Sensing with Multipolar Second Harmonic Generation from Spherical

Letter pubs.acs.org/NanoLett

Sensing with Multipolar Second Harmonic Generation from Spherical Metallic Nanoparticles Jérémy Butet, Isabelle Russier-Antoine, Christian Jonin, Noel̈ le Lascoux, Emmanuel Benichou, and Pierre-François Brevet* Laboratoire de Spectrométrie Ionique et Moléculaire (LASIM), UMR CNRS 5579, Université Claude Bernard Lyon 1, 43 Boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex, France ABSTRACT: We show that sensing in the nonlinear optical regime using multipolar surface plasmon resonances is more sensitive in comparison to sensing in the linear optical regime. Mie theory, and its extension to the second harmonic generation from a metallic nanosphere, is used to describe multipolar second harmonic generation from silver metallic nanoparticles. The standard figure of merit of a potential plasmonic sensor based on this principle is then calculated. We finally demonstrate that such a sensor is more sensitive to optical refraction index changes occurring in the vicinity of the metallic nanoparticle than its linear counterpart. KEYWORDS: Silver nanoparticles, nonlinear optical sensing, plasmonics, second harmonic generation

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practical applications.13−15 This experimental work has also been successfully supported by theoretical investigations, analytical methods, or numerical simulations.16−18 SHG can be enhanced if the fundamental or the harmonic wavelengths are tuned close to LSPR with similar advantages to the linear optical case. However, to our knowledge, this property has never been exploited for sensing purposes. In this Letter, based on our recent experimental results we therefore theoretically investigate the sensing of refractive index changes using the SHG response from silver nanospheres. First, we address the linear case of the quadrupolar mode, which has good sensing properties but a challenging experimental observation. We then show that this mode dominates the total SH scattering cross section for silver nanoparticles the diameter of which is 60 nm and we discuss how the sensitivity to the refractive index changes is increased due to the intrinsic properties of the SHG response. The impact of the size on sensing is also discussed, pointing out that the best figure of merit is obtained for 60−80 nm silver nanospheres. Our results demonstrate in a simple case that nonlinear optical processes can already increase sensors efficiency. Using Mie theory and the multipolar expansion of the electromagnetic fields,19 the extinction, scattering and absorption cross sections for a 60 nm diameter silver nanoparticle can be calculated. The weight of each multipole in the internal and scattered fields is simply obtained with the application of the boundary conditions at the nanoparticle surface. The total

etallic nanoparticles support localized surface plasmon resonances (LSPR), that is, the collective excitation of the conduction electrons, leading to unique optical properties. These resonances are versatile tools since their width and position depend on the size, shape, composition, and dielectric constant of the surrounding medium.1,2 This latter dependence has opened the way to one of the most promising use of metallic nanoparticles: sensing using LSPR .3−5 Sensors based on this principle are thus able to detect small changes into the surrounding medium through the monitoring of the LSPR position shift. Recently, new coherent effects have been observed in plasmonic nanostructures such as Fano resonances or electromagnetically induced transparency. These phenomena are also offering new possibilities for the design of high sensitivity sensors.6−8 Fano resonances are obtained owing to the coupling of plasmonic modes supported by subregions of complicated nanostructures. This is the case for asymmetric nanocavities or coupled plasmonic nanoparticles.6,9,10 Fano resonances lead to very sharp peaks, the positions of which are very sensitive to the dielectric constant of the surrounding medium. This property makes them attractive for highly sensitive LSPR sensors. At the same time, efforts have been devoted to the study of the nonlinear optical properties of plasmonic nanoparticles.11 Among all the nonlinear optical processes, second harmonic generation (SHG), whereby two photons at the fundamental frequency are converted into one at the harmonic frequency, is the simplest. The polarization and shape dependence of the second harmonic (SH) intensity has been addressed for nanoparticles dispersed in liquid solutions or deposited on substrates.12 Several studies have reported the observation of SHG from single metallic nanoparticles thereby paving the way for a deeper understanding of the nonlinear interaction of light with the nanoparticle and, eventually, for the design of future © 2012 American Chemical Society

Received: January 17, 2012 Revised: February 27, 2012 Published: February 29, 2012 1697

dx.doi.org/10.1021/nl300203u | Nano Lett. 2012, 12, 1697−1701

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extinction cross section, which is the sum of the scattering and absorption cross sections, is then given by 2π

Nevertheless, the sensitivity is not the only relevant parameter to characterize a plasmonic sensor. Indeed, the width of the resonance is also important. Van Duyne and co-workers have therefore introduced a figure of merit (FOM) defined as the ratio between the sensitivity and the full width at half maximum (fwhm) for a given LSPR.21 For a refractive index n = 1.33, the fwhm of the dipolar and quadrupolar resonances are 51 and 11 nm, respectively, leading to a corresponding FOM of 3.8 and 9.5. To our knowledge, the predicted FOM for the quadrupolar LSPR is one of the highest reported for silver nanoparticles embedded in a homogeneous medium. The highest predicted value has been calculated for single silver nanocubes supported on ZnSe substrate (FOM = 20 in a particular situation).22 Experimentally though, the quadrupolar mode from a spherical nanoparticle can be observed with sensitive single nanoparticle detection experimental set-ups using linear optical processes but the determination of its exact spectral position is difficult to achieve.23 We now turn our attention to the nonlinear optical regime using 60 nm silver nanospheres. We perform calculations using Mie theory generalized to the case of SHG. The generalization of Mie theory to SHG has been developed previously in several works.24−26 Briefly, the fundamental electric fields are calculated using Mie theory and then used to calculate the nonlinear polarization oscillating at the second harmonic frequency. To this end, the fundamental electric field is evaluated just above the interface, inside the metallic nanoparticle.27 We consider only the component χsurf,⊥⊥⊥ of the surface susceptibility tensor, where ⊥ denotes the direction normal to the surface. Since the breaking of the centrosymmetry occurs along this direction, this element is known to dominate the surface response of metallic nanoparticles.28,29 Then, the nonlinear polarization can be written

∞

Cext = 2 ∑ (2l + 1)Re{al + bl} k l

(1)

where al and bl are the weights of the different modes present in the scattered field. k is the fundamental wavevector. The dipolar and quadrupolar modes are simply computed using l = 1 and l = 2, respectively. Results with the values of 1.33 and 1.57 for the optical refractive index describing the surrounding medium are depicted in Figure 1a. The bulk dielectric constant for the

Psurf, ⊥(r, 2ω) = χsurf, ⊥⊥⊥E⊥(r, ω)E⊥(r, ω)

(2)

The multipolar development of the second harmonic scattered field is obtained applying the appropriate set of boundary conditions, considering a nonlinear polarization sheet at the interface between the nanoparticle and the surrounding medium.30 In the case of the χsurf,⊥⊥⊥ element, only transverse magnetic modes are excited since the nonlinear polarization sheet does not possess any tangential component. The total SH scattering cross section can then be written as a mode superposition with the following expression

Figure 1. (a) Extinction spectrum of 60 nm silver nanoparticles for two different optical refraction indices of the surrounding medium, (continuous line) n = 1.33 and (dashed line) n = 1.57. The extinction cross sections considering independently the first two modes are shown, (red) dipolar mode (l = 1) and (blue) quadrupolar mode (l = 2). (b) Wavelength of the maximum SH intensity of the (square) dipolar mode and (circle) quadrupolar mode as a function of the optical refractive index. Lines are linear fits.

∞

2π l Csca(2ω) = 2 ∑ (2l + 1)|AM (2ω)|2 k2ω l

(3)

I AM (2ω)

where are the parameters calculated for the SH scattered wave. As in the case of linear extinction, the contributions of the dipolar and quadrupolar modes to the total SH scattering cross section are calculated using l = 1 and l = 2, respectively. Only the dipolar and quadrupolar modes are considered here. The octupolar one that has recently been observed for larger nanoparticles still remains negligible for nanoparticles with diameter of 60 nm.31 The spectrum for the SH cross-section is shown in Figure 2(a) for a refractive index equal to 1.33. In opposition to the linear extinction case, the dipolar contribution to the SH intensity is weaker than the quadrupolar one, see Figure 2a. This is a surprising result at first sight, but it can be interpreted as follows. The most efficient mechanism for a dipolar SH emission is the E1 + E2 → E1 mechanism. We use

silver nanoparticles is taken from ref 20. As the refractive index of the surrounding medium increases, the dipolar and quadrupolar resonances both shift to longer wavelengths. The graphs of the wavelengths corresponding to the dipolar and quadrupolar LSPR maxima as function of the refractive index are shown on the Figure 1b. The shift of the dipolar resonance with the optical index is larger than the quadrupolar resonance one as shown by the sensitivity values obtained by fitting procedures. The dipolar mode has a sensitivity of 196 nm/RIU whereas the quadrupolar mode of only 104 nm/RIU. Here, RIU stands for refractive index unit. These values are far smaller than the one usually obtained for the best plasmonic sensors.4 1698


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response at the fundamental wavelength, between 650 and 1000 nm in the present case. On the other hand, the SH quadrupolar mode that is excited by coupling twice the dipolar mode at the fundamental frequency does not suffer from this limitation and therefore largely dominates the total SH response. To determine the sensing properties of the SH quadrupolar mode, we performed calculations for different optical refractive indices. Figure 2b shows the wavelength of the maximum of the SH response as a function of the refractive index for 60 nm diameter silver nanospheres. A sensitivity of 208 nm/RIU is determined, twice the one found in the case of linear extinction. The quadrupolar LSPR is resonantly excited at the harmonic frequency, see Figure 1, and the fundamental wavelength has to be increased by 2 nm to increase the harmonic wavelength by 1 nm. For this reason, the sensitivity is increased by a factor of 2 due to the SHG process itself. One can note that a factor of 3 can be obtained using third harmonic generation. Similarly to the case of sensitivity, the SH quadrupolar resonance fwhm is twice as large as the one of the quadrupolar contribution to the linear extinction case. Hence, the FOM is identical. The main advantage of the SHG process therefore lies in the possibility to easily observe the quadrupolar mode. Interestingly, this observation can be taken down to single nanoparticle measurement.14 The properties of a LSPR, its position and width for instance, depend on the nanoparticle size. Sensing is optimized by the selection of the appropriate one. Several simulations have been performed considering nanoparticles with diameters ranging from 20 nm up to 100 nm. Figure 3a depicts the behavior of the fundamental wavelength, corresponding to the maximum of the SH quadrupolar mode, as a function of the refractive index. The corresponding sensitivities are obtained by adjustment procedures. The sensitivity is enhanced as the nanoparticle diameter increases from 157 nm/RIU for a 20 nm diameter up to 283 nm/RIU for 100 nm diameter silver nanoparticles, see Figure 3b. The corresponding FOM as a function of the diameter is depicted in Figure 3b. It is obvious that the FOM maximum value is obtained for 60−80 nm silver nanospheres. Indeed, not only does the LSPR shift faster toward longer wavelengths for larger nanoparticles, but the LSPR width also increases with the nanosphere diameter. The competition between these two effects leads to a local maximum and an optimum nanopshere diameter of about 60 nm, the most appropriate diameter for sensing purposes. Finally, we discuss how the SH quadrupolar mode can be isolated experimentally in the SH scattered wave. Recently, based on theoretical predictions by Dadap and co-workers, we have experimentally demonstrated using hyper-Rayleigh scattering that even and odd modes are perfectly decoupled when the SH intensity is collected perpendicularly to the direction of the incident fundamental laser beam.25,31In this configuration, even and odd SH emission modes are selected using an analyzer since they are polarized perpendicular and parallel to the scattering plane respectively. Figure 4 shows the SH intensity as a function of the incident polarization angle for a radiated SH wave polarized perpendicular (Figure 4a) and parallel (Figure 4b) to the scattering plane. The four lobes pattern observed in Figure 4a is characteristic of a pure quadrupolar SH where only the SH quadrupolar mode contribute. On the contrary, the SH dipolar mode is oriented parallel to the incident fundamental beam propagation direction and its strength is independent of the linear

Figure 2. (a) SH scattering cross section (integrated in all spatial directions) of 60 nm silver nanoparticles for an optical index refraction of the surrounding medium n = 1.33. The SH scattering cross section considering independently the first two modes are shown, (red) dipolar mode (l = 1) and (blue) quadrupolar mode (l = 2). (b) Wavelength of the maximum of the quadrupolar mode excited resonantly at the harmonic frequency as function of the optical refractive index. The line is a linear fit.

here the standard formalism where the two terms on the left of the arrow refer to the nature of the two exciting fundamental modes whereas the right term describes the SH emission mode. Explicitly, this mechanism corresponds to a dipolar emission E1 arising from the combination of an electric dipole E1 and an electric quadrupolar mode E2. The E1 + E1 → E1 mechanism, that is, the lowest order mode of the SH emission, is forbidden here because we consider centrosymmetric silver nanospheres. This is a specificity of even order nonlinear optical processes like SHG. This mode is therefore forbidden since it does not preserve the overall parity of the SHG process. The SH dipolar emission requires a retardation effects at the fundamental frequency. This is obtained with the introduction of the quadrupolar mode. On the other hand, the quadrupolar mode for the SH emission can be excited without retardation effects at the fundamental frequency. This mode arises with the E1 + E1 → E2 mechanism. Neglecting all resonances, the dipolar and quadrupolar emission modes have the same dependence with the scattering parameter x = ka, where a is the nanosphere diameter and k the fundamental wavevector. Both scattering modes scale with an x6 dependence. However, the relative weight of these multipoles can be modified by the proximity of LSPRs arising either at the fundamental or the harmonic frequencies. As discussed above, the SH dipolar mode requires retardation at the fundamental wavelength. However, the quadrupolar mode only weakly contributes to the optical 1699


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to the SH response, whatever the detection direction, except the forward and the backward directions. In these two directions, the SH quadrupolar mode vanishes altogether. This configuration may turn to be more versatile than the right angle configuration for ease of experimental implementation. In conclusion, we have demonstrated in the specific case of the SH quadrupolar mode emission from silver spherical nanoparticles that SHG offers advantages for sensing. Based on the observation of higher multipolar modes and rather narrow resonances, we show how the optical refractive index sensing can take advantage from the SHG nonlinear optical process despite the weak overall intensity. Furthermore, the present results can be extended to other nonlinear spectroscopy techniques like third harmonic generation, offering new possibilities for the monitoring of LSPR. The combination of the most efficient plasmonic sensors, like the ones supporting Fano resonances, and nonlinear optics is thus a promising way to push forward the sensor sensitivity.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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Figure 3. (a) Fundamental wavelength of the maximum of the SH quadrupolar mode as a function of the optical refractive index for silver nanospheres with varying diameters. (b) FOM (left axis) and sensitivity (right axis) as a function of the nanoparticle diameter for an optical refractive index n = 1.41 (dashed lines are guides to the eyes).

Figure 4. SH intensity recorded at right angle with respect to the fundamental wave as a function of the incident polarization angle for a SH wave polarized (a) perpendicular and (b) parallel to the scattering plane.

polarization angle of the fundamental wave. The SH intensity collected at right angle from the fundamental propagation direction is therefore independent of the incident polarization angle, see Figure 4b. In a recent study, we have shown that the strategy described above can be successfully applied with a standard (×16, NA = 0.32) microscope objective and a (focal length = 25 mm, NA = 0.5) collection lens.14 It is though emphasized that the use of tighter focusing conditions may lead to an additional longitudinal component of the electric field and therefore to corrections of the plan wave Mie theory approach. To discriminate between these dipolar and quadrupolar modes, another possibility would be to use an incident fundamental beam circularly polarized.32 Indeed, in this case, the SH dipolar mode is not excited and only the quadrupolar mode contributes 1700


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Sensing with Multipolar Second Harmonic Generation from Spherical

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