Fluorescence enhancement and quenching in tip-enhanced fluorescence spectroscopy

Justin R. Isaac; Huizhong Xu

doi:10.1364/OSAC.1.000899

1. Introduction

Tip-enhanced Raman spectroscopy (TERS) has gained increasing attention in the recent years due to the combined advantages of nanometer spatial resolution, single-molecule sensitivity, and flexibility in probing different regions of the sample [1–5]. Unlike the extremely large Raman enhancement in TERS, enhancement in fluorescence signal in tip-enhanced fluorescence (TEF) [6–11] is significantly smaller as a result of the competition between enhancement in local electromagnetic fields and fluorescence quenching via nonradiative energy transfer [12]. Since the high specificity of fluorescence spectroscopy can reveal information complementary to that of Raman spectroscopy, it is desirable to optimize TERS setups for efficient measurement of both Raman and fluorescence signal in the same setup [13].

Field enhancement in a nanometer-sized gap formed between the tip end and a flat metal surface has been well studied [14–17], and is largely responsible for the superior sensitivity and resolution in TERS [3,4]. With a radius of curvature on the order of tens of nanometers, the end of the tip can be approximated by an induced electric dipole whose magnitude depends on the material and geometry of the tip, and the illumination condition [18,19]. The dipole often exhibits plasmonic resonance and can produce strong field enhancement near the tip apex at resonance. When the gap size is on the order of a few nanometers, this induced dipole together with its image counterpart inside the metal substrate interact and result in extremely large field enhancement inside the gap [17,20]. In the case of a dielectric tip, while the effect of plasmonic resonance is less pronounced, the induced dipole can still produce appreciable field enhancement for a sharp tip of high dielectric constant [21]. The field enhancement is also heavily influenced by the material of substrate. For dielectric substrates, the image dipole inside the substrate will be significantly smaller compared to those found in metal substrates [22], resulting in less field enhancement inside the gap.

In addition to field enhancement, the introduction of a metal tip near a dipole emitter also alters the total decay rate of its excited atomic state, a result that is now well known owing to the pioneering discovery by Purcell [23]. The total decay rate, with contributions from both radiative and nonradiative decays, depends on the electromagnetic local density of states (LDOS) at the location of the emitter [24] and can be significantly enhanced near a metal surface [25–30]. Furthermore, it is the balance of the radiative and nonradiative rates that determines the amount of fluorescence signal to be detected in the far field. Thus, in the case of plasmonic structure-enhanced fluorescence [31–33], the goal is to optimize the configuration to not only increase the field enhancement but also balance the decay rates, thus maximizing the fluorescence signal.

In this study, we use finite element method simulations to study the effect of different tip dimensions and varying tip-substrate distances on fluorescence enhancement and quenching in a TEF setup. First, we study the field enhancement and fluorescence quenching for a dipole emitter situated between a silver tip and a glass substrate. While a glass substrate may not produce the extremely high field enhancement seen in gap-mode TERS setups, it is chosen here given its common use in fluorescence microscopy and its potential for reducing fluorescence quenching compared with metal substrates. The effect of tip radius on enhancement and quenching is also studied. Next, we study the effect of substrate materials on enhancement and quenching. It is well known that surface plasmon polaritons at a metal-dielectric interface can be resonantly excited if the dielectric constants of the respective mediums are equal and opposite [34], i.e.

ε_{1} + ε_{2} = 0.

This condition has also been employed to achieve extraordinary transmission through isolated dielectric nanowire waveguides with sizes as small as one tenth of the wavelength [35,36], and for deep subwavelength confinement in hybrid nanowire waveguides [37]. Therefore we choose TiO₂ as the substrate such that this condition is approximately satisfied in order to resonantly excite the gap plasmons between the tip and substrate. The results are then compared with those for a silver tip over a glass substrate. Fluorescence enhancement can be further improved for a fictitious metal tip with a dielectric constant perfectly matched to that of TiO₂. As recent research has shown the promise of using all-dielectric silicon nanogaps to enhance fluorescence [38], we also investigate the role of tip material choice in the context of a high dielectric silicon tip over substrates of both low and high refractive indices and compare the results with those for a silver tip. It has been shown that quantum mechanical effects such as electron tunneling and nonlocal screening become important as the tip-substrate distance approaches the sub-nanometer scale [39]. However, the gap sizes considered in this study are generally above 1 nm where deviation between quantum mechanical treatment and classical approach is not severe, thus the fields will be treated with classical electromagnetic theory here. The results obtained here should provide a reasonably reliable picture of the effect of various tip and substrate parameters on fluorescence enhancement in a TEF setup.

2. Materials and methods

A silver conical tip with an apex angle of 30° is positioned above a glass substrate as shown in Fig. 1

Fig. 1 A schematic illustration of the tip-enhanced fluorescence (TEF) setup. A silver tip of conical shape is positioned directly above a dipole molecule situated 0.5 nm above a glass substrate. Linearly polarized light is incident from the side with an angle of incidence 40° and the polarization is in the plane of incidence.

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. A single dipole molecule is situated 0.5 nm above the surface of the substrate. Since the scattered fields near the tip are dominated by the z-components, horizontally orientated dipoles will not be strongly affected by the presence of the tip. Therefore we choose the dipole moment to be orientated along the z-axis in this study. Linearly polarized light with a wavelength of 532 nm is incident from the side with an angle of incidence 40° and polarization in the plane of incidence. We choose the above condition for incident light as it falls inside the range for optimal field enhancement for TERS [40].

To figure out the fluorescence signal from the dipole emitter, we need to examine excitation and emission of the molecule separately. Excitation of the molecule depends on the z-component of the local field at the position of the molecule and can be drastically enhanced due to the huge field enhancement near the tip. We define the field enhancement factor (EF) to be:

f = \int {| E_{z} |}^{2} d^{3} \vec{r} / \int {| {\vec{E}}_{0} |}^{2} d^{3} \vec{r},

where E_z is the z-component of the field in the presence of the tip and

{\vec{E}}_{0}

is the field in the absence of a tip, and the integration is performed over a sphere of radius 0.25 nm centered at the molecule.

The total decay rate of a dipole emitter can be calculated by modeling it as a two-level system with transition dipole moment $\vec{p}$ and transition frequency ω [12]. The total spontaneous decay rate according to Fermi’s golden rule is expressed as [41]:

γ = \frac{π ω p^{2}}{3 ℏ ε_{0}} ρ ({\vec{r}}_{0}, ω),

where p is the magnitude of the dipole moment located at

{\vec{r}}_{0}

. The local density of states at the location of the molecule,

ρ ({\vec{r}}_{0}, ω)

, can be obtained by solving the Green’s function of the system [41]:

ρ ({\vec{r}}_{0}, ω) = \frac{6 ω}{π c^{2}} [\vec{u} \cdot Im {\overset{\leftrightarrow}{G} ({\vec{r}}_{0}, {\vec{r}}_{0})} \cdot \vec{u}] = \frac{6 ε_{0}}{π ω p} Im [\vec{u} \cdot {\vec{E}}_{m} ({\vec{r}}_{0})],

where

\overset{\leftrightarrow}{G}

is the dyadic Green’s function,

\vec{u}

is the unit vector in the direction of the dipole moment, and

{\vec{E}}_{m}

is the electric field emitted by the dipole molecule. Using Eq. (3) and the local density of states in free space

ρ_{0} = ω^{2} / (π^{2} c^{3})

, we can obtain the spontaneous decay rate in free space to be

γ_{0} = ω^{3} p^{2} / (3 π ε_{0} ℏ c^{3})

. The total decay rate for an arbitrary electromagnetic environment can be normalized by

γ_{0}

as:

\frac{γ}{γ_{0}} = \frac{6 π ε_{0} c^{3}}{ω^{3} p} Im [\vec{u} \cdot {\vec{E}}_{m} ({\vec{r}}_{0})] .

Alternatively, one can calculate the ratio of the two spontaneous decay rates as the ratio of the power P radiated by the dipole in the presence of the tip to that radiated in free space [41]:

\frac{γ}{γ_{0}} = \frac{P}{P_{0}},

where

P_{0} = ω^{4} p^{2} / (12 π ε_{0} c^{3})

is the power emitted by a classical dipole in free space.

However not every photon emitted by the molecule is detectable as far-field radiation due to non-radiative loss to the nearby metal. The far-field radiation as a percentage of the total emission of the molecule is represented by the quantum yield:

q_{a} = γ_{r} / γ = 1 - γ_{nr} / γ,

where

γ_{r}

and

γ_{nr}

are the radiative and nonradiative decay rates respectively. The nonradiative rate is a result of Ohmic loss and is given by [25]:

\frac{γ_{nr}}{γ_{0}} = \frac{1}{2 P_{0}} \int_{V} Re {\vec{J} (\vec{r}) \cdot {\vec{E}}_{m}^{*} (\vec{r})} d^{3} \vec{r},

where

\vec{J} (\vec{r})

is the induced current density in the dissipative medium, and the integration is performed over a finite volume V where dissipation occurs.

The competition between local field enhancement and fluorescence quenching can then be used to calculate the fluorescence enhancement factor (FEF), which is the product of the field enhancement factor and the quantum yield:

FEF = γ_{em} / γ_{em}^{0} = f \cdot q_{a} .

where

γ_{em}

and

γ_{em}^{0}

are the fluorescence emission rates near the tip and in free space, respectively. For simplicity, we have assumed the intrinsic quantum yield q₀ of the molecule to be unity. In general, the apparent quantum yield is proportional to the intrinsic quantum yield q₀ of the molecule, therefore the fluorescence enhancement factor is not affected by q₀.

To calculate the field enhancement factor and the decay rates, we have applied the finite element method (COMSOL Wave Optics Module) to a physical domain of 750 × 750 × 1050 nm³ in three dimensions. The physical domain consists of a 250-nm-thick substrate, a tip, and the air medium above the substrate. It is surrounded by a perfectly matched layer (PML) of thickness 150 nm in all directions to reduce reflection of fields at the boundaries. The tip as shown in Fig. 1 extends vertically to the edge of the physical domain and continues into the PML to closely model the effect of a real-sized tip. An electric point dipole orientated perpendicular to the substrate surface is placed directly below the tip at a fixed distance of 0.5 nm above the substrate with the tip-substrate distance being varied. To calculate the nonradiative rates, the integration in Eq. (8) is performed over the portion of the tip inside the physical domain. We have found the integral is dominated by contributions from the tip apex region where most nonradiative energy transfer occurs. For the field calculations, the top and side walls of the physical domain are chosen as the port for the incident plane wave with the same PML boundary condition used in the simulations of dipole radiation. The fields are calculated in the presence of the metal tip as well as in the absence of it, with the normalization being a division of the former by the latter. The optical constants for silver and silicon are taken from [42,43], respectively.

3. Results and discussion

3.1 Silver tip on a glass substrate

Figure 2(a)

Fig. 2 Finite element simulation of fluorescence enhancement for a 20-nm-radius silver tip above a glass substrate as shown in Fig. 1. (a) Distribution of the normalized electric field strength |E/E₀| and (b) magnitude of the time-averaged Poynting vector normalized by its value at the location of the molecule on a logarithmic scale for a tip-substrate distance of 2.2 nm. (c) Field enhancement factor, (d) total (solid lines) and nonradiative (dashed lines) decay rates normalized by the spontaneous decay rate of the molecule in free space, (e) quantum yield, and (f) fluorescence enhancement factor as a function of tip-substrate distance.

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shows finite element method calculations of field enhancement as a function of tip-substrate distance for a 20-nm-radius silver tip placed above a glass substrate as shown in Fig. 1. For a tip-substrate distance of a few nanometers, the field is strongly localized and enhanced near the tip apex as a result of both the lightning rod effect and tip plasmon resonances [Fig. 2(a)]. As shown in Fig. 2(c), the field enhancement factor increases rapidly as the tip is brought closer to the substrate and reaches around 5000 for a gap size of 1.0 nm.

The dipole radiation pattern of the emitter is clearly observed in the presence of the tip [Fig. 2(b)]. The total decay rate and the nonradiative decay rate are then figured out by using the imaginary part of the electric field at the location of the molecule and calculating the Ohmic loss inside the tip respectively. We also use the power ratio in Eq. (6) to obtain the total decay rates which are within numerical errors of the results obtained using Eq. (5). Both rates are seen to increase as the tip is brought closer to the molecule, as shown in Fig. 2(d). However, the nonradiative rate increases more rapidly when the tip is within a few nanometers of the molecule as a result of nonradiative energy transfer to the metal tip, leading to fluorescence quenching as shown by the quantum yield curve in Fig. 2(e). As fluorescence EF is the product of field enhancement and quantum yield, the increase in field enhancement leads to an increase in fluorescence EF for larger gap sizes where the quantum yield is nearly constant. As the gap size falls in the range of a few nanometers, the rapid decrease in quantum yield overshadows the increase in field enhancement, leading to a decrease in fluorescence EF. As a result, a maximum FEF of ~1500 is found at a tip-substrate distance of 2.2 nm as shown in Fig. 2(f).

The field enhancement, the radiation pattern of the dipole molecule, and the decay rates are controllable through a set of parameters including the tip radius and the substrate material. As shown in Fig. 3

Fig. 3 Fluorescence enhancement for silver tips of different radii above a glass substrate as shown in Fig. 1. (a) Field enhancement factors, (b) quantum yields, and (c) fluorescence enhancement factors as a function of tip-substrate distance for three different tip radii: 10 nm (solid lines), 20 nm (dashed lines), and 50 nm (dotted lines).

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, a tip radius of 10 nm produces a maximum FEF of ~10⁴ [Fig. 3(c)], roughly a fivefold increase compared with a 20-nm-radius tip. For a tip of smaller radius of curvature, nonradiative loss is decreased due to a reduction in surface area for the decay channel. The loss becomes appreciable only at smaller tip-substrate distances where the solid angle subtended by the tip surface at the location of the molecule becomes large enough to cause significant nonradiative energy transfer. As a result, the decrease in quantum yield occurs at smaller tip-substrate distances as shown in Fig. 3(b). In addition, an increase in field enhancement is also observed due to a more pronounced lightning rod effect [Fig. 3(a)]. The converse is true for a tip of larger radius of curvature 50 nm, resulting in a smaller maximum FEF of ~100.

3.2 Silver tip on a TiO₂ substrate

In the configuration considered above, the plasmonic contribution to enhancement is due mostly to the induced dipole at the tip apex as the image dipole inside the glass substrate is not very strong. It has been shown that well-confined plasmonic propagating modes can exist inside a 1-nm air gap between a dielectric nanowire and a metal surface when the dielectric constants of the two are matched to satisfy Eq. (1) [37]. Here, we use a TiO₂ substrate with a refractive index of 2.67 at 532 nm [44] to pair with the silver tip providing a reasonably good match between the two dielectric constants. We find, as a result of matching dielectric constants, additional plasmonic coupling between tip and substrate occurs, leading to an increase in field enhancement.

As shown in Fig. 4(a)

Fig. 4 Finite element simulation of field enhancement and radiation pattern for a 20-nm-radius silver tip above a TiO₂ substrate. Distribution of the normalized electric field strength for a 20-nm-radius silver tip placed: (a) 1.2 nm and (b) 10 nm above a TiO₂ substrate. Magnitude of time-averaged Poynting vector normalized by its value at the location of the molecule on a logarithmic scale for a 20-nm-radius silver tip placed: (c) 1.2 nm and (d) 10 nm above a TiO₂ substrate.

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, the field for a tip-substrate distance of 1.2 nm, where the fluorescence EF reaches maximum [see Fig. 5(c)

Fig. 5 Fluorescence enhancement for a 20-nm-radius silver tip above glass and TiO₂ substrates. (a) Field enhancement factors, (b) quantum yields, and (c) fluorescence enhancement factors as a function of the tip-substrate distance for a 20-nm-radius silver tip placed above glass (solid lines) and TiO₂ (dashed lines) substrates.

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], is strongly enhanced inside the gap due to the resonant excitation of gap plasmons. When the gap size is increased to 10 nm where the plasmonic interaction between the silver tip and the TiO₂ substrate is greatly reduced, a much weaker field enhancement results [Fig. 4(b)]. The dipole radiation patterns of the emitter for a gap size of 1.2 nm and 10 nm are shown in Figs. 4(c) and 4(d) respectively. At a gap size of 1.2 nm, there is significant extension of electric fields into the metal tip which increases the nonradiative energy transfer thus decreasing the quantum yield.

A comparison between the results for the glass and TiO₂ substrates is shown in Fig. 5. Compared with that of a non-dielectric-matched configuration, we can see an order of magnitude improvement in field enhancement as the tip-TiO₂ substrate distance approaches 1.0 nm [Fig. 5(a)]. Furthermore, the relatively high refractive index of TiO₂ also mitigates quenching, due to a decreased confinement volume and therefore an increased LDOS, leading to an increase in quantum yield, as shown in Fig. 5(b). These factors lead to an appreciable increase in fluorescence EF. As shown in Fig. 5(c), a maximum FEF of ~8500, is seen at a tip-substrate spacing of 1.2 nm, a roughly six-fold improvement. The shift of the maximum fluorescence EF to an even smaller tip-substrate spacing for the TiO₂ substrate is the result of a faster increase in field enhancement and a slower decrease of quantum yield with decreasing gap size.

We note that Eq. (1) is not exactly satisfied by the refractive indexes of silver (n_Ag = 0.054 + 3.429i) and TiO₂ (2.67) at 532 nm. To test the case of perfect dielectric matching, we have calculated the field enhacnement, quantum yield and fluorescene EF for a fictitious metal tip (n_metal = 0.054 + 2.67i), whose dielectric constant is perfectly matched to that of TiO₂. As shown in Fig. 6(a)

Fig. 6 Fluorescence enhancement for a 20-nm-radius silver tip and a 20-nm-radius fictitious metal tip above a TiO₂ substrate. The latter material is chosen to match the dielectric constant of TiO₂ perfectly. (a) Field enhancement factors, (b) quantum yields, and (c) fluorescence enhancement factors as a function of the tip-substrate distance for the silver tip (solid lines) and the fictitious metal tip (dashed lines).

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, compared with a silver tip, the field enhancement almost doubles due to more efficient excitation of gap plasmons. However, the fictitious metal is less effective in screening electric fields due to the smaller imaginary part of its refractive index, resulting in more ohmic loss and thus a decrease in quantum yield [see Fig. 6(b)]. The field enhancement is still large enough to overcome these nonradiative losses, leading to an improved fluorescence enhancement factor of ~11000 as shown in Fig. 6(c).

3.3 Silicon tip

To study the dependence of fluorescence enhancement on the tip material, the same calculations are carried out for a silicon tip. In this case, Eq. (1) is not satisfied for both glass and TiO₂ substrates. Figure 7

Fig. 7 Finite element simulation of field enhancement and radiation pattern for a 20-nm-radius silicon tip above glass and TiO₂ substrates. Distribution of the normalized electric field strength |E/E₀| for a 20-nm-radius silicon tip placed: (a) 3.0 nm above a glass substrate and (b) 1.8 nm above a TiO₂ substrate. Magnitude of time-averaged Poynting vector normalized by its value at the location of the molecule on a logarithmic scale for a 20-nm-radius silicon tip placed: (c) 3.0 nm above a glass substrate and (d) 1.8 nm above a TiO₂ substrate.

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shows a comparison of the field distribution and the dipole radiation pattern for the glass substrate at a tip-substrate distance of 3.0 nm and the TiO₂ substrate at a tip-substrate distance of 1.8 nm. The fluorescence enhancement factors are found to reach maxima at these gap sizes [see Fig. 8(c)

Fig. 8 Fluorescence enhancement for a 20-nm-radius silicon tip above glass and TiO₂ substrates. (a) Field enhancement factors, (b) quantum yields, and (c) fluorescence enhancement factors as a function of the tip-substrate distance for a 20-nm-radius silicon tip placed above glass (solid lines) and TiO₂ (dashed lines) substrates.

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]. The field enhancement factors, quantum yields, and FEFs as a function of the tip-substrate distance are plotted in Fig. 8.

From Fig. 7(a), we can see field enhancement for a silicon tip above a glass substrate is still present but is significantly smaller compared with that for a silver tip. On the other hand, the advantage of a TiO₂ substrate is apparent in improving both field enhancement and quantum yield [Figs. 8(a) and 8(b)]. For a silicon tip above a glass substrate, the field enhancement is largely due to the induced dipole at the tip apex as a result of its high refractive index [21]. In the case of a silicon tip above a TiO₂ substrate, further enhancement results from the image dipole within the substrate, whose magnitude is boosted as a result of the large index contrast at the air-TiO₂ boundary. However, since gap plasmons are not resonantly excited in this case, fluorescence enhancement reaches a maximum of about 400 at a tip-substrate distance of 1.8 nm, which is more than 20 times smaller than that obtained for a silver tip above a TiO₂ substrate.

4. Conclusion

In summary, we have studied fluorescence enhancement and quenching for a dipole emitter placed between a tip and different dielectric substrates. We have found fluorescence enhancement displays a resonant behavior where both the maximum fluorescence enhancement factor and the corresponding tip-substrate distance can be tuned by choosing different tip materials and dimensions. As the tip radius decreases, we have found the maximum fluorescence enhancement generally increases and the resonance occurs at smaller tip-substrate distances. Furthermore, our results demonstrate that the enhancement in fluorescence signal can also be tuned through the choice of substrate material. In particular, using a dielectric substrate with dielectric constant matching that of the metal tip, gap plasmons can be resonantly excited leading to a significant increase in both field enhancement and quantum yield. The results obtained here may find use in optimizing tip-enhanced Raman spectroscopy setups for efficient measurement of fluorescence signal.

Funding

San Francisco State University CCLS Mini-Grant program; National Institutes of Health (NIH) (1R15GM116043-01).

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Fluorescence enhancement and quenching in tip-enhanced fluorescence spectroscopy

Abstract

1. Introduction

2. Materials and methods