Light emission from plasmonic nanostructures

Light emission from plasmonic nanoparticles can be applied in imaging^1–7 and sensing,^8–12 accurately probing local temperature^13–17 and chemical reactions at the nanoscale.^18–21 It also contributes to the background of surface-enhanced Raman scattering (SERS)^22–25 and plasmon enhanced fluorescence.^26–29 Thus, the emission mechanism is a critical area of study. Photon emission from metals was first investigated in bulk gold and copper by Mooradian,³⁰ and later, the enhanced emission from roughened surfaces was reported by Boyd et al.³¹ and Beversluis et al.³² Mohamed et al.³³ with others following (Refs. 34–38) then observed strong emission from an ensemble of metal nanoparticles. While this Perspective focuses on emission following continuous wave (cw) excitation, many reports have examined emission following multi-photon absorption using pulsed laser excitation.^39–45 Furthermore, emission from metal clusters showing molecular-type luminescence features has been an active area of research. Both topics, however, are beyond the scope of this article.^46–51 Tcherniak et al.⁵² and Gaiduk et al.⁵³ reported the first spectroscopic characterization of the one-photon emission from single plasmonic gold nanorods (AuNRs) and nanospheres, respectively. Meixner and co-workers definitively linked the luminescence to the plasmon in 2013.^54,55 While most studies analyzed the Stokes emission component, Mooradian also reported an anti-Stokes component,³⁰ which has received renewed interest recently.^56,57 Later work investigated the emission from metallic nanoparticles of different sizes^58–60 and morphologies^61–65 as well as from coupled nanostructures,^66–72 confirming and deepening the understanding of the plasmonic enhancement effect.

Most optical properties associated with the collective motion of conduction band electrons in metals, named the surface plasmon,^73–77 can be well predicted by classical electromagnetic theory^78–80 when the particle size is larger than a few nanometers.⁸¹ However, the light emission from plasmonic nanoparticles is beyond the scope of Maxwell’s equations involving transitions of single electrons.^{30,32,82–84} Building a quantitative predictive model for the light emission from plasmonic nanostructures can be challenging, considering the large number of electronic states and the strong electron–electron scattering as well as electron–phonon coupling involved.^82,84 While it is well accepted that the localized surface plasmon resonance (LSPR) can enhance the emission,^{52,62,85–87} the ongoing debate focuses on whether a real or a virtual electronic state is involved in the emission process, corresponding to photoluminescence (PL)^{30,31,34,85,88–92} and electronic Raman scattering mechanisms, respectively.^14,15,22,93

Here, we summarize our studies on the emission spectroscopy of single AuNRs placed on insulating transparent supports and excited with cw lasers of varying wavelengths and powers, following both Stokes and anti-Stokes emission. We begin with a summary of the general properties of AuNR emission and discuss its potential origins. Then, we summarize the results from our laboratory, proposing that emission is the result of PL and can be explained by a Purcell effect enhancement mechanism. We show the effects that varying excitation wavelength and power as well as the AuNR size have on the PL and relate quantitative single particle PL quantum yields (QYs) to their corresponding Purcell factors and electromagnetic local density of states (LDOS)^94–96 by analyzing darkfield scattering (DFS) quality factors (Q-factors). We find that these results extend to lithographically prepared, polycrystalline nanostructures. Finally, we discuss cw laser excitation induced anti-Stokes emission resulting from multiphoton excitation. We emphasize the need for a quantitative analysis, which we achieve through correlated single particle emission spectroscopy, electron microscopy, and finite difference time domain (FDTD) simulations to obtain QYs and Purcell factors, in each case for a large number of AuNRs, i.e., at least several dozen. This approach has allowed for unique mechanistic insight into the emission mechanism of AuNRs and, as we will demonstrate, suggests that light emission from single AuNRs on insulating transparent substrates is caused by PL.

When a AuNR is excited with cw light, the resulting emission is stable and scales linearly with the laser excitation power (Fig. 1). To demonstrate these properties, we employed a confocal microscope to image single AuNRs on a quartz substrate, used to minimize background luminescence, and recorded photon counts with an avalanche photodiode.^52,62 A typical emission image excited with a circularly polarized 532 nm laser is shown in Fig. 1(a), with the SEM images of the corresponding AuNRs included as insets. Compared to the corresponding DFS image [Fig. 1(b)], the emission image gives better spatial resolution because the excitation laser can be focused to a diffraction-limited spot. Unlike the fluorescence of inorganic quantum dots,⁹⁷ the emission time trajectory of a AuNR displays no blinking or photobleaching [Fig. 1(c)]. An example illustrating the scaling of the emission intensity with excitation power is plotted in Fig. 1(d) for 514 nm excitation. As seen in Fig. 1(d) and generally reported in the literature, the Stokes emission from single AuNRs scales linearly with the excitation power, indicating a one-photon absorption process.^{52,61,62,85,98} However, electronic Raman scattering would also be consistent with the properties described in Fig. 1.²² 

The light emitted from single AuNRs has unique spectral properties that suggest a close relationship with the LSPR,^54,99 as the emission spectra follow the corresponding DFS spectral lineshape. Spectra from single AuNRs were collected by using a spectrometer equipped with a charge-coupled device camera. The wavelength dependent detection efficiency of the entire setup was corrected with a calibrated white light lamp. Emission from a single gold nanosphere (AuNS), with a diameter of 45 nm and illuminated with a 514 nm laser, follows its DFS spectrum [Fig. 2(a)]. The emission intensity depends weakly on the polarization of the detected light [inset of Fig. 2(a)], consistent with the colloidal AuNSs not being perfect spheres. The 514 and 633 nm excited emission spectra of a single AuNR, shown in the SEM image in the inset of Fig. 2(b), both display a resonance close to the longitudinal LSPR observed in DFS [Fig. 2(b)]. To demonstrate that the emission spectrum tracks the DFS spectrum, Fig. 2(c) shows single particle DFS (blue and cyan) and 514 nm excited emission (red and magenta) spectra for a 33 × 70 nm AuNR on a substrate measured in air and water. A redshift of about 50 nm is seen for both the DFS and emission resonance maxima. When the effective refractive index of the surrounding medium changes from 1.25 as in the case of the spectra taken on a substrate in air to 1.4 for the spectra taken with water on top of the sample, the emission spectrum shifts in the same way as the DFS spectrum, i.e., the emission from AuNRs tracks their LSPRs.

The main resonance in the emission spectrum of a single 34 × 68 nm AuNR, excited at 514 and 633 nm, modulates in phase with DFS when changing the detection polarization [Fig. 2(d)]. In contrast, a weak polarization dependency is observed for the emission near the excitation wavelength.^98,100 The modulation depth of the DFS and emission intensities from the same AuNR as a function of the detection polarization angle are given in the inset of Fig. 2(d). The polarization dependencies were fit to I(θ) = N(1 + M cos 2(θ − φ)), where I is the intensity, θ is the polarizer angle, φ represents the angle of the longest projected dipole axis, N is a normalization factor, and M is the modulation depth.¹⁰¹ An average modulation depth of 0.95 ± 0.05 obtained from ten individual AuNRs confirmed the expected perfect dipole behavior for DFS. Emission following 633 nm excitation almost reproduces the amplitude and phase of DFS with a modulation depth of 0.94 ± 0.05. Because of the weak polarization dependency at short wavelengths with 514 nm excitation, the modulation depth is slightly lower when integrating the emission spectra over the entire acquisition range (0.90 ± 0.07).

The close resemblance between the emission and DFS spectra are further demonstrated when varying the aspect ratio of AuNRs and hence resonance energies.^62, Figure 3 illustrates the emission and DFS spectra of four representative AuNRs with different aspect ratios. The characteristic LSPR mode is seen in DFS spectra, while the emission spectra closely follow the DFS spectra. To more quantitatively assess the similarity between the emission and DFS spectra, the emission and DFS maxima, λ_max^PL and λ_max^DFS, of 82 single AuNRs are correlated. A small blueshift of the emission compared to the DFS, independent of the AuNR aspect ratio, is observed and will be discussed in more detail below. We note that while we always observed a blueshift relative to the DFS spectrum, the Orrit group reported a redshift for high aspect ratio AuNRs immersed in glycerol.⁵⁸ This dissimilarity may be due to a combination of several experimental factors that differed, such as nanorod width, embedding medium, and excitation power. In particular, as discussed below, we found that raising the excitation power further blueshifts the emission maximum. The results discussed so far suggest that the surface plasmon of AuNRs acts like an antenna enhancing their emission.^58,89,102 While there is general agreement about the role the LSPR plays in emission enhancement, two mechanistic interpretations of the emission from plasmonic nanostructures have been developed and will be discussed next.

A plasmonic nanoparticle can be described as an antenna, enhancing the light emission radiating into the far-field,³³ consistent with other spectroscopic signals being plasmon enhanced by either increasing photon absorption or emission.^103–105 However, the important finding that the cw laser excited emission spectra always follow the elastic scattering lineshape, which represents the LSPR supported by the nanoparticle,^52,62,106 is insufficient to properly interpret the phenomenon of light emission. For proper interpretation, we must consider the electronic transitions occurring in the metal. Mooradian³⁰ and Boyd et al.³¹ attributed the emission from gold and copper films to the interband transitions between the d-band and sp-band [Fig. 4(a)]. Based on measurements on thin films and nanoparticles, Beversluis et al. proposed that the intraband transitions within the sp-band of gold can also contribute to the emission [Fig. 4(c)].³² These results indicate a PL mechanism involving real electronic states and have led to the development of theoretical frameworks that consider PL as the radiative recombination of d-band holes and sp-band electrons, although these models focused on spherical particles where interband transitions dominate the emission.^83,107 While both interband and intraband transitions can contribute to PL, it is important to consider them separately because interband transitions do not require a change of momentum, while intraband transitions do in order to satisfy momentum conservation rules.¹⁰⁸ Studies on the emission from plasmonic nanoparticles later adopted these interpretations and considered that emission originates from the recombination of the energetic carriers generated by the incident photon, i.e., PL.^{59,62,89,102,109}

In addition to PL, electronic Raman scattering has been suggested as the mechanism for light emission from plasmonic nanostructures.^14,22,108 Because electronic Raman scattering requires a smaller momentum change compared to intraband transitions [Fig. 4(d)],²² it has been argued that, in particular, the emission at wavelengths longer than the threshold for interband transitions is more favorably interpreted as electronic Raman scattering. This inelastic scattering of a photon from electrons, involving only one intermediate state in a single scattering event, is a coherent process and stops after dephasing.¹¹⁰ In contrast, in the case of a PL mechanism, a real excited state is created by the absorption of a photon, and subsequent momentum and energy changes occur through electron–electron and electron–phonon interactions before the emission of a photon via radiative charge carrier recombination.¹¹¹ Next, we discuss our research into metal nanoparticle emission using steady state emission spectroscopy. We provide indirect but supportive evidence for a PL mechanism by demonstrating the effect of the band structure on emission efficiency.

Single AuNRs support a well characterized longitudinal LSPR, which can be tuned by varying their aspect ratio and size, and thus are a good model system for emission spectroscopy studies.^{32,33,47,78,112–116} In particular, for small aspect ratio AuNRs, the longitudinal LSPR partially overlaps with the interband transition of gold, while for large aspect ratio AuNRs, the plasmon can be shifted to energies lower than the interband transition threshold, resulting in only intraband excitation following plasmon decay. Light emission at these longer wavelengths where interband transitions are not possible is especially debated compared to interband emission at shorter wavelengths and has led to the two opposing views of light emission below the interband threshold, i.e., intraband PL vs electronic Raman scattering. We therefore studied AuNRs with varying aspect ratios using excitation energies both below and above the interband gap of gold at 1.8 eV.^117,118 As discussed, cw laser excited emission from the AuNRs follows the plasmonic spectral lineshape and polarization.^32,34,52 To allow for a quantitative comparison between the AuNRs with varying longitudinal LSPR energies and excited at different wavelengths, we determined the emission quantum yield (QY) as the ratio of emitted photons to absorbed photons.¹¹⁹ Quantitatively evaluating efficiencies, including when an electronic Raman process is stipulated, is absolutely essential for the comparison of results from different plasmonic systems measured by a variety of groups.

Specifically, we used cw lasers operating at 405, 488, 532, and 633 nm above and 785 nm below the interband gap [Fig. 5(a)]. Figures 5(b)–5(e) show the emission spectra when the incident photon energy is larger than the interband gap. The spectral features near the excitation wavelengths are assigned to interband PL, as illustrated in Fig. 4(a). This interband PL is not observed with 785 nm excitation [Fig. 5(f)] because the photon energy is below the interband gap of gold. The long wavelength spectral features in the emission spectra [Figs. 5(b)–5(f)] resemble the LSPR as determined by DFS [Fig. 5(g)], consistent with the results in Fig. 3. Within a PL mechanistic picture, for 405, 488, 532, and 633 nm excitation, the dominant long wavelength resonance could still occur due to interband transitions between a d-band hole and electrons below the Fermi level. However, for 785 nm excitation, only intraband PL is possible [Fig. 4(b)]. Because of the otherwise indistinguishable spectral shape of the long wavelength emission for all excitation wavelengths, it is likely that intraband PL also occurs for excitation energies larger than the interband gap, both after plasmon decay directly into intraband excitations as well as following an Auger process, where one electron fills the d-band hole and transfers the energy to create an intraband excitation [Fig. 4(b)]. QYs discussed below further confirm this interpretation.

The emission spectra were accurately simulated according to a PL mechanism involving the radiative recombination of excited charge carriers by considering the LDOS modulated by the LSPR as the Purcell enhancement factor,^96,120 giving rise to the emission peak. The simulations of the emission spectra assumed a simplified band structure for gold with a large d-band electronic density of states and parameterized transition matrix elements. Nevertheless, this simplified model successfully recovers the emission features in both the interband and LSPR spectral regions [Figs. 5(h)–5(k)].

Because we correlated the emission QYs for each of the 80 single AuNRs among all excitation wavelengths used, we were able to separate interband and intraband PL. Excitation energies above the interband energy yield higher QYs than the 785 nm excited pure intraband PL because interband recombination constitutes a direct momentum allowed transition.³² The single AuNR QYs are very close for all excitation wavelengths above the interband gap [Figs. 5(n) and 5(o)] with a slight enhancement seen when the LSPR overlaps with the interband emission peak for 633 nm excitation [Fig. 5(p)]. In that case, increased QYs are observed due to plasmonic enhancement of the interband emission. This enhancement is consistent with previous theoretical studies.^83,107 In contrast, when exciting below the interband gap, as in the case of 785 nm excitation, the emission QY is lower by a factor of about 2. We attribute the lower QY for pure intraband PL to its indirect momentum forbidden nature. However, selection rules are relaxed in nano-confined systems, as we discuss next, and a difference of only 2 suggests that intraband PL is likely also present after interband excitation following an Auger scattering process [Fig. 4(b)],⁸⁵ especially when also considering that d-band holes have a short lifetime of only <50 fs.^121,122

In addition to identifying the spectral contributions, the effect of the hot carrier distribution on emission spectra was demonstrated through the relative shift of the emission spectrum compared to the DFS spectrum as a function of incident laser power density. For both interband and intraband excitations, higher laser powers lead to increased blueshifted emission because the hot carrier distribution is shifted to larger energies [Figs. 6(a) and 6(b)]. The blueshift is not accounted for by thermal effects as the calculated temperature change of the AuNRs (<30 K) does not cause a noticeable change in the LSPR, as confirmed by acquiring DFS spectra while illuminating the AuNRs with the same laser excitation. Another notable observation is that the blueshift between the emission and DFS spectra is consistent irrespective of the excitation wavelength and only differs in magnitude [Figs. 6(c) and 6(d)]. Excitation with higher energy photons causes larger blueshifts, likely because higher incident photon energies lead to an initially higher energy electron distribution, akin to the power dependent blueshift. In conclusion, our excitation wavelength and power dependent studies of the Stokes emission from single AuNRs support our proposed Purcell effect enhanced emission model,^62,85 while theoretical modeling considering the effect of the gold band structure yields excellent agreement with the measured emission spectra.⁸² 

We further investigated the emission from single AuNRs with similar aspect ratios but different volumes to systematically determine the size dependency of the inter- and intraband PL.⁹⁸ We utilized AuNRs from three different samples of colloidal AuNRs with different widths but similar aspect ratios and therefore similar longitudinal LSPR energies with comparable contributions from interband damping.¹⁰⁰ Our results demonstrate that the effect of plasmonic enhancement, expressed through the Purcell factor, alone cannot explain the measured size dependency of emission intensities, and we therefore conclude that the transition matrix elements must also change with the AuNR size. These changes in transition matrix elements are due to an increased intraband contribution assisted by the electric field confinement in smaller AuNRs.

AuNR emission peak intensities decrease at the LSPR wavelength as the size increases, while the emission intensity for interband transitions is relatively independent of size [Fig. 7(a)]. To quantitatively compare the emission intensities of different AuNR sizes, we used the QY to re-scale the initially measured intensities of the emission spectra. The decrease in the main emission peak intensity for larger AuNRs partially comes from a reduced plasmonic enhancement due to a smaller Purcell factor because of increased radiative plasmon damping.^123–125 The interband emission intensities, on the other hand, do not follow a similar size dependence because interband transitions are an intrinsic property of gold and lack a size dependency for the AuNR sizes studied here.^100,119,126 Correspondingly, spectrally resolved LDOS profiles determined from finite element method calculations follow a similar trend as the experimental emission spectra [Fig. 7(b)]. The LDOS close to longitudinal LSPR decrease with increasing AuNR size, similar to the experimental results. However, the relative changes of LDOS are smaller than those seen for the experimental emission intensities as the size increases. This excess emission intensity decrease can be attributed to a reduction in the contribution from intraband PL to the total PL spectrum for larger AuNRs.

Correlating the Purcell factor and QY scaled emission at the longitudinal LSPR wavelength allowed us to quantify contributions from inter- and intraband transitions to the PL of AuNRs. Based on the mechanism of a Purcell effect enhanced PL, the emission enhancement is proportional to the calculated LDOS or the Purcell factor. Instead of simulating the LDOS as shown in Fig. 7, the Purcell factor can be derived experimentally using the Q-factor, mode volume, and emission wavelength of individual AuNRs.^120,127 The Q-factors, calculated mode volumes, and physical volumes of the AuNRs studied as a function of their width are presented in Fig. 8(a). Mode volumes (green line and circles) of smaller AuNRs are comparable to their physical volumes (blue circles). However, as the AuNR size increases, the mode volume starts to differ from the physical volume. Figure 8(b) illustrates the QY scaled PL intensities at the LSPR wavelength as a function of the calculated Purcell factor for all 120 AuNRs investigated. In Fig. 8(b), the gray circles present the simulated emission intensity vs the calculated and scaled LDOS (which is proportional to the Purcell factor).¹²⁰ It is worth noting that the calculated PL intensities for the eight AuNRs used here are directly comparable to their QY scaled emission intensities without requiring any adjustments in the simulations. A linear fit to these simulated data points and its extrapolation to larger AuNR sizes provide predicted PL intensities based only on the enhancement by the LDOS ignoring any potential changes to the transition matrix elements [see gray line in Fig. 8(b)]. This simulated trend is followed by AuNRs with widths between 25 and 35 nm [Fig. 8(b), green symbols] but is inconsistent with the measurements for AuNRs with widths ranging from 40 to 55 nm [Fig. 8(b), orange symbols] and 65–100 nm [Fig. 8(b), purple symbols]. The observed deviations increase with increasing AuNR size and suggest that contributions from intraband transitions to the emission decrease. Consistent with these results, FDTD simulations of the electric field intensity distribution inside the AuNRs found a 2.5 times stronger electric field confinement in the smaller AuNRs, providing the necessary momentum for efficient intraband transitions.^32,128 Our results highlight the important role of the AuNRs size in determining the inter- and intraband PL efficiency. Intraband PL in confined metallic nanostructures can be enhanced, while interband emission is mostly independent of size.

As discussed in the previous section regarding size effects the Purcell effect based PL mechanism indicates that the plasmonic enhancement depends on the quality of the resonator cavity and the resulting LDOS. We therefore expect the general mechanistic properties of PL to extend to lithographically fabricated AuNRs with a QY decrease that reflects the reduced quality of the LSPR. To demonstrate this prediction directly without having to consider changes in the transition matrix elements due to size variations, we characterized the emission from single AuNRs falling in the same size range but having different degrees of plasmon damping. We compared highly crystalline colloidal AuNRs and polycrystalline electron-beam lithography fabricated AuNRs with and without a Ti adhesion layer. Both the polycrystalline nature^9,129,130 and the Ti adhesion layer¹³¹ increase plasmon damping of metallic nanostructures fabricated through metal evaporation, leading to smaller Q-factors.

The emission spectra of lithographically fabricated AuNRs follow the same general properties as discussed above for the highly crystalline chemically prepared AuNRs [Fig. 9(a)]. We investigated AuNRs with aspect ratios ranging from 1.5 to 2.5. Their emission lineshapes are again similar to the corresponding DFS spectra; AuNRs with larger aspect ratios have lower energy DFS and emission maxima and the emission maxima are blueshifted slightly compared to the DFS maxima. We furthermore found that AuNRs with larger Q-factors have larger QYs [Fig. 9(b)]. The AuNR DFS spectra were used to characterize the LSPR Q-factors. When comparing AuNRs of similar sizes, the Q-factors decrease in the order of chemically synthesized > Ti free lithographically prepared >2 nm Ti adhesion layer lithographically prepared AuNRs. Electron scattering at grain boundaries and defects caused by polycrystallinity increases plasmon damping.^9,129,130 Although the Ti adhesion layer can dramatically improve the success of the lithography process, it introduces significant chemical interface damping to the LSPR.¹³¹ This additional plasmon damping due to polycrystallinity and the secondary metal adhesion layer cause broader DFS spectra and hence reduced Q-factors. A roughly linear correlation between the Q-factors of AuNRs fabricated by all three approaches and their emission QYs was observed, consistent with the results presented in the previous section discussing size effects.⁹⁸ This connection between the Q-factor and the Purcell factor was supported by LDOS simulations with the degree of plasmon damping tuned by adjusting the Drude–Lorentz term in the dielectric function of gold.¹³² 

We further varied the crystallinity of a single AuNR using a gradual photothermal annealing method and determined the effect on its QY. Thermal annealing is known to improve the crystallinity of metal nanostructures and thus reduces plasmon damping.^133,134 Exposing the lithographically fabricated AuNRs to a focused 488 nm laser and increasing the power slowly over a time of 2 h led to blue-shifted DFS spectra and a Q-factor increase of ∼2. During this photothermal annealing process, the emission intensity increased by a factor of ∼1.5× despite virtually no change in the shape of the AuNRs occurring.

While these results are not necessarily surprising, given the fact that the only meaningful difference between lithographically fabricated AuNRs and chemically synthesized AuNRs is the underlying crystal structure of the gold, these studies nevertheless fill an important gap in the literature. Other studies had demonstrated that the quality of the plasmonic resonance of lithographically fabricated nanostructures is diminished compared to their chemically synthesized counterparts,¹³¹ but the emission properties of such samples were previously unknown.

Up to this point, we have considered one-photon processes that lead to Stokes emission. However, a comprehensive characterization of AuNR emission must also consider anti-Stokes emission.^30,88,91 According to Fig. 10, for 405 nm excitation [Figs. 10(a) and 10(d)], the emission follows the LSPR for each AuNR [Figs. 10(c) and 10(f)] as expected and previously discussed as a Purcell effect enhanced PL. For 633 [Fig. 10(b)] and 785 nm [Fig. 10(c)] excitation, AuNRs that have longitudinal LSPRs overlapping with the excitation exhibit both the lower energy Stokes emission, as seen with 405 nm (and other non–longitudinal LSPR resonant) excitation, and a higher energy anti-Stokes emission peak. The 633 [Fig. 10(b)] and 785 nm [Fig. 10(e)] excited anti-Stokes emission from single AuNRs occurs mainly in the spectral region covered by the longitudinal LSPR [Figs. 10(c) and 10(f)]. For the anti-Stokes emission, the intensity scales nonlinearly with excitation power [Fig. 10(g)], in contrast to the linear excitation power dependence for the one-photon Stokes emission from AuNRs.^14,62,91 We therefore interpret the anti-Stokes emission as the Purcell effect enhanced radiative recombination of charge carriers with energies exceeding the excitation wavelength due to multi-photon absorption and electron–electron scattering leading to an increased hot electron energy distribution.⁸⁸ 

Additionally, the power law exponents for the anti-Stokes emission increase with the emitted photon energy. Figure 10(h) shows the power law exponents, extracted from the emission intensities at different excitation power, as a function of energy shift between emission and excitation wavelength. The number of incident photons needed for emitting an anti-Stokes photon increases with the emission energy, involving hot carriers with higher energies, faster decay rates, and smaller occupation numbers. Electron–electron scattering creates these highly excited electrons from continuous excitation events with a cw laser and provides the energy for the anti-Stokes shift. A similar trend was observed for pulsed laser excited gold nanostructures.^135,136 The power law exponents in the pulsed laser case are larger than 2 though in contrast to the smaller values seen here for cw laser excitation [Fig. 10(h)].

Temperatures can be extracted based on the ratio of Stokes and anti-Stokes emission from resonantly excited AuNRs (Fig. 11). The measured ratios for 633 and 785 nm excitation are displayed in Fig. 11(a). The emission spectra were fitted using the DFS spectra and a Bose–Einstein distribution to model phonon occupation and a Boltzmann distribution to describe plasmon-generated hot carriers. The extracted distributions can be assigned effective temperatures, which are plotted in Fig. 11(b) for Bose–Einstein and Fig. 11(d) for Boltzmann statistics. In particular, for 785 nm excitation, the temperatures extracted from a Bose–Einstein phonon distribution are higher than 1000 K, which is unrealistic for the AuNR lattice temperature considering that AuNRs readily reshape at 400 K.¹³⁷ Since AuNR melting was not observed⁸⁸ and the calculated steady state lattice temperatures are less than 100 K above room temperature [Fig. 11(c)], Boltzmann statistics describing the hot carrier energy distribution is more reasonable. In fact, estimating the lattice temperature after energy exchange with the hot carrier distribution yields values similar to the steady state lattice temperatures.

In summary, we have shown that our proposed Purcell effect enhanced hot carrier PL mechanism explains all features of Stokes and anti-Stokes emission from single AuNRs.^85,88 The wavelength, excitation power, and size dependence of inter- and intraband emission efficiencies highlight the effect of confinement and the band structure of gold in determining the spectral lineshape and QY of the emission. The slight changes in observed emission indicate different hot carrier energy distributions and suggest that it should be possible through further theoretical studies to determine hot carrier distributions from emission spectroscopy using cw excitation, which more accurately mimics low level and solar irradiation. The impact of the Purcell factor enhancement on the emission was demonstrated by quantitatively determining for individual AuNRs their emission lineshape and maximum, QY, Q-factor, and mode volume. While these relationships also persist in lithographically fabricated AuNRs, their emission QY is reduced because they are polycrystalline, leading to increased LSPR damping. Overall, our experimental and theoretical studies support a PL mechanism for light emission from AuNRs, with hot carriers playing a critical role. Finally, our results are consistent with work from other groups showing that Stokes emission from plasmonic nanoparticles is a one-photon process and tracks the LSPR lineshape.^58,61,62

We also analyzed anti-Stokes emission excited with cw lasers and extracted an effective electron temperature corresponding to an excited charge carrier distribution. Compared to Stokes emission, anti-Stokes emission is more sensitive to the energy distribution of the system because it requires an energy exceeding that of just one incident photon.¹³ In comparison, the large excitation power density during the short duration of femtosecond pulses often leads to multi-photon (>2) excited emission.^138–141 When the incident laser power is concentrated within a short pulse duration, a broader hot carrier distribution skewed to higher energies is obtained and the emission spans to more than 1 eV above the excitation. Such emission following nonlinear excitation of AuNRs has been explained using a PL mechanism characterized by an increased LDOS at energies corresponding to both the longitudinal and transverse plasmon modes.¹⁴² In contrast, cw excitation, having a 2 orders of magnitude lower photon flux,^135,136 gives much narrower anti-Stokes emission spectra.¹⁴ Nevertheless, both excitation conditions are well explained by a hot carrier driven PL mechanism considering the agreement in the increased power law exponent with higher emission energy and the high extracted effective electron temperatures from the anti-Stokes spectra.

We observed the cw laser excited anti-Stokes emission from single AuNRs under interband (633 nm) and intraband (785 nm) excitation and operated in the power density region of 0.1–1 MW cm⁻². Other studies using cw excitation assumed thermal equilibrium between electrons and phonons and explained the anti-Stokes emission with a phonon-mediated charge carrier recombination^13,56 or a thermally activated electronic Raman scattering mechanism.²² In these studies, the temperatures extracted from the emission spectra were attributed only to the lattice, in contrast to the electronic temperature we assigned it to. It is worth noting that these mechanistic views are not contradictory in the low excitation power region when the electron temperature does not deviate much from the lattice temperature.¹³ However, we observed that the efficiency of Stokes and anti-Stokes emission depends on the electronic band structure, a fact that cannot be easily explained by electronic Raman scattering because the scattering cross sections at the two excitation wavelengths are similar. Raman enhancement by resonant interband transitions at 633 nm also cannot explain our data as a previous study indicated that resonance Raman enhancement is related to the imaginary part of the dielectric function,¹⁴³ which for gold is larger at 785 nm than at 633 nm.¹⁴⁴ We therefore conclude that our interpretation presents a unified mechanistic view of anti-Stokes and Stokes emission from single AuNRs under cw laser excitation modeled as the Purcell effect enhanced radiative recombination of hot carriers and is furthermore consistent with emission studies using ultrafast laser excitation.

We want to emphasize though that we do not necessarily generalize our conclusions to all plasmonic systems, such as coupled nanostructures including particle on a mirror configurations¹⁰⁸ or other plasmonic metals with different band structures.¹⁴⁵ Future research is needed to quantify light emission from different plasmonic materials coupled with well-designed metal–metal, metal–semiconductor, and metal–molecule interfaces.¹⁴⁶ In particular, to compare results among different plasmonic nanostructures excited at varying wavelengths, it is necessary that quantitative QYs or alternatively absolute electronic Raman scattering cross sections are consistently reported in the literature. It is furthermore conceivable that both PL and electronic Raman scattering occur for the same nanoparticle, but their relative amplitudes depend strongly on the metal, size, shape, and environment, where the latter could selectively quench the PL.

To help resolve the debate on the emission mechanism, time-resolved emission lifetime measurements based on femtosecond luminescence upconversion would be helpful.^92,147–149 The emission lifetime for a PL process is expected to be on time scale of reaching thermal equilibration of the electron sea and the lattice (∼1 ps), significantly longer than the electronic Raman scattering process, which lives only for the duration of the femtosecond excitation pulse. However, previous ensemble studies of the time-resolved emission from plasmonic nanoparticles have provided conflicting results,^147,148 yielding both support for and against both mechanisms. Lifetime measurements performed on a single nanoparticle or a pristine nanoparticle array would eliminate possible contaminations present in ensemble solutions but have yet to be accomplished.

We would like to end by stating that it is important to resolve this debate about the emission mechanism because light emission, if interpreted correctly, can provide detailed insight into the electron and phonon distributions (i.e., temperatures) following photon absorption. Such knowledge is particularly beneficial to the ongoing quest to characterize hot carrier distributions and lifetimes in plasmonic nanostructures for their use as photocatalysts.^18,150–152 Anti-Stokes emission spectra have recently been employed as a probe to determine temperatures of nanoparticles and their local environment.^13,15,153 In an impressive recent study, the determination of electron temperatures from anti-Stokes emission has been extended to time-resolved measurements.¹⁵⁴ Further resolving the time-resolved PL at different excitation wavelengths and powers would not only help determine the emission mechanism but also open observation windows for characterizing hot carriers for various environments, interfaces, and chemical processes.

Y.-Y.C. and L.J.T. contributed equally to this work.

The work discussed in this paper was supported by the Robert A. Welch Foundation (Grant No. C-1664), the Office of Naval Research (Grant No. N00014-10-1-0989), the Air Force Office of Scientific Research (Grant No. MURI FA9550-15-1-0022), the National Science Foundation (Grant Nos. CHE-0955286, ECCS-1608917, and EEC-0647452), the American Chemical Society Petroleum Research Fund (Grant No. 50191-DNI6), and a 3M Nontenured Faculty Grant. We would like to thank all previous members of the Link group who participated in the research summarized here. In particular, we would like to thank Dr. Alexei Tchemiak, Dr. Ying Fang, Dr. Sergio Dominguez-Medina, and Dr. Da Huang and also our collaborators Professor Christy Landes, Professor Wei-Shun Chang, and Professor Peter Nordlander. We would also like to thank Dr. Anneli Joplin for creating the cover art image.