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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 5 — Mar. 1, 2010
  • pp: 4316–4328
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Fluorescence enhancement of quantum emitters with different energy systems near a single spherical metal nanoparticle

Yingjie Zhang, Ruoyang Zhang, Qingru Wang, Zhishuai Zhang, Haibo Zhu, Jiadong Liu, Feng Song, Shanxin Lin, and Edwin Yue Bun Pun  »View Author Affiliations


Optics Express, Vol. 18, Issue 5, pp. 4316-4328 (2010)
http://dx.doi.org/10.1364/OE.18.004316


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Abstract

We present a theoretical study of the influence of a single spherical metal nanoparticle (MNP) on the fluorescence intensity of nearby emitters with two-level and multi-level energy systems. The enhancement factors of the excitation and relaxation processes are deduced. To reveal the interrelationship between the excitation and relaxation processes we adopt the rate equations of two-level fluorescent systems and upconversion fluorescent systems, and deduce the expression for the fluorescence enhancement factor. Our calculated results for the two-level systems agree well with reported experimental data. As to the upconversion fluorescent systems, our numerical results provide the first theoretical prediction showing that the MNP may selectively enhance a certain fluorescence process among various ones.

© 2010 OSA

1. Introduction

The influence of the surrounding environment on the fluorescence process of quantum emitters has been studied extensively, starting off with Purcell [1

1. E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

]. Among various materials that affect fluorescence, metals are of great interest due to the plasmonic resonance of the free electrons with the excitation field. This plasmonic resonance, in turn, can couple strongly with the fluorescence process of nearby emitters. Theoretical and experimental studies of the influence of metallic nanostructures (surfaces, wires, particles, etc.) on fluorescence processes have been developed [2

2. P. Andrew and W. L. Barnes, “Molecular fluorescence above metallic gratings,” Phys. Rev. B 64(12), 125405 (2001). [CrossRef]

17

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

]. Nowadays, single molecule detection and spectroscopy are made possible as a result of the near-field optical techniques. In order to improve the detection efficiency, metal tips of various shapes are used to enhance the fluorescence intensity of single emitters [10

10. M. Thomas, J.-J. Greffet, R. Carminati, and J. R. Arias-Gonzalez, “Single-molecule spontaneous emission close to absorbing nanostructures,” Appl. Phys. Lett. 85(17), 3863–3865 (2004). [CrossRef]

14

14. R. Esteban, M. Laroche, and J.-J. Greffet, “Influence of metallic nanoparticles on upconversion processes,” J. Appl. Phys. 105(3), 033107 (2009). [CrossRef]

]. According to currently developed theories, metal nanoparticles in the state of Localized Surface Plasmon Resonance (LSPR) can both enhance the excitation probability of the emitter and quench the fluorescent emission by absorbing energy from it [11

11. S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006). [CrossRef] [PubMed]

17

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

]. Numerical calculations with experimental proof have been carried out to illustrate the interaction of a single metal nanoparticle with fluorescent emitters, which are approximated to be simple two-level systems [11

11. S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006). [CrossRef] [PubMed]

13

13. P. Bharadwaj, P. Anger, and L. Novotny, “Nanoplasmonic enhancement of single-molecule fluorescence,” Nanotechnology 18(4), 044017 (2007). [CrossRef]

], or three-level systems [14

14. R. Esteban, M. Laroche, and J.-J. Greffet, “Influence of metallic nanoparticles on upconversion processes,” J. Appl. Phys. 105(3), 033107 (2009). [CrossRef]

].

Currently there has been an increasing interest in probing electromagnetic local fields with erbium ions, in which the infrared fluorescence and upconversion fluorescence both exists [18

18. E. Verhagen, L. Kuipers, and A. Polman, “Enhanced nonlinear optical effects with a tapered plasmonic waveguide,” Nano Lett. 7(2), 334–337 (2007). [CrossRef] [PubMed]

,19

19. E. Verhagen, L. Kuipers, and A. Polman, “Field enhancement in metallic subwavelength aperture arrays probed by erbium upconversion luminescence,” Opt. Express 17(17), 14586–14598 (2009). [CrossRef] [PubMed]

]. The interaction of a metal nanoparticle with upconversion processes is discussed in a theoretical work [14

14. R. Esteban, M. Laroche, and J.-J. Greffet, “Influence of metallic nanoparticles on upconversion processes,” J. Appl. Phys. 105(3), 033107 (2009). [CrossRef]

], which has only explored one emission process of the upconversion fluorescent system. To the best of our knowledge, there has been no study of the real erbium ion system which involves the emission of photons with several ranges of frequencies.

In this paper, we present theoretical calculation of the interaction between a spherical metal nanoparticle (MNP) and the surrounding fluorescent emitter excited by external electromagnetic field. We treat the excitation and relaxation processes of the fluorescent emitter as dipole transitions, and regard the relaxation process as classical electric dipole radiation. With the aid of Mie theory [20

20. C. F. Bohern, and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

], we can calculate the enhancement factor of the excitation probability which depends on the wavelength of the incident field. As to the relaxation processes, a series of expressions for the enhancement factors of various relaxation pathways can be deduced [21

21. M. Kerker, D.-S. Wang, and H. Chew, “Surface enhanced Raman scattering (SERS) by molecules adsorbed at spherical particles: errata,” Appl. Opt. 19(24), 4159 (1980). [CrossRef] [PubMed]

23

23. R. Ruppin, “Decay of an excited molecule near a small metal sphere,” J. Chem. Phys. 76(4), 1681–1684 (1982). [CrossRef]

]. To reveal the mechanism of the enhancement of fluorescence intensity, we adopt the steady state rate equations, which show the interrelationship of the excitation and relaxation processes, and provide expressions for the fluorescence enhancement factor. The calculated enhancement factor of fluorescence intensity for a two-level system is in well agreement with the reported experimental data, which shows the validity of the rate equation method and our calculation for various enhancement factors in the excitation and relaxation processes. Finally, we extend our calculation to the complex upconversion fluorescence process. After deriving the enhancement factor of the fluorescence intensity of erbium ions, we provide numerical results showing that the MNP with various sizes can either enhance or weaken the upconversion green fluorescence and the infrared fluorescence. The relative enhancement factor of the green light with respect to the infrared light is also calculated, and is shown to vary significantly with the MNP radius and the MNP-dipole distance. Therefore, we may enhance specific dipole transitions by changing these two factors. This result may be applied to tune erbium-doped lasers/fiber amplifiers [24

24. X. M. Liu, X. F. Yang, F. Y. Lu, J. H. Ng, X. Q. Zhou, and C. Lu, “Stable and uniform dual-wavelength erbium-doped fiber laser based on fiber Bragg gratings and photonic crystal fiber,” Opt. Express 13(1), 142–147 (2005). [CrossRef] [PubMed]

,25

25. E. Desurvire, J. R. Simpson, and P. C. Becker, “High-gain erbium-doped traveling-wave fiber amplifier,” Opt. Lett. 12(11), 888–890 (1987). [CrossRef] [PubMed]

] to emit/amplify light with a specific, single wavelength.

The paper is organized as follows. In section 2, the generalized theory of fluorescence enhancement near a single spherical metal nanoparticle is provided. In section 3, we deduce the enhancement factor of the fluorescence intensity for two-level systems and compare the result with the reported experimental data. In section 4, we calculate the enhancement factor of both the upconversion fluorescence and the infrared fluorescence of erbium ions, showing that LSPR may enhance either process. Section 5 is a summary of this article.

2. Generalized theory on the fluorescence enhancement

Generally, fluorescence consists of two kinds of processes, i.e., excitation and relaxation. Excitation denotes the transition from lower energy levels to higher levels by absorption of photons, while relaxation can occur both radiatively via the emission of photons and nonradiatively via various pathways. For the fluorescent emitter near the MNP, excitation is enhanced due to the enhancement of the local field. As to the relaxation process, radiative decay probability is affected and a new channel of nonradiative decay is introduced. The theory of the fluorescence enhancement is provided as follows.

2.1 Excitation

Suppose that an x-polarized plane wave is incident on a homogeneous, isotropic spherical metal particle with wave vector k parallel to the z axis. A fluorescent emitter is located on the x axis with distance r from the center of the sphere with radius a, as is shown in Fig. 1
Fig. 1 Configuration of the theoretical model. The sphere represents the metal particle, and the dipole represents the fluorescent emitter.
. The fluorescent emitter is excited by the local field which is the sum of the incident field and the field scattered by the sphere. As an approximation, we treat the excitation process as a dipole transition with dipole moment p. According to Fermi’s golden rule, the probability that the emitter is excited R is proportional to the square of the modulus of the perturbation Hamiltonian |pE|2. Therefore, the enhancement factor of R is obtained as:
hex(ω)=|pE(r)|2|pEi(r)|2
(1)
where ω is the angular frequency of the incident wave, Ei is the incident electric field, andE(r) is the local field at the dipole point, which can be written as:

E(r)=Ei(r)+Es(r).
(2)

Here Es is the scattered field, the expression of which can be obtained from [20

20. C. F. Bohern, and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

]. We assume that only the dipole oriented along the the x axis is excited [17

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

], as is shown in Fig. 1. The enhancement factor can then be reduced to a simpler form:

hex(ω)=|E(r)|2|Ei(r)|2
(3)

2.2 Emission

In the calculation of the emission enhancement, we regard the excited fluorescent emitter as a classical electric dipole. In order to reveal the influence of the MNP on the relaxation process, we ignore the incident plane wave and regard the primary dipole field Edip as the field incident on the MNP. The magnetic permeabilities of the sphere and the surrounding medium are assumed to be equal to the magnetic permeability of the vacuum μ0. The angular frequency of the oscillating dipole ω can be different from the angular frequency of the incident field ω, and may have one or several continuous range of values, depending on the fluorescence spectrum of the emitter. The incident dipole field and the scattered field can be obtained following the procedures provided in [21

21. M. Kerker, D.-S. Wang, and H. Chew, “Surface enhanced Raman scattering (SERS) by molecules adsorbed at spherical particles: errata,” Appl. Opt. 19(24), 4159 (1980). [CrossRef] [PubMed]

].

The total power for radiative decay, nonradiative decay, and energy transfer process of a fluorescent emitter is:

Ptotal=Pr+Pnr0+Pabs.
(4)

Here Pnr0 is the intrinsic nonradiative decay power and is independent of the environment, thus it does not change because of the plasmonic oscillation inside the MNP.

γ0=P0ω.
(5)

The total decay probability and the nonradiative decay probability are obtained as:

γtotal0=γ0η,
(6)
γnr0=Pnr0ω=1ηηγ0.
(7)

Here we have introduced η as the intrinsic quantum efficiency, defined as the fraction of emission probability to the total decay probability.

As to the dipole in the vicinity of the MNP, the radiative decay probability and total decay probability are modified due to the interaction of the dipole and the localized plasmonic oscillation inside the MNP:

γr=Prω,
(8)
γtotal=Ptotalω.
(9)

The enhancement factor of the total decay probability is obtained as:

hdecay=γtotalγtotal0=ηPtotalP0.
(10)

The presence of the MNP introduces energy transfer from the dipole to the MNP as a new channel to dissipate energy. The energy transfer probability is:

γET=Pabsω.
(11)

The quantum efficiency of the dipole coupled to the MNP is obtained as follows:

η=γrγtotal=PrPtotal.
(12)

The enhancement factor of the quantum efficiency is:

hq=ηη=1ηPrPtotal.
(13)

Up till now, we have obtained the expressions for the excitation enhancement factor and the enhancement of the total decay probability, together with the enhancement of the quantum efficiency of the florescent emitter near the MNP. While the excitation enhancement depends on the wavelength of the incident plane wave, the modification of the various factors in the relaxation process does not rely on the excitation field, and is dependent on the emitted photon energy ω (determined by the energy difference between the upper and lower transition levels) and the orientation of the dipole moment p.

3. Enhanced fluorescence intensity of two-level systems

Currently, the enhancement of fluorescence intensity near metal nanoparticle(s) is generally viewed as the result of two independent processes: excitation enhancement and emission enhancement [11

11. S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006). [CrossRef] [PubMed]

13

13. P. Bharadwaj, P. Anger, and L. Novotny, “Nanoplasmonic enhancement of single-molecule fluorescence,” Nanotechnology 18(4), 044017 (2007). [CrossRef]

,15

15. T. Härtling, P. Reichenbach, and L. M. Eng, “Near-field coupling of a single fluorescent molecule and a spherical gold nanoparticle,” Opt. Express 15(20), 12806–12817 (2007). [CrossRef] [PubMed]

17

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

]. However, when taking into account the time evolution of the fluorescence process under continuous pumping, the excitation and relaxation processes of the fluorescent emitter should be interrelated. To show the relation of these two processes, we adopt the rate equations of the fluorescence process to deduce the expression for the fluorescence enhancement factor.

For two-level systems, the energy levels are shown in Fig. 2
Fig. 2 Schematic diagram of a two-level system.
. Note that for each electronic level, there are many vibrational levels around it. In general, the relaxation processes between these vibrational levels are much faster than the transition between the two electronic levels. Therefore, it is reasonable to ignore these vibrational relaxation processes when writing the rate equations of the system. Thus, we can easily obtain the rate equations as follows:
dN0dt=N0R+N1W,dN1dt=N0RN1W,N0+N1=N.
(14)
where R and W are the excitation probability and total decay probability, respectively. And N is the total population of the fluorescent emitter, while N0 and N1 are the population of state |0 and state |1, separately. For a single emitter, N = 1, and N0, N1 denotes the probability that the emitter is at each energy level at the time t.

In the steady state, we can obtain the following results:

N0=NWW+R,N1=NRW+R.
(15)

The fluorescence rate is obtained as:

Γfluo=N1Wη.
(16)

It should be noted that the fluorescence rate here means the number of photons emitted per unit time, and is different from the excitation and decay probability which is the probability of transition per unit time.

For weak excitation, the fluorescent emitter is in the thermal equilibrium state, thus satisfy the Boltzmann distribution law. Under this condition,
N1/N0=exp(E1E0kBT)=exp(ωkBT),
(17)
where E1 and E0 are the energy eigenvalues of the state |1 and |0, respectively. When the radiation wavelength is in the range of visible or infrared spectrum, we can get the relation:

N1<<N0.
(18)

Noting that R/W=N1/N0, we obtain:

R<<W,
(19)
N1=NRW,
(20)
Γfluo=NRη.
(21)

Equation (21) shows that the fluorescence rate is proportional to the excitation probability and the quantum efficiency, which corresponds to the excitation and relaxation process, respectively. Thus, the enhancement factor of the fluorescence intensity is:

hfluo=hexhq.
(22)

This result is in agreement with those reported in [11

11. S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006). [CrossRef] [PubMed]

17

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

]. To calculate this enhancement factor, we choose gold as the material for the metal nanoparticle, and the fluorescent emitter is taken to be Nile Blue, which has a simple two-level system. The dielectric constant of gold is obtained from [26

26. P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

], and various other parameters are taken from [12

12. P. Bharadwaj and L. Novotny, “Spectral dependence of single molecule fluorescence enhancement,” Opt. Express 15(21), 14266–14274 (2007). [CrossRef] [PubMed]

], which are listed as follows: η=1, λ=637nm, n0=1, a=40nm. The calculated results for the two-level system are shown in Fig. 3
Fig. 3 (a) Excitation enhancement factor of the dipole in the vicinity of the MNP with a radius of 40nm. (b) Enhancement factor of quantum efficiency. (c) Fluorescence enhancement factor.
.

We can see that hex decreases rapidly with the decrease of dipole-MNP distance, while hq rises until reaching unity. As to the fluorescence enhancement factor, it reaches maximum when the distance is 5nm. Below this distance, the enhancement factor drops as a result of the quenching effect. It should be noted that classical electrodynamics will be invalid when the distance becomes too small (less than 2nm), so will our calculated results. At larger distance, the fluorescence enhancement also decreases due to the decrease of excitation enhancement, and ultimately reaches unity, which means that the MNP will have no effect on the fluorescent dipole.

Taking into account the specific condition that the dielectric layer at the surface of the MNP increases the fluorescence enhancement by a factor 2-3 in the close vicinity of the MNP as reported in [12

12. P. Bharadwaj and L. Novotny, “Spectral dependence of single molecule fluorescence enhancement,” Opt. Express 15(21), 14266–14274 (2007). [CrossRef] [PubMed]

], our calculated results for the fluorescence enhancement are in well agreement with the experimental data in this reference.

4. Influence of MNP on nearby upconversion fluorescence systems

In this section, we focus on the simplification of multi-level fluorescence systems, and calculate the fluorescence enhancement factors of different fluorescence processes. The theory is outlined below with numerical results provided, showing the tunability of specific fluorescent transitions by using MNP.

4.1 Theory

To understand the fluorescence process of quantum emitters with complex energy levels, we can illustrate the interrelationship of the excitation and relaxation processes with the aid of the rate equations of the system. As an example, we have calculated the fluorescence intensity of green light (which generally dominates the visible spectrum) and infrared light for erbium ions. For simplicity, we only consider the excited state absorption (ESA) upconversion processes which results in green emission with the transition H211/2I415/2 and S43/2I415/2, together with the direct transition I413/2I415/2 which produces infrared light. Thus, we reduce the complex energy level diagram of erbium ions to a simple form, as shown in Fig. 4
Fig. 4 Schematic diagram of energy levels for erbium ions.
.

Similar to the treatment of the vibrational relaxation processes in two-level fluorescence systems, we assume that the MPR (Multi-phonon assisted Relaxation) processes |2(F47/2)|2(H211/2), |2|2(S43/2) and |1(I411/2)|1(I413/2) (which is common in erbium doped crystals) are much faster than the excitation and emission processes. Therefore, we regard level |1 and level |1 as one single level (level |1), and combine level |2, |2, |2 to two separate levels |2 and |2 (i.e. “move” the population of level |2 to|2 and |2). For simplicity, we write level |2 and |2 as level |2 and |3 in the following calculation. We further assume that the branching ratio from higher excited states |2 and |3 to the ground state |0(I415/2) equals to 1, and the rate equations can be written as follows:
dN0dt=R01N0+W1N1+W2N2+W3N3,dN1dt=R01N0(W1+R12)N1,dN2dt=α2R12N1W2N2,dN3dt=α3R12N1W3N3,N0+N1+N2+N3=N,
(23)
where we have introduced α2 and α3 (α2+α3=1) as the probabilities that the erbium ion at state F47/2 relaxes to state S43/2 and state H211/2, respectively. Ni is the population of level |i (i = 0, 1, 2, 3), and N is the total population of erbium ions. At steady state we can obtain the following results:

N1=NW1+R12R01+1+α2R12W2+α3R12W3,N2=α2R12W2N1,N3=α3R12W3N1.
(24)

The fluorescence rate of the transition |i|0 (i = 0, 1, 2, 3) can be written as:
Γfluoi=NiWiηi,
(25)
where ηi is the intrinsic quantum efficiency of the transition |i|0. We can see that the fluorescence rate of every level depends on all the parameters R and W. To calculate the enhancement factor of the fluorescence rate, we need to know the parameters R and W for the isolated emitter, together with the enhancement factor for each R and W for the emitter in the vicinity of the MNP.

However, the results can be much simpler when we calculate the relative enhancement factor of the green light compared to the infrared light. In fact, the ratio of the fluorescence intensity of the transition |i|0 (i = 2, 3) with respect to that of |1|0 can easily be obtained by using Eq. (25) as:

ΓfluoiΓfluo1=NiWiηiN1W1η1.
(26)

According to Eq. (24), Ni/N1=αiR12/Wi. Therefore,

ΓfluoiΓfluo1=αiR12ηiW1η1.
(27)

Assume that αi do not change because of the presence of the MNP, we get the relative enhancement factor:
hfluoihfluo1=hexhqihdecay1hq1.
(28)
where hfluoi,hqi and hfluo1,hq1are the enhancement of fluorescence rate and quantum efficiency for the dipole transition |i|0 and |1|0, respectively. hdecay1 is the enhancement of total decay probability for the transition |1|0.

In order to understand the basic enhancement mechanisms of the upconversion process in the vicinity of the MNP, we would like to reduce Eqs. (24-25) to simpler forms. To reach this goal, we need to restrict the excitation condition to the weak excitation, where the erbium ions are in the thermal equilibrium state. Hence, similar to Eq. (17), we have:
Ni/N1=exp(EiE1kBT),Ni/N1Wi/W1=Wi/W1exp(EiE1kBT).
(29)
where Ei (i = 2, 3) and E1 are the energy eigenvalues of the state |i and |1, respectively. Normally, for erbium ions, we can obtain the following relations:

Ni/N1<<1,Ni/N1Wi/W1<<1.
(30)

Noting that Ni/N1=αiR12/Wi, we get the relations:

R12/Wi<<1,R12/W1<<1.
(31)

Since the excitation wavelength for the transition I415/2I411/2 and I411/2F47/2 are the same, we can write:

R01R12.
(32)

Thus, Eq. (24) is reduced to:
N1=NR01W1,Ni=αiNR01R12W1Wi.(i=2,3)
(33)
Substituting Eq. (33) into Eq. (25), we obtain:

Γfluo1=NR01η1,Γfluoi=αiNR01R12ηi/W1.
(34)

So far, we have made several assumptions about the excitation condition and the fluorescent transition processes. Nevertheless, the results expressed by Eq. (34) are quite reasonable. The expression for Γfluo1 denotes that the enhancement factor is equal to the product of the excitation enhancement and the enhancement of quantum efficiency, which is in good agreement with that of the two-level fluorescent system. In fact, since R12<<W1, the fluorescent transition occurs mainly between the states |0 and |1. Therefore, the infrared fluorescence process can be approximated to be two-level transitions. As for the expression of Γfluoi, it also includes the two-step excitation probability R01R12 and the quantum efficiency of the emission process ηi. Besides, there’s one more item τ1=1/W1, which is the lifetime of the metastable energy level |1. This is due to the fact that the population of level |1 is proportional to its lifetime and that the transition rate from level |1 to level |i is proportional to the population of level |1. Thus, we can easily obtain the relation Γfluoiτ1.

The enhancement factor of each emission rate is obtained as:

hfluo1=hexhq1,hfluoi=hex2hqihdecay1.
(35)

Using Eqs. (3) (10) (13) (28) (35), we are able to calculate the exact value of hfluoi/hfluo1, and the value of hfluo1 and hfluoi in the weak excitation regime.

4.2 Numerical results

We have calculated the enhancement of the 547nm upconversion fluorescence (|2|0), the enhancement of the 1533nm infrared fluorescence (|1|0), and their relative enhancement for erbium ions near the MNP with three different values of radius: 50nm, 100nm, 150nm. The quantum efficiencies of erbium ions in absence of the MNP and the refractive index of the medium used in our calculation are taken from [27

27. H. Lin, E. Y. B. Pun, S. Q. Man, and X. R. Liu, “Optical transitions and frequency upconversion of Er3+ ions in Na2O⋅Ga3Al2Ge3O12 glasses,” J. Opt. Soc. Am. B 18(5), 602–609 (2001). [CrossRef]

]. Specifically, the quantum efficiencies of the 547nm upconversion fluorescence and the 1533nm infrared fluorescence are taken to be 0.0085 and 1, respectively. The excitation wavelength is 973nm, and the refractive index of the medium (Na2OCa3Al2Ge3O12 glass) is calculated using the equation n0=A+B/λ2, where A=1.6013, B=8457nm2. The calculated results are shown in Fig. 5
Fig. 5 The red dashed curve and the green solid curve in (a) (c) (e) denote the infrared and green fluorescence enhancement factors of erbium ions in the vicinity of MNP with radius 50nm, 100nm and 150nm, respectively. The blue solid curve in (b) (d) (f) is the relative enhancement of the 537nm upconversion fluorescence with respect to the 1533nm infrared fluorescence of erbium ions near MNP with radius 50nm, 100nm and 150nm, separately.
.

It can be seen that both the infrared fluorescence and the upconversion fluorescence are enhanced when the MNP radius is 50nm. As to the case when the MNP radius is 100nm or 150nm, both processes may either be enhanced or weakened with the change of the MNP-dipole distance. For the relative enhancement factor, it is greater than 1 when the MNP radius is 50nm, revealing that the MNP favors the upconversion process. When the MNP becomes larger, this factor drops. For MNP with radius 100nm, this factor is greater than 1 when the dipole-MNP distance is smaller than 26nm, and falls under 1 as the distance becomes larger. As to the 150nm radius MNP, the fluorescence enhancement of the infrared emission is larger than that of the upconversion fluorescence when the dipole-MNP distance is smaller than 287nm.

These numerical results show that the MNP may either enhance or weaken the infrared fluorescence and the upconversion fluorescence of the nearby erbium ions. By tuning the MNP radius and the dipole-MNP distance, we can selectively enhance either fluorescence process.

5. Conclusion

In conclusion, we have studied and provided insights into the effect of a metal nanoparticle on the fluorescence process of nearby emitters. Specifically, we have calculated the fluorescence enhancement factor of quantum emitters with two-level and multi-level energy systems near a single spherical metal nanoparticle. Our results show that the presence of MNP makes it possible to selectively enhance either the upconversion fluorescence or the infrared fluorescence of erbium ions.

Acknowledgments

This work was supported by NSFC90923035, 973 Program2006CB302904, NSFCJ0730315, and the “100 Projects” of Creative Research for Undergraduates of Nankai University under project No. BX6-293.

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K. L. Shuford, M. A. Ratner, S. K. Gray, and G. C. Schatz, “Electric field enhancement and light transmission in cylindrical nanoholes,” J. Comput. Theor. Nanosci. 4, 239–246 (2007).

7.

M. H. Chowdhury, K. Ray, S. K. Gray, J. Pond, and J. R. Lakowicz, “Aluminum nanoparticles as substrates for metal-enhanced fluorescence in the ultraviolet for the label-free detection of biomolecules,” Anal. Chem. 81(4), 1397–1403 (2009). [CrossRef] [PubMed]

8.

Y. Ito, K. Matsuda, and Y. Kanemitsu, “Mechanism of photoluminescence enhancement in single semiconductor nanocrystals on metal surfaces,” Phys. Rev. B 75(3), 033309 (2007). [CrossRef]

9.

C. Hagglund, M. Zach, and B. Kasemo, “Enhanced charge carrier generation in dye sensitized solar cells by nanoparticle plasmons,” Appl. Phys. Lett. 92(1), 013113 (2008). [CrossRef]

10.

M. Thomas, J.-J. Greffet, R. Carminati, and J. R. Arias-Gonzalez, “Single-molecule spontaneous emission close to absorbing nanostructures,” Appl. Phys. Lett. 85(17), 3863–3865 (2004). [CrossRef]

11.

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006). [CrossRef] [PubMed]

12.

P. Bharadwaj and L. Novotny, “Spectral dependence of single molecule fluorescence enhancement,” Opt. Express 15(21), 14266–14274 (2007). [CrossRef] [PubMed]

13.

P. Bharadwaj, P. Anger, and L. Novotny, “Nanoplasmonic enhancement of single-molecule fluorescence,” Nanotechnology 18(4), 044017 (2007). [CrossRef]

14.

R. Esteban, M. Laroche, and J.-J. Greffet, “Influence of metallic nanoparticles on upconversion processes,” J. Appl. Phys. 105(3), 033107 (2009). [CrossRef]

15.

T. Härtling, P. Reichenbach, and L. M. Eng, “Near-field coupling of a single fluorescent molecule and a spherical gold nanoparticle,” Opt. Express 15(20), 12806–12817 (2007). [CrossRef] [PubMed]

16.

M. Ringler, A. Schwemer, M. Wunderlich, A. Nichtl, K. Kürzinger, T. A. Klar, and J. Feldmann, “Shaping emission spectra of fluorescent molecules with single plasmonic nanoresonators,” Phys. Rev. Lett. 100(20), 203002 (2008). [CrossRef] [PubMed]

17.

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

18.

E. Verhagen, L. Kuipers, and A. Polman, “Enhanced nonlinear optical effects with a tapered plasmonic waveguide,” Nano Lett. 7(2), 334–337 (2007). [CrossRef] [PubMed]

19.

E. Verhagen, L. Kuipers, and A. Polman, “Field enhancement in metallic subwavelength aperture arrays probed by erbium upconversion luminescence,” Opt. Express 17(17), 14586–14598 (2009). [CrossRef] [PubMed]

20.

C. F. Bohern, and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

21.

M. Kerker, D.-S. Wang, and H. Chew, “Surface enhanced Raman scattering (SERS) by molecules adsorbed at spherical particles: errata,” Appl. Opt. 19(24), 4159 (1980). [CrossRef] [PubMed]

22.

Y.-L. Xu, “Electromagnetic scattering by an aggregate of spheres,” Appl. Opt. 34(21), 4573–4588 (1995). [CrossRef] [PubMed]

23.

R. Ruppin, “Decay of an excited molecule near a small metal sphere,” J. Chem. Phys. 76(4), 1681–1684 (1982). [CrossRef]

24.

X. M. Liu, X. F. Yang, F. Y. Lu, J. H. Ng, X. Q. Zhou, and C. Lu, “Stable and uniform dual-wavelength erbium-doped fiber laser based on fiber Bragg gratings and photonic crystal fiber,” Opt. Express 13(1), 142–147 (2005). [CrossRef] [PubMed]

25.

E. Desurvire, J. R. Simpson, and P. C. Becker, “High-gain erbium-doped traveling-wave fiber amplifier,” Opt. Lett. 12(11), 888–890 (1987). [CrossRef] [PubMed]

26.

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

27.

H. Lin, E. Y. B. Pun, S. Q. Man, and X. R. Liu, “Optical transitions and frequency upconversion of Er3+ ions in Na2O⋅Ga3Al2Ge3O12 glasses,” J. Opt. Soc. Am. B 18(5), 602–609 (2001). [CrossRef]

OCIS Codes
(190.7220) Nonlinear optics : Upconversion
(240.6680) Optics at surfaces : Surface plasmons
(260.2510) Physical optics : Fluorescence
(160.4236) Materials : Nanomaterials

ToC Category:
Optics at Surfaces

History
Original Manuscript: December 16, 2009
Revised Manuscript: January 13, 2010
Manuscript Accepted: January 14, 2010
Published: February 17, 2010

Citation
Yingjie Zhang, Ruoyang Zhang, Qingru Wang, Zhishuai Zhang, Haibo Zhu, Jiadong Liu, Feng Song, Shanxin Lin, and Edwin Yue Bun Pun, "Fluorescence enhancement of quantum emitters with different energy systems near a single spherical metal nanoparticle," Opt. Express 18, 4316-4328 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-5-4316


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References

  1. E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).
  2. P. Andrew and W. L. Barnes, “Molecular fluorescence above metallic gratings,” Phys. Rev. B 64(12), 125405 (2001). [CrossRef]
  3. K. T. Shimizu, W. K. Woo, B. R. Fisher, H. J. Eisler, and M. G. Bawendi, “Surface-enhanced emission from single semiconductor nanocrystals,” Phys. Rev. Lett. 89(11), 117401 (2002). [CrossRef] [PubMed]
  4. J. Kalkman, C. Strohhöfer, B. Gralak, and A. Polman, “Surface plasmon polariton modified emission of erbium in a metallodielectric grating,” Appl. Phys. Lett. 83(1), 30–32 (2003). [CrossRef]
  5. Y. Wang and Z. P. Zhou, “Strong enhancement of erbium ion emission by a metallic double grating,” Appl. Phys. Lett. 89(25), 253122 (2006). [CrossRef]
  6. K. L. Shuford, M. A. Ratner, S. K. Gray, and G. C. Schatz, “Electric field enhancement and light transmission in cylindrical nanoholes,” J. Comput. Theor. Nanosci. 4, 239–246 (2007).
  7. M. H. Chowdhury, K. Ray, S. K. Gray, J. Pond, and J. R. Lakowicz, “Aluminum nanoparticles as substrates for metal-enhanced fluorescence in the ultraviolet for the label-free detection of biomolecules,” Anal. Chem. 81(4), 1397–1403 (2009). [CrossRef] [PubMed]
  8. Y. Ito, K. Matsuda, and Y. Kanemitsu, “Mechanism of photoluminescence enhancement in single semiconductor nanocrystals on metal surfaces,” Phys. Rev. B 75(3), 033309 (2007). [CrossRef]
  9. C. Hagglund, M. Zach, and B. Kasemo, “Enhanced charge carrier generation in dye sensitized solar cells by nanoparticle plasmons,” Appl. Phys. Lett. 92(1), 013113 (2008). [CrossRef]
  10. M. Thomas, J.-J. Greffet, R. Carminati, and J. R. Arias-Gonzalez, “Single-molecule spontaneous emission close to absorbing nanostructures,” Appl. Phys. Lett. 85(17), 3863–3865 (2004). [CrossRef]
  11. S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006). [CrossRef] [PubMed]
  12. P. Bharadwaj and L. Novotny, “Spectral dependence of single molecule fluorescence enhancement,” Opt. Express 15(21), 14266–14274 (2007). [CrossRef] [PubMed]
  13. P. Bharadwaj, P. Anger, and L. Novotny, “Nanoplasmonic enhancement of single-molecule fluorescence,” Nanotechnology 18(4), 044017 (2007). [CrossRef]
  14. R. Esteban, M. Laroche, and J.-J. Greffet, “Influence of metallic nanoparticles on upconversion processes,” J. Appl. Phys. 105(3), 033107 (2009). [CrossRef]
  15. T. Härtling, P. Reichenbach, and L. M. Eng, “Near-field coupling of a single fluorescent molecule and a spherical gold nanoparticle,” Opt. Express 15(20), 12806–12817 (2007). [CrossRef] [PubMed]
  16. M. Ringler, A. Schwemer, M. Wunderlich, A. Nichtl, K. Kürzinger, T. A. Klar, and J. Feldmann, “Shaping emission spectra of fluorescent molecules with single plasmonic nanoresonators,” Phys. Rev. Lett. 100(20), 203002 (2008). [CrossRef] [PubMed]
  17. P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96(11), 113002 (2006). [CrossRef] [PubMed]
  18. E. Verhagen, L. Kuipers, and A. Polman, “Enhanced nonlinear optical effects with a tapered plasmonic waveguide,” Nano Lett. 7(2), 334–337 (2007). [CrossRef] [PubMed]
  19. E. Verhagen, L. Kuipers, and A. Polman, “Field enhancement in metallic subwavelength aperture arrays probed by erbium upconversion luminescence,” Opt. Express 17(17), 14586–14598 (2009). [CrossRef] [PubMed]
  20. C. F. Bohern, and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  21. M. Kerker, D.-S. Wang, and H. Chew, “Surface enhanced Raman scattering (SERS) by molecules adsorbed at spherical particles: errata,” Appl. Opt. 19(24), 4159 (1980). [CrossRef] [PubMed]
  22. Y.-L. Xu, “Electromagnetic scattering by an aggregate of spheres,” Appl. Opt. 34(21), 4573–4588 (1995). [CrossRef] [PubMed]
  23. R. Ruppin, “Decay of an excited molecule near a small metal sphere,” J. Chem. Phys. 76(4), 1681–1684 (1982). [CrossRef]
  24. X. M. Liu, X. F. Yang, F. Y. Lu, J. H. Ng, X. Q. Zhou, and C. Lu, “Stable and uniform dual-wavelength erbium-doped fiber laser based on fiber Bragg gratings and photonic crystal fiber,” Opt. Express 13(1), 142–147 (2005). [CrossRef] [PubMed]
  25. E. Desurvire, J. R. Simpson, and P. C. Becker, “High-gain erbium-doped traveling-wave fiber amplifier,” Opt. Lett. 12(11), 888–890 (1987). [CrossRef] [PubMed]
  26. P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]
  27. H. Lin, E. Y. B. Pun, S. Q. Man, and X. R. Liu, “Optical transitions and frequency upconversion of Er3+ ions in Na2O⋅Ga3Al2Ge3O12 glasses,” J. Opt. Soc. Am. B 18(5), 602–609 (2001). [CrossRef]

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