On the SERS Depolarization Ratio

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 Raman scattering (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 spectroscopy 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 spectroscopies 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 Raman spectroscopy (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].

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