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Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 21 — Oct. 21, 2013
  • pp: 25026–25034
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The contribution of nonlocal electro-opto-thermal interaction to single molecule nonlinear Raman enhancement

Chao-Yi Tai and Wen-Hsiang Yu  »View Author Affiliations


Optics Express, Vol. 21, Issue 21, pp. 25026-25034 (2013)
http://dx.doi.org/10.1364/OE.21.025026


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Abstract

we develop a precise modelling where nonlocal electro-opto-thermal interactions are comprehensively included for the analysis of nonlinear Raman enhancement and plasmonic heating. An interaction enhancement factor GIEF is introduced to quantify the coupling between the electromagnetic field and the temperature field which is rarely considered in the estimation of Raman enhancement. For the case of isolated single nanosphere, GIEF can be up to ten, indicating a thermal origin which well explains the observed temperature rise, shortened blinking period, and the nonlinearly enhanced Raman cross-section. For the case of nanodimer, the suppression of plasmon heating was analyzed, demonstrating the great capability to mitigate biomolecular degradation and blinking.

© 2013 Optical Society of America

1. Introduction

Essentially, EM field and temperature field are coupled. Electromagnetic absorption results from the excitation of LSPs can induce tremendous nonlocal hot-electrons. Upon oscillation, not only the EM response of metals but the spatial distribution of the EM field and the temperature field are altered. The significance of this study is that the nonlinear Raman enhancement and mitigation of Raman blinking can be simultaneously obtained. This has been accounted never possible in the past and proper models fall short till now. Through plasmonic inter-modal coupling, we show that this problem can be solved. To illustrate the concept, two prototype cases are considered: the isolated nanosphere and nanodimer. The formal case is used to illustrate the nonlinear enhancement of the GEF and the latter is for the suppression of the temperature rise. The nonlinear relations between the SERS signal, illumination intensity and environmental temperatures were explored in both cases. To verify our modeling, results are comprehensively compared with those reported in literatures [15

15. S. R. Emory, R. A. Jensen, T. Wenda, M. Han, and S. Nie, “Re-examining the origins of spectral blinking in single-molecule and single-nanoparticle SERS,” Faraday Discuss. 132, 249–259, discussion 309–319 (2006). [CrossRef] [PubMed]

, 16

16. A. M. Michaels, J. Jiang, and L. Brus, “Ag nanocrystal junctions as the site for surface-enhanced Raman scattering of single rhodamine 6G molecules,” J. Phys. Chem. B 104(50), 11965–11971 (2000). [CrossRef]

, 23

23. P. T. Leung, M. H. Hider, and E. J. Sanchez, “Surface-enhanced Raman scattering at elevated temperatures,” Phys. Rev. B Condens. Matter 53(19), 12659–12662 (1996). [CrossRef] [PubMed]

, 24

24. L. Xu and Y. Fang, “Temperature-induced effect on surface-enhanced Raman scattering of p, m-hydroxybenzoic acid on silver nanoparticles,” Spectroscopy 18, 26–31 (2003).

], and close agreement was found. Our study provides a more accurate way to estimate the temperature in steady state [25

25. A. M. Gobin, M. H. Lee, N. J. Halas, W. D. James, R. A. Drezek, and J. L. West, “Near-infrared resonant nanoshells for combined optical imaging and photothermal cancer therapy,” Nano Lett. 7(7), 1929–1934 (2007). [CrossRef] [PubMed]

], pointing out a potential inaccuracy in temperature determination by the intensity ratio of the Stokes to anti-Stokes scattering [26

26. R. C. Maher, L. F. Cohen, P. Etchegoin, H. J. N. Hartigan, R. J. C. Brown, and M. J. T. Milton, “Stokes/anti-Stokes anomalies under surface enhanced Raman scattering conditions,” J. Chem. Phys. 120(24), 11746–11753 (2004). [CrossRef] [PubMed]

].

2. Model and numerical procedures

Our model is established by linking the Maxwell’s equations and the thermal diffusion equation which can be expressed as follows [27

27. G. Baffou, R. Quidant, and F. J. García de Abajo, “Nanoscale control of optical heating in complex plasmonic systems,” ACS Nano 4(2), 709–716 (2010). [CrossRef] [PubMed]

]:
[κ(r)T(r)]=ρ(r)
(1)
T(r) represents the spatial distribution of the temperature field, κ(r) represents the position dependent thermal conductivity, and ρ(r) stands for the heat source density (HSD) as a consequence of EM absorption. For monochromatic wave with angular frequency ω0, ρ(r)can be expressed by Eq. (2),
ρ(r)=ω0ε''(r)<E(r,t)2>
(2)
where ε''(r) stands for the imaginary part of the permittivity, and the bracket gives the time-average light intensity. Combining Eq. (1) and Eq. (2) can only obtain the temperature rise caused by the EM absorption and is widely used in most of the research up to date. However, according to the study of Wiedemann and Franz [28

28. R. Franz and G. Wiedemann, “Ueber die wärme-leitungsfähigkeit der metalle,” Annalen der Physik 165(8), 497–531 (1853). [CrossRef]

], the electrical conductivity σ(r) is highly correlated to the temperature of the metal itself. The EM response thereby changes correspondingly as the temperature rises. This recurrence relation should be taken into account repeatedly until reaching steady-state in order to reveal material properties with high fidelity.
κ(r)/σ(r)T(r)=L
(3)
Eq. (3) is the well-known law proposed by Wiedemann and Franz, which is used to describe the relations between the temperatureT(r), thermal conductivityκ(r), and the electrical conductivity σ(r) of the metal in consideration. In Eq. (3), L is the so-called Lorenz number which is intrinsically material dependent. For noble metals such as gold and silver, L and κ(r) can be treated as temperature-independent constants. Hence, the electrical conductivity is inversely proportional to the temperature. Once the incident light impinges on the structure, the electro-opto-thermal interaction is initiated. The risen temperature results in a reduced conductivity which in turn causes the redistribution of the EM fields according to the Ampère’s law, as shown in Eq. (4). Based on Eq. (2), this further affects the HSD, and the temperature field will be deviated correspondingly from the initial condition (according to Eq. (1)). This process repeats until the system reaches steady state.

×H(r,t)=σE(r,t)+jωε'E(r,t)
(4)

The numerical procedures are detailed as follows: The transport behavior of hot-electrons is modeled by thermal diffusion equation under thermal equilibrium; the nonlocal hot-electrons contributed to the electrical conductivity is governed by the law of Wiedemann-Franz; and the heat source density (HSD) resulted from the electromagnetic absorption is governed by the interacted Maxwell’s equation. The full vectorial finite difference time domain (FDTD) method is used to simulate the enhanced localization of electromagnetic field around the isolated gold nanosphere and nanodimers, where the dispersion relation of gold is modeled by Lorentz-Drude model and the incident plane wave is introduced by total and scattering field boundaries. Twelve perfectly matched layers are allocated on each boundary to absorb the outgoing electromagnetic waves. Time and space grid set in FDTD are 8.34 × 10−19 s and 1.25nm × 1.25nm × 1.25nm respectively, which ensures the simulation yields convergent and accurate results.

The iterative finite difference method of the explicit form and the modified Gauss-Seidel algorithm were applied to model the distribution of the temperature field that accelerated the numerical procedure effectively. For the purpose of obtaining a realistic temperature distribution in a wider region, non-uniform grids are applied to extend the simulation domain by over 550 μm3. Numerically, the undisturbed steady-state electromagnetic fields are calculated first. Subsequently, the thermal diffusion equation was solved to obtain the undisturbed steady-state temperature field. The temperature field then feeds back to the electrical conductivity and the discrete Maxwell’s equations are solved again to acquire the redistributed electromagnetic fields. The HSD is renewed correspondingly as a result of the redistributed electromagnetic field, which is then substituted back into the thermal diffusion equation to obtain a renewed temperature field again. The iterative calculation between the discrete Maxwell’s equations and the thermal diffusion equation should be computed repeatedly until the system reaches self-consistence. Typically, fifteen to forty loops are included in this process. The flow chart of the numerical procedure is schematically shown in Fig. 1.
Fig. 1 The flow chart of the computational procedure.

3. Results and discussion

In order to illustrate how the mutual interaction enhances the absorption cross section, an isolated gold nanosphere (50 nm in radius) immobilized on the glass substrate subject to the illumination of monochromatic plane wave was studied. When the localized surface plasmons are excited, intense EM fields are induced around the rim of the gold nanosphere.

In order to quantify the intensity dependentGEF(r), the interaction enhancement factor GIEF(r) was introduced as follows:
GIEF(r)=|Eint(r)|4|Enonint(r)|4
Eint(r) is the electric field considering the effect of electro-opto-thermal interaction whileEnonint(r) is that without interaction considered. Since GIEF(r) is a function of coordinates, GIEF(r)Sur, defining by the spatially-averaged GIEF(r) on the surface of the gold nanosphere, is introduced to quantify the nonlinear amplification of the GEF(r).

Compared to the result calculated by the non-interaction model (the blue-dashed line in Fig. 3), GIEF(r)Suris proportional to the illumination intensity, exhibiting a nonlinear enhancement due to plasmon heating. (the blue solid-line in Fig. 3). In contrast toGIEF(r)Sur, the surface temperature grows almost linearly with the increase of the illumination intensity. With electro-opto-thermal interaction considered, the surface temperature is slightly higher than that calculated without interaction, as shown by the red line in Fig. 3.
Fig. 3 The surface temperature and spatially averaged interaction enhancement factor as a function of the illumination intensity. The bottom level of each bar gives the degradation temperature for the noted molecules. The values on top axis give the degradation intensities.

Interestingly, one may find that interaction enhancement accompany blinking was rarely reported in literatures, especially for bio-molecular systems. An intuitive interpretation is that light induced temperature rise may accelerate the degradation of bio-molecules, and the threshold degradation intensity is far below that required for observable enhancement or blinking. To illustrate how accurate our modeling defines the boundary which separates regimes between interaction enhancement and thermal degradation, the degradation temperature of some commonly used molecules were converted to the illumination intensity. As shown in Fig. 3, the degradation temperature for erythrocyte and nerve fiber are 45 °C and 60 °C [30

30. K. Linko and K. Hynynen, “Erythrocyte damage caused by the Haemotherm microwave blood warmer,” Acta Anaesthesiol. Scand. 23(4), 320–328 (1979). [CrossRef] [PubMed]

, 31

31. M. I. Hafez, S. Zhou, R. R. H. Coombs, and I. D. McCarthy, “The effect of irrigation on peak temperatures in nerve root, dura, and intervertebral disc during laser-assisted foraminoplasty,” Lasers Surg. Med. 29(1), 33–37 (2001). [CrossRef] [PubMed]

], and the corresponding degradation intensities are calculated to be 0.1 mW/μm2 and 0.2 mW/μm2, respectively. It should be noted that the degradation temperature for the abovementioned molecules lies below the curve of GIEF(r)Sur even under very weak illumination, indicating that the interaction enhancement is very difficult to be observed. In contrast to bio-molecules, the interaction enhancement is relatively easy to be observed for non-biomolecules as long as the illumination intensity is sufficiently moderate. Examples can be indeed found in literatures. For instance, the degradation temperature for polyvinylpyrrolidone (PVP), crystal violet (CV), polystyrene (PS), rhodamine 6G (R6G), and benzenethiol (BT) are around 150 °C, 200 °C, 240°C, 325°C, and 650°C, respectively [15

15. S. R. Emory, R. A. Jensen, T. Wenda, M. Han, and S. Nie, “Re-examining the origins of spectral blinking in single-molecule and single-nanoparticle SERS,” Faraday Discuss. 132, 249–259, discussion 309–319 (2006). [CrossRef] [PubMed]

, 32

32. S. W. Kuo and F. C. Chang, “Studies of miscibility behavior and hydrogen bonding in blends of poly(vinylphenol) and poly(vinylpyrrolidone),” Macromolecules 34(15), 5224–5228 (2001). [CrossRef]

34

34. D. E. Johnson, “Pyrolysis of benzenethiol,” Fuel 66(2), 255–260 (1987). [CrossRef]

]. The corresponding degradation intensities were calculated to be 0.7 mW/μm2, 0.9 mW/μm2, 1.1 mW/μm2, 1.4 mW/μm2, and 1.5 mW/μm2 respectively.

Since the tunability of resonance in metal nanosphere is limited, nanoparticles of various shapes, such as ellipsoid, prism, disk, dimer, trimer, etc. have been investigated to tailor the resonant wavelength so as to increase the resonant strength. Through structural engineering, the temperature rise due to plasmon heating may also be suppressed. Here an isolated gold nanodimer immobilized on glass substrate was considered to demonstrate the suppression of plasmonic heating. The same particle size (50 nm in radius) with an inter-particle distance of 10nm is assumed in the calculation. In comparison with the far field characteristics of gold nanosphere without electro-opto-thermal interaction, the resonant wavelength of the nanodimer is red shifted owing to strong inter-modal coupling, as shown by the black stars in Fig. 4(a).
Fig. 4 Near and far-field characteristics of isolated gold nanodimer. (a) The absorption cross section as functions of the incident wavelength and illumination intensity. (b) The enhanced electromagnetic field and the temperature field as a function of the illumination intensity in the near-field region. (c) The nonlinear relationship of the gap temperature and the GIEF as a function of the illumination intensity.
To calculate the intensity dependent absorption cross section, a commonly used wavelength (λ = 633nm) close to the LSPR was chosen. In contrast to the case of nanosphere, the absorption cross section drops with the increase of the illumination intensity, as shown by the red stars in Fig. 4(a). In the near field, the coupled plasmonic mode produces an intense electromagnetic field within the gap, yielding an EF as high as 107 accompanied by a much suppressed temperature rise, as shown in Fig. 4(b). With the illumination intensity varied from 0.1 mW/μm2 to 1.0 mW/μm2, the GEF(r) changes insignificantly around 107. Meanwhile, the surface temperature rises from 39 °C to 145 °C, which is lower than the degradation temperature for most of the analytes. In order to quantify the electromagnetic field and temperature field in the gap, values of the temperature and GIEF(r) at the coordinate center of the gap are extracted from the simulation. Figure 4(c) gives the results (solid lines) compared to those (broken lines) obtained without the electro-opto-thermal interaction. Since the electromagnetic energy is more concentrated in the dielectric gap region instead of on the metallic surface, the contribution from the coupling between the electromagnetic field and the temperature field to the enhancement factor is very limited. In addition, the nanoparticle dimer forms a structure similar to a tapered slit, mimicking the propagation characteristics of the extraordinary transmission (EOT) like behavior [35

35. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]

, 36

36. R. Gordon, “Light in a subwavelength slit in a metal: propagation and reflection,” Phys. Rev. B 73(15), 153405 (2006). [CrossRef]

]. In EOT, the electromagnetic energy is concentrated within the gap and the plasmonic gap mode is insensitive to the change of the material parameters of the consisting metals. As a result, the magnification of GEF(r) is only very moderate which is insufficient to counteract the decrease of the absorption coefficient (proportional to the σ) as in the case of the nanosphere. Hence GIEF(r)tends to saturate at high illumination intensities and the decrease of the absorption cross section is mainly attributed to the decrease of the absorption coefficient as a consequence of temperature increase. This result renders isolated nanodimer as an appropriate platform for molecular sensing without suffering severe thermal issues. The degradation intensities for bio- and nonbio-molecules are higher as compared to the case of nanosphere. For erythrocyte and nerve fiber, the degradation intensities are 0.15 mW/μm2 and 0.35 mW/μm2, respectively. For PVP, CV, PS, R6G, and BT, the degradation intensities are all higher than 1.2 mW/μm2.

For practical use, we provide fitting functions of GIEF(I), GIEF(T), and T(I) in Table 1

Table 1. Fitting Functions of GIEF(I), GIEF(T), and T(I) near LSPR for Gold Nanosphere and Gold Nanodimer.

table-icon
View This Table
. For the case of isolated nanosphere (nanodimer), the sign of the second-order terms are all positive (negative), indicating nonlinearly enhanced (suppressed) growth with the illumination intensity or the global temperature. Finally, to verify our modeling, results extracted from several other studies are compared. The magnification of GEF(r) as a function of light intensity is observed in [16

16. A. M. Michaels, J. Jiang, and L. Brus, “Ag nanocrystal junctions as the site for surface-enhanced Raman scattering of single rhodamine 6G molecules,” J. Phys. Chem. B 104(50), 11965–11971 (2000). [CrossRef]

]. Up to 10 times magnification were obtained which coincides with our calculation. In addition, the nonlinear magnification of GEF(r)as a function of the global temperature is consistent with [15

15. S. R. Emory, R. A. Jensen, T. Wenda, M. Han, and S. Nie, “Re-examining the origins of spectral blinking in single-molecule and single-nanoparticle SERS,” Faraday Discuss. 132, 249–259, discussion 309–319 (2006). [CrossRef] [PubMed]

], and the temperature rise as a function of the illumination intensity is also compared with [22

22. H. H. Richardson, M. T. Carlson, P. J. Tandler, P. Hernandez, and A. O. Govorov, “Experimental and theoretical studies of light-to-heat conversion and collective heating effects in metal nanoparticle solutions,” Nano Lett. 9(3), 1139–1146 (2009). [CrossRef] [PubMed]

], [27

27. G. Baffou, R. Quidant, and F. J. García de Abajo, “Nanoscale control of optical heating in complex plasmonic systems,” ACS Nano 4(2), 709–716 (2010). [CrossRef] [PubMed]

], and [37

37. L. R. Hirsch, R. J. Stafford, J. A. Bankson, S. R. Sershen, B. Rivera, R. E. Price, J. D. Hazle, N. J. Halas, and J. L. West, “Nanoshell-mediated near-infrared thermal therapy of tumors under magnetic resonance guidance,” Proc. Natl. Acad. Sci. U.S.A. 100(23), 13549–13554 (2003). [CrossRef] [PubMed]

]. Note that in our result, the predicted temperature rise is a bit higher. This is because the surrounding medium is air, having relatively lower thermal conductivity as opposed to water in the given references. The agreements between our predictions and those reported in literatures are well within the same order of magnitude, showing that the present model considering the electro-opto-thermal interaction is very reliable and superior to many existing estimations of the enhancement factor for SERS.

4. Conclusion

We developed a numerical technique to analyze the contribution of nonlocal electro-opto-thermal interactions to the enhancement of the electromagnetic field as well as the plasmonic heating, and is applicable to any nanostructures. For the gold nanosphere under weak light illumination (I<1.5 mW/μm2), the spatially averaged interaction enhancement factor GIEF(r)Surwas amplified by ~10 times and the surface temperature was raised to over 300°C, showing very close agreement with experimental observations in literatures. For the nanodimer, a large field enhancement factor of 107 accompanied by much suppressed plasmonic heating was demonstrated, showing potential contribution to mitigate molecule degradation and blinking. We conclude that the interaction enhancement factor is more appropriate than the conventional definition for SERS, where the electro-opto-thermal interactions are all included to reveal the electromagnetic and temperature field with high fidelity.

Acknowledgments

References and links

1.

M. Fleischmann, P. J. Hendra, and A. J. McQuillan, “Raman spectra of pyridine adsorbed at a silver electrode,” Chem. Phys. Lett. 26(2), 163–166 (1974). [CrossRef]

2.

S. L. McCall and P. M. Platzman, “Raman scattering from chemisorbed molecules at surfaces,” Phys. Rev. B 22(4), 1660–1662 (1980). [CrossRef]

3.

J. R. Lombardi, R. L. Birke, T. Lu, and J. Xu, “Charge-transfer theory of surface enhanced Raman spectroscopy: Herzberg–Teller contributions,” J. Chem. Phys. 84(8), 4174–4180 (1986). [CrossRef]

4.

F. Le, D. W. Brandl, Y. A. Urzhumov, H. Wang, J. Kundu, N. J. Halas, J. Aizpurua, and P. Nordlander, “Metallic nanoparticle arrays: a common substrate for both surface-enhanced Raman scattering and surface-enhanced infrared absorption,” ACS Nano 2(4), 707–718 (2008). [CrossRef] [PubMed]

5.

T. R. Jensen, M. L. Duval, K. L. Kelly, A. A. Lazarides, G. C. Schatz, and R. P. Van Duyne, “Nanosphere lithography: effect of the external dielectric medium on the surface plasmon resonance spectrum of a periodic array of silver nanoparticles,” J. Phys. Chem. B 103(45), 9846–9853 (1999). [CrossRef]

6.

V. L. Schlegel and T. M. Cotton, “Silver-island films as substrates for enhanced Raman scattering: effect of deposition rate on intensity,” Anal. Chem. 63(3), 241–247 (1991). [CrossRef] [PubMed]

7.

J. T. Bahns, F. Yan, D. Qiu, R. Wang, and L. Chen, “Hole-enhanced Raman scattering,” Appl. Spectrosc. 60(9), 989–993 (2006). [CrossRef] [PubMed]

8.

K. Imura, H. Okamoto, M. K. Hossain, and M. Kitajima, “Visualization of localized intense optical fields in single gold-nanoparticle assemblies and ultrasensitive Raman active sites,” Nano Lett. 6(10), 2173–2176 (2006). [CrossRef] [PubMed]

9.

P. Hildebrandt and M. Stockburger, “Surface-enhanced resonance Raman spectroscopy of rhodamine 6G adsorbed on colloidal silver,” J. Phys. Chem. 88(24), 5935–5944 (1984). [CrossRef]

10.

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]

11.

K. Kneipp, H. Kneipp, R. Manoharan, E. B. Hanlon, I. Itzkan, R. R. Dasari, and M. S. Feld, “Extremely large enhancement factors in surface-enhanced Raman scattering for molecules on colloidal gold clusters,” Appl. Spectrosc. 52(12), 1493–1497 (1998). [CrossRef]

12.

A. M. Michaels, M. Nirmal, and L. E. Brus, “Surface enhanced Raman spectroscopy of individual rhodamine 6G molecules on large Ag nanocrystals,” J. Am. Chem. Soc. 121(43), 9932–9939 (1999). [CrossRef]

13.

M. Nirmal, B. O. Dabbousi, M. G. Bawendi, J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Brus, “Fluorescence intermittency in single cadmium selenide nanocrystals,” Nature 383(6603), 802–804 (1996). [CrossRef]

14.

Th. Basché, S. Kummer, and C. Bräuchle, “Direct spectroscopic observation of quantum jumps of a single molecule,” Nature 373(6510), 132–134 (1995). [CrossRef]

15.

S. R. Emory, R. A. Jensen, T. Wenda, M. Han, and S. Nie, “Re-examining the origins of spectral blinking in single-molecule and single-nanoparticle SERS,” Faraday Discuss. 132, 249–259, discussion 309–319 (2006). [CrossRef] [PubMed]

16.

A. M. Michaels, J. Jiang, and L. Brus, “Ag nanocrystal junctions as the site for surface-enhanced Raman scattering of single rhodamine 6G molecules,” J. Phys. Chem. B 104(50), 11965–11971 (2000). [CrossRef]

17.

A. L. Efros and M. Rosen, “Random telegraph signal in the photoluminescence intensity of a single quantum dot,” Phys. Rev. Lett. 78(6), 1110–1113 (1997).

18.

K. A. Bosnick, J. Jiang, and L. E. Brus, “Fluctuations and local symmetry in single-molecule rhodamine 6G Raman scattering on silver nanocrystal aggregates,” J. Phys. Chem. B 106(33), 8096–8099 (2002). [CrossRef]

19.

Z. Wang and L. J. Rothberg, “Origins of blinking in single-molecule Raman spectroscopy,” J. Phys. Chem. B 109(8), 3387–3391 (2005). [CrossRef] [PubMed]

20.

Y. Maruyama, M. Ishikawa, and M. Futamata, “Thermal activation of blinking in SERS signal,” J. Phys. Chem. B 108(2), 673–678 (2004). [CrossRef]

21.

G. Baffou, C. Girard, and R. Quidant, “Mapping heat origin in plasmonic structures,” Phys. Rev. Lett. 104(13), 136805 (2010). [CrossRef] [PubMed]

22.

H. H. Richardson, M. T. Carlson, P. J. Tandler, P. Hernandez, and A. O. Govorov, “Experimental and theoretical studies of light-to-heat conversion and collective heating effects in metal nanoparticle solutions,” Nano Lett. 9(3), 1139–1146 (2009). [CrossRef] [PubMed]

23.

P. T. Leung, M. H. Hider, and E. J. Sanchez, “Surface-enhanced Raman scattering at elevated temperatures,” Phys. Rev. B Condens. Matter 53(19), 12659–12662 (1996). [CrossRef] [PubMed]

24.

L. Xu and Y. Fang, “Temperature-induced effect on surface-enhanced Raman scattering of p, m-hydroxybenzoic acid on silver nanoparticles,” Spectroscopy 18, 26–31 (2003).

25.

A. M. Gobin, M. H. Lee, N. J. Halas, W. D. James, R. A. Drezek, and J. L. West, “Near-infrared resonant nanoshells for combined optical imaging and photothermal cancer therapy,” Nano Lett. 7(7), 1929–1934 (2007). [CrossRef] [PubMed]

26.

R. C. Maher, L. F. Cohen, P. Etchegoin, H. J. N. Hartigan, R. J. C. Brown, and M. J. T. Milton, “Stokes/anti-Stokes anomalies under surface enhanced Raman scattering conditions,” J. Chem. Phys. 120(24), 11746–11753 (2004). [CrossRef] [PubMed]

27.

G. Baffou, R. Quidant, and F. J. García de Abajo, “Nanoscale control of optical heating in complex plasmonic systems,” ACS Nano 4(2), 709–716 (2010). [CrossRef] [PubMed]

28.

R. Franz and G. Wiedemann, “Ueber die wärme-leitungsfähigkeit der metalle,” Annalen der Physik 165(8), 497–531 (1853). [CrossRef]

29.

N. W. Ashcroft and N. D. Mermin, Solid State Physics, (Harcourt Brace College Publishers, 1976), Chap. 1.

30.

K. Linko and K. Hynynen, “Erythrocyte damage caused by the Haemotherm microwave blood warmer,” Acta Anaesthesiol. Scand. 23(4), 320–328 (1979). [CrossRef] [PubMed]

31.

M. I. Hafez, S. Zhou, R. R. H. Coombs, and I. D. McCarthy, “The effect of irrigation on peak temperatures in nerve root, dura, and intervertebral disc during laser-assisted foraminoplasty,” Lasers Surg. Med. 29(1), 33–37 (2001). [CrossRef] [PubMed]

32.

S. W. Kuo and F. C. Chang, “Studies of miscibility behavior and hydrogen bonding in blends of poly(vinylphenol) and poly(vinylpyrrolidone),” Macromolecules 34(15), 5224–5228 (2001). [CrossRef]

33.

J. R. Wünsch, “Polystyrene-synthesis, production and applications,” Rapra Review Reports 10, 15 (2000).

34.

D. E. Johnson, “Pyrolysis of benzenethiol,” Fuel 66(2), 255–260 (1987). [CrossRef]

35.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]

36.

R. Gordon, “Light in a subwavelength slit in a metal: propagation and reflection,” Phys. Rev. B 73(15), 153405 (2006). [CrossRef]

37.

L. R. Hirsch, R. J. Stafford, J. A. Bankson, S. R. Sershen, B. Rivera, R. E. Price, J. D. Hazle, N. J. Halas, and J. L. West, “Nanoshell-mediated near-infrared thermal therapy of tumors under magnetic resonance guidance,” Proc. Natl. Acad. Sci. U.S.A. 100(23), 13549–13554 (2003). [CrossRef] [PubMed]

OCIS Codes
(190.4870) Nonlinear optics : Photothermal effects
(240.6680) Optics at surfaces : Surface plasmons
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Plasmonics

History
Original Manuscript: July 22, 2013
Revised Manuscript: September 14, 2013
Manuscript Accepted: September 29, 2013
Published: October 14, 2013

Citation
Chao-Yi Tai and Wen-Hsiang Yu, "The contribution of nonlocal electro-opto-thermal interaction to single molecule nonlinear Raman enhancement," Opt. Express 21, 25026-25034 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-21-25026


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References

  1. M. Fleischmann, P. J. Hendra, and A. J. McQuillan, “Raman spectra of pyridine adsorbed at a silver electrode,” Chem. Phys. Lett.26(2), 163–166 (1974). [CrossRef]
  2. S. L. McCall and P. M. Platzman, “Raman scattering from chemisorbed molecules at surfaces,” Phys. Rev. B22(4), 1660–1662 (1980). [CrossRef]
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