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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 22 — Nov. 4, 2013
  • pp: 26483–26492
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Molecular fluorescence in the vicinity of a charged metallic nanoparticle

H. Y. Chung, P. T. Leung, and D. P. Tsai  »View Author Affiliations


Optics Express, Vol. 21, Issue 22, pp. 26483-26492 (2013)
http://dx.doi.org/10.1364/OE.21.026483


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Abstract

The modified fluorescence properties of a molecule in the vicinity of a metallic nanoparticle are further studied accounting for the possible existence of extraneous charges on the particle surface. This is achieved via a generalization of the previous theory of Bohren and Hunt for light scattering from a charged sphere, with the results applied to the calculation of the various decay rates and fluorescence yield of the admolecule. Numerical results show that while charge effects will in general blue-shift all the plasmonic resonances of the metal particle, both the quantum yield and the fluorescence yield can be increased at emission frequencies close to that of the surface plasmon resonance of the particle due to the suppression of the nonradiative decay rate. This provides a possibility of further enhancing the particle-induced molecular fluorescence via the addition of surface charge to the metal particle.

© 2013 Optical Society of America

1. Introduction

Since the first discovery of surface-enhanced Raman scattering (SERS) four decades ago and the subsequent understanding of the phenomenon to be largely caused by the resonant excitation of the surface plasmons in metallic nano structures, it has been widely recognized that such plasmonic enhancement can be applied to almost any molecular spectroscopy [1

1. For a good recent review on this topic, see, e.g.H. Chen, G. C. Schatz, and M. A. Ratner, “Experimental and theoretical studies of plasmon-molecule interactions,” Rep. Prog. Phys. 75(9), 096402 (2012). [CrossRef] [PubMed]

]. In particular, the modified fluorescence properties of molecules in the vicinity of a metallic nanoparticle (MNP) have been actively studied by many researchers in recent years [2

2. F. Tam, G. P. Goodrich, B. R. Johnson, and N. J. Halas, “Plasmonic enhancement of molecular fluorescence,” Nano Lett. 7(2), 496–501 (2007). [CrossRef] [PubMed]

4

4. G. P. Acuna, M. Bucher, I. H. Stein, C. Steinhauer, A. Kuzyk, P. Holzmeister, R. Schreiber, A. Moroz, F. D. Stefani, T. Liedl, F. C. Simmel, and P. Tinnefeld, “Distance dependence of single-fluorophore quenching by gold nanoparticles studied on DNA origami,” ACS Nano 6(4), 3189–3195 (2012). [CrossRef] [PubMed]

]. It has been established that depending on many factors such as the emission frequency, the orientation of the emitting dipole, the distance of the molecule from the MNP, the geometry and material of the MNP, etc., the molecule fluorescence can both be enhanced and suppressed in the presence of the MNP. In general, for a radial-oriented emitting molecular dipole at a certain optimal distance from the MNP, fluorescence can be significantly enhanced when the emission frequency is close to the dipole surface plasmon resonance of the particle.

Theoretically, both quantum and classical theories have been developed in the literature [1

1. For a good recent review on this topic, see, e.g.H. Chen, G. C. Schatz, and M. A. Ratner, “Experimental and theoretical studies of plasmon-molecule interactions,” Rep. Prog. Phys. 75(9), 096402 (2012). [CrossRef] [PubMed]

]. In the quantum approach, density functional theory is often applied to treat both the molecule and the MNP; whereas for MNP of greater size or in case of molecule being far from the MNP, classical electrodynamics can also be applied which models the system as an oscillating dipole interacting with a metallic sphere which is characterized by a dielectric function. In this latter approach, further simplifications can be obtained via the long wavelength approximation when the characteristic dimensions are much smaller than the optical wave length. In addition, hybrid quantum/classical formulations are also available such as that adopting the multi-scale Maxwell-Schrodinger equation [1

1. For a good recent review on this topic, see, e.g.H. Chen, G. C. Schatz, and M. A. Ratner, “Experimental and theoretical studies of plasmon-molecule interactions,” Rep. Prog. Phys. 75(9), 096402 (2012). [CrossRef] [PubMed]

, 5

5. C. Arntsen, K. Lopata, M. R. Wall, L. Bartell, and D. Neuhauser, “Modeling molecular effects on plasmon transport: Silver nanoparticles with tartrazine,” J. Chem. Phys. 134(8), 084101 (2011). [CrossRef] [PubMed]

], and that introducing quantum effects of the MNP through a nonlocal dielectric response function [6

6. See, e.g.,H. Y. Chung, P. T. Leung, and D. P. Tsai, “Fluorescence characteristics of a molecule in the vicinity of a plasmonic nanomatryoska: nonlocal optical effects,” Opt. Commun. 285(8), 2207–2211 (2012). [CrossRef]

]. Moreover, all the existing studies so far have been limited to neutral MNP’s and hence the possible effects due to the presence of a net extraneous charge on the particle have seldom been investigated in this context when a light source (i.e. the fluorescing molecule) is in close proximity. Nevertheless, the classic Lorenz-Mie scattering theory has indeed been generalized to allow for the presence of extraneous charge by Bohren and Hunt [7

7. C. F. Bohren and A. J. Hunt, “Scattering of electromagnetic waves by a charged sphere,” Can. J. Phys. 55(21), 1930–1935 (1977). [CrossRef]

] and far-field scattering from such a sphere has been studied actively in the literature in recent years [8

8. J. Klačka and M. Kocifaj, “Scattering of electromagnetic waves by charged spheres and some physical consequences,” J. Quant. Spectrosc. Radiat. Transf. 106(1-3), 170–183 (2007). [CrossRef]

11

11. R. L. Heinisch, F. X. Bronold, and H. Fehske, “Mie scattering by a charged dielectric particle,” Phys. Rev. Lett. 109(24), 243903 (2012). [CrossRef] [PubMed]

]. In addition, although to a lesser extent, experimental study on light scattering from charged particle has also been carried out with noticeable difference observed from millimeter-wave scattered by neutral versus charged water droplets [12

12. A. Heifetz, H. T. Chien, S. Liao, N. Gopalsami, and A. C. Raptis, “Millimeter-wave scattering from neutral and charged water droplets,” J. Quant. Spectrosc. Radiat. Transf. 111(17–18), 2550–2557 (2010). [CrossRef]

]; with the observed results being consistent with the generalized theory [7

7. C. F. Bohren and A. J. Hunt, “Scattering of electromagnetic waves by a charged sphere,” Can. J. Phys. 55(21), 1930–1935 (1977). [CrossRef]

].

In a recent study [13

13. H. Y. Chung, P. T. Leung, and D. P. Tsai, “Effects of extraneous surface charges on the enhanced Raman scattering from metallic nanoparticles,” J. Chem. Phys. 138(22), 224101 (2013). [CrossRef] [PubMed]

], we have taken a first step in applying this extended Lorenz-Mie theory [7

7. C. F. Bohren and A. J. Hunt, “Scattering of electromagnetic waves by a charged sphere,” Can. J. Phys. 55(21), 1930–1935 (1977). [CrossRef]

] to investigate the extraneous charge effects on MNP-enhanced molecular spectroscopy. In particular, we have studied the effects on SERS and have concluded that such effects will in general lead to blue-shifted resonances [14

14. J. Rostalski and M. Quinten, “Effect of a surface charge on the halfwidth and peak position of cluster plasmons in colloidal metal particles,” Colloid Polym. Sci. 274(7), 648–653 (1996). [CrossRef]

] and greater enhancements. Moreover, our theory was not a fully-electrodynamic one due to the complexity of the SERS problem which involves the modeling of the scattering of incident plane waves from a dipole-sphere system. We were then limited to merging the electrodynamic theory of Bohren and Hunt [7

7. C. F. Bohren and A. J. Hunt, “Scattering of electromagnetic waves by a charged sphere,” Can. J. Phys. 55(21), 1930–1935 (1977). [CrossRef]

] with the static model of Gersten and Nitzan [15

15. J. Gersten and A. Nitzan, “Electromagnetic theory of enhanced Raman scattering by molecules adsorbed on rough surfaces,” J. Chem. Phys. 73(7), 3023–3037 (1980). [CrossRef]

], with improvement of the model’s accuracy relative to a full electrodynamic approach via implementation of the modified long wavelength approximation [16

16. M. Meier and A. Wokaun, “Enhanced fields on large metal particles: dynamic depolarization,” Opt. Lett. 8(11), 581–583 (1983). [CrossRef] [PubMed]

].

It is the purpose of this paper to launch our spectroscopic study on another very important process: molecular fluorescence, which for applications is no less significant than SERS. In particular, we shall study the charge effects on the MNP-modified fluorescence for molecules in close proximity to the particle. Since in fluorescence, unlike Raman scattering, the emission process is completely independent of the initial absorption (i.e. both photons are not linked to each other in a coherent and instantaneous way) [17

17. P. G. Etchegoin and E. C. Le Ru, Surface Enhanced Raman Spectrocopy: Analytical, Biophysical and Life Science Applications (edited by S. Schlucker), pp 1–37 (Wiley-VCH, 2011).

], we shall see that the modeling for the MNP-modified fluorescence process is simpler than that for SERS and we can also implement a fully-electrodynamic model. However, in order to incorporate the charge effects, we have to first extend the theory of Bohren and Hunt [7

7. C. F. Bohren and A. J. Hunt, “Scattering of electromagnetic waves by a charged sphere,” Can. J. Phys. 55(21), 1930–1935 (1977). [CrossRef]

] to have the incident plane wave replaced by a localized source in the form of an emitting dipole in the proximity of the charged sphere. For the neutral sphere case, this extension has been accomplished by Ruppin [18

18. R. Ruppin, “Decay of an excited molecule near a small metal sphere,” J. Chem. Phys. 76 (4), 1681–1684 (1982). Note that the first work that studied the scattering of dipole radiation from a sphere was in B. van der Pol and H. Bremmer, ” The diffraction of electromagnetic waves from an electrical point source round a finitely conducting sphere, with applications to radiotelegraphy and the theory of the rainbow. Part I,” Philos. Mag. 24(159), 141–176 (1937) (however, Ruppin was the first to apply this theory to study the problem of molecular fluorescence near a sphere.).

] in his study of molecular decay rates near a spherical particle. In the following, we shall first extend Ruppin’s theory to allow for the presence of surface charge on the sphere, in a way parallel to that of Bohren and Hunt [7

7. C. F. Bohren and A. J. Hunt, “Scattering of electromagnetic waves by a charged sphere,” Can. J. Phys. 55(21), 1930–1935 (1977). [CrossRef]

] in their generalization of the Lorenz-Mie theory to charged sphere. Following this we shall apply our extended Ruppin theory to the study of the modifications of molecular fluorescence in the vicinity of a charged MNP.

2. Theory

2.1 Generalization of Ruppin’s theory to a charged sphere

In Ruppin’s theory, the full electrodynamics of the scattering of a harmonically emitting dipole from a sphere has been worked out with the scattered and transmitted fields (into the sphere) expanded in terms of the vector spherical waves and the well-known Mie coefficients [18

18. R. Ruppin, “Decay of an excited molecule near a small metal sphere,” J. Chem. Phys. 76 (4), 1681–1684 (1982). Note that the first work that studied the scattering of dipole radiation from a sphere was in B. van der Pol and H. Bremmer, ” The diffraction of electromagnetic waves from an electrical point source round a finitely conducting sphere, with applications to radiotelegraphy and the theory of the rainbow. Part I,” Philos. Mag. 24(159), 141–176 (1937) (however, Ruppin was the first to apply this theory to study the problem of molecular fluorescence near a sphere.).

]. In deriving his solutions, Ruppin had applied the ordinary boundary conditions with the tangential components of both the electric and magnetic fields to be continuous:
n×(E1E2)=0,
(1)
and

n×(H1H2)=0.
(2)

However, in the presence of extraneous surface charges on the sphere, shown in Fig. 1
Fig. 1 Schematic of the dipole-sphere system with extraneous surface charges.
, the condition in Eq. (2) must be modified to account for the free current (K) arising from the interaction of these charges with the external field:

n×(H1H2)=K.
(3)

To study how this will modify Ruppin’s results, it turns out that it is not necessary to solve the boundary value problem with a dipole source starting from the beginning, since the same problem with an incident plane wave has already been worked out in the literature [7

7. C. F. Bohren and A. J. Hunt, “Scattering of electromagnetic waves by a charged sphere,” Can. J. Phys. 55(21), 1930–1935 (1977). [CrossRef]

].

In their pioneering work, Bohren and Hunt had extended the classic Mie theory for an incident plane wave with the boundary conditions (1) and (3) implemented and correlated by introducing a parameter known as surface conductivity via Ohm’s law: K=σSE1t=σSE2t. The results from this generalized Lorenz-Mie theory [7

7. C. F. Bohren and A. J. Hunt, “Scattering of electromagnetic waves by a charged sphere,” Can. J. Phys. 55(21), 1930–1935 (1977). [CrossRef]

] show that all one has to do for the charged sphere scattering is to replace the various Mie coefficients to include the contributions from this surface conductivity. For example, the standard Mie scattering coefficients will now take the following form [7

7. C. F. Bohren and A. J. Hunt, “Scattering of electromagnetic waves by a charged sphere,” Can. J. Phys. 55(21), 1930–1935 (1977). [CrossRef]

]:
an=ψn(x)ψn(mx)ψn(x)[mψn(mx)iτψn(mx)]ξ(x)ψn(mx)ξn(x)[mψn(mx)iτψn(mx)],
(4)
bn=ψn(x)ψn(mx)ψn(x)[mψn(mx)+iτψn(mx)]ξn(x)ψn(mx)ξ(x)[mψn(mx)+iτψn(mx)],
(5)
where ψn and ξn are the Riccati-Bessel functions, x=ka is the size parameter of the sphere, m=ε is the refraction index of the (nonmagnetic) sphere, and τ=4πσS(ω)/c with c the speed of light.

Now the observation is that in Ruppin’s original solution to the dipole-sphere problem, the fields are all expanded in terms of the vector spherical waves modulated by a dipole source term. When the conditions (1) and (2) are matched across the sphere boundary, the expansion coefficients are found to be the same as those in the original plane wave Lorenz-Mie theory [18

18. R. Ruppin, “Decay of an excited molecule near a small metal sphere,” J. Chem. Phys. 76 (4), 1681–1684 (1982). Note that the first work that studied the scattering of dipole radiation from a sphere was in B. van der Pol and H. Bremmer, ” The diffraction of electromagnetic waves from an electrical point source round a finitely conducting sphere, with applications to radiotelegraphy and the theory of the rainbow. Part I,” Philos. Mag. 24(159), 141–176 (1937) (however, Ruppin was the first to apply this theory to study the problem of molecular fluorescence near a sphere.).

]. Hence if one were to generalize the theory of Bohren and Hunt [7

7. C. F. Bohren and A. J. Hunt, “Scattering of electromagnetic waves by a charged sphere,” Can. J. Phys. 55(21), 1930–1935 (1977). [CrossRef]

] to the case of an emitting dipole interacting with a charged sphere, one can imagine that the same algorithm as Ruppin’s can simply be applied leading to identical results as in Ruppin’s theory with the standard Mie coefficients replaced by those in Eqs. (4) and (5) to account for the effects of the surface charges. We thus in the following simply apply Ruppin’s results together with Eqs. (4) and (5) to study the charge effects on molecular fluorescence near a non-neutral MNP.

2.2 Calculation of fluorescence characteristics

As explained above, fluorescence is governed by two relatively independent processes (absorption and emission), one can thus introduce a MNP-modified fluorescence rate as follows [19

19. P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96(11), 113002 (2006). [CrossRef] [PubMed]

]:
γF=|EE0|2(γrγr+γnr),
(6)
where |E/E0|2 is the field enhancement ratio and
Y=γrγr+γnr
(7)
is the quantum yield of the molecule in the presence of the MNP. Note that |E/E0|2 also describes the excitation probability of the molecule in the absence of saturation of fluorescence, and Yindicates the probability of receiving the emitted photons in the far field (radiation efficiency), where γr and γnr are the radiatve and nonradiative decay rates, respectively.

Since for a dipole-sphere system, the quantities in Eqs. (6) and (7) have all been worked out in the literature starting from Ruppin’s work [18

18. R. Ruppin, “Decay of an excited molecule near a small metal sphere,” J. Chem. Phys. 76 (4), 1681–1684 (1982). Note that the first work that studied the scattering of dipole radiation from a sphere was in B. van der Pol and H. Bremmer, ” The diffraction of electromagnetic waves from an electrical point source round a finitely conducting sphere, with applications to radiotelegraphy and the theory of the rainbow. Part I,” Philos. Mag. 24(159), 141–176 (1937) (however, Ruppin was the first to apply this theory to study the problem of molecular fluorescence near a sphere.).

] for an uncharged sphere, we simply collect some of these in the following [18

18. R. Ruppin, “Decay of an excited molecule near a small metal sphere,” J. Chem. Phys. 76 (4), 1681–1684 (1982). Note that the first work that studied the scattering of dipole radiation from a sphere was in B. van der Pol and H. Bremmer, ” The diffraction of electromagnetic waves from an electrical point source round a finitely conducting sphere, with applications to radiotelegraphy and the theory of the rainbow. Part I,” Philos. Mag. 24(159), 141–176 (1937) (however, Ruppin was the first to apply this theory to study the problem of molecular fluorescence near a sphere.).

, 20

20. Y. S. Kim, P. T. Leung, and T. F. George, “Classical decay rates for molecules in the presence of a spherical surface: A complete treatment,” Surf. Sci. 195(1–2), 1–14 (1988). [CrossRef]

, 21

21. H. Y. Chung, P. T. Leung, and D. P. Tsai, “Equivalence between the mechanical model and energy-transfer theory for the classical decay rates of molecules near a spherical particle,” J. Chem. Phys. 136(18), 184106 (2012). [CrossRef] [PubMed]

], where we have assumed the molecular intrinsic quantum yield to be unity for simplicity [19

19. P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96(11), 113002 (2006). [CrossRef] [PubMed]

]. For a radial oriented dipole, we have:
EE0=1+n=1in+1bn(2n+1)Pn1(0)hn(xd)xd,
(8)
γ=1+32Ren=1n(n+1)(2n+1)bn(hn(xd)xd)2,
(9)
γr=32n=1n(n+1)(2n+1)|jn(xd)+bnhn(xd)|2xd2,
(10)
and
γnr=3x2xd2n=1n(n+1)|βnhn(xd)|2[(n+1)In1+nIn+1],
(11)
where γ=γr+γnr is the total decay rate (all normalized to the free decay value), which can also be obtained from the mechanical oscillator model in linear systems [21

21. H. Y. Chung, P. T. Leung, and D. P. Tsai, “Equivalence between the mechanical model and energy-transfer theory for the classical decay rates of molecules near a spherical particle,” J. Chem. Phys. 136(18), 184106 (2012). [CrossRef] [PubMed]

]. The other quantities including the special functions and Mie coefficients are in obvious notations with xd=kd and d being the distance of the molecule from the sphere center [18

18. R. Ruppin, “Decay of an excited molecule near a small metal sphere,” J. Chem. Phys. 76 (4), 1681–1684 (1982). Note that the first work that studied the scattering of dipole radiation from a sphere was in B. van der Pol and H. Bremmer, ” The diffraction of electromagnetic waves from an electrical point source round a finitely conducting sphere, with applications to radiotelegraphy and the theory of the rainbow. Part I,” Philos. Mag. 24(159), 141–176 (1937) (however, Ruppin was the first to apply this theory to study the problem of molecular fluorescence near a sphere.).

]. Note that the Mie coefficient bn is simply the one in Eq. (5) without the surface charge term, and In is a result from an integral obtained previously in the form In=Im[x1*jn1*(x1)jn(x1)] with x1=εka [21

21. H. Y. Chung, P. T. Leung, and D. P. Tsai, “Equivalence between the mechanical model and energy-transfer theory for the classical decay rates of molecules near a spherical particle,” J. Chem. Phys. 136(18), 184106 (2012). [CrossRef] [PubMed]

].

Similarly, for a tangential oscillating dipole, we have:
EE0=1+n=1in2n+1n(n+1){anP'n(0)hn(xd)+ibnPn1(0)[xdhn(xd)]xd},
(12)
γ=1+34Ren=1(2n+1)[anhn2(xd)+bn(ξ(xd)xd)2],
(13)
γr=34n=1(2n+1){|jn(xd)+anhn(xd)|2+1xd2|ψn(xd)+bnξn(xd)|2},
(14)
and
γnr=3x4n=1{(2n+1)|αnhn(xd)|2In+|βnξn(xd)xd|2[(n+1)In1+nIn+1]},
(15)
where again γ=γr+γnr is the total decay rate [21

21. H. Y. Chung, P. T. Leung, and D. P. Tsai, “Equivalence between the mechanical model and energy-transfer theory for the classical decay rates of molecules near a spherical particle,” J. Chem. Phys. 136(18), 184106 (2012). [CrossRef] [PubMed]

].

3. Numerical results

We have performed some numerical studies of the charge effects on the MNP-modified fluorescence for a molecule in the vicinity of a silver sphere with the same dielectric function given in [13

13. H. Y. Chung, P. T. Leung, and D. P. Tsai, “Effects of extraneous surface charges on the enhanced Raman scattering from metallic nanoparticles,” J. Chem. Phys. 138(22), 224101 (2013). [CrossRef] [PubMed]

], in which a fit to the Drude function with limitation of the mean free path is adopted in the following way:
ε=εAg(ω)=1ωp2ω(ω+iΓ),
(16)
where ωp=1.36×1016s1 and Γ=ΓB+AvF/a with ΓB=2.56×1013s1, vF=1.38×108cm/s and the coefficient A in the term accounting for surface damping is simply taken as unity. In order to manifest these effects, we have considered relatively large values of surface charge density and small MNP size of 5 nm radius, though our formalism is fully dynamic and applicable to particles of any size. We expect the qualitative feature of the effects will remain if realistic values of the charge turn out to be smaller, and also for larger MNP sizes. The molecule is located at 1 nm from the MNP surface for all spectral calculations.

We first study the effects on the various decay rates of the molecule. Figure 2
Fig. 2 The spectrum of the normalized total decay rate as a function of the emission frequency of the molecule with (a) radial and (b) tangential orientation for the molecule at a distance of 1 nm from a silver sphere of radius 5 nm. The extraneous surface charges on the silver sphere are q0=0, q1=1.67×1016C, and q2=5×1016C as indicated in the figure.
shows the normalized total decay rate as a function of emission frequency. It is interesting to observe that for the neutral (q0) case, the strongest induced decay emerges at higher multipole (=3) SP resonance instead of the dipole SP resonance (ω/ωp~0.57) due to the dominance of nonradiative transfer at such close molecule-sphere distance (see below). As extraneous charge is added to the sphere, the total molecular decay is in general suppressed with the resonance blue-shifted (due to an effective increase of free charge density and hence the plasmon frequency [13

13. H. Y. Chung, P. T. Leung, and D. P. Tsai, “Effects of extraneous surface charges on the enhanced Raman scattering from metallic nanoparticles,” J. Chem. Phys. 138(22), 224101 (2013). [CrossRef] [PubMed]

, 14

14. J. Rostalski and M. Quinten, “Effect of a surface charge on the halfwidth and peak position of cluster plasmons in colloidal metal particles,” Colloid Polym. Sci. 274(7), 648–653 (1996). [CrossRef]

]), and a larger number of multipolar resonance being manifested. In addition, we see that the decay rates for tangential dipoles (Fig. 2(b)) are smaller than those for radial dipoles (Fig. 2(a)) as expected, even in the presence of extraneous charges on the MNP.

In order to understand the results better, we have decomposed the total decay into radiative and nonradiative rates and plotted in Figs. 3
Fig. 3 Same as Fig. 2, but for the normalized radiative decay rate.
and 4
Fig. 4 Same as Fig. 2, but for the normalized nonradiative rate.
, respectively. Figure 3 shows the expected result with the enhanced radiative rate due exclusively to the dipole surface plasmon resonance of the MNP. Moreover, while the charge-induced blue shifted resonances and the molecular orientation effects are as observed in the total decay rate, it is seen that the extraneous charge will now increase the radiative rate at resonance due to greater effective oscillating dipole moment for the MNP. This will be significant for enhancement of fluorescence as we shall see in the following.

To have more definitive conclusion about the overall effects on the fluorescence of the molecule, we plot in Figs. 5
Fig. 5 Same as Fig. 2, but for the quantum yield.
and 6
Fig. 6 Same as Fig. 2, but for the normalized fluorescence rate.
the quantum yield (Eq. (7)) and fluorescence rate (Eq. (6)) of the molecule in the presence of a charged MNP. Figure 5 shows that despite the rather different results for the various decay rates for the two different oriented molecules, the overall quantum yields are very similar and rather small (a few percent) for such a close molecule-MNP distance due to the dominance of the nonradiative rates. However, the addition of charges to the MNP will mostly lead to an increase of the yield (except for a small range of frequency due to the blue-shift effect). This is expected since we have already demonstrated in the above the decrease in nonradiative and increase in radiate rates due to charge effects, together with the fact that the radiative rate is much smaller than that of the nonradiative. Such charge-induced enhancement of MNP modified fluorescence is even more apparent from Fig. 6 where we have plotted the fluorescence rates, in which the enhancement at the dipole surface plasmon resonance is definite with the increase of surface charge of the MNP. More interestingly, we see that in spite of very close quantum yield values for the two different oriented molecules shown in Fig. 5, the enhanced fluorescence rate is several times greater in the case with radial molecular dipoles. This reveals that the enhanced field in the radial dipole case must be much stronger which is expected if one simply compares the relative orientations of the image dipoles between the radial and the tangential molecules, where in one case the image is parallel to and in the other case anti-aligned with the source (molecular) dipole. In addition, it is worth noting that such MNP enhanced fluorescence is in general much more modest as compared to SERS [13

13. H. Y. Chung, P. T. Leung, and D. P. Tsai, “Effects of extraneous surface charges on the enhanced Raman scattering from metallic nanoparticles,” J. Chem. Phys. 138(22), 224101 (2013). [CrossRef] [PubMed]

] as is well explained in the literature [23

23. G. Sun, J. B. Khurgin, and D. P. Tsai, “Comparative analysis of photoluminescence and Raman enhancement by metal nanoparticles,” Opt. Lett. 37(9), 1583–1585 (2012). [CrossRef] [PubMed]

].

Finally, we study the dependence of the enhanced fluorescence on the molecule-MNP distance d. It has been established that due to the competing nature of the field enhancement and the nonradiative decay as a function of this distance, there exists an optimal location for the molecule to experience the greatest overall fluorescence enhancement [19

19. P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96(11), 113002 (2006). [CrossRef] [PubMed]

]. This happens since at very close distances, the nonradiative transfer is too large and at far distances, the enhanced field becomes too weak. In Fig. 7
Fig. 7 Normalized fluorescence rate as a function of distance from the silver surface. The molecule is along (a) radial and (b) tangential directions. The emission frequencies are set at each of the dipole resonance for the cases q0, q1, and q2 with values equal to 0.57ωp, 0.58ωp, and 0.58ωp, respectively. Other parameters are the same as in Fig. 2.
, we have plotted the fluorescence rate (Eq. (1)) as a function of d for the three differently charged MNP’s at fixed emission frequencies equal to the respective dipole surface plasmon resonance for each sphere (Fig. 6). The results show that while for such a small MNP (5 nm radius) the optimal distances are all within 1 nm, this distance decreases as the charge of the MNP is increased. This is again conceivable as a consequence of the decrease in nonradiative rate due to the charge effects, so that one does not need to go too far from the sphere to have this rate significantly decreased. Furthermore, one sees that this optimal distance is not sensitive to the different orientations of the molecular dipoles.

4. Conclusion

Acknowledgments

The authors gratefully acknowledge the financial support of the National Science Council of Taiwan (NSC 102-2745-M-002-005-ASP, 102-2911-I-002-505, 101-2911-I-002-107, 100-2923-M-002-007-MY3, 101-2112-M-002-023-, 100-2112-M-019 −003 -MY3). They are also grateful to National Center for Theoretical Sciences, Taipei Office, Molecular Imaging Center of National Taiwan University, National Center for High-Performance Computing, Taiwan, and Research Center for Applied Sciences, Academia Sinica, Taiwan for their support.

References and links

1.

For a good recent review on this topic, see, e.g.H. Chen, G. C. Schatz, and M. A. Ratner, “Experimental and theoretical studies of plasmon-molecule interactions,” Rep. Prog. Phys. 75(9), 096402 (2012). [CrossRef] [PubMed]

2.

F. Tam, G. P. Goodrich, B. R. Johnson, and N. J. Halas, “Plasmonic enhancement of molecular fluorescence,” Nano Lett. 7(2), 496–501 (2007). [CrossRef] [PubMed]

3.

Y. Fu, J. Zhang, and J. R. Lakowicz, “Plasmonic enhancement of single-molecule fluorescence near a silver nanoparticle,” J. Fluoresc. 17(6), 811–816 (2007). [CrossRef] [PubMed]

4.

G. P. Acuna, M. Bucher, I. H. Stein, C. Steinhauer, A. Kuzyk, P. Holzmeister, R. Schreiber, A. Moroz, F. D. Stefani, T. Liedl, F. C. Simmel, and P. Tinnefeld, “Distance dependence of single-fluorophore quenching by gold nanoparticles studied on DNA origami,” ACS Nano 6(4), 3189–3195 (2012). [CrossRef] [PubMed]

5.

C. Arntsen, K. Lopata, M. R. Wall, L. Bartell, and D. Neuhauser, “Modeling molecular effects on plasmon transport: Silver nanoparticles with tartrazine,” J. Chem. Phys. 134(8), 084101 (2011). [CrossRef] [PubMed]

6.

See, e.g.,H. Y. Chung, P. T. Leung, and D. P. Tsai, “Fluorescence characteristics of a molecule in the vicinity of a plasmonic nanomatryoska: nonlocal optical effects,” Opt. Commun. 285(8), 2207–2211 (2012). [CrossRef]

7.

C. F. Bohren and A. J. Hunt, “Scattering of electromagnetic waves by a charged sphere,” Can. J. Phys. 55(21), 1930–1935 (1977). [CrossRef]

8.

J. Klačka and M. Kocifaj, “Scattering of electromagnetic waves by charged spheres and some physical consequences,” J. Quant. Spectrosc. Radiat. Transf. 106(1-3), 170–183 (2007). [CrossRef]

9.

E. Rosenkrantz and S. Arnon, “Enhanced absorption of light by charged nanoparticles,” Opt. Lett. 35(8), 1178–1180 (2010). [CrossRef] [PubMed]

10.

M. Kocifaj and J. Klačka, “Scattering of electromagnetic waves by charged spheres: near-field external intensity distribution,” Opt. Lett. 37(2), 265–267 (2012). [CrossRef] [PubMed]

11.

R. L. Heinisch, F. X. Bronold, and H. Fehske, “Mie scattering by a charged dielectric particle,” Phys. Rev. Lett. 109(24), 243903 (2012). [CrossRef] [PubMed]

12.

A. Heifetz, H. T. Chien, S. Liao, N. Gopalsami, and A. C. Raptis, “Millimeter-wave scattering from neutral and charged water droplets,” J. Quant. Spectrosc. Radiat. Transf. 111(17–18), 2550–2557 (2010). [CrossRef]

13.

H. Y. Chung, P. T. Leung, and D. P. Tsai, “Effects of extraneous surface charges on the enhanced Raman scattering from metallic nanoparticles,” J. Chem. Phys. 138(22), 224101 (2013). [CrossRef] [PubMed]

14.

J. Rostalski and M. Quinten, “Effect of a surface charge on the halfwidth and peak position of cluster plasmons in colloidal metal particles,” Colloid Polym. Sci. 274(7), 648–653 (1996). [CrossRef]

15.

J. Gersten and A. Nitzan, “Electromagnetic theory of enhanced Raman scattering by molecules adsorbed on rough surfaces,” J. Chem. Phys. 73(7), 3023–3037 (1980). [CrossRef]

16.

M. Meier and A. Wokaun, “Enhanced fields on large metal particles: dynamic depolarization,” Opt. Lett. 8(11), 581–583 (1983). [CrossRef] [PubMed]

17.

P. G. Etchegoin and E. C. Le Ru, Surface Enhanced Raman Spectrocopy: Analytical, Biophysical and Life Science Applications (edited by S. Schlucker), pp 1–37 (Wiley-VCH, 2011).

18.

R. Ruppin, “Decay of an excited molecule near a small metal sphere,” J. Chem. Phys. 76 (4), 1681–1684 (1982). Note that the first work that studied the scattering of dipole radiation from a sphere was in B. van der Pol and H. Bremmer, ” The diffraction of electromagnetic waves from an electrical point source round a finitely conducting sphere, with applications to radiotelegraphy and the theory of the rainbow. Part I,” Philos. Mag. 24(159), 141–176 (1937) (however, Ruppin was the first to apply this theory to study the problem of molecular fluorescence near a sphere.).

19.

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96(11), 113002 (2006). [CrossRef] [PubMed]

20.

Y. S. Kim, P. T. Leung, and T. F. George, “Classical decay rates for molecules in the presence of a spherical surface: A complete treatment,” Surf. Sci. 195(1–2), 1–14 (1988). [CrossRef]

21.

H. Y. Chung, P. T. Leung, and D. P. Tsai, “Equivalence between the mechanical model and energy-transfer theory for the classical decay rates of molecules near a spherical particle,” J. Chem. Phys. 136(18), 184106 (2012). [CrossRef] [PubMed]

22.

H. Y. Chung, P. T. Leung, and D. P. Tsai, “Decay rates of a molecule in the vicinity of a spherical surface of an isotropic magnetodielectric material,” Phys. Rev. B 86(15), 155413 (2012). [CrossRef]

23.

G. Sun, J. B. Khurgin, and D. P. Tsai, “Comparative analysis of photoluminescence and Raman enhancement by metal nanoparticles,” Opt. Lett. 37(9), 1583–1585 (2012). [CrossRef] [PubMed]

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(260.2510) Physical optics : Fluorescence
(260.3910) Physical optics : Metal optics
(300.6280) Spectroscopy : Spectroscopy, fluorescence and luminescence
(160.4236) Materials : Nanomaterials

ToC Category:
Plasmonics

History
Original Manuscript: July 31, 2013
Revised Manuscript: September 17, 2013
Manuscript Accepted: October 8, 2013
Published: October 28, 2013

Citation
H. Y. Chung, P. T. Leung, and D. P. Tsai, "Molecular fluorescence in the vicinity of a charged metallic nanoparticle," Opt. Express 21, 26483-26492 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-22-26483


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References

  1. For a good recent review on this topic, see, e.g.H. Chen, G. C. Schatz, and M. A. Ratner, “Experimental and theoretical studies of plasmon-molecule interactions,” Rep. Prog. Phys.75(9), 096402 (2012). [CrossRef] [PubMed]
  2. F. Tam, G. P. Goodrich, B. R. Johnson, and N. J. Halas, “Plasmonic enhancement of molecular fluorescence,” Nano Lett.7(2), 496–501 (2007). [CrossRef] [PubMed]
  3. Y. Fu, J. Zhang, and J. R. Lakowicz, “Plasmonic enhancement of single-molecule fluorescence near a silver nanoparticle,” J. Fluoresc.17(6), 811–816 (2007). [CrossRef] [PubMed]
  4. G. P. Acuna, M. Bucher, I. H. Stein, C. Steinhauer, A. Kuzyk, P. Holzmeister, R. Schreiber, A. Moroz, F. D. Stefani, T. Liedl, F. C. Simmel, and P. Tinnefeld, “Distance dependence of single-fluorophore quenching by gold nanoparticles studied on DNA origami,” ACS Nano6(4), 3189–3195 (2012). [CrossRef] [PubMed]
  5. C. Arntsen, K. Lopata, M. R. Wall, L. Bartell, and D. Neuhauser, “Modeling molecular effects on plasmon transport: Silver nanoparticles with tartrazine,” J. Chem. Phys.134(8), 084101 (2011). [CrossRef] [PubMed]
  6. See, e.g.,H. Y. Chung, P. T. Leung, and D. P. Tsai, “Fluorescence characteristics of a molecule in the vicinity of a plasmonic nanomatryoska: nonlocal optical effects,” Opt. Commun.285(8), 2207–2211 (2012). [CrossRef]
  7. C. F. Bohren and A. J. Hunt, “Scattering of electromagnetic waves by a charged sphere,” Can. J. Phys.55(21), 1930–1935 (1977). [CrossRef]
  8. J. Klačka and M. Kocifaj, “Scattering of electromagnetic waves by charged spheres and some physical consequences,” J. Quant. Spectrosc. Radiat. Transf.106(1-3), 170–183 (2007). [CrossRef]
  9. E. Rosenkrantz and S. Arnon, “Enhanced absorption of light by charged nanoparticles,” Opt. Lett.35(8), 1178–1180 (2010). [CrossRef] [PubMed]
  10. M. Kocifaj and J. Klačka, “Scattering of electromagnetic waves by charged spheres: near-field external intensity distribution,” Opt. Lett.37(2), 265–267 (2012). [CrossRef] [PubMed]
  11. R. L. Heinisch, F. X. Bronold, and H. Fehske, “Mie scattering by a charged dielectric particle,” Phys. Rev. Lett.109(24), 243903 (2012). [CrossRef] [PubMed]
  12. A. Heifetz, H. T. Chien, S. Liao, N. Gopalsami, and A. C. Raptis, “Millimeter-wave scattering from neutral and charged water droplets,” J. Quant. Spectrosc. Radiat. Transf.111(17–18), 2550–2557 (2010). [CrossRef]
  13. H. Y. Chung, P. T. Leung, and D. P. Tsai, “Effects of extraneous surface charges on the enhanced Raman scattering from metallic nanoparticles,” J. Chem. Phys.138(22), 224101 (2013). [CrossRef] [PubMed]
  14. J. Rostalski and M. Quinten, “Effect of a surface charge on the halfwidth and peak position of cluster plasmons in colloidal metal particles,” Colloid Polym. Sci.274(7), 648–653 (1996). [CrossRef]
  15. J. Gersten and A. Nitzan, “Electromagnetic theory of enhanced Raman scattering by molecules adsorbed on rough surfaces,” J. Chem. Phys.73(7), 3023–3037 (1980). [CrossRef]
  16. M. Meier and A. Wokaun, “Enhanced fields on large metal particles: dynamic depolarization,” Opt. Lett.8(11), 581–583 (1983). [CrossRef] [PubMed]
  17. P. G. Etchegoin and E. C. Le Ru, Surface Enhanced Raman Spectrocopy: Analytical, Biophysical and Life Science Applications (edited by S. Schlucker), pp 1–37 (Wiley-VCH, 2011).
  18. R. Ruppin, “Decay of an excited molecule near a small metal sphere,” J. Chem. Phys. 76 (4), 1681–1684 (1982). Note that the first work that studied the scattering of dipole radiation from a sphere was in B. van der Pol and H. Bremmer, ” The diffraction of electromagnetic waves from an electrical point source round a finitely conducting sphere, with applications to radiotelegraphy and the theory of the rainbow. Part I,” Philos. Mag.24(159), 141–176 (1937) (however, Ruppin was the first to apply this theory to study the problem of molecular fluorescence near a sphere.).
  19. P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett.96(11), 113002 (2006). [CrossRef] [PubMed]
  20. Y. S. Kim, P. T. Leung, and T. F. George, “Classical decay rates for molecules in the presence of a spherical surface: A complete treatment,” Surf. Sci.195(1–2), 1–14 (1988). [CrossRef]
  21. H. Y. Chung, P. T. Leung, and D. P. Tsai, “Equivalence between the mechanical model and energy-transfer theory for the classical decay rates of molecules near a spherical particle,” J. Chem. Phys.136(18), 184106 (2012). [CrossRef] [PubMed]
  22. H. Y. Chung, P. T. Leung, and D. P. Tsai, “Decay rates of a molecule in the vicinity of a spherical surface of an isotropic magnetodielectric material,” Phys. Rev. B86(15), 155413 (2012). [CrossRef]
  23. G. Sun, J. B. Khurgin, and D. P. Tsai, “Comparative analysis of photoluminescence and Raman enhancement by metal nanoparticles,” Opt. Lett.37(9), 1583–1585 (2012). [CrossRef] [PubMed]

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