Gold nanorods emit strong photoluminescence under two photon excitation; the efficient two photon lumininescence (TPL) arises from the local field enhancement assisted by surface plasmons. The surface plasmon effects on the TPL efficiency and spectrum are investigated by measuring the TPL of gold nanorods with various aspect ratios. A large TPL efficiency is found when incident light wavelength coincides with the longitudinal surface plasmon mode of the gold nanorods. However, the emission spectra of nanorods with various aspect ratios look similar and exhibit modest surface plasmon features, which implies a major non-radiative decay of excited surface plasmons.
©2009 Optical Society of America
The photoluminescence of gold metal was first reported in 1969 by Mooradian . The photoemission is thought to arise from the direct transitions between electrons in the conduction band below the Fermi level and holes in the d bands. Although suggested by Mooradian as a band-structure probe, the photoluminescence of noble metals remained relatively unexplored for nearly two decades until 1986, when Boyd  reported multiphoton-induced luminescence on roughened noble metal surfaces. Since the efficiency of single photon luminescence is very small, ~10-10 , even the luminescence can be excited by multiphoton absorption, it is not likely to be detected without an enhancement mechanism. There are two important effects contributing to the local field enhancement on roughened metal surfaces. First, fields tend to concentrate at the protrusions on metal surfaces, known as the lightning-rod effect . Second, the collective oscillation of the electrons on metal surfaces can be induced by optical fields; the resonance greatly amplifies the local field, which is referred to as the local-plasmon effect .
In recent years, there has been a renewed interest in photoluminescence from metal surfaces, primarily in the photoluminescence from noble metal nanoparticles. Much of the interest is generated by the potential biomedical applications of nanoparticles. Two photon luminescence (TPL) is particularly appealing for biomedical use because of its high resolution, low photodamage and 3D-imaging capability. Besides, the near-infrared excitation light is where the absorption of water and biological samples are minimized. The two photon luminescence of various gold nanoparticles, including nanospheres, nanorods and nanoshells, has been tested and reported to be highly efficient [4–8]. Similar to the mechanism on a roughened surface, the photoluminescence is enhanced through the mediation of surface plasmons (SPs). The efficient, non-bleaching and non-blinking photoluminescence makes gold nanoparticles an ideal probe in imaging, as it is used as a contrast agent in most reports [7–9]. However, the photoluminescence of gold nanoparticles has not yet reached its full potential for applications. Since surface plasmon modes are sensitive to the local dielectric properties, the local ionic movement or fluctuation of charge density could modify the surface plasmon mode by affecting the local dielectric constant and thus causes a change in the photoluminescence. Thus, by monitoring the photoluminescence of the targeted nanoparticles, it is possible to sense local biological events that involve charge density changes, such as the action potential firing of neurons. Yet, prior to the promising use of photoluminescence as a sensor, the local plasmon effects on the photoluminescence spectra need to be well studied.
This article is intended to study the local plasmon effects on the two photon luminescence of gold nanorods. It is well known that the surface plasmon modes can be modulated by varying the aspect ratio of gold nanorods or by modifying the ambient refractive index. Hence, we measured the two photon luminescence of gold nanorods with various aspect ratios and in media with different refractive index. The experiment was carried out for gold nanorods in aqueous solution, very similar to the previous work on single photon luminescence done by Mohamed et al. , but simply on a two-photon basis. Unlike the single photon luminescence of gold nanorods, which has a spectrum peak strongly dependent on the aspect ratios of the nanorods , the difference in the TPL spectrum for nanorods with various aspect ratios is quite modest. We have observed quite similar TPL spectra for gold nanorods with aspect ratios from 1.3 to 5.3 and in media of varied refractive index. However, a great variation in the emission efficiency was observed among the nanorods with various aspect ratios. The variation in the TPL efficiency is also clearly seen when the ambient refractive index is varied. This indicates that the surface plasmon plays an important role in TPL efficiency, but the emission spectrum is determined by the intrinsic electronic properties of the rod particles.
Gold nanorods were synthesized by using the seed-mediated methods as described elsewhere . In short, Au seeds were prepared by mixing solutions of 0.1M NaBH4 and 2.5×10-4M HAuCl4, followed by vigorous stirring. For the rod formation, a sufficient amount of surfactant, cetyltrimetyl ammonium bromide (CTAB), was added into the solution. By varying the amount of surfactant, gold nanorods with different aspect ratios can be obtained.
The extinction spectra of gold nanorods with various aspect ratios were measured by a UV-Visible spectrophotometer (Cary 50Conc, Varian) and the longitudinal surface plasmon (LSP) peaks are found to be at 540, 590, 680, 740, 790, 820, and 930nm, which is equivalent to aspect ratios from 1.3 to 5.3 according to the linear dependence of LSP peaks on the aspect ratios of gold nanorods  (see Fig. 1). The axial length of the nanorods is between 10 and 15nm as indicated by the TEM (transmission electron microscopy) images. The concentration of each nanorod solution was adjusted so the optical density (OD) of LSP band is about 1; the nanorod solutions are then used for the TPL measurement.
The setup for TPL measurements is schematically shown in Fig. 2. The light source was a Ti:sapphire laser (Tsunami, Spectra Physics) at a 80 MHz repetition rate with a pulse width <100 fs. The TPL spectrum was recorded by a liquid N2 cooled spectrometer (iHR550, Horiba) connected to the backport; the TPL intensity at the selected wavelength (band-pass filter HQ660/50, Chroma Technology) was recorded by a highly sensitive and low-dark-count photomultiplier (H7422 P, Hamamatsu) at the side port. The average incident power on sample was about 2 mW, corresponding to a peak intensity of about 1.25GW/m2 in the focus.
2.2 Estimation of the local field factor
Mohamed et al.  measured the photoluminescence from gold nanorods (with aspect ratios of 2.0–5.4) by single photon excitation at 480 nm. They observed a photoluminescence enhanced by a factor of over a million compared to that of gold metal; this is due to the enhanced absorption facilitated by the transverse surface plasmon mode (~520 nm). More interestingly, the efficiency increases and the emission wavelength peak red-shifts as the length of the rods increases. To explain this phenomenon, they employed the local field correction idea used by Boyd et al. [3 3] to estimate the field enhancement on the rough metal surface. The local field factor L of a hemispheroid is the product of LLR and Lp, which are the lightning rod factor and the local plasmon factor, respectively. LLR is only related to the hemispheroid shape, given by the aspect ratio (a detailed formula for LLR and Lp can be found in the reference). The calculated local field factor L(ω), though successfully predicts certain trends in the data, does not give a quantitatively accurate estimation. First, the theory predicts a fast increase in the emission strength as the rod length becomes very long, but in fact a decrease in emission is observed for very long nanorods. Second, it vastly overestimates the emission peak wavelength for nanorods with high aspect ratios . Therefore, for a quantitative analysis in our study, the local field enhancement factor is evaluated with the help of linear extinction spectroscopy, where the transmission minimum is associated with the localized surface plasmon . The characterization technique by extinction spectroscopy, though lacking in spatial resolution, is considered quite reliable. It should be applicable to our experiment, as the extinction and TPL spectra were obtained on the same samples using far-field incident light, which completely smears the spatial information. The samples were gold nanorod aqueous solutions with rods of aspect ratios ranging from 1.3 to 5.3, and the concentration was adjusted so that the OD of the LSP band was 1. For each gold nanorod solution with OD~1, the exact particle concentration in each solution was slightly different; the nanorods with higher aspect ratios had slightly lower particle concentrations. In order to compare the TPL efficiency on a single particle basis, we must at least know the relative particle concentration among the nanorod solutions. The relative concentrations of the gold nanorod solutions were calculated using the molar extinction coefficient of the LSP band . Since the reference only offers the molar extinction coefficient for nanorods with aspect ratios up to 4.5 (equivalent to LSP band at 850 nm), we only make comparisons in this range. Taking the particle concentration of the nanorod solution with LSP band at 820 nm as 1, we obtain a concentration ratio ranging from 3.1 to 0.7 for the nanorod solutions used in the experiment.
where Iext, Iabs, Isca, and Iin are the intensity of extinction, absorption, scattering and incident light, respectively; α(ω) and β(ω) are the constants that include the intrinsic spectrum of absorption and scattering; γ (ω) is the sum of α(ω) and β(ω) ; N is the number of nanorods in the light path; E 0 is the incident electrical field. According to Eq. (1), the local field factor for each sample can be deducted from the measured absorbance A
where It is the transmission intensity. The L(ω) for incident and outgoing light of each gold nanorod sample can be computed with the measured absorbance.
2.3 Estimation of the TPL efficiency
where ω 2 and ω 1 are the luminescence and incident light frequencies, respectively, N is the number of particles in the excitation volume, and η is a factor related to the intrinsic luminescence spectrum of the material. In the experiment measuring the TPL efficiency of nanorods with different aspect ratios, the power and wavelength of the incident light was set as constant (λext=815 nm), and the emission intensity was measured at ~660±25 nm. In our experiment, the nanorod solution with LSPR at 820 nm was found to have the maximum emission. If we consider the TPL efficiency of a nanorod with LSPR at 790 nm and compare it to that of a nanorod with LSPR at 820 nm, we have the relative TPL efficiency Pr for the nanorod with LSPR at 790 nm
Where PLSPR =790 and P LSPR=820 are the measured emission intensity for the gold nanorod solutions (OD=1) with LSP band at 790 and 820nm, respectively; N 1 and N 2 are the numbers of gold nanorods in the excitation volume for solutions with LSP band at 820 nm and 790 nm, respectively. is the concentration ratio mentioned in last section. Based on the definition of Pr in Eq. (4), we can integrate Eq. (3) into Eq. (4) and acquire a Pr predicted by the local field model described above, where Pr is
According to Eq. (4), the Pr can also be experimentally obtained from the measured intensity and particle concentration ratio for each nanorod solution. The measured Pr is compared to the one estimated by calculating the local field factor as described in Eq. (2) and Eq. (5).
3. Results and Discussion
3.1 The TPL efficiencies and spectra of gold nanorods with different aspect ratios
To verify the two photon origin of the observed luminescence, the TPL yield was measured against the excitation power. A fit to the logarithm of the data reveals a slope of 2.05, indicative of a dominant two photon process. The relative TPL efficiency Pr of the nanorods with aspect ratios from 1.3 to 4.2 (equivalent to LSP modes from 540 to 820 nm) was measured and is shown in Fig. 3. With the excitation wavelength set at 815 nm, it is not surprising to see that the nanorod with LSP mode of 820 nm has the greatest TPL efficiency, due to its quadratic dependence on excitation power. For nonlinear processes such as TPL, the incoming field intensity plays a dominant role in PL efficiency; the largest enhancement happens when the incoming light couples with the longitudinal surface plasmons of the nanorods and greatly increases the absorption cross section. Part of the excited surface plasmons decay nonradiatively into electron-hole pairs via interband excitation ; the subsequent relaxation and recombination of electron-hole pairs lead to the observed TPL. The radiative recombination of electron-hole pairs may likewise excite surface plasmons and produce a second enhancement, as the local plasmon effect would enhance both incoming and outgoing electrical fields [2,3]. Equation (5) includes the enhancement of both the incident and emission electric fields; the result is calculated and shown as the dotted line in Fig. 3. The result exhibits a larger TPL for the nanorods with LSPR at 680 and 740 nm, and the decrease in TPL is mild when the LSP mode varies from 790 to 680nm. However, we have consistently measured a sharper TPL decrease in this range. In contrast, the calculation considering only the field enhancement of incident light gives a better estimation, as shown in Fig. 3. If a substantial part of the emission is indeed enhanced by the support of surface plasmon excitation, we would expect different spectrum shapes for nanorods with varied LSP modes. However, the observed spectra are quite similar in each case, with peaks at roughly the same positions, as shown in Fig. 4. The observation suggests a likely weak coupling of the emission to surface plasmons, or, if efficient coupling indeed occurs, the excited SPs may be subject to nonradiative decay and thus are not detected as photons.
Although the gold nanorod spectrum in Fig. 4 is an ensemble average excited by far-field light, it still bears much resemblance to the results obtained on a single nanorod. Imura et al.  have measured the spectrum of a single gold nanorod using near-field excitation, in which two peaks near 540 and 650 nm are found. The peak positions are close to the emission peaks of gold crystal, which is expected at 520 and 650 nm according to the calculated band structure. The emission peaks of gold crystal originate from the interband transitions near the X and L symmetry points of the first Brillouin zone due to the large density of states near the symmetry points. The 650 and 540 nm peaks observed on a single nanorod are thus assigned to the electron-hole recombinations near the X and L symmetry points, respectively. Similarly, we also observed peaks at 680 and 540 nm, which possibly represent the transition at the X and L symmetry points. While the spectra in Fig. 4 look similar, the relative intensities Ix/IL of these two spectral components vary for different nanorods. Imura et al.  reported a Ix/IL ratio ranging from 0.5 to 2; they ascribed the variation of this ratio to the difference in the plasmon modes excited. For nanorods with LSP modes at 680 to 930 nm, the Ix/IL ratio measured in our experiment is between 1 and 2, as listed in Table 1. The nanorod with LSP mode at 680 nm has the highest Ix/IL ratio, 1.47, while the ratio for the nanorod with LSP mode at 930 nm is the lowest. Apparently, the nanorods with LSP wavelengths overlapping the emission from the X region have higher Ix/IL ratios; this strongly suggests that the emission from X region is in resonance with the LSP of the nanorods.
Bouhelier et al.  have measured TPL spectra of relatively large gold nanorods; the TPL spectra they observed almost overlap with the scattering spectra, reflecting pronounced surface plasmon characteristics. Compared to their results, the TPL spectra observed in our experiment do not exhibit prominent surface plasmon features. The discrepancy may arise from the different ways by which the excited surface plasmons (SPs) decay. The coupling of TPL to SP can be large, but only part of the captured energy by SPs reradiates as photons, with part of the energy dissipated in the metal. The relative strength of these two processes depends on the geometry of the nanoparticle, and the geometry is exactly the major difference between the nanorods used by Bouhelier et al. and those used by us. We used smaller nanorods, with an axial length only 1/3 of that of their nanorods, and the nanorods produced by wet chemical methods may carry more shape irregularity compared to e-beam fabricated nanorods. As the dissipation dominates the plasmon decay for nanoparticles with small sizes, this is likely the reason why we do not see a clear surface plasmon feature in the emission.
3.2 The TPL efficiency of gold nanorods in medium with different refractive index
The sensitivity of TPL to the LSP mode of nanorods implies the possibility of sensing the local refractive index change by TPL, as the ambient refractive index can modify the peak position of the LSPR . To verify this, 1 cc gold nanorod solutions were diluted with 1 cc DI water and 1 cc glycerol. The 50% glycerol solution had a refractive index of 1.4, which caused a red shift of about 20nm in the LSP wavelength of the gold nanorods, as shown in Fig. 5(a). The TPL efficiency of the nanorods was measured at various wavelengths from 754 nm to 860 nm. The TPL efficiency of the nanorods in the 50% glycerol solution is compared to that of the nanorods in 100% DI water, and the results are presented in Fig. 5(b). As the ambient refractive changes from 1.33 to 1.40, depending on the choice of excitation wavelength, the TPL intensity can change up to 50%. If an event occurring near the nanorod involves drastic refractive index changes, then it can be detected simply by measuring the TPL intensity of the nanorod. According to Fig. 5(b), the excitation wavelength that produces an equal TPL efficiency is at ~815 nm. When excited at 815nm, the TPL spectra of gold nanorods in 100% DI water and 50% glycerol are nearly identical, as shown in Fig. 5(c). Note that if we only consider the local field enhancement by surface plasmons, then the TPL efficiency should be roughly the same when the excitation wavelength is set at 800 nm. Apparently, the TPL intensity in 50% glycerol is slightly lower than expected. This can be due to scattering losses of emitted light in a more dense medium like glycerol.
4. Conclusion and Perspectives
In conclusion, we have measured the strong dependence of the TPL efficiency on the LSP modes of nanorods. The enhanced TPL efficiency arises mostly from the enhanced absorption by surface plasmons, which then increases the pumping rate of electron-hole pairs. The plasmon-supported photoemission was observed, but the effects on the TPL efficiency were not significant in our case. A possible explanation for the relatively weak plasmon-supported PL is the nonradiative dissipation of excited surface plasmons. We have also investigated the PL intensity change as the ambient refractive index changes from 1.33 to 1.40, and we observed a large intensity change up to 50%, which is a quite an encouraging result. As some biological events are generated by drastic ionic movement, which can induce a fluctuation in the local refractive index, PL can be a promising tool to detect these events. An excellent example for this type of applications is to monitor the fast membrane potential signals of neurons; this requires a method to attach the nanoparticle directly to the cell membrane. Based on our results, the biological use of gold nanorods is not limited to an imaging probe, but can be simultaneously extended to monitor fast dynamic events, which are of great biological significance.
This work is financially supported by the Ministry of Education, Taiwan, R.O.C, under the grant No.980061-01.
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