Abstract

Studying the interaction between molecules and surface plasmon polaritons (SPPs) is of great important in understanding surface-enhanced Raman scattering (SERS). While it is known that SERS consists of excitation and emission enhancements, each of them is manifested by several sub-steps which individually also deserve attention. For example, for emission enhancement, the energy from the excited molecules is first coupled to SPPs, which then radiatively scatter to far-field. To understand these two sequential processes completely, differentiating them one by one is necessary. Here, we decouple them and determine the coupling efficiency of molecules to SPPs by using a phenomenological rate equation model. We find the coupling efficiency, defined as the ratio of the coupling rate from molecules to SPPs to the direct Raman decay rate, can be expressed as the SERS intensity ratio and the SPP absorption and radiative decay rates, which all can be determined by polarization- and angle-dependent Raman and reflectivity spectroscopy. As a demonstration, the coupling efficiencies of 6-mercaptopurine to SPPs propagating in Γ-X direction on Ag nanohole array are measured for several Raman emission wavelengths.

© 2013 OSA

1. Introduction

Raman scattering provides fingerprint-like signature of molecules and thus is a promising technique for high specific chemical identification [1]. Unlike fluorescence, Raman scattering is a label-free technique in which tagging to targets is not necessary [2]. Unfortunately, the Raman cross-section is usually very small, around 12-14 orders of magnitude lower than that of fluorescence. In other words, for every 1010-12 photons incident on a molecule, only one or less undergoes Raman scattering [1,3,4]. Therefore, Raman scattering does not generate strong signal and is not very applicable when the concentration of target analyte is very low. However, when the molecules are placed in close proximity to a metal surface, much stronger Raman signal can be produced due to the excitation of surface plasmon polaritons (SPPs) [3,4]. Molecules can be excited and dissipated via SPPs, which extraordinarily enhance both Raman excitation and emission [3,4]. This electromagnetic mediated Raman process leads to the well-known surface-enhanced Raman scattering (SERS). Since the sensitivity is greatly improved, SERS can now be used as practical molecular probe with detection limit possibly down to one single molecule [5].

As a result, the ability to generate desired enhancement is of crucial in SERS and this requires in-depth understanding of the entire process. Although the first order E4 approximation provides good estimation of the total Raman enhancement for practical use, it reveals no details of SERS other than the contributions from excitation and emission enhancements [3,4]. In particular, it is known that several sequential steps are involved in determining the overall SERS [6,7]. As shown in Fig. 1, the excitation photon at ηωexc is first resonantly coupled to the metal surface to produce ingoing SPPs for excitation. Then, theses SPPs, which possess much stronger field strength than that of the incident field, induce large dipole moments of the molecules, resulting in the excitation enhancement [8]. When the molecules depolarized, they radiate at several frequencies including the non-resonant Rayleigh and the Stokes and anti-Stokes Raman scattering. For the Stokes emission, for example, the energy is coupled into outgoing SPPs at ηωscatt before radiatively scattering into far-field, giving rise to emission enhancement. Therefore, the whole Raman enhancement depends on several coupling and decay processes and each contributes distinctively to SERS. To study them in greater detail, differentiating them one by one is essential. However, to date, effort on this issue is rarely seen primarily because of the difficulty in decoupling the process.

 

Fig. 1 An illustration to describe the SPP mediated Raman scattering process. Molecule can be excited by the ingoing SPPs generated by the excitation. The molecule can transfer its energy either directly to far-field at rate Γr or to the outgoing SPPs at ΓckSPP. The outgoing SPPs propagate at wavevector kSPP will dissipate energy either by Ohmic absorption at ΓabskSPPor radiative scattering at mΓradkSPP,m through multiple channels. Each radiative decay channel yields SPP mediated Raman emission at a well-defined angle.

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In this work, we propose a simple method to determine the coupling efficiency of energy from excited molecules to outgoing SPPs in periodic array by using a phenomenological rate equation model. For SPPs with a given propagating wavevector, we find the coupling rate ratio can be determined by measuring the absorption and radiative decay rates of the outgoing SPPs and the Raman intensity ratio. As a proof of concept, we determine the coupling efficiency of 6-mercaptopurine to SPPs propagating in Γ-X direction supported on Ag nanohole array.

2. Theory

First, we describe how one can determine the coupling efficiency in periodic array based on a rate equation model. From Fig. 1, for emission enhancement, we assume, other than the Rayleigh and anti-Stokes emission decays, the excited molecules with energy [M] can dissipate via several radiative decay channels at the Stokes frequency ωscatt to produce the overall SERS response. For example, they can scatter at rate Γr without involving SPPs, resulting in non-SPP related or direct emission. On the other hand, the rest of the energy can be coupled into outgoing SPPs at coupling rate ΓckSPP. These SPPs then propagate with vectorial wavevectors kSPP that have the same magnitude |kSPP|=neffωc, where neffis the effective refractive index, but different directions. While propagating, they lose their energy either by intrinsic Ohmic loss or radiation damping [9]. The radiation damping in fact yields the SPP mediated Raman emission. Therefore, under the conservation of energy, the rate equation of the SPPs with energy [SPPkSPP] and kSPP can be written as d[SPPkSPP]dt=ΓckSPP[M]ΓtotkSPP[SPPkSPP], where the first term denotes the power coupled to the SPPs from the molecules whereas the second one indicates the total SPP power losses. The total decay rate is the addition of absorption and radiative decay rates ΓtotkSPP=ΓabskSPP+ΓradkSPP and the radiative decay rate sums up the individual rates from all emission ports ΓradkSPP=mΓradkSPP,m. The number of m emission ports is governed by the phase-matching equation given as kSPP=(ωcsinθcosφ+2nxπa)x^+(ωcsinθsinφ+2nyπa)y^, where a is the period and nx and ny are the integers defining the order of Bragg scattering. From the equation, we see the SPP mediated Raman emissions emerge at well-defined polar θ and azimuthal φ angles depending on the combination of nx and ny [6,1013]. As a result, the total Raman response is the summation of direct Pd=Γr[M] and total SPP mediated mPSPPkSPP,m(θ,φ)=mΓradkSPP,m[SPPkSPP]. To determine ΓckSPP for each kSPP, we consider the steady state where d[SPPkSPP]dt=0 and the Raman power ratio between one of the SPP emission ports, e.g. the nth port, and the direct channel is

PSPPkSPP,nPd=ΓckSPPΓrΓradkSPP,nΓtotkSPP.
From the above equation, strong SPP mediated Raman emission requires both large coupling and radiative decay rates. In addition, one sees by measuring the total decay rate, the direct emission as well as the SPP mediated emission and the radiative decay rate of only one of the nth ports, the ratio between coupling and direct rates ΓckSPP/Γr, defined as the coupling efficiency here, for kSPP can be determined. ΓckSPPcan be estimated once Γr is known.

While the power ratio can be obtained from angle-resolved Raman spectroscopy [10], the acquisition of SPP decay rates relies on polarization- and angle-dependent reflectivity spectroscopy and temporal coupled mode theory (CMT) [1417]. In fact, following [1618], we consider an optically thick periodic system supporting one resonance is excited at a fixed incident angle, the p-polarized diffraction coefficient of the pth output port can be written as: cp+Γrad1Γradpeiϕpi(ωωres)+Γtot/2, where ωres is resonant frequency, cp and ϕp are the nonresonant diffraction efficiency and the phase-shift of SPPs. The numerator also contains the multiplication of the square root of the in- and out-coupling radiative decay rates Γrad1 and Γradp provided the excitation is input from the 1st port. For the 0th order diffraction, i.e. specular reflection, since the 1st port is also the output port, the equation can be expressed as: |c1+Γrad1eiϕ1i(ωωres)+Γtot/2|2, yielding Fano-like resonance [15]. In addition, by using Jones calculus, under orthogonal or cross polarization configuration, it is possible to eliminate c1 and attain Lorentzian lineshape given as 14(Γrad1)2(ωωres)2+(Γtot/2)2 in which both Γtot and Γrad1 can be determined accordingly [16].

3. Experiment

We attempt to experimentally measure the coupling efficiency based on the above formulations. Interference lithography is used to prepare Ag nanohole array with period = 670 nm, hole depth and radius = 100 and 140 nm [10] and its scanning electron microscopy (SEM) image is shown in the inset of Fig. 2(a). The array is then immersed in an ethanolic solution of 6-mercaptopurine at concentration of 5 mM for 18 hours to form a self-assembled monolayer [19]. The sample is mounted on a goniometer for reflectivity and Raman measurements. A pair of incident polarizer and detection analyzer is used for polarization-dependent spectroscopy [15,16]. For reflectivity, a collimated white light is illuminated on the sample at different incident angles and the specular reflections are collected. The polarizer is placed at 45° with respect to the incidence plane and the analyzer is oriented at 45° and −45°, resulting in parallel and orthogonal polarizations. Given the incident and the reflection Jones vectors are [11] and [rp+Γrad1eiϕ1i(ωωres)+Γtot/2rs], where rp and rs are the p- and s-nonresonant reflection coefficients, the two specular reflectivity spectra from CMT thus can be expressed as:

14|2rp+Γrad1eiϕ1i(ωωres)+Γtot/2|2  and  14(Γrad1)2(ωωres)2+(Γtot/2)2,
for parallel and orthogonal assuming rp ≈rs [16]. On the other hand, for Raman spectroscopy, a p-polarized 514 nm Ar laser with power ~20 mW is incident on the sample at 10° and the signals are collected at detection angles scanning from 15°-50° without the analyzer. All spectra are taken in Γ-X direction.

 

Fig. 2 (a) Parallel and (b) orthogonal reflectivity mappings of 6-mercaptopurine coated Ag nanohole array. The dash lines identify different (nx,ny) SPP modes. Inset: the SEM image of the array. The (c) parallel and (d) orthogonal (1,0) reflectivity spectra extracted from the mappings. The dash lines are the best fits by using coupled mode theory. (e) The plots of deduced (1,0) radiative and total decay rates of SPPs as a function of resonant wavelength in logarithmic scale. The dash line is the linear fit showing a λ-6.95 dependence.

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Figures 2(a) and 2(b) show the parallel and orthogonal polarized angle-dependent reflectivity mappings of 6-mercaptopurine coated Ag array. The mappings, also known as dispersion relations, identify the excitation of different SPP modes by using the phase-matching equation. The dash lines are labeled near the reflectivity dips in the parallel mapping indicating (−1,0), (0, ± 1), (1,0), (−1, ± 1), (1, ± 1), and (−2,0) Ag/air SPPs are excited. Likewise, the orthogonal mapping displays almost identical features as the parallel counterpart except the dips are now flipped into peaks. Here, we only focus on the decay rates of (1,0) SPPs since they will be used for determining the coupling efficiency in positive Γ-X direction. We extract the (1,0) reflectivity spectra from λ = 500 – 600 nm and incident angle = 15°-25° and display them in Fig. 2(c) and 2(d). While the parallel spectra exhibit Fano-like profiles, the orthogonal spectra show Lorentzian lineshapes, which both agree with the predictions from CMT. We fit both spectra simultaneously by using Eq. (2) and the best fits are shown as the dash lines for reference. The deduced (1,0) SPP Γrad and Γtot are plotted in logarithmic scale against wavelength in Fig. 2(e) showing they decrease with increasing wavelength. In fact, the radiative decay rates display a λ-6.95 dependence as indicated by the dash line, revealing a Mie-like scattering behavior [9]. It has been shown that the wavelength dependence is very sensitive to hole geometry such as size and shape [9,20]. In particular, within the range of geometries and wavelengths considered here, the behavior of Γrad can be understood as the result of the scattering of SPPs by single isolated holes. Our results [9] show Γrad exhibits close to λ−4 dependence when the hole size is small [16] but becomes more λ-4 to −8 when hole size increases.

After determining the decay rates, we turn our attention to the Raman scattering. Figure 3(a) shows the detection angle-dependent Raman mapping taken at an off-resonant incident angle of 10o, which does not generate any SPPs at 514 nm, thus minimizing excitation enhancement. The mapping features two strong dispersive bands which bare close resemblance with the p-polarized reflectivity mapping as shown in Fig. 3(b) in the same scale. Therefore, one can conclude the strong emissions originate from the (1,0) and (−2,0) SPPs. However, it is reminded that although both (1,0) and (−2,0) are observed in Γ-X direction, they arise from SPPs propagating with different vectorial wavevectors. The SPPs that give rise to (1,0) emissions propagate in positive Γ-X direction whereas the (−2,0) counterpart propagates in negative Γ-X direction. Therefore, their coupling efficiencies could/could not be the same. In addition, the SPPs that generate (1,0) Bragg scattering can at the same time produce other (nx,ny) emissions at different angles. Nevertheless, from Eq. (1), we see only the information of one single port is sufficient to calculate the coupling efficiency in positive Γ-X. We plot the Raman spectra taken at several detection angles in Fig. 3(c). We see a number of peaks superimposed on a broad background and their spectral positions are at 537, 542, 550, and 558 nm in consistent with the Stoke Raman signatures of 6-mercaptopurine [10]. No peak is found at 592 nm indicating the absence of S-H bond, confirming a single monolayer is formed on the metal surface [19]. The board emission background is of fluorescence origin and several speculations have been proposed [21,22]. We believe it is not SERS relevant even though its intensity also varies closely with the dispersion relation very well. Therefore, to extract the Raman emissions, we angularly plot the peak intensities in Fig. 3(d)-3(f) for λ = 537, 550, and 558 nm after subtracting them from the fluorescence background. The angular p-polarized reflectivity plots are also shown for reference, indicating that the SERS peaks are closely related to the (1,0) and (−2,0) SPPs. Finally, for comparison with the array, the background subtracted angular intensities obtained from 6-mercaptopurine coated on flat Ag film are also plotted and they simply display weak direct emissions. We assume a uniform coverage of monolayer on the array and the film and a factor of 1πR2/P2 is used to roughly correct the intensities the flat surface so that two sets of data contain the same number of molecules.

 

Fig. 3 The angle-dependent (a) Raman scattering and (b) p-polarized reflectivity mappings plotted in the same scale. The dash lines indicate the (1,0) and (−2,0) SPPs. (c) The Raman spectra of the array taken from different detection angles. The spectra are vertical shifted for visualization. The dash lines indicate the Raman peaks at 537, 550, and 558 nm. The angular plots of Raman intensities at (d) 537 nm, (e) 550 nm, and (f) 558 nm (squares) after subtracting the fluorescence background. The angular plots of intensities obtained from a flat film at the same wavelengths are also shown (circles). The corresponding p-polarized reflectivity as a function of incident angle (solid lines). The dash lines are the best-fits.

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To calculate the Raman power ratio PSPPΓX,(1,0)/Pdas well as the coupling efficiency ΓcΓX/Γr, we first fit the angular plots in Fig. 3(d)-3(f) to obtain the (1,0) SPP and the flat Raman emissions. The best fits for (1,0) SPPs are shown as the dash lines in the figures and the results are plotted in Fig. 4(a). However, the background powers in Fig. 4(a) do not represent the complete direct emission since they provide only a portion of it from θ = 0°-55° at φ = 0°. The entire half space is required for the direct emission. To roughly estimate them, we find our detection system supports a solid angle of Δφ ≈2° and thus Pd is simply assumed to be equal to Pbackground × 360°/2° considering that direct emission should possess a full circular symmetry over φ and the power ratios are plotted in Fig. 4(b). The decay rate ratio, ΓradkSPP,(1,0)/ΓtotkSPP,(1,0), can be readily obtained from Fig. 2(e) and is shown in Fig. 4(c). Therefore, by using Eq. (1), the calculated coupling efficiencies for three wavelengths are plotted in Fig. 4(d). Since the knowledge of Γr for 6-mercaptopurine is not yet available, we do not attempt to estimate the coupling rate. However, once Γr is being measured, we believe the coupling rate can be determined accordingly.

 

Fig. 4 (a) The plot of integrated powers of background and SPP mediated emissions (squares and circles) against wavelength. (b) The power ratio between SPP mediated and direct emissions. (c) The (1,0) SPP total to radiative decay rate ratio. (d) The calculated coupling efficiency as a function of wavelength.

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Finally, we briefly comment on the dependence of coupling efficiency on wavelength. The coupling efficiency remains almost constant with wavelength although there is a slight increase at 550 nm. The reason behind this is still unknown but is unlikely due to the electromagnetic origin as the decay rates and the rate ratio given in Fig. 2(e) and 4(c) show a monotonic variation with wavelength, suggesting the field strength would follow similarly. It is noted that Le Ru et al have studied the relative enhancement ratios of different SERS peaks for different molecular probes and find they behave differently [23]. While rhodamine 6G exhibits a gradual decrease of enhancement with increasing Raman shift that can be attributed to the SPP effect due to the different degrees of excitation and emission enhancements, 3-methoxy-4-(5′-azobenzotriazolyl)phenylamine and crystal violet (CV) display a more complicated behavior. In particular, for CV, the enhancement is found similar to our case in which the ratio increases with Raman shift initially but decrease afterwards. They attribute this trend to the surface selection rule where the geometry of molecules absorbed on the surface, the induced image charges, etc, play important roles in governing the resulting enhancement [24]. Nevertheless, more study is required for quantification.

4. Conclusion

In summary, by combining the rate equation model and the temporal coupled mode theory, we measure the coupling efficiency of 6-mercaptopurine to SPPs in Γ-X direction supported on periodic Ag nanohole array for several Raman emission wavelengths. This simple method resolves the coupling process and the radiative decay of SPPs in the excitation enhancement. We expect the coupling efficiency could provide much information about the underlying physics of SERS and shed light in controlling it in the future.

Acknowledgments

This research was supported by the Chinese University of Hong Kong through the RGC Competitive Earmarked Research Grants (402908, 402909 and 403310), the Shun Hing Institute of Advanced Engineering (BME-p3-11), UGC special equipment grant (SEG_CUHK07), and CRF CUHK1/CRF/12G.

References and links

1. J. R. Ferraro, K. Nakamoto, and C. Brown, Introductory Raman Spectroscopy (Academic Press, 2003).

2. J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008). [CrossRef]   [PubMed]  

3. E. Le Ru and P. Etchegoin, Principles of Surface Enhanced Raman Spectroscopy: and Related Plasmonic Effects (Elsevier Science, 2008).

4. K. Kneipp and M. Moskovits, H. Kneipp ed., Surface Enhanced Raman Scattering – Physics and Application (Springer, 2006).

5. S. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science 275(5303), 1102–1106 (1997). [CrossRef]   [PubMed]  

6. J. J. Baumberg, T. A. Kelf, Y. Sugawara, S. Cintra, M. E. Abdelsalam, P. N. Bartlett, A. E. Russell, and A. E. Russell, “Angle-resolved surface-enhanced raman scattering on metallic nanostructured plasmonic crystals,” Nano Lett. 5(11), 2262–2267 (2005). [CrossRef]   [PubMed]  

7. P. Etchegoin, L. F. Cohen, H. Hartigan, R. J. C. Brown, M. J. T. Milton, and J. C. Gallop, “Electromagnetic contribution to surface enhanced Raman scattering revisited,” J. Chem. Phys. 119(10), 5281 (2003). [CrossRef]  

8. D. W. Ball, “Theory of Raman spectroscopy,” Spectroscopy 16, 32 (2001).

9. D. Y. Lei, J. Li, A. I. Fernández-Domínguez, H. C. Ong, and S. A. Maier, “Geometry dependence of surface plasmon polariton lifetimes in nanohole arrays,” ACS Nano 4(1), 432–438 (2010). [CrossRef]   [PubMed]  

10. C. Y. Chan, J. B. Xu, M. Y. Waye, and H. C. Ong, “Angle resolved surface enhanced Raman scattering (SERS) on two-dimensional metallic arrays with different hole sizes,” Appl. Phys. Lett. 96(3), 033104 (2010). [CrossRef]  

11. L. Baltog, N. Primeau, R. Reinisch, and J. L. Coutaz, “Surface enhanced Raman scattering on silver grating: Optimized antennalike gain of the stokes signal of 104,” Appl. Phys. Lett. 66(10), 1187 (1995). [CrossRef]  

12. S. Ushioda and Y. Sasaki, “Raman scattering mediated by surface-plasmon polariton resonance,” Phys. Rev. B 27(2), 1401–1404 (1983). [CrossRef]  

13. J. P. Goudonnet, T. Inagaki, E. T. Arakawa, and T. Ferrell, “Angular and polarization dependence of surface-enhanced Raman scattering in attenuated-total-reflection geometry,” Phys. Rev. B Condens. Matter 36(2), 917–921 (1987). [CrossRef]   [PubMed]  

14. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

15. H. Y. Lo, C. Y. Chan, and H. C. Ong, “Direct measurement of radiative scattering of surface plasmon polariton resonance from metallic arrays by polarization-resolved reflectivity spectroscopy,” Appl. Phys. Lett. 101(22), 223108 (2012). [CrossRef]  

16. Z. L. Cao, H. Y. Lo, and H. C. Ong, “Determination of absorption and radiative decay rates of surface plasmon polaritons from nanohole array,” Opt. Lett. 37(24), 5166–5168 (2012). [CrossRef]   [PubMed]  

17. J. Yoon, K. H. Seol, S. H. Song, and R. Magnusson, “Critical coupling in dissipative surface-plasmon resonators with multiple ports,” Opt. Express 18(25), 25702–25711 (2010). [CrossRef]   [PubMed]  

18. S. Wu, Z. Wang, and S. H. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multi-mode cavities,” IEEE, J. Quantum Elect. 40(10), 1511–1518 (2004). [CrossRef]  

19. H. Yang, Y. Liu, Z. Liu, Y. Yang, J. Jiang, Z. Zhang, G. Shen, and R. Yu, “Raman mapping and in situ SERS spectroelectrochemical studies of 6-Mercaptopurine SAMs on the gold electrode,” J. Phys. Chem. B 109(7), 2739–2744 (2005). [CrossRef]   [PubMed]  

20. K. C. Hui, J. T. K. Wan, J. B. Xu, and H. C. Ong, “Dependence of anisotropic surface plasmon lifetimes of two-dimensional hole arrays on hole geometry,” Appl. Phys. Lett. 95(6), 063110 (2009). [CrossRef]  

21. C. Farcau and S. Astilean, “Evidence of a surface plasmon-mediated mechanism in the generation of the SERS background,” Chem. Commun. (Camb.) 47(13), 3861–3863 (2011). [CrossRef]   [PubMed]  

22. S. Mahajan, R. M. Cole, J. D. Speed, S. H. Pelfrey, A. E. Russell, P. N. Bartlett, S. M. Barnett, and J. J. Baumberg, “Understanding the surface-enhanced Raman spectroscopy ‘background’,” J. Phys. Chem. C 114(16), 7242–7250 (2010). [CrossRef]  

23. E. C. LeRu, M. Blackie.E, Meyer, and P. G. Etchegoin, “Surface enhanced Raman scattering enhancement factors: A comprehensive study,” J. Phys. Chem. C 111(37), 13794–13803 (2007). [CrossRef]  

24. M. Moskovits and J. S. Suh, “Surface selection rules for surface-enhanced Raman spectroscopy: calculations and application to the surface-enhanced Raman spectrum of phthalazine on silver,” J. Phys. Chem. 88(23), 5526–5530 (1984). [CrossRef]  

References

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  1. J. R. Ferraro, K. Nakamoto, and C. Brown, Introductory Raman Spectroscopy (Academic Press, 2003).
  2. J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater.7(6), 442–453 (2008).
    [CrossRef] [PubMed]
  3. E. Le Ru and P. Etchegoin, Principles of Surface Enhanced Raman Spectroscopy: and Related Plasmonic Effects (Elsevier Science, 2008).
  4. K. Kneipp and M. Moskovits, H. Kneipp ed., Surface Enhanced Raman Scattering – Physics and Application (Springer, 2006).
  5. S. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science275(5303), 1102–1106 (1997).
    [CrossRef] [PubMed]
  6. J. J. Baumberg, T. A. Kelf, Y. Sugawara, S. Cintra, M. E. Abdelsalam, P. N. Bartlett, A. E. Russell, and A. E. Russell, “Angle-resolved surface-enhanced raman scattering on metallic nanostructured plasmonic crystals,” Nano Lett.5(11), 2262–2267 (2005).
    [CrossRef] [PubMed]
  7. P. Etchegoin, L. F. Cohen, H. Hartigan, R. J. C. Brown, M. J. T. Milton, and J. C. Gallop, “Electromagnetic contribution to surface enhanced Raman scattering revisited,” J. Chem. Phys.119(10), 5281 (2003).
    [CrossRef]
  8. D. W. Ball, “Theory of Raman spectroscopy,” Spectroscopy16, 32 (2001).
  9. D. Y. Lei, J. Li, A. I. Fernández-Domínguez, H. C. Ong, and S. A. Maier, “Geometry dependence of surface plasmon polariton lifetimes in nanohole arrays,” ACS Nano4(1), 432–438 (2010).
    [CrossRef] [PubMed]
  10. C. Y. Chan, J. B. Xu, M. Y. Waye, and H. C. Ong, “Angle resolved surface enhanced Raman scattering (SERS) on two-dimensional metallic arrays with different hole sizes,” Appl. Phys. Lett.96(3), 033104 (2010).
    [CrossRef]
  11. L. Baltog, N. Primeau, R. Reinisch, and J. L. Coutaz, “Surface enhanced Raman scattering on silver grating: Optimized antennalike gain of the stokes signal of 104,” Appl. Phys. Lett.66(10), 1187 (1995).
    [CrossRef]
  12. S. Ushioda and Y. Sasaki, “Raman scattering mediated by surface-plasmon polariton resonance,” Phys. Rev. B27(2), 1401–1404 (1983).
    [CrossRef]
  13. J. P. Goudonnet, T. Inagaki, E. T. Arakawa, and T. Ferrell, “Angular and polarization dependence of surface-enhanced Raman scattering in attenuated-total-reflection geometry,” Phys. Rev. B Condens. Matter36(2), 917–921 (1987).
    [CrossRef] [PubMed]
  14. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).
  15. H. Y. Lo, C. Y. Chan, and H. C. Ong, “Direct measurement of radiative scattering of surface plasmon polariton resonance from metallic arrays by polarization-resolved reflectivity spectroscopy,” Appl. Phys. Lett.101(22), 223108 (2012).
    [CrossRef]
  16. Z. L. Cao, H. Y. Lo, and H. C. Ong, “Determination of absorption and radiative decay rates of surface plasmon polaritons from nanohole array,” Opt. Lett.37(24), 5166–5168 (2012).
    [CrossRef] [PubMed]
  17. J. Yoon, K. H. Seol, S. H. Song, and R. Magnusson, “Critical coupling in dissipative surface-plasmon resonators with multiple ports,” Opt. Express18(25), 25702–25711 (2010).
    [CrossRef] [PubMed]
  18. S. Wu, Z. Wang, and S. H. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multi-mode cavities,” IEEE, J. Quantum Elect.40(10), 1511–1518 (2004).
    [CrossRef]
  19. H. Yang, Y. Liu, Z. Liu, Y. Yang, J. Jiang, Z. Zhang, G. Shen, and R. Yu, “Raman mapping and in situ SERS spectroelectrochemical studies of 6-Mercaptopurine SAMs on the gold electrode,” J. Phys. Chem. B109(7), 2739–2744 (2005).
    [CrossRef] [PubMed]
  20. K. C. Hui, J. T. K. Wan, J. B. Xu, and H. C. Ong, “Dependence of anisotropic surface plasmon lifetimes of two-dimensional hole arrays on hole geometry,” Appl. Phys. Lett.95(6), 063110 (2009).
    [CrossRef]
  21. C. Farcau and S. Astilean, “Evidence of a surface plasmon-mediated mechanism in the generation of the SERS background,” Chem. Commun. (Camb.)47(13), 3861–3863 (2011).
    [CrossRef] [PubMed]
  22. S. Mahajan, R. M. Cole, J. D. Speed, S. H. Pelfrey, A. E. Russell, P. N. Bartlett, S. M. Barnett, and J. J. Baumberg, “Understanding the surface-enhanced Raman spectroscopy ‘background’,” J. Phys. Chem. C114(16), 7242–7250 (2010).
    [CrossRef]
  23. E. C. LeRu, M. Blackie.E, Meyer, and P. G. Etchegoin, “Surface enhanced Raman scattering enhancement factors: A comprehensive study,” J. Phys. Chem. C111(37), 13794–13803 (2007).
    [CrossRef]
  24. M. Moskovits and J. S. Suh, “Surface selection rules for surface-enhanced Raman spectroscopy: calculations and application to the surface-enhanced Raman spectrum of phthalazine on silver,” J. Phys. Chem.88(23), 5526–5530 (1984).
    [CrossRef]

2012

H. Y. Lo, C. Y. Chan, and H. C. Ong, “Direct measurement of radiative scattering of surface plasmon polariton resonance from metallic arrays by polarization-resolved reflectivity spectroscopy,” Appl. Phys. Lett.101(22), 223108 (2012).
[CrossRef]

Z. L. Cao, H. Y. Lo, and H. C. Ong, “Determination of absorption and radiative decay rates of surface plasmon polaritons from nanohole array,” Opt. Lett.37(24), 5166–5168 (2012).
[CrossRef] [PubMed]

2011

C. Farcau and S. Astilean, “Evidence of a surface plasmon-mediated mechanism in the generation of the SERS background,” Chem. Commun. (Camb.)47(13), 3861–3863 (2011).
[CrossRef] [PubMed]

2010

S. Mahajan, R. M. Cole, J. D. Speed, S. H. Pelfrey, A. E. Russell, P. N. Bartlett, S. M. Barnett, and J. J. Baumberg, “Understanding the surface-enhanced Raman spectroscopy ‘background’,” J. Phys. Chem. C114(16), 7242–7250 (2010).
[CrossRef]

J. Yoon, K. H. Seol, S. H. Song, and R. Magnusson, “Critical coupling in dissipative surface-plasmon resonators with multiple ports,” Opt. Express18(25), 25702–25711 (2010).
[CrossRef] [PubMed]

D. Y. Lei, J. Li, A. I. Fernández-Domínguez, H. C. Ong, and S. A. Maier, “Geometry dependence of surface plasmon polariton lifetimes in nanohole arrays,” ACS Nano4(1), 432–438 (2010).
[CrossRef] [PubMed]

C. Y. Chan, J. B. Xu, M. Y. Waye, and H. C. Ong, “Angle resolved surface enhanced Raman scattering (SERS) on two-dimensional metallic arrays with different hole sizes,” Appl. Phys. Lett.96(3), 033104 (2010).
[CrossRef]

2009

K. C. Hui, J. T. K. Wan, J. B. Xu, and H. C. Ong, “Dependence of anisotropic surface plasmon lifetimes of two-dimensional hole arrays on hole geometry,” Appl. Phys. Lett.95(6), 063110 (2009).
[CrossRef]

2008

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater.7(6), 442–453 (2008).
[CrossRef] [PubMed]

2007

E. C. LeRu, M. Blackie.E, Meyer, and P. G. Etchegoin, “Surface enhanced Raman scattering enhancement factors: A comprehensive study,” J. Phys. Chem. C111(37), 13794–13803 (2007).
[CrossRef]

2005

J. J. Baumberg, T. A. Kelf, Y. Sugawara, S. Cintra, M. E. Abdelsalam, P. N. Bartlett, A. E. Russell, and A. E. Russell, “Angle-resolved surface-enhanced raman scattering on metallic nanostructured plasmonic crystals,” Nano Lett.5(11), 2262–2267 (2005).
[CrossRef] [PubMed]

H. Yang, Y. Liu, Z. Liu, Y. Yang, J. Jiang, Z. Zhang, G. Shen, and R. Yu, “Raman mapping and in situ SERS spectroelectrochemical studies of 6-Mercaptopurine SAMs on the gold electrode,” J. Phys. Chem. B109(7), 2739–2744 (2005).
[CrossRef] [PubMed]

2004

S. Wu, Z. Wang, and S. H. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multi-mode cavities,” IEEE, J. Quantum Elect.40(10), 1511–1518 (2004).
[CrossRef]

2003

P. Etchegoin, L. F. Cohen, H. Hartigan, R. J. C. Brown, M. J. T. Milton, and J. C. Gallop, “Electromagnetic contribution to surface enhanced Raman scattering revisited,” J. Chem. Phys.119(10), 5281 (2003).
[CrossRef]

2001

D. W. Ball, “Theory of Raman spectroscopy,” Spectroscopy16, 32 (2001).

1997

S. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science275(5303), 1102–1106 (1997).
[CrossRef] [PubMed]

1995

L. Baltog, N. Primeau, R. Reinisch, and J. L. Coutaz, “Surface enhanced Raman scattering on silver grating: Optimized antennalike gain of the stokes signal of 104,” Appl. Phys. Lett.66(10), 1187 (1995).
[CrossRef]

1987

J. P. Goudonnet, T. Inagaki, E. T. Arakawa, and T. Ferrell, “Angular and polarization dependence of surface-enhanced Raman scattering in attenuated-total-reflection geometry,” Phys. Rev. B Condens. Matter36(2), 917–921 (1987).
[CrossRef] [PubMed]

1984

M. Moskovits and J. S. Suh, “Surface selection rules for surface-enhanced Raman spectroscopy: calculations and application to the surface-enhanced Raman spectrum of phthalazine on silver,” J. Phys. Chem.88(23), 5526–5530 (1984).
[CrossRef]

1983

S. Ushioda and Y. Sasaki, “Raman scattering mediated by surface-plasmon polariton resonance,” Phys. Rev. B27(2), 1401–1404 (1983).
[CrossRef]

Abdelsalam, M. E.

J. J. Baumberg, T. A. Kelf, Y. Sugawara, S. Cintra, M. E. Abdelsalam, P. N. Bartlett, A. E. Russell, and A. E. Russell, “Angle-resolved surface-enhanced raman scattering on metallic nanostructured plasmonic crystals,” Nano Lett.5(11), 2262–2267 (2005).
[CrossRef] [PubMed]

Anker, J. N.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater.7(6), 442–453 (2008).
[CrossRef] [PubMed]

Arakawa, E. T.

J. P. Goudonnet, T. Inagaki, E. T. Arakawa, and T. Ferrell, “Angular and polarization dependence of surface-enhanced Raman scattering in attenuated-total-reflection geometry,” Phys. Rev. B Condens. Matter36(2), 917–921 (1987).
[CrossRef] [PubMed]

Astilean, S.

C. Farcau and S. Astilean, “Evidence of a surface plasmon-mediated mechanism in the generation of the SERS background,” Chem. Commun. (Camb.)47(13), 3861–3863 (2011).
[CrossRef] [PubMed]

Ball, D. W.

D. W. Ball, “Theory of Raman spectroscopy,” Spectroscopy16, 32 (2001).

Baltog, L.

L. Baltog, N. Primeau, R. Reinisch, and J. L. Coutaz, “Surface enhanced Raman scattering on silver grating: Optimized antennalike gain of the stokes signal of 104,” Appl. Phys. Lett.66(10), 1187 (1995).
[CrossRef]

Barnett, S. M.

S. Mahajan, R. M. Cole, J. D. Speed, S. H. Pelfrey, A. E. Russell, P. N. Bartlett, S. M. Barnett, and J. J. Baumberg, “Understanding the surface-enhanced Raman spectroscopy ‘background’,” J. Phys. Chem. C114(16), 7242–7250 (2010).
[CrossRef]

Bartlett, P. N.

S. Mahajan, R. M. Cole, J. D. Speed, S. H. Pelfrey, A. E. Russell, P. N. Bartlett, S. M. Barnett, and J. J. Baumberg, “Understanding the surface-enhanced Raman spectroscopy ‘background’,” J. Phys. Chem. C114(16), 7242–7250 (2010).
[CrossRef]

J. J. Baumberg, T. A. Kelf, Y. Sugawara, S. Cintra, M. E. Abdelsalam, P. N. Bartlett, A. E. Russell, and A. E. Russell, “Angle-resolved surface-enhanced raman scattering on metallic nanostructured plasmonic crystals,” Nano Lett.5(11), 2262–2267 (2005).
[CrossRef] [PubMed]

Baumberg, J. J.

S. Mahajan, R. M. Cole, J. D. Speed, S. H. Pelfrey, A. E. Russell, P. N. Bartlett, S. M. Barnett, and J. J. Baumberg, “Understanding the surface-enhanced Raman spectroscopy ‘background’,” J. Phys. Chem. C114(16), 7242–7250 (2010).
[CrossRef]

J. J. Baumberg, T. A. Kelf, Y. Sugawara, S. Cintra, M. E. Abdelsalam, P. N. Bartlett, A. E. Russell, and A. E. Russell, “Angle-resolved surface-enhanced raman scattering on metallic nanostructured plasmonic crystals,” Nano Lett.5(11), 2262–2267 (2005).
[CrossRef] [PubMed]

Blackie.E, M.

E. C. LeRu, M. Blackie.E, Meyer, and P. G. Etchegoin, “Surface enhanced Raman scattering enhancement factors: A comprehensive study,” J. Phys. Chem. C111(37), 13794–13803 (2007).
[CrossRef]

Brown, R. J. C.

P. Etchegoin, L. F. Cohen, H. Hartigan, R. J. C. Brown, M. J. T. Milton, and J. C. Gallop, “Electromagnetic contribution to surface enhanced Raman scattering revisited,” J. Chem. Phys.119(10), 5281 (2003).
[CrossRef]

Cao, Z. L.

Chan, C. Y.

H. Y. Lo, C. Y. Chan, and H. C. Ong, “Direct measurement of radiative scattering of surface plasmon polariton resonance from metallic arrays by polarization-resolved reflectivity spectroscopy,” Appl. Phys. Lett.101(22), 223108 (2012).
[CrossRef]

C. Y. Chan, J. B. Xu, M. Y. Waye, and H. C. Ong, “Angle resolved surface enhanced Raman scattering (SERS) on two-dimensional metallic arrays with different hole sizes,” Appl. Phys. Lett.96(3), 033104 (2010).
[CrossRef]

Cintra, S.

J. J. Baumberg, T. A. Kelf, Y. Sugawara, S. Cintra, M. E. Abdelsalam, P. N. Bartlett, A. E. Russell, and A. E. Russell, “Angle-resolved surface-enhanced raman scattering on metallic nanostructured plasmonic crystals,” Nano Lett.5(11), 2262–2267 (2005).
[CrossRef] [PubMed]

Cohen, L. F.

P. Etchegoin, L. F. Cohen, H. Hartigan, R. J. C. Brown, M. J. T. Milton, and J. C. Gallop, “Electromagnetic contribution to surface enhanced Raman scattering revisited,” J. Chem. Phys.119(10), 5281 (2003).
[CrossRef]

Cole, R. M.

S. Mahajan, R. M. Cole, J. D. Speed, S. H. Pelfrey, A. E. Russell, P. N. Bartlett, S. M. Barnett, and J. J. Baumberg, “Understanding the surface-enhanced Raman spectroscopy ‘background’,” J. Phys. Chem. C114(16), 7242–7250 (2010).
[CrossRef]

Coutaz, J. L.

L. Baltog, N. Primeau, R. Reinisch, and J. L. Coutaz, “Surface enhanced Raman scattering on silver grating: Optimized antennalike gain of the stokes signal of 104,” Appl. Phys. Lett.66(10), 1187 (1995).
[CrossRef]

Emory, S. R.

S. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science275(5303), 1102–1106 (1997).
[CrossRef] [PubMed]

Etchegoin, P.

P. Etchegoin, L. F. Cohen, H. Hartigan, R. J. C. Brown, M. J. T. Milton, and J. C. Gallop, “Electromagnetic contribution to surface enhanced Raman scattering revisited,” J. Chem. Phys.119(10), 5281 (2003).
[CrossRef]

Etchegoin, P. G.

E. C. LeRu, M. Blackie.E, Meyer, and P. G. Etchegoin, “Surface enhanced Raman scattering enhancement factors: A comprehensive study,” J. Phys. Chem. C111(37), 13794–13803 (2007).
[CrossRef]

Fan, S. H.

S. Wu, Z. Wang, and S. H. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multi-mode cavities,” IEEE, J. Quantum Elect.40(10), 1511–1518 (2004).
[CrossRef]

Farcau, C.

C. Farcau and S. Astilean, “Evidence of a surface plasmon-mediated mechanism in the generation of the SERS background,” Chem. Commun. (Camb.)47(13), 3861–3863 (2011).
[CrossRef] [PubMed]

Fernández-Domínguez, A. I.

D. Y. Lei, J. Li, A. I. Fernández-Domínguez, H. C. Ong, and S. A. Maier, “Geometry dependence of surface plasmon polariton lifetimes in nanohole arrays,” ACS Nano4(1), 432–438 (2010).
[CrossRef] [PubMed]

Ferrell, T.

J. P. Goudonnet, T. Inagaki, E. T. Arakawa, and T. Ferrell, “Angular and polarization dependence of surface-enhanced Raman scattering in attenuated-total-reflection geometry,” Phys. Rev. B Condens. Matter36(2), 917–921 (1987).
[CrossRef] [PubMed]

Gallop, J. C.

P. Etchegoin, L. F. Cohen, H. Hartigan, R. J. C. Brown, M. J. T. Milton, and J. C. Gallop, “Electromagnetic contribution to surface enhanced Raman scattering revisited,” J. Chem. Phys.119(10), 5281 (2003).
[CrossRef]

Goudonnet, J. P.

J. P. Goudonnet, T. Inagaki, E. T. Arakawa, and T. Ferrell, “Angular and polarization dependence of surface-enhanced Raman scattering in attenuated-total-reflection geometry,” Phys. Rev. B Condens. Matter36(2), 917–921 (1987).
[CrossRef] [PubMed]

Hall, W. P.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater.7(6), 442–453 (2008).
[CrossRef] [PubMed]

Hartigan, H.

P. Etchegoin, L. F. Cohen, H. Hartigan, R. J. C. Brown, M. J. T. Milton, and J. C. Gallop, “Electromagnetic contribution to surface enhanced Raman scattering revisited,” J. Chem. Phys.119(10), 5281 (2003).
[CrossRef]

Hui, K. C.

K. C. Hui, J. T. K. Wan, J. B. Xu, and H. C. Ong, “Dependence of anisotropic surface plasmon lifetimes of two-dimensional hole arrays on hole geometry,” Appl. Phys. Lett.95(6), 063110 (2009).
[CrossRef]

Inagaki, T.

J. P. Goudonnet, T. Inagaki, E. T. Arakawa, and T. Ferrell, “Angular and polarization dependence of surface-enhanced Raman scattering in attenuated-total-reflection geometry,” Phys. Rev. B Condens. Matter36(2), 917–921 (1987).
[CrossRef] [PubMed]

Jiang, J.

H. Yang, Y. Liu, Z. Liu, Y. Yang, J. Jiang, Z. Zhang, G. Shen, and R. Yu, “Raman mapping and in situ SERS spectroelectrochemical studies of 6-Mercaptopurine SAMs on the gold electrode,” J. Phys. Chem. B109(7), 2739–2744 (2005).
[CrossRef] [PubMed]

Kelf, T. A.

J. J. Baumberg, T. A. Kelf, Y. Sugawara, S. Cintra, M. E. Abdelsalam, P. N. Bartlett, A. E. Russell, and A. E. Russell, “Angle-resolved surface-enhanced raman scattering on metallic nanostructured plasmonic crystals,” Nano Lett.5(11), 2262–2267 (2005).
[CrossRef] [PubMed]

Lei, D. Y.

D. Y. Lei, J. Li, A. I. Fernández-Domínguez, H. C. Ong, and S. A. Maier, “Geometry dependence of surface plasmon polariton lifetimes in nanohole arrays,” ACS Nano4(1), 432–438 (2010).
[CrossRef] [PubMed]

LeRu, E. C.

E. C. LeRu, M. Blackie.E, Meyer, and P. G. Etchegoin, “Surface enhanced Raman scattering enhancement factors: A comprehensive study,” J. Phys. Chem. C111(37), 13794–13803 (2007).
[CrossRef]

Li, J.

D. Y. Lei, J. Li, A. I. Fernández-Domínguez, H. C. Ong, and S. A. Maier, “Geometry dependence of surface plasmon polariton lifetimes in nanohole arrays,” ACS Nano4(1), 432–438 (2010).
[CrossRef] [PubMed]

Liu, Y.

H. Yang, Y. Liu, Z. Liu, Y. Yang, J. Jiang, Z. Zhang, G. Shen, and R. Yu, “Raman mapping and in situ SERS spectroelectrochemical studies of 6-Mercaptopurine SAMs on the gold electrode,” J. Phys. Chem. B109(7), 2739–2744 (2005).
[CrossRef] [PubMed]

Liu, Z.

H. Yang, Y. Liu, Z. Liu, Y. Yang, J. Jiang, Z. Zhang, G. Shen, and R. Yu, “Raman mapping and in situ SERS spectroelectrochemical studies of 6-Mercaptopurine SAMs on the gold electrode,” J. Phys. Chem. B109(7), 2739–2744 (2005).
[CrossRef] [PubMed]

Lo, H. Y.

H. Y. Lo, C. Y. Chan, and H. C. Ong, “Direct measurement of radiative scattering of surface plasmon polariton resonance from metallic arrays by polarization-resolved reflectivity spectroscopy,” Appl. Phys. Lett.101(22), 223108 (2012).
[CrossRef]

Z. L. Cao, H. Y. Lo, and H. C. Ong, “Determination of absorption and radiative decay rates of surface plasmon polaritons from nanohole array,” Opt. Lett.37(24), 5166–5168 (2012).
[CrossRef] [PubMed]

Lyandres, O.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater.7(6), 442–453 (2008).
[CrossRef] [PubMed]

Magnusson, R.

Mahajan, S.

S. Mahajan, R. M. Cole, J. D. Speed, S. H. Pelfrey, A. E. Russell, P. N. Bartlett, S. M. Barnett, and J. J. Baumberg, “Understanding the surface-enhanced Raman spectroscopy ‘background’,” J. Phys. Chem. C114(16), 7242–7250 (2010).
[CrossRef]

Maier, S. A.

D. Y. Lei, J. Li, A. I. Fernández-Domínguez, H. C. Ong, and S. A. Maier, “Geometry dependence of surface plasmon polariton lifetimes in nanohole arrays,” ACS Nano4(1), 432–438 (2010).
[CrossRef] [PubMed]

Meyer,

E. C. LeRu, M. Blackie.E, Meyer, and P. G. Etchegoin, “Surface enhanced Raman scattering enhancement factors: A comprehensive study,” J. Phys. Chem. C111(37), 13794–13803 (2007).
[CrossRef]

Milton, M. J. T.

P. Etchegoin, L. F. Cohen, H. Hartigan, R. J. C. Brown, M. J. T. Milton, and J. C. Gallop, “Electromagnetic contribution to surface enhanced Raman scattering revisited,” J. Chem. Phys.119(10), 5281 (2003).
[CrossRef]

Moskovits, M.

M. Moskovits and J. S. Suh, “Surface selection rules for surface-enhanced Raman spectroscopy: calculations and application to the surface-enhanced Raman spectrum of phthalazine on silver,” J. Phys. Chem.88(23), 5526–5530 (1984).
[CrossRef]

Nie, S.

S. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science275(5303), 1102–1106 (1997).
[CrossRef] [PubMed]

Ong, H. C.

Z. L. Cao, H. Y. Lo, and H. C. Ong, “Determination of absorption and radiative decay rates of surface plasmon polaritons from nanohole array,” Opt. Lett.37(24), 5166–5168 (2012).
[CrossRef] [PubMed]

H. Y. Lo, C. Y. Chan, and H. C. Ong, “Direct measurement of radiative scattering of surface plasmon polariton resonance from metallic arrays by polarization-resolved reflectivity spectroscopy,” Appl. Phys. Lett.101(22), 223108 (2012).
[CrossRef]

C. Y. Chan, J. B. Xu, M. Y. Waye, and H. C. Ong, “Angle resolved surface enhanced Raman scattering (SERS) on two-dimensional metallic arrays with different hole sizes,” Appl. Phys. Lett.96(3), 033104 (2010).
[CrossRef]

D. Y. Lei, J. Li, A. I. Fernández-Domínguez, H. C. Ong, and S. A. Maier, “Geometry dependence of surface plasmon polariton lifetimes in nanohole arrays,” ACS Nano4(1), 432–438 (2010).
[CrossRef] [PubMed]

K. C. Hui, J. T. K. Wan, J. B. Xu, and H. C. Ong, “Dependence of anisotropic surface plasmon lifetimes of two-dimensional hole arrays on hole geometry,” Appl. Phys. Lett.95(6), 063110 (2009).
[CrossRef]

Pelfrey, S. H.

S. Mahajan, R. M. Cole, J. D. Speed, S. H. Pelfrey, A. E. Russell, P. N. Bartlett, S. M. Barnett, and J. J. Baumberg, “Understanding the surface-enhanced Raman spectroscopy ‘background’,” J. Phys. Chem. C114(16), 7242–7250 (2010).
[CrossRef]

Primeau, N.

L. Baltog, N. Primeau, R. Reinisch, and J. L. Coutaz, “Surface enhanced Raman scattering on silver grating: Optimized antennalike gain of the stokes signal of 104,” Appl. Phys. Lett.66(10), 1187 (1995).
[CrossRef]

Reinisch, R.

L. Baltog, N. Primeau, R. Reinisch, and J. L. Coutaz, “Surface enhanced Raman scattering on silver grating: Optimized antennalike gain of the stokes signal of 104,” Appl. Phys. Lett.66(10), 1187 (1995).
[CrossRef]

Russell, A. E.

S. Mahajan, R. M. Cole, J. D. Speed, S. H. Pelfrey, A. E. Russell, P. N. Bartlett, S. M. Barnett, and J. J. Baumberg, “Understanding the surface-enhanced Raman spectroscopy ‘background’,” J. Phys. Chem. C114(16), 7242–7250 (2010).
[CrossRef]

J. J. Baumberg, T. A. Kelf, Y. Sugawara, S. Cintra, M. E. Abdelsalam, P. N. Bartlett, A. E. Russell, and A. E. Russell, “Angle-resolved surface-enhanced raman scattering on metallic nanostructured plasmonic crystals,” Nano Lett.5(11), 2262–2267 (2005).
[CrossRef] [PubMed]

J. J. Baumberg, T. A. Kelf, Y. Sugawara, S. Cintra, M. E. Abdelsalam, P. N. Bartlett, A. E. Russell, and A. E. Russell, “Angle-resolved surface-enhanced raman scattering on metallic nanostructured plasmonic crystals,” Nano Lett.5(11), 2262–2267 (2005).
[CrossRef] [PubMed]

Sasaki, Y.

S. Ushioda and Y. Sasaki, “Raman scattering mediated by surface-plasmon polariton resonance,” Phys. Rev. B27(2), 1401–1404 (1983).
[CrossRef]

Seol, K. H.

Shah, N. C.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater.7(6), 442–453 (2008).
[CrossRef] [PubMed]

Shen, G.

H. Yang, Y. Liu, Z. Liu, Y. Yang, J. Jiang, Z. Zhang, G. Shen, and R. Yu, “Raman mapping and in situ SERS spectroelectrochemical studies of 6-Mercaptopurine SAMs on the gold electrode,” J. Phys. Chem. B109(7), 2739–2744 (2005).
[CrossRef] [PubMed]

Song, S. H.

Speed, J. D.

S. Mahajan, R. M. Cole, J. D. Speed, S. H. Pelfrey, A. E. Russell, P. N. Bartlett, S. M. Barnett, and J. J. Baumberg, “Understanding the surface-enhanced Raman spectroscopy ‘background’,” J. Phys. Chem. C114(16), 7242–7250 (2010).
[CrossRef]

Sugawara, Y.

J. J. Baumberg, T. A. Kelf, Y. Sugawara, S. Cintra, M. E. Abdelsalam, P. N. Bartlett, A. E. Russell, and A. E. Russell, “Angle-resolved surface-enhanced raman scattering on metallic nanostructured plasmonic crystals,” Nano Lett.5(11), 2262–2267 (2005).
[CrossRef] [PubMed]

Suh, J. S.

M. Moskovits and J. S. Suh, “Surface selection rules for surface-enhanced Raman spectroscopy: calculations and application to the surface-enhanced Raman spectrum of phthalazine on silver,” J. Phys. Chem.88(23), 5526–5530 (1984).
[CrossRef]

Ushioda, S.

S. Ushioda and Y. Sasaki, “Raman scattering mediated by surface-plasmon polariton resonance,” Phys. Rev. B27(2), 1401–1404 (1983).
[CrossRef]

Van Duyne, R. P.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater.7(6), 442–453 (2008).
[CrossRef] [PubMed]

Wan, J. T. K.

K. C. Hui, J. T. K. Wan, J. B. Xu, and H. C. Ong, “Dependence of anisotropic surface plasmon lifetimes of two-dimensional hole arrays on hole geometry,” Appl. Phys. Lett.95(6), 063110 (2009).
[CrossRef]

Wang, Z.

S. Wu, Z. Wang, and S. H. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multi-mode cavities,” IEEE, J. Quantum Elect.40(10), 1511–1518 (2004).
[CrossRef]

Waye, M. Y.

C. Y. Chan, J. B. Xu, M. Y. Waye, and H. C. Ong, “Angle resolved surface enhanced Raman scattering (SERS) on two-dimensional metallic arrays with different hole sizes,” Appl. Phys. Lett.96(3), 033104 (2010).
[CrossRef]

Wu, S.

S. Wu, Z. Wang, and S. H. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multi-mode cavities,” IEEE, J. Quantum Elect.40(10), 1511–1518 (2004).
[CrossRef]

Xu, J. B.

C. Y. Chan, J. B. Xu, M. Y. Waye, and H. C. Ong, “Angle resolved surface enhanced Raman scattering (SERS) on two-dimensional metallic arrays with different hole sizes,” Appl. Phys. Lett.96(3), 033104 (2010).
[CrossRef]

K. C. Hui, J. T. K. Wan, J. B. Xu, and H. C. Ong, “Dependence of anisotropic surface plasmon lifetimes of two-dimensional hole arrays on hole geometry,” Appl. Phys. Lett.95(6), 063110 (2009).
[CrossRef]

Yang, H.

H. Yang, Y. Liu, Z. Liu, Y. Yang, J. Jiang, Z. Zhang, G. Shen, and R. Yu, “Raman mapping and in situ SERS spectroelectrochemical studies of 6-Mercaptopurine SAMs on the gold electrode,” J. Phys. Chem. B109(7), 2739–2744 (2005).
[CrossRef] [PubMed]

Yang, Y.

H. Yang, Y. Liu, Z. Liu, Y. Yang, J. Jiang, Z. Zhang, G. Shen, and R. Yu, “Raman mapping and in situ SERS spectroelectrochemical studies of 6-Mercaptopurine SAMs on the gold electrode,” J. Phys. Chem. B109(7), 2739–2744 (2005).
[CrossRef] [PubMed]

Yoon, J.

Yu, R.

H. Yang, Y. Liu, Z. Liu, Y. Yang, J. Jiang, Z. Zhang, G. Shen, and R. Yu, “Raman mapping and in situ SERS spectroelectrochemical studies of 6-Mercaptopurine SAMs on the gold electrode,” J. Phys. Chem. B109(7), 2739–2744 (2005).
[CrossRef] [PubMed]

Zhang, Z.

H. Yang, Y. Liu, Z. Liu, Y. Yang, J. Jiang, Z. Zhang, G. Shen, and R. Yu, “Raman mapping and in situ SERS spectroelectrochemical studies of 6-Mercaptopurine SAMs on the gold electrode,” J. Phys. Chem. B109(7), 2739–2744 (2005).
[CrossRef] [PubMed]

Zhao, J.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater.7(6), 442–453 (2008).
[CrossRef] [PubMed]

ACS Nano

D. Y. Lei, J. Li, A. I. Fernández-Domínguez, H. C. Ong, and S. A. Maier, “Geometry dependence of surface plasmon polariton lifetimes in nanohole arrays,” ACS Nano4(1), 432–438 (2010).
[CrossRef] [PubMed]

Appl. Phys. Lett.

C. Y. Chan, J. B. Xu, M. Y. Waye, and H. C. Ong, “Angle resolved surface enhanced Raman scattering (SERS) on two-dimensional metallic arrays with different hole sizes,” Appl. Phys. Lett.96(3), 033104 (2010).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

An illustration to describe the SPP mediated Raman scattering process. Molecule can be excited by the ingoing SPPs generated by the excitation. The molecule can transfer its energy either directly to far-field at rate Γr or to the outgoing SPPs at Γ c k SPP . The outgoing SPPs propagate at wavevector k SPP will dissipate energy either by Ohmic absorption at Γ abs k SPP or radiative scattering at m Γ rad k SPP ,m through multiple channels. Each radiative decay channel yields SPP mediated Raman emission at a well-defined angle.

Fig. 2
Fig. 2

(a) Parallel and (b) orthogonal reflectivity mappings of 6-mercaptopurine coated Ag nanohole array. The dash lines identify different (nx,ny) SPP modes. Inset: the SEM image of the array. The (c) parallel and (d) orthogonal (1,0) reflectivity spectra extracted from the mappings. The dash lines are the best fits by using coupled mode theory. (e) The plots of deduced (1,0) radiative and total decay rates of SPPs as a function of resonant wavelength in logarithmic scale. The dash line is the linear fit showing a λ-6.95 dependence.

Fig. 3
Fig. 3

The angle-dependent (a) Raman scattering and (b) p-polarized reflectivity mappings plotted in the same scale. The dash lines indicate the (1,0) and (−2,0) SPPs. (c) The Raman spectra of the array taken from different detection angles. The spectra are vertical shifted for visualization. The dash lines indicate the Raman peaks at 537, 550, and 558 nm. The angular plots of Raman intensities at (d) 537 nm, (e) 550 nm, and (f) 558 nm (squares) after subtracting the fluorescence background. The angular plots of intensities obtained from a flat film at the same wavelengths are also shown (circles). The corresponding p-polarized reflectivity as a function of incident angle (solid lines). The dash lines are the best-fits.

Fig. 4
Fig. 4

(a) The plot of integrated powers of background and SPP mediated emissions (squares and circles) against wavelength. (b) The power ratio between SPP mediated and direct emissions. (c) The (1,0) SPP total to radiative decay rate ratio. (d) The calculated coupling efficiency as a function of wavelength.

Equations (2)

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P SPP k SPP ,n P d = Γ c k SPP Γ r Γ rad k SPP ,n Γ tot k SPP .
1 4 | 2 r p + Γ rad 1 e i ϕ 1 i(ω ω res )+ Γ tot /2 | 2   and   1 4 ( Γ rad 1 ) 2 (ω ω res ) 2 + ( Γ tot /2 ) 2 ,

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