracy, thus providing the framework for automatic background removal of large sets of data (typically obtained in time-series or spatial mappings). A MATLAB((R)) based application that utilizes the iterative algorithm developed here is freely available to download from http://www.victoria.ac.nz/raman/publis/codes/cobra.aspx.

Single-molecule vibrational pumping in SERS.

Single-molecule vibrational pumping in surface-enhanced Raman scattering (SERS) is demonstrated rigorously using the bi-analyte SERS method at low temperatures. These experiments reveal a systematic difference between the radiative SERS cross section estimated from the Stokes intensity and that obtained by pumping itself (from the anti-Stokes-to-Stokes ratio), the latter being always larger. This difference can only be reliably demonstrated in the single-molecule SERS regime, for it is otherwise affected by complications of the averaging (over the enhancement distribution) of the signals of several molecules. The findings in this paper highlight the limitations of the pumping cross-section, which cannot (in general) be taken as a reliable measure of the SERS cross-section itself. We provide a discussion of the main possible explanations for the systematic difference of the two estimates.

Plasmon-dispersion corrections and constraints for surface selection rules of single molecule SERS spectra.

The problem of extracting information from relative intensities of Raman peaks in surface-enhanced-Raman-scattering (SERS) is intimately related to several important topics in the technique. Among them: (i) the possibility (or sometimes impossibility) of observing surface selection rules in different situations, (ii) the role of analyte resonance conditions, (iii) the crucial inclusion of plasmon-resonance dispersion corrections in the analysis of relative Raman intensities among peaks, and (iv) the connection of these phenomena with (broader) issues like surface-enhanced fluorescence (SEF). This paper deals with the underlying connections among these (apparently disconnected at first sight) topics. The technique is now at a mature stage to review the aforementioned phenomena from a unified point of view; thus pinpointing the most important issues, clarifying concepts that have been historically confusing (or treated in isolation), and paving the road for future developments.

Ultrafast nonradiative decay rates on metallic surfaces by comparing surface-enhanced Raman and fluorescence signals of single molecules.

By the simultaneous observation of surface-enhanced Raman scattering and surface-enhanced fluorescence signals from a single molecule, we can measure and quantify the modification of the total decay rate of emitters in very close proximity to metals, even down to adsorbed molecules. This modified decay rate is shown to be largely dominated by its nonradiative component, which would be extremely difficult to estimate with conventional approaches. The method provides an indirect measurement of ultrafast (approximately 25 fs) mechanisms, which would be impossible to gain with time-resolved spectroscopy of a single molecule.

Guiding molecules with electrostatic forces in surface enhanced Raman spectroscopy.

In surface enhanced raman scattering (SERS) the problem of drawing molecules to the places where surface plasmon resonance enhancements will produce signals is one of the most basic ones, and the initial obstacle to every application of the effect. We explore the possibility of using electrostatic forces as a means to "guide" charged molecules in solution toward SERS active substrates. We also show explicitly the possibility of selectively enhancing different types of dyes according to their charge, and we discuss briefly possible extensions for other applications where "electrostatic guiding" could be an option.

A perspective on single molecule SERS: current status and future challenges.

We present an overview of a some of the basic principles underlying current research in single-molecule surface-enhanced Raman scattering (SM-SERS). We summarize, by the same token, a series of conditions and characteristics that are common to most SM-SERS conditions, and discuss their implications for the understanding of data and for the comparison among different methods. We try to emphasize aspects of the problem that are not conventionally discussed in detail in the literature. In particular, we provide a full length discussion on the topics of: (i) the minimum SERS enhancement necessary to observe a single molecule, and (ii) the spatial distribution of the enhancement factor (EF) around hot-spots (which affects the statistics of SM-SERS events). A brief outlook into future perspectives of the different techniques used in SM-SERS and a few outstanding questions are also provided.

Bi-analyte SERS with isotopically edited dyes.

Isotopically substituted rhodamine dyes provide ideal probes for the study of single-molecule surface enhanced Raman scattering (SM-SERS) events through multiple-analyte techniques. Isotopic editing should, in principle, provide probes that have identical chemical properties (and surface chemistries); while exhibiting at the same time distinct Raman features which enable us to identify single-molecule SERS events. We present here a specific example of two-analyte SM-SERS based on the isotopic substitution of a methyl ester rhodamine dye. The dyes are carefully characterized (in both standard and SERS conditions) to confirm experimentally their similar chemical properties. We then demonstrate their utility for bi-analyte SERS (BiASERS) experiments and, as an example, highlight the transition from a single, to a few, to many molecules in the statistics of SM-SERS signals.

Vibrational pumping in surface enhanced Raman scattering (SERS).

In this tutorial review, the underlying principles of vibrational pumping in surface enhanced Raman scattering (SERS) are summarized and explained within the framework of their historical development. Some state-of-the-art results in the field are also presented, with the aim of giving an overview on what has been established at this stage, as well as hinting at areas where future developments might take place.

Statistics of single molecule SERS signals: is there a Poisson distribution of intensities?

This paper is aimed at clarifying the statistics of single molecule (SM) surface enhanced Raman scattering (SERS) signals. The argument of the possible existence of a Poisson distribution in the statistics of intensities in SM-SERS has been used many times in the last decade as a proof of single molecule detection. We show theoretically and experimentally that the conditions under which a Poisson distribution would be present are so unlikely to exist in a real system that there is no other option but to attribute the claims to poor statistical sampling. We believe the argument based on Poisson statistics should be dropped as a proof of single molecule detection in SERS.

Enhancement factor averaging and the photostability of probes in SERS vibrational pumping.

The technique of temperature dependent vibrational pumping in surface enhanced Raman scattering (SERS) has been recently demonstrated as a promising new tool to estimate SERS cross-sections. In this paper we expand on the previous developments and study several details around the implementation and physics of the vibrational pumping technique in SERS. Here we concentrate on two specific aspects related to: (i) the different averaging properties (over the distribution of enhancements) of the Stokes and anti-Stokes signals in the pumping regime; and (ii) the role of the finite photostability of the probes. The fact that the anti-Stokes signal is averaged differently from the Stokes counterpart leads to some unique phenomena in Raman spectroscopy that can only be observed under the conditions of vibrational pumping in SERS.

Statistics of single-molecule surface enhanced Raman scattering signals: fluctuation analysis with multiple analyte techniques.

The mathematical background, based on a variation of the principal component analysis (PCA) method, is developed for the understanding of fluctuating multiple analyte single-molecule (SM) surface enhanced Raman scattering (SERS) signals; with emphasis on the bianalyte SERS technique developed recently. The method and its significance are presented to provide a systematic framework with which several aspects of the statistics of SM-SERS signals can be analyzed in general. We also apply the method to a concrete example of bianalyte statistics in silver colloidal solutions and discuss related topics around experimental issues and the interpretation of single-molecule SERS data.