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Surface plasmon-enhanced and quenched two-photon excited fluorescence

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Abstract

This study investigated theoretically and experimentally that two-photon excited fluorescence is enhanced and quenched via surface plasmons (SPs) excited by total internal reflection with a silver film. The fluorescence intensity is fundamentally affected by the local electromagnetic field enhancement and the quantum yield change according to the surrounding structure and materials. By utilizing the Fresnel equation and classical dipole radiation modeling, local electric field enhancement, fluorescence quantum yield, and fluorescence emission coupling yield via SPs were theoretically analyzed at different dielectric spacer thicknesses between the fluorescence dye and the metal film. The fluorescence lifetime was also decreased substantially via the quenching effect. A two-photon excited total internal reflection fluorescence (TIRF) microscopy with a time-correlated single photon counting device has been developed to measure the fluorescence lifetimes, photostabilities, and enhancements. The experimental results demonstrate that the fluorescence lifetimes and the trend of the enhancements are consistent with the theoretical analysis. The maximum fluorescence enhancement factor in the surface plasmon-total internal reflection fluorescence (SP-TIRF) configuration can be increased up to 30 fold with a suitable thickness SiO2 spacer. Also, to compromise for the fluorescence enhancement and the fluorophore photostability, we find that the SP-TIRF configuration with a 10 nm SiO2 spacer can provide an enhanced and less photobleached fluorescent signal via the assistance of enhanced local electromagnetic field and quenched fluorescence lifetime, respectively.

©2010 Optical Society of America

1. Introduction

The scattering of one-photon total internal reflection fluorescence (TIRF) for bio-imaging applications causes excitation photons to leak into deeper cell regions, resulting in the fluorescence image being excited by both near- and far-field components [1]. The confinement of one-photon TIRF excitation is gradually loosed in its propagation direction, and therefore the biological fluorescent image is generated by the excitation of the superposition of an evanescent field and a scattered light component [2]. Therefore, a two-photon TIRF image close to a cell-substrate interface excited by a femtosecond infrared laser has been demonstrated [2]. Benefiting from the nonlinearity and the longer excitation wavelength of multiphoton excitation and the spatial nonhomogeneity of the evanescent field, the two-photon TIRF excitation can largely decrease the out-of-focus fluorescence excited by scattered light. Furthermore, two-photon fluorescence excitation represents the quadratic intensity dependence. Even though the two-photon fluorescence excitation utilizes a longer wavelength, the effective evanescent field penetration depths of one and two-photon TIRF excitations are comparable. Therefore, compared with one-photon TIRF excitation, two-photon TIRF excitation obviously increased the signal-to-noise ratio (SNR) by suppressing background fluorescence [3]. However, the fluorescence intensity excited by two-photon wide-field TIRF microscopy in chemical and biological samples is still in need of being improved if dynamic signals of the molecular interactions are to be acquired [4,5].

Metallic surfaces or particles have been exploited to enhance the fluorescence of the fluorophores in order to develop more efficient fluorescence immunoassays [69]. In these techniques, surface plasmons (SPs) or localized SPs on the metallic surfaces or nanoparticles enhance the local electro-magnetic (EM) field around the fluorophore, and therefore increase the intensity of the detected fluorescence signal [9]. SPs are oscillations of the free electrons located on the surface of a metal film and can be usually excited by incident light based on the prism-coupled total internal reflection or grating-coupled diffraction methods [10]. Conveniently, the prism-coupled excitation can be substituted via the excitation of a highly oblique collimating beam that is generated by focusing a light beam on the outer regions of the back focal plane (BFP) of a high numerical aperture (NA) objective [11]. When the wave vector of an incident evanescent transverse magnetic (TM) light matches that of the SPs, the so-called surface plasmon resonance (SPR) phenomenon occurs. This results in the SPR associated with the EM field being greatly enhanced [10], while the intensity of the two-photon excited fluorescence could be enhanced via the SPs.

The emission efficiency of the fluorophores is usually not only affected by the local SP-enhanced electric field, but also the quenching by the SPs. Therefore, the fluorescence quantum yield and emission coupling yield combined with the local electric field enhancement will dominate the final fluorescence emission efficiency. In the interaction of the SPs with fluorophores located within a very short metal-fluorophore distance (approximately < 10 nm), the dipole field is dominated by the near field, the strength of the fluorescence is quenched, and the excitation fluorescent energy dissipates into the metal in the form of heat [12]. For intermediate separation distances, the emission fluorescence can be effectively coupled back to the SPs of the metal surface by matching the momentum of the fluorophores with that of the SPs. Subsequently, the emission SPs are re-radiated into the glass prism with a hollow cone of intense light around angles near the SPR angle [13]. In one previous study, however, it had been shown that the SP-coupled emission did not lead to any improvement, where the metal film actually reduced the sensitivity of fluorescence detection [14]. The result related to the fluorescent emission rate is therefore still inconsistent. For larger separation distances, the fluorescent emission rate can be predicted by considering the classic mechanism of a dipole, which is influenced by the back-reflected field caused by its dipole image [15]. Therefore, through the moderate modifications of a metal film or particles on a substrate and the metal-fluorophore distance, the SPs obviously contribute to the increase in the quantum yield for achieving a brighter fluorescent signal, a reduction in the fluorescence lifetime for attaining better photostability, and a specific orientation in the typically isotropic emission for providing more information. These effects are not due to the reflection of the emitted fluorescence, but rather as the result of the fluorophore dipole interacting with free electrons in the metal [16,17].

Our previous studies have shown that the SP-enhanced one and two-photon TIRF microscopy can increase the brightness and acquisition frame rate of live cell membrane images [18,19]. In this study, we attempt to identify a suitable spacer between the fluorophore and the metal surface as a trade-off between the fluorescence enhancement and quenching in two-photon excited TIRF microscopy. Therefore, this study investigated systemically that two-photon excited fluorescence is enhanced and quenched via the SPs first. The local electric field enhancement, fluorescence lifetime and quantum yield, and fluorescence emission coupling yield by the SPs with a spacer between the dye and the metal surface are theoretically studied by using the Fresnel equation and classical dipole radiation modeling [2023]. Also, a two-photon TIRF microscopy with a time-correlated single photon counting (TCSPC) module has been developed to observe the fluorescence lifetime, photostability, and enhancements. From the simulations and the experiments, the trend of the enhancement and the fluorescence lifetimes based on the surface plasmon-total internal reflection fluorescence (SP-TIRF) setup are consistent. We can find that the maximum fluorescence enhancement has been increased up to 30 fold with suitable SiO2 spacers. The experimental results demonstrate that the configuration with an optimal SiO2 spacer not only clearly reveals a brighter fluorescent signal compared to that of conventional TIRF, but also improves fluorescence photostability compared to that of a less quenching setup with a thicker spacer.

2. Principle and experimental setup

2.1. Two-photon excited fluorescence by SP-TIRF

The optical setup is based on the oil-immersion objective-coupled TIRF microscopy shown in Fig. 1(a) . A 780 nm femtosecond Ti:sapphire laser (Tsunami, Spectra-Physics) with a pulse width of 100 fs and repetition rate of 80 MHz passes through a half-wave plate and a linear polarizer to control the polarization and power of the laser beam. Then, the beam is reflected by mirrors and is funneled into the microscope by a focusing lens. The optical components are fixed on a linear translation stage in order to adjust the position of the focus point on the back focus plane (BFP) of a high NA oil-immersion objective (60 × , NA = 1.49, Nikon). After that, a parallel laser beam is formed after the objective. The incident angle of the parallel beam is manipulated by adjusting the focusing position on the BFP via moving the linear translation stage. The fluorescence is collected by the same objective and passes through a dichroic mirror, a shortpass filter (SPF, λ < 680 nm, Semrock) and a bandpass filter (BPF, λ = 500 - 535 nm, Semrock). Finally, the fluorescence is focused into a photomultiplier tube (PMT) (H5783P, Hamamatsu) by a lens. The fluorescent signals are counted by a TCSPC module (PicoHarp 300, PicoQuant) to estimate the fluorescence intensity and lifetime.

 figure: Fig. 1

Fig. 1 (a) Schematic diagram of the optical setup of the two-photon excited fluorescence by objective-coupled TIRF and (b) the configuration of the SP-TIRF chip.

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The complex dielectric constants of gold and silver have large negative real numbers in the visible and near infrared light region. Compared with thin gold films, superior fluorescence enhancement is able to be obtained by the excitation of thin silver films with an excitation wavelength of 780 nm. Therefore, the configuration of the SP-TIRF chip with a silver film as a five-layer structure such as 0/1/2/3/4 (BK7/Ag/SiO2/Alq3/Air) is shown in Fig. 1(b). A 0.17 mm cover slip (BK7) is coated with a thin silver film (Ag, d 1 = 40 nm), and a dielectric spacer (SiO2, d 2 = 0 - 100 nm) via a radio frequency sputtering deposition process. After that, a fluorescent dye (Tris(8-hydroxyquinolinato)aluminum, Alq3, d 3 = 10 nm) layer is coated by thermal evaporation process. For a conventional TIRF chip without SPs, there is only an Alq3 fluorescent layer directly coated on a cover slip. Undoubtedly, a 50 nm silver film can provide very strong local electric field enhancement in the SP-TIRF configuration. However, the transmittance of excited fluorescence into the objective is reduced by the 50 nm silver film, and hence the fluorescence emission coupling yield is decreased. Therefore, to collect brighter SP-enhanced two-photon excited fluorescence by the objective-coupled TIRF microscope, a silver film with a thickness of 40 nm is adopted according to the local electric field enhancement and the fluorescence emission coupling yield. According to the simulation of the configuration, a decrease of the silver film thickness decreases the SPR angle so as to resolve the restriction associated with the maximum incident angle imposed by the finite NA value of the objective. When the thickness of the SiO2 spacer is increased, the SPR angle is also increased. Under the maximum incident angle restriction of 79.5° of the adopted 1.49 NA objective, the spacer thickness should be designed to be below 200 nm in order to achieve a better SP excitation.

2.2. Local electric field enhancement via SPs

The local electric field enhancement at different dielectric spacer thicknesses is simulated by utilizing the Fresnel equation. According to the orientation of the fluorescent molecules on the SiO2 spacer, the local electric field to excite the fluorescent molecules can be classified as both the vertical and horizontal electric field, whose polarizations are perpendicular and parallel to the configuration, respectively. Figure 2 shows the local electric field enhancement factors in the 10 nm fluorescent layer based on the SP-TIRF configuration with an excitation wavelength of 780 nm. The five-layer structure of BK7/Ag/SiO2/Alq3/Air has the refractive indices of n 0 = 1.5188, n 1 = 0.1432 + j5.1304, n 2 = 1.4537, n 3 = 1.6895, and n 4 = 1.0 at the excitation wavelength of 780 nm, respectively. For the vertical electric field, the local electric field enhancement factor is monotonically decreased according to the increase of the spacer thickness. The SPs are excited on the metallic surface to enhance the electric field near the metal film, so the electric field intensity decreases as the distance between the metallic surface and fluorescent dye is increased. Therefore, the vertical electric field enhancement factor decays with the increase of the spacer thickness. For the horizontal electric field, the local electric field enhancement factor is proportional to the spacer thickness prior to a spacer thickness of about 50 nm and has a maximum value of about 14 at 50 nm. When the spacer thickness is greater than 50 nm, the enhancement factor gradually decreases as the spacer thickness is increased. However, the dielectric spacer provides a waveguide cavity to modulate the electric field distribution in the fluorescent layer. When the SP effect is removed, i.e. the configuration as the conventional TIRF, the horizontal and vertical electric field enhancements reduce to 0.7 at the incident angle of 51.0°.

 figure: Fig. 2

Fig. 2 Local electric field enhancement factors for (a) vertical electric field and (b) horizontal electric field.

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2.3. Fluorescence lifetime and quantum yield

The above described local field enhancement can increase the intensity of the fluorescence emission. Furthermore, the fluorescence quantum yield and emission coupling yield are also two other key factors that influence the fluorescence emission efficiency. In order to simulate the fluorescence quantum yield, the fluorescent molecule can first be regarded as the electric dipole. Then, the vibrated characteristic of the dipole moment is modulated by its reflected electric field when the dipole is hosted in the five-layer 0/1/2/3/4 structure. The motion of the dipole is presented as [20,21]

p¨+b0p˙+ω02p=(q2m)E,
where p is the dipole moment, b 0 is an initial damping rate, ω 0 is the natural frequency, q is the effective charge, m is the effective mass, and E is the reflected electric field which is parallel to the dipole moment. The dipole moment and the electric field are oscillated at the same complex frequency Ω=ωjb/2, so Eq. (1) can be simplified to
bb0=1Q0+Q00I(u)du,
where b/b 0 is the normalized damping rate and its inverse is the normalized lifetime, Q 0 is the initial quantum yield, and I is the power dissipation by the dipole and is also the function of the orientation of the dipole. To consider the orientation of the dipole, the two types of the normalized damping rate can be denoted as the vertical electric dipole (VED) and the horizontal electric dipole (HED), which are perpendicular and parallel to the interface, respectively. They can be expressed as
(bb0)VED=1Q0+Q032Re(0duu31u2(1+r3210pej2k3zh)(1+r34pej2k3z(d3h)))1r3210pr34pej2k3zd3),
(bb0)HED=1Q0+Q034Re(0duu1u2((1u2)(1r3210pej2k3zh)(1r34pej2k3z(d3h))1r3210pr34pej2k3zd4                                                                                +(1+r3210sej2k3zh)(1+r34sej2k3z(d3h))1r3210sr34sej2k3zd3)),
where u is the normalized transverse wave number, rpand rs are the Fresnel reflection amplitude coefficients for the TM mode and the transverse electric (TE) mode, h is the distance between the fluorescent dye and the interface of the 2/3 (SiO2/Alq3), and k3z is the vertical component of the wave number in layer 3. From Eqs. (3) and (4), the normalized fluorescence lifetime τ for an isotropic distributed dipole can be defined as
τ=1/[13(bb0)VED+23(bb0)HED],
and the modified fluorescence quantum yield is

Q=01I(u)du/0I(u)du.

Because the power dissipation is a function for the orientation of the dipole, the modified quantum yield can be separated into QVED and QHED. Therefore, the dissipated power spectrum of the fluorescent dye can be calculated to evaluate the fluorescence lifetime and modified quantum yield from the theoretical models.

In our experimental configuration, the emission wavelength is assumed to be approximately 530 nm for Alq3 [24]. The initial quantum yield Q 0 is 0.3, while the initial fluorescence lifetime is 12.0 ns. The refractive indexes of the SP TIRF configuration are 1.5196 (BK7), 0.1294 + j3.1772 (Ag), 1.4608 (SiO2), 1.7023 (Alq3), and 1.0 (Air) at the emission wavelength of 530 nm. Figure 3(a) and 3(b) exhibit the fluorescence lifetime and modified quantum yield with various spacer thicknesses from 0 to 100 nm. The fluorescence lifetime is directly quenched down to less than 9.0 ns via the metal film without the spacer of SiO2, arises quickly with increasing the spacer thickness, and then approaches 12.0 ns when the spacer thickness is greater than about 10 nm. Similarly, the modified quantum yields rapidly increase when the spacer thickness is less than about 40 nm, and then slowly rises after the thickness of 40 nm. The non-radiated energy is greater increased via the SPs on the 0/1 interface and the quenching effect by the silver film when the fluorescent dye is near the silver film. Hence, the fluorescence lifetime and modified quantum yield affected by the quenching effect are decreased. When the spacer thickness is increased, the non-radiated power rapidly lowers and the quenching effect is also reduced. The fluorescence lifetime and modified quantum yield are increased with a thicker spacer thickness. Furthermore, the fluorescence lifetime is estimated at 13.8 ns and the modified quantum yield is set at the standard of 1.0 in the conventional TIRF configuration by using the above same theoretical analysis.

 figure: Fig. 3

Fig. 3 The variations of (a) the fluorescence lifetime and (b) modified quantum yield as function of dielectric spacer thickness.

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2.4. Fluorescence emission coupling yield

The radiation pattern of the fluorescent dye is similar to dipole radiation. As the fluorescence penetrates the Alq3 layer, the radiation pattern transmitted through the layer will be transformed into [22,23]

P(θ)=P3(θ3)T3210|1+r34ej2k3z(d3h)1r3210r34ej2k3zd3|2n0k0zn3k3ze|Im(2k3zh)|,
where T 3210 is the transmittance from layer 3 to layer 0, P3 is the radiation pattern according to the orientation and emission angle θ3 of the dipole in the dye layer, and k0z is the vertical component of the wave number in layer 0. The overall emission power, which can be collected by a high NA objective into the detector, can integrate the radiation pattern from the entire emission angle and be described as

EP=0π/22πP(θ)sinθdθ.

Based on the theoretical simulation, the emission pattern obviously reveals that the emission power is confined to a specific emission angle in the SP-TIRF configuration. In the VED case, the emission polarization occurs only in the TM mode, so that the SPs could be excited by the VED emission. The maximum emission intensity is decreased and the specific emission angle increased when the thickness of the spacer is increased. This phenomenon is called the surface plasmon-coupled emission (SPCE) [2529]. In the HED case, the emission polarizations occur in both the TM and TE modes. The characteristics of the HED emission pattern are almost the same as the VED when the spacer thickness is thinner than about 60 nm; thereupon, the SPCE dominates the emission power. When the spacer thickness is thicker than 70 nm, the TE waveguide mode dominates the emission characteristic for the HED, and therefore the emission power is increased based on the waveguide resonance mechanism. The emission characteristics in the TIRF configuration are also obtained by using the theoretical simulation. In the TIRF configuration, the emission power is confined to near the critical angle. The fluorescence emission yield is defined as the overall emission power normalized by that in the conventional TIRF configuration, as shown in Fig. 4 . For the VED case, the overall emission power is slightly higher than that in the TIRF configuration with a spacer thickness of less than 70 nm. This enhancement is caused from the SPCE. However, there is no improvement for the HED, with the overall emission power being lower than that in the conventional TIRF configuration. The TE mode emission from the HED is dissipated by the silver layer.

 figure: Fig. 4

Fig. 4 Fluorescence emission coupling yield in the SP-TIRF configuration compared to that in the conventional TIRF configuration.

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2.5. Simulated fluorescence enhancement

The fluorescence emission intensity is governed by the local electric field in Sec. 2B, the quantum yield in Sec. 2C, and the emission coupling yield in Sec. 2D. For two-photon excited fluorescence, the fluorescence emission intensity is proportional to

F(I0FE)2QEP
where I0 is the excitation power, FE is the local electric field enhancement factor, Q is the modified quantum yield, and EP is the emission power related to the emission coupling yield. The simulated fluorescence enhancement factor is defined as the F in the SP-TIRF configuration normalized by that in the conventional TIRF configuration under a fixed excitation power. Figure 5 shows the simulated enhancement factor as a function of spacer thickness. In Fig. 5, the fluorescence enhancement is separated into three regions. The enhancement factor rapidly rises and reaches a maximum enhancement factor of 75 at a spacer thickness of about 30 nm. This trend is dominated by the modified quantum yield, as shown in Fig. 3(b). The SPCE from the VED in Fig. 4 also contributes to the trend. Between 30 nm and 80 nm, the factor decreases monotonically. After 80 nm, the increasing trend is governed by the HED emission coupling yield with assistance from the TE waveguide mode, as shown in Fig. 4.

 figure: Fig. 5

Fig. 5 Simulated fluorescence enhancement factor governed by the local electric field enhancement factor, the quantum yield, and the emission coupling yield as function of spacer thickness.

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3. Experimental results and discussions

In this section, the experimental results for the SP and conventional TIRF configurations are studied to verify the theoretical simulation in Sec. 2. The quenching effect is first tested by detecting the fluorescence lifetime on different spacer thicknesses. Then, the photostability test is used to verify the relationship between the fluorescence lifetime and photostability: the shorter the lifetime, the better the photostability. To account for all the effects, such as the local electric enhancement, the fluorescence quantum yield, and the fluorescence emission coupling yield, the overall fluorescence emissions with different spacer thicknesses in the SP-TIRF configuration are normalized to that in the conventional TIRF configuration to show the overall fluorescence emission enhancement factor via SPs.

3.1. Fluorescence lifetime and photostability

Figure 6(a) shows the measured fluorescence lifetime vs. different spacer thicknesses in the SP-TIRF excitation. Here, the laser power is fixed at 5 mW. The fluorescence lifetime is similar to the theoretical prediction in Fig. 3(a). The lifetime is extended up to 12.0 ns when the thickness of the spacer is greater than 10 nm. Furthermore, the fluorescence lifetime is also measured from the TIRF excitation. The fluorescence lifetime is 13.9 ns and 13.8 ns for the measurement and the theoretical prediction, respectively. Therefore, the theoretical modeling is appropriate to estimate the actual lifetime in the SP- and conventional TIRF configurations. The experimental results and the theoretical simulation both demonstrate that the fluorescence lifetimes and quantum yields are seriously influenced by the metal surface when the fluorescent dye is near the surface. Figure 6(b) exhibits that the two-photon excited fluorescence intensity decays with time when the laser power is at 15 mW. These experimental results show that the fluorescence intensity decays rapidly when the spacer thickness is increased to greater than 20 nm, and therefore reveals that a better photostability can be provided when the spacer thickness is less than 20 nm. After the 10 nm thickness, the photostability quickly decreases when the spacer thickness increases. Therefore, the quenching effect dominates the characteristics of the two-photon excited fluorescence lifetime and quantum yield when the spacer thickness is thinner than 10 nm. Although the quenching effect reduces the fluorescence emission, it shortens its lifetime to enhance fluorophore photostability.

 figure: Fig. 6

Fig. 6 Experimental results for the fluorescence (a) lifetime and (b) photostability as function of spacer thickness.

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3.2. Overall fluorescence enhancement

The overall fluorescence enhancement factor is defined as the two-photon excited fluorescence intensity in the SP-TIRF configuration normalized by that in the conventional TIRF configuration. Figure 7 shows the overall enhancement factor of the fluorescence intensity as a function of spacer thickness. The trend of the overall fluorescence enhancement is similar to the simulated result by comparing Fig. 7 to Fig. 5. The maximum enhancement factor in the experimental results can be enhanced up to 30 fold at the spacer thickness of 30 nm, as shown in Fig. 7. However, the fluorescence enhancement only reaches 40% of the maximum (70 fold) based on the theoretical simulation. Hence, some other effects to influence the two-photon excitation of the fluorescent dye in the SP-TIRF configuration are not considered in the theoretical analysis. We believe that the two photon absorption cross-section of the fluorescent dye differs depending on configuration. Based on the assumption, the two-photon absorption cross-section in the conventional TIRF configuration is about 2.5 times (70 fold/ 30 fold) higher than that in the SP-TIRF configuration. The maximum enhancement factor of 30 fold is attained with a 30 nm spacer, but better fluorophore photostability can be achieved when the spacer thickness is decreased to less than 20 nm [Fig. 6(b)]. Therefore, to compromise for the fluorescence enhancement and the fluorophore photostability, we find that the SP-TIRF configuration with an SiO2 spacer of 10 nm not only clearly reveals an enhanced fluorescent signal compared to that of conventional TIRF, but also significantly improves fluorescence photostability compared to that of a less quenching setup with a thicker spacer.

 figure: Fig. 7

Fig. 7 The overall enhancement factor of the fluorescence intensity as function of spacer thickness.

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4. Conclusions

This study investigated that two-photon excited fluorescence is enhanced and quenched via SPs. The enhancement and quenching effects by the SPs are theoretically estimated by utilizing the Fresnel equation and classical dipole radiation modeling. From the experimental results, we have demonstrated that the fluorescence lifetimes and the trend of the fluorescence enhancements with different spacers are consistent with the theoretical analysis. The quenching reduces the overall fluorescence enhancement. However, the lifetime of the dye is shortened so that the fluorescence photostability is increased. The maximum fluorescence enhancement has been increased 30 fold, and the photostability can be also significantly improved with suitable SiO2 spacers. Therefore, the SP-enhanced and quenched two-photon TIRF microscopy can provide a brighter and less photobleached fluorescent image with the assistance of an enhanced local electromagnetic field and reduced fluorescence lifetime, respectively.

Acknowledgments

This work was supported by the National Research Program for Genomic Medicine (NRPGM) of the National Science Council (NSC) in Taiwan (NSC 97-3112-B-006-013), NSC 97-3111-B-006-004, and Advanced Optoelectronic Technology Center of National Cheng Kung University.

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Figures (7)

Fig. 1
Fig. 1 (a) Schematic diagram of the optical setup of the two-photon excited fluorescence by objective-coupled TIRF and (b) the configuration of the SP-TIRF chip.
Fig. 2
Fig. 2 Local electric field enhancement factors for (a) vertical electric field and (b) horizontal electric field.
Fig. 3
Fig. 3 The variations of (a) the fluorescence lifetime and (b) modified quantum yield as function of dielectric spacer thickness.
Fig. 4
Fig. 4 Fluorescence emission coupling yield in the SP-TIRF configuration compared to that in the conventional TIRF configuration.
Fig. 5
Fig. 5 Simulated fluorescence enhancement factor governed by the local electric field enhancement factor, the quantum yield, and the emission coupling yield as function of spacer thickness.
Fig. 6
Fig. 6 Experimental results for the fluorescence (a) lifetime and (b) photostability as function of spacer thickness.
Fig. 7
Fig. 7 The overall enhancement factor of the fluorescence intensity as function of spacer thickness.

Equations (9)

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p ¨ + b 0 p ˙ + ω 0 2 p = ( q 2 m ) E ,
b b 0 = 1 Q 0 + Q 0 0 I ( u ) d u ,
( b b 0 ) V E D = 1 Q 0 + Q 0 3 2 Re ( 0 d u u 3 1 u 2 ( 1 + r 3210 p e j 2 k 3 z h ) ( 1 + r 34 p e j 2 k 3 z ( d 3 h ) ) ) 1 r 3210 p r 34 p e j 2 k 3 z d 3 ) ,
( b b 0 ) H E D = 1 Q 0 + Q 0 3 4 Re ( 0 d u u 1 u 2 ( ( 1 u 2 ) ( 1 r 3210 p e j 2 k 3 z h ) ( 1 r 34 p e j 2 k 3 z ( d 3 h ) ) 1 r 3210 p r 34 p e j 2 k 3 z d 4                                                                                   + ( 1 + r 3210 s e j 2 k 3 z h ) ( 1 + r 34 s e j 2 k 3 z ( d 3 h ) ) 1 r 3210 s r 34 s e j 2 k 3 z d 3 ) ) ,
τ = 1 / [ 1 3 ( b b 0 ) V E D + 2 3 ( b b 0 ) H E D ] ,
Q = 0 1 I ( u ) d u / 0 I ( u ) d u .
P ( θ ) = P 3 ( θ 3 ) T 3210 | 1 + r 34 e j 2 k 3 z ( d 3 h ) 1 r 3210 r 34 e j 2 k 3 z d 3 | 2 n 0 k 0 z n 3 k 3 z e | Im ( 2 k 3 z h ) | ,
E P = 0 π / 2 2 π P ( θ ) sin θ d θ .
F ( I 0 F E ) 2 Q E P
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