Nanospectroscopy 2015; 1: 26–32

Research Article Open Access

Antonino Foti, Cristiano D’Andrea, Elena Messina, Alessia Irrera, Onofrio M. Maragò, Barbara Fazio, Pietro G. Gucciardi* On the SERS depolarization ratio

Abstract: The Raman depolarization ratio is a quantity According to the E4 model,[18-24] in SERS the that can be easily measured experimentally and offers nanoantenna plays a twofold role: firstly it amplifies the unique information on the Raman polarizability tensor local field (excitation-field enhancement) confining it to of molecular vibrations. In Surface Enhanced Raman nanoscale regions (hot spots), and secondly it magnifies Scattering (SERS), molecules are near-field coupled with the (re-radiation enhancement). optical nanoantennas and their scattering properties Molecules lying in the hot spots (located at the edges of are strongly affected by the radiation patterns of the individual nanoantennas or in the nanocavities between nanoantenna. The polarization of the SERS photons is near-field coupled NPs[15,25-29]) experience an amplified consequently modified, affecting, in a non trivial way, the local field and an enhanced re-radiation whenever both measured value of the SERS depolarization ratio. In this the wavelengths of the laser pump (λL) and of the induced article we elaborate a model that describes how the SERS Raman dipole (λR) are close to the LSPR wavelength (λLSPR) depolarization ratio is influenced by the nanoantenna [24]. It is well known that the enhanced local field is re-radiation properties, suggesting how to retrieve polarization sensitive. The only component of the incident information on the Raman polarizability from SERS field yielding the local field amplification is the one experiments. capable of exciting the LSPR of the antenna [30-33]. On the other hand, in near-field coupled nanoantennas the Keywords: Raman scattering, Depolarization ratio, SERS re-radiation effect yields a selective enhancement of the Raman dipole component parallel to the nanocavity axis at the single molecule level, linearizing the polarization of DOI 10.1515/nansp-2015-0001 the Raman field [34-38]. Received July 21, 2014; accepted November 6, 2014 The re-radiation effect, therefore, causes a strong modification of the polarization of the SERS field, whose 1 Introduction components will be altered with respect to what would have been measured in normal Raman Arranged in either isolated or near-field coupled in absence of the nanoantennas. In addition, such an architectures, optical nanoantennas [1,2] are nowadays alteration is dependent on the orientation of the antenna. used for a broad set of plasmon enhanced A measurable quantity that will be strongly affected (PlEnS) such as Surface Enhanced Raman Scattering from such dependence is the depolarization ratio [39]. It (SERS), [3-5] Metal Enhanced Fluorescence (MEF), [6-8] is defined in (for linear excitation and Surface-Enhanced Infrared Absorption-Scattering polarization) as the ratio between the intensity of the (SEIRA-SEIRS) [9,10]. PlEnS enable the development of Raman field polarized orthogonal to the laser field (I ) high sensitivity, multiband spectroscopic nanosensors and the intensity of the Raman field polarized parallel⟘ for label-free detection of chemical and biomolecular to the laser field (I ). The depolarization ratio provides compounds [11-17]. information on the Raman� polarizability tensor (α) of the vibration considered and is therefore a very useful tool. It was recognized early on that in SERS the relationship *Corresponding author: Pietro G. Gucciardi: CNR, Istituto per i Processi Chimico-Fisici, Viale F. Stagno D’Alcontres 37, Messina, between the depolarization ratio and the components of I-98158, Italy, E-mail: [email protected] the Raman polarizability tensor was not straightforward Antonino Foti, Cristiano D’Andrea, Elena Messina, Alessia Irrera, [3]. One striking example is provided by Fazio and Onofrio M. Maragò, Barbara Fazio: CNR, Istituto per i Processi coworkers, [38] where the polarized SERS intensity is Chimico-Fisici, Viale F. Stagno D’Alcontres 37, Messina, I-98158, Italy found to be at a maximum in the direction orthogonal Antonino Foti: Dipartimento di Fisica e Scienze della Terra, Universi- to the excitation field, whereas in Raman spectroscopy tà di Messina, Viale F. Stagno D’Alcontres, 31, 98166 Messina, Italy

© 2015 Antonino Foti et al., licensee De Gruyter Open. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License. On the SERS depolarization ratio 27 the polarized signal is always maximum in the direction The depolarization ratio only depends on the parallel to the excitation field. Such a discrepancy, caused excitation/detection geometry and provides information by nanoantenna re-radiation properties, suggests that a on the orientation averaged components of the Raman precise model of the SERS depolarization ratio is needed polarizability tensor [39] (with i,j = x,y,z) The to understand how to retrieve the molecular information calculation of ρ in the backscattering configuration gives out of signals measured experimentally. In this article we will analyze how the SERS (4) depolarization ratio is related to the molecular where we have introduced [39] the rotation invariants depolarization factor in the presence of near-field coupling a2, γ2 and δ2. Eq. 4 remarkably shows that the depolarization with nanonatenna dimers and we highlight how the ratio is bound between 0 ≤ ρ ≤ 3/4 and consequently that ratio can be used to gain information on the orientation- we have always I < I . averaged non-diagonal components of the Raman tensor Together with⟘ the� Raman depolarization ratio, the of the probe molecule. degree of Raman polarization is another quantity easily measurable experimentally and provides information about the polarizability tensor [35]. Analogues to the 2 Results and Discussion visibility parameter, the degree of Raman depolarization is defined as: 2.1 Raman depolarization ratio (5) Note that is always greater than zero and bound In the classical treatment of the Raman effect when a between 1/7 ≤ σ ≤ 1. molecule interacts with an electromagnetic field, , an electric dipole moment, , is induced: 2.2 Polarized SERS signal (1) SERS differs from normal Raman spectroscopy because where is the molecular Raman polarizability of the presence of a third element, the nanoantenna, tensor. The Raman polarizability is a symmetric rank-2 which enters into play in the coupling between the tensor and its elements are a function of the nuclei electromagnetic field and the molecular vibration. positions and hence of the molecule’s vibrational state. According to the E4 model, if both the excitation and Raman In the most general case of molecules randomly oriented photon energies are within the plasmonic resonance of and non-totally symmetric modes, the Raman dipoles the nanoantenna, the antenna enhances both the local will be oriented differently with respect to the excitation excitation and the re-radiated fields. We can model SERS field, i.e. the Raman field radiated by randomly oriented as a three step phenomenon: [34,38] molecules is expected to be unpolarized. If we put a 1. enhancement of the excitation field at wavelength polarization analyzer before the detector, the intensity λ and the generation of hot spots of the orientation-averaged Raman signal along a given L direction, ê , will be det (6) 2. generation of a molecular Raman dipolar field at (2) λR wavelength

where ϕ, ϴ, ψ are the Euler angles associated to (7) the 3D spatial rotations of the molecule in the reference 3. amplification of the SERS field at wavelength for frame considered. I is expected to be different from zero molecules located at hot spots for any êdet, and in particular when êdet is orthogonal to the excitation field polarization vector ê . For linearly exc (8) polarized excitations, we therefore define the Raman depolarization ratio as: where we have introduced the excitation field (3) enhancement tensor, , and the re-radiation where I and I are, respectively, the intensity of the enhancement tensor, , to describe the Raman scattered fields polarized orthogonally (ê · ê = 0) ⟘ � exc det amplification of the excitation and the Raman field and and parallel (ê · ê = 1) to the laser field polarization. exc det which are, in principle, wavelength-dependent. Using 28 A. Foti et al.

tensors helps us to account for the different amplification Notably ρSERS does not depend only on the Raman of the three components of the electromagnetic fields. We polarizability but also on ϴ, the excitation polarization consider a nanoantenna dimer (see Figure 1) in the base angle and, in turn, on the coupling between the optical

{x, y , z} where x is the dimer axis (or nanocavity axis) fields and the nanoantenna. and z the la,ser field propagation direction. We can write Values of ρSERS~5, i.e. ρSERS ¾, have been observed on the field enhancement tensor as: molecules adsorbed on near-field coupled nanowires [38] as ≫ a consequence of the SERS field polarization modification (9) induced by the nanocavities. An explicit model of such

coupling is thus needed to relate ρSERS to ρmol. and the re-radiation enhancement tensor as: Analogous considerations can be drawn for the SERS degree of depolarization, which can be defined as: (10) (13)

in which we assume that the excitation and the σSERS has been observed to assume values lower than re-radiated field components along the nanocavity axis zero in dimers and trimers,[34-37] whereas only positive

x are amplified by the factors and , values, greater or equal to 1/7 are expected in normal and that the components along the other two axes are left Raman scattering (Eq. 44). unperturbed. We use the factor (1+ɛ) to distinguish the excitation field enhancement factor from the re-radiation 2.4 SERS depolarization ratio in nanoan- factor. The two are, in principle, different because of the tenna dimers. wavelength dependence of the SERS amplification [40]. The SERS intensity for many randomly oriented For a nanoantenna dimer the SERS intensities can be molecules as a function of the angle ϴ, between the laser easily calculated in the E4 approximation (i.e. keeping only field and the nanocavity, and the angle φ, between the the first term in eq. 11), giving, for the SERS depolarization polarization analyzer and the laser field, is found to be ratio, the following expression: [38] (14)

(11)

Eq. 11 contains a term proportional to that can be found within the E4 approximation, as well as terms beyond the E4 approximation that, although less intense (by approximately a factor ), bring valuable information.

2.3 SERS depolarization ratio

The Raman depolarization ratio measured on a set of randomly oriented molecules, once the excitation/ detection geometry is defined, is a parameter related only to the intrinsic molecular Raman polarizability tensor. For this reason we will call ρ the “molecular depolarization Figure 1: Schematics of a dimer-like nanoantenna excited with a ratio” and indicate it with ρ . In analogy with Eq. 3, we mol planar wave propagating along the direction of and polarized can define and measure the SERS depolarization ratio as along , forming an angle ϴ with the nanocavity axis, . the ratio between the cross- and the parallel-polarized The component of the backscattered radiation is analyzed with a SERS intensities, i.e. polarizer along the direction that forms an angle ϕ with . When ϕ is equal to 0 we detect the parallel-polarized SERS inten- (12) sity, , while when ϕ is π/2 we detect the cross-polarized SERS intensity, . On the SERS depolarization ratio 29

Notably the SERS depolarization ratio only depends light-nanoantenna coupling parameters ϴ and Г. Figure 4 on the coupling between the light and the nanoantenna 2a compares the plots of ρSERS(ϴ) calculated with the E and does not bring any information on the Raman approximation (blue line) with a plot which includes polarizability tensor. This implies that SERS experiments the terms beyond the E4 approximation (red line). No cannot be used to probe the Raman polarizability tensor divergences occur in the latter case, the maximum of 2 of molecules lying in the nanocavity unless we are able to ρSERS(ϴ) being limited to ρmolГ . Additionally, the minimum access the signal contribution given by the terms beyond is found to be different from zero, assuming the value 4 2 2 the E approximation, these being the only terms that ρmol/Г . Indeed the two models tend to coincide for Г 1, bring information on the non-diagonal components of the regime in which the E4 approximation holds. ≫ the Raman tensor [38]. Equation 14 explains also why the ρmol can be retrieved by multiplying the SERS SERS depolarization ratio, in contrast to the molecular depolarization ratios measured at ϴ = 0,π/2, i.e. depolarization ratio, can be higher than ¾, and even (16) diverges for (see Figure 2a, blue line). A more allowing one to extract the molecular information physical, non divergent expression of ρSERS(ϴ) is obtained from the SERS measurements. Remarkably, Eq. 16 also when considering the terms beyond the E4 approximation. holds if the excitation and the re-radiation enhancement In the specific case when the excitation and the factors are not equal. re-radiation enhancement factors are equal, i.e. ε = 0, A closer look to ρSERS(ϴ) shows that there are two without loosing any physical insight, we find possible analytical trends as a function of ρmol. For

molecular depolarization ratios ρmol≥1/2, ρSERS(ϴ) behaves (15) as plotted in Figure 2a (red line) with the intensity maxima 2 This expression explicitly shows that ρSERS(ϴ) is ρmolГ at angles ϴ = (n+1/2)π (n is an integer), and the 2 linked to ρmol in a non straightforward way through the intensity minima ρmol/Г for ϴ = nπ. The opposite effect

2 ρmol Γ 4 2 1 + Γ - 2Γ (1 - 2ρmol) 2 4Γ (1 - ρmol) SERS ρ SERS 2 ρ ρmol Γ 2 ρmol / Γ

0 π/23π π/2 2π 0 π/2 π 3π/2 2π a Angle θ (rad) b Angle θ (rad)

0.7 1.0 0.6 0.5 0.5 0.4

mol 0.0 ρ 0.3 SERS σ 0.2 -0.5 0.1 0.0 -1.0 1 10 100 1000 10 4 0 π/2 π 3π/2 2π c SERS enhancement Γ 4 d Angle θ (rad)

Figure 2: (a) Plot of the SERS depolarization ratio in the E4 approximation (blue line) and including the terms beyond the E4 approximation (red line) for a vibrational mode featuring a depolarization ratio of 0.5. (b) Angular dependence of the SERS depolarization ratios calculated for a nanoantenna featuring a SERS enhancement Г4~ 100 on which are deposited molecules with different molecular depolarization ratios:

ρmol= 0.47 (red line), ρmol= 0.3 (yellow line) and ρmol= 0 (blue line). The additional local minimum observed in the SERS depolarization ratios for ϴ = (n+1/2)π (b, yellow and blue lines) is found to occur only when the molecular depolarization ratio and the SERS signal enhancement fall within the shaded area in (c), otherwise an absolute maximum is expected for ϴ = (n+1/2). (d) Plot of the SERS degree of polarization 4 4 in the E approximation (blue line) and beyond the E approximation (red line) for a vibrational mode featuring ρmol= 0. The nanoantenna is assumed to provide SERS enhancement Г4~ 100. 30 A. Foti et al.

4 is observed for ρmol<1/2 where two different regimes are E approximation (blue line), possibly explaining the expected, depending on the specific value of ρmol and Г. experimental results. This is highlighted in Figure 2b where we compare the angular behavior of ρSERS(ϴ) for a nanoantenna featuring 2.5 SERS depolarization ratio in randomly a SERS enhancement Г4~102 for three different values of distributed near-field coupled nanoparticles. the molecular depolarization ratio, namely ρmol = 0.47 (red line), ρmol = 0.3 (dark yellow line) and ρmol = 0 (blue line). Randomly distributed nanoparticles grown or cast on While in the first case we still expect absolute maxima solid substrates represent one of the most easy to fabricate occurring at ϴ = (n+1/2)π separated by minima at ϴ = nπ, and reproducible, yet highly efficient, class of SERS-active for lower and lower molecular depolarization ratios local substrates. When densely packed with average distances of minima start to be observed at ϴ = (n+1/2)π, decreasing to few nanometers, spherical nanoparticles can be modeled zero when ρmol = 0. It can be demonstrated that the local as an ensemble of randomly oriented nanocavities. Such minima are expected only when the condition systems can be easy described by averaging the polarized 2 2 0 ≤ ρmol ≤ (Г -1)/2 Г (17) SERS response over all the possible nanocavities is met, corresponding to the couples of parameters orientations or, equivalently, averaging the response of a 4 (ρmol, Г ) evidenced by the shaded area in Figure 2c. single dimer over all the possible incident polarizations in Note that even if the SERS depolarization ratio has a the plane. The SERS depolarization ratio can be therefore local minimum at ϴ = (n+1/2)π, ρSERS(ϴ) is still a limited calculated as quantity and the relationship given by Eq. 16 to retrieve (20) the molecular depolarization ratio still holds. Assuming equal excitation and re-radiation The SERS degree of depolarization σ has been SERS enhancements, we get used in refs. [34-36] as a physical quantity to prove the (21) linear polarization induced by nanoantenna dimers to where we have neglected the terms in 1/Г4. To the the SERS scattering of molecules in the cavities. In the E4 first order, the SERS depolarization ratio turns out to approximation be 1/3, constant for every molecule, as experimentally σ (ϴ) = cos 2ϴ (18) SERS verified [21,38]. Again, information on ρ is brought by which varies between -1 and 1 and, as for the SERS mol the terms beyond E4 approximation, and can be obtained depolarization ratio, does not bring any information on the with such nanostructures, provided the SERS substrate molecular Raman polarizability tensor. The discrepancy is homogeneous enough and provides an enhancement to what expected in normal Raman spectroscopy (σ >0) SERS factor such that the experimental error is below 1/Г2. is, again explained by the polarization changes induced SERS enhancement factors Г4>104 are typical for such by the nanoantenna radiation properties. Equation 18 nanostructures, requiring an experimental accuracy and has been experimentally verified [34,36] in nano-spheres homogeneity of the sample of ~ 0.1% to measure molecular dimers or clusters with a single hotspot. Nevertheless, depolarization ratios of 0.5, quite difficult to achieve with it is often observed that the minimum σ (ϴ= π/2) SERS the current synthesis techniques. measured is higher than -1 without any clear explanation [35-37]. Notably, if we include the terms beyond the E4 approximation, assuming for simplicity equal 3 Conclusions enhancement factors (ε=0), we find that the SERS degree of polarization becomes The SERS depolarization ratio is an intriguing physical quantity that can provide information on the Raman polarizability tensor and on the molecular orientation (19) at the single molecule level. Here we have developed On one hand, we retrieve the information on the a model to extract the Raman polarizability tensor molecular depolarization ratio, as expected, although information encoded in the SERS depolarization ratio encoded by the molecule-nanoantenna coupling for dimers and disordered arrays of metal nanoparticles parameters. On the other hand, we observe that when near-field coupled. We have shown how the nanoantenna the terms beyond the E4 approximation are taken into re-radiation properties play an intriguing role in the account in the calculation of σSERS (ϴ) (Figure 2d, red line), polarization of the SERS fields making deficient the models the minimum gets higher than -1 and the curve is slightly developed for conventional Raman spectroscopy to relate shifted with respect to the cos 2ϴ trend expected in the the depolarization ratio to the Raman polarizability tensor. On the SERS depolarization ratio 31

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