1. Introduction

Total internal reflection fluorescence (TIRF) microscopy, also known as evanescent wave microscopy, has been widely used in bioimaging [1,2], chemical sensing [3,4], and biophysical applications [5,6]. This method provides low-noise, high-quality images of specimen containing fluorophores, such as quantum dots or fluorescent molecules. When light traveling in a glass substrate strikes the glass-water interface at an angle larger than the total internal reflection (TIR) critical angle, an evanescent field is produced in the water. This exponentially decaying field generates a thin layer of illumination at the interface where the specimens of interest, for example, bio-molecules or cells, are attached. For a penetration depth ≳100 nm, the evanescent field excites the specimens in the proximity of the surface selectively and intensively, and minimizes the background signals.

Although TIRF microscopy has been successful in improving the signal-to-noise ratio of conventional fluorescence microscopes, several details about it remain to be clarified, as elaborated upon in the following text. First, the achievable penetration depth of the evanescent field is limited by the refractive indices of the water and glass substrate, and thus, it is barely customizable for various applications. For example, in the single molecule detection, the evanescent tail is still sufficiently long, whereby it cannot resolve a target molecule from among the molecules. Second, conventional optics cannot provide the horizontal confinement of TIRF illumination at the deep subwavelength scale beyond the optical diffraction limit. This indicates that conventional TIRF microscopy would not be suitable for observing biophysical phenomena on the scale of a few tens of nanometers, such as molecular reactions or protein transfers [7]. Lastly, strong field concentrations at the deep subwavelength scale are required to enhance not only the excitation of the fluorophores but also their fluorescence emission. The high Purcell enhancement of the fluorescence emission can improve signal quality of the TIRF microscopy significantly.

Plasmonic nano-antennas offer an efficient solution to convert light propagating in free-space into local electromagnetic field within a subwavelength volume and vice versa [8]. They can also manipulate the absorption or emission properties of quantum emitters [9] including radiation direction [10]. In particular, there has much research into using the strong field confinement of the antennas to enhance fluorescence signals from fluorescent molecules [11], or photoluminescent quantum dots [12,13], control electroluminescence from quantum well [14], improve surface enhanced Raman scattering [15], and generate second harmonic signals [16]. Despite the significant advantages of plasmonic nano-antennas, little research has been conducted on using plasmonic nano-antennas in combination with TIRF microscopy. In this study, we propose a modified bow-tie nano-antenna, which can improve the performance of TIRF microscopy. The proposed nano-antenna not only concentrates the TIR evanescent field at the deep subwavelength scale, but also enhances the spontaneous fluorescence emission by the Purcell effect [17]. Finite-difference time-domain (FDTD) calculations were performed to obtain the resonant spectra and field distributions of individual resonant modes. In addition, we calculated the far-field radiation patterns for each mode and confirmed the strong correlation between the far-field pattern and enhancement of the excitation light.

2. Design scheme of plasmonic nano-antenna for TIRF microscopy

Figure 1(a) shows a schematic diagram of the plasmonic nano-antenna coupled with TIRF microscopy. The nano-antenna is formed on a glass substrate and submerged in water. The TIR critical angle at the glass-water interface is ~66.5°. By employing its plasmonic resonant modes, the metallic nano-antenna can efficiently manipulate the TIR evanescent fields generated by the excitation light, which is incident at an angle larger than the TIR critical angle of the glass-water interface. In particular, plasmonic nano-antennas with a central nano-gap can strongly concentrate TIR evanescent fields into the nano-gap and overcome the optical diffraction limit in the complete three dimensions. This confined field selectively excites the fluorophores at the gap and makes their fluorescence signals stronger than the background signals, with a high signal-to-noise ratio.

 

Fig. 1 (a) Schematic diagram of a plasmonic nano-antenna coupled to TIRF microscopy. The nano-antenna is formed on a glass substrate and covered with water. The blue cone represents the TIR critical angle. The excitation light is injected at an angle larger than the TIR critical angle and the output fluorescence emission is detected in the upward or downward direction. The modified bow-tie nano-antenna concentrates the evanescent excitation illumination at the sub-wavelength nano-gap and boosts the spontaneous fluorescence emission simultaneously. (b) Schematic spectra of the resonant modes of the plasmonic nano-antenna. When the resonance peak of the two separated antenna modes (red and blue solid lines) overlaps with the emission (red dotted line) and excitation (blue dotted line) bands of fluorophores, the fluorescence process performance is doubly enhanced. (c) Expected plasmonic charge distributions of the lowest three modes from the modified bow-tie nano-antenna.

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When the nano-antenna supports multiple plasmonic resonant modes at different wavelengths, one of the resonances can be used for intensifying the emission, while the other one at a lower wavelength can be used for the excitation. If both the resonant modes have electric field profiles concentrated at the central gap, and their wavelengths are tuned to the excitation and emission spectra as shown in Fig. 1(b), the total fluorescence output can be enhanced doubly [18]. Since the fluorescence emission and excitation process is enhanced by |E_{emission mode}|² and |E_{excitation mode}|², respectively, a total enhancement of |E_{emission mode}|²|E_{excitation mode}|² is achievable and a larger increase in the total fluorescence output is expected. This concept is analogous to the concept of surface enhanced Raman spectroscopy (SERS), in which the total enhancement is approximately proportional to |E|⁴. However, a single-mode antenna showing unequal field enhancement for all frequencies does not show an |E|⁴ enhancement since both the excitation and emission stages cannot be maximally enhanced. In addition, engineered plasmonic nano-antennas tend to induce fluorescence emissions in the upward or downward direction, in which fluorescence signals are collected by microscope objectives, thus providing a high collection efficiency.

Here, we propose a gold modified bow-tie antenna structure supporting multiple plasmonic antenna resonances, as illustrated in Fig. 1(c). Both the first and third modes have an anti-symmetric charge distribution, which provides not only a strong confinement of electric fields at the central nano-gap, but also a well-defined dipole moment that interfaces with the confined fields with efficient free-space radiation. In contrast, the second resonant mode, a dark mode with a symmetric charge distribution, does not confine electric fields at the central nano-gap or exhibit good coupling with free-space radiation.

3. Plasmonic resonant modes of the modified bow-tie nano-antenna

Figure 2 shows the characteristics of the resonant modes supported by a typical gold modified bow-tie antenna. We calculated the resonance spectra, charge distributions, and electric field distributions of the lowest three resonant modes. Here, the length, width, and thickness of the nano-antenna were 450, 150, and 55 nm respectively. The antenna has a right-angled apex at the bow-tie and a gap size of 30 nm. The resonance spectra of the first and third modes shown in Fig. 2(a) were obtained by calculating and normalizing the electric field intensity enhancement at the antenna center when a plane wave was normally incident from the glass substrate. For the second mode, that is, for dark to normal incidence, we imposed an artificial plane wave with an anti-symmetric E_x field distribution and calculated the field intensity enhancement at the position shifted by 10 nm from the center. The resonant wavelengths of the antenna modes were well-separated and the first mode shows a line width much broader than the others show. The detail spectral characteristics of the first and third modes are discussed in the next section.

 

Fig. 2 (a) Normalized electric field intensity enhancement spectra of the resonant modes. The resonant wavelengths of the first, second, and third modes were approximately 1150, 890, and 670 nm, respectively. The length, width, gap size, and thickness of the antenna were 450, 150, 30, and 55 nm, respectively. (b) Calculated plasmonic charge distributions at the horizontal cross section. Red and blue colors in the scale bars represent the positive and negative signs of the charges. (c) Normalized electric field intensity distribution. Both the first and third modes support the strong field confinement at the nano-gap of the antenna. The distribution was calculated at the cross section of the antenna, 20 nm above the glass substrate. (d) Normalized electric field energy density distribution at the same cross section as (c).

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The charge distribution obtained by taking the divergence of the electric fields can be used to explain the origins of the antenna resonant modes [Fig. 2(b)]. The bonding and anti-bonding combinations of the dipolar charge oscillations from each antenna arm result in the first and second modes, respectively. The anti-bonding mode has a shorter resonant wavelength due to the larger restoring force of the charge oscillation compared to the bonding mode [19]. The third mode exhibits the bonding combination of the longitudinal quadrupole oscillations. The in-phase bonding combinations of the plasmonic oscillations support the strong electric field concentration at the central nano-gap, as shown in Fig. 2(c). We also calculated the mode area of the antenna mode, defined as total energy of electric fields divided by the maximum value of the electric field energy density: $A_m={\displaystyle \iint \epsilon {\left|E\right|}^{2}da}/\max \left(\epsilon {\left|E\right|}^2\right)$. For the metals, we employed the effective dielectric constant, ${\epsilon }_{eff}=\mathrm{Re}\left[d\left(\omega \epsilon \right)/d\omega \right]$, of which the value for gold is ~82 and ~34 at the wavelengths of the first and third modes, respectively [20,21]. The mode areas of the first and third modes are only ~1.6 × 10⁻³ and 4.2 × 10⁻³ μm², corresponding to ~0.002 (λ_1st/n_water)² and ~0.02 (λ_3rd/n_water)², respectively. Due to the boundary condition, the electric field amplitude drops by a factor of ${\epsilon }_{water}/{\epsilon }_{metal}$ from water to metal. As a result, the amount of electric field energy penetrated into the metal is approximately proportional to $1/{\epsilon }_{metal}$: ${\epsilon }_{metal}{\left|E\right|}^2\propto {\epsilon }_{metal}\times {\left({\epsilon }_{water}/{\epsilon }_{metal}\right)}^2\propto 1/{\epsilon }_{metal}$. The electric field energy density distribution in Fig. 2(d) clearly shows that the third mode with a lower effective dielectric constant of gold has more electric field energy in the metal region and a larger mode area than the first mode.

The decay length of the evanescent field along the z-axis was calculated to be only ~76 nm and ~60 nm from the glass surface for both of the first and third mode, respectively. It is remarkable that this value is much smaller than the decay length at the bare glass-water interface. For example, at the incident angle of 70°, the decay length is ~180 nm for the wavelength of 665 nm. This corresponds to the resonant wavelength of the third mode. On the other hand, the second mode is not suitable for concentrating the TIR evanescent fields since its electric field profile is widely distributed over the antenna and has a null electric field energy at the nano-gap center.

In the 3D FDTD simulations, gold was modeled with the Drude dielectric function of a free electron gas: ε(ω) = ε_∞ - ω_p² / (ω² + iγω). The Drude model was used to fit the experimentally determined dielectric function of gold in the spectral range from 580 to 1600 nm [22]. The background dielectric constant ε_∞, plasma frequency ω_p, and collision frequency γ at room temperature were set at 10.48, 1.376 × 10¹⁶ s⁻¹, and 1.177 × 10¹⁴ s⁻¹, respectively. The domain and grid sizes were 1400 × 950 × 1200 nm³ and 4 nm, respectively. The uniaxial perfectly matched layer (UPML) was used as the absorbing boundary condition. The refractive index of water and glass was set as 1.33 and 1.45, respectively.

4. Spectral characteristics of the plasmonic resonant modes

In order to maximize the plasmonic fluorescence enhancement in the TIRF microscopy, it is necessary to tune the resonant wavelength of the antenna modes to the excitation or emission wavelength of fluorophores in use. We examined the spectral properties of the resonant modes by calculating the enhancement, of total electric field intensity, |E|², as a function of the wavelength (Fig. 3). The enhancement is the intensity ratio at the center of the nano-gap between the presence and absence of the antenna. Since a plane wave normally incident on the antenna plane was employed, the second mode was not excited. One can easily see that the resonant modes of the modified bow-tie antenna can be widely tuned by changing its length as shown in Fig. 3(a). As the length increases from 300 to 500 nm, the first mode shifts from ~830 to ~1260 nm and the third mode, from ~580 to ~690 nm. The wide spectral tuning is able to deal with diverse fluorophores having different excitation or emission wavelengths. As a result, they are highly flexible for the desired application [23]. In particular, we set the first mode to operate over the entire near infrared (NIR) range, which consists of frequencies to which most biological materials, including proteins, cells, and even tissues, are transparent, and in which no damage or destruction occurs from direct light absorption [24,25]. In addition, the resonant wavelength of the third mode is sufficiently separated from the interband electronic transition range of gold [22]. The interband transition causes a considerable loss in gold at wavelengths of ~500 nm or less and limits the practicality of using plasmonic nano-structures for many applications [26]. For an application requiring operation in the visible or even ultraviolet wavelength range, gold can be substituted with other metals, such as silver [27] or aluminum [28]. In contrast to the effect of the antenna length, changing the width does not significantly influence the resonance wavelengths, as shown in Fig. 3(b). During the width increase from 130 to 170 nm, the enhancement peak of the third mode is the only mode that exhibits a slight rise with a red shift.

 

Fig. 3 Electric field intensity enhancement spectra of the first and third modes depending on the antenna geometry: (a) length, (b) width, (c) gap size, and (d) thickness. The enhancement was calculated at the center of the nano-gap 10 nm above the substrate. Here, we set the initial geometric parameters, namely, antenna length, width, gap size, thickness, as 450, 150, 30, 55 nm and varied only one of the parameters.

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The gap size predominantly determines the field enhancement, leaving the resonant wavelength nearly fixed as shown in Fig. 3(c). It is well known that the narrower the gap size, the stronger the field confinement [29]. The first mode supports a strong field intensity enhancement factor of ~180 and ~50 for a gap size of 30 and 50 nm, respectively. Here, the curvature radius of the tip was 4 nm. In order to examine the effect of sharpness of the tip edge, we also performed simulations with a tip curvature of 12 nm. When the gap size is fixed to be 30 nm, the field enhancement for a tip curvature of 12 nm is ~220, which is even higher than that for a tip curvature of 4 nm, ~180. It is because the electric field diffuses from the gap of extremely sharp tips more rapidly than that of blunt tips, even though the sharp tip has a stronger field right at the tip edge. The sharpness of the tip does not show significant influence on the field enhancement at the nano-gap center at least 15 nm apart from the tip edge. We can also change the thickness of the antenna in order to control the enhancement and resonant wavelength of the antenna mode as shown in Fig. 3(d). As the thickness decreases from 85 to 35 nm, the field enhancement of the first mode increases from ~130 to ~250 due to a stronger charge density at the apex. Above 65 nm, another higher order mode based on the plasmonic resonance along the thickness direction appears and an even coupling between the third and higher order modes complicates the spectral behavior. Thus, an antenna with a thin metal layer can intensify the fluorescence emission by the first mode and can also excite a quantum emitter with a well-isolated third mode.

The field enhancement at the first mode resonance shows a monotonic increase as the antenna is lengthened. The first mode has a far-field radiation pattern with a prominent lobe in the normal direction, which is similar to that of a single dipole emitter on the glass substrate. Since the lobe shape and intensity of the dipole-like emission pattern are not sensitive to wavelength changes, the degree of enhancement is approximately proportional to the physical cross section of the antenna. Contrastively, the enhancement produced by the third mode tends to drop at the antenna length of ~400 nm. The far-field pattern of a higher order mode is more likely to have multiple lobes, and their intensities and directions are highly dependent on both the antenna geometry and the wavelength of light. Thus, the third mode spectral behavior is highly sensitive to both the wavelength and the angle of the incident light. In order to fully understand the influence of the incident angle on excitation light capture and field enhancement, especially under TIR conditions, a rigorous study of the far-field radiation pattern of each antenna mode is required.

5. Far-field radiation pattern of the first and third mode

In order to obtain the far-field radiation patterns of the antenna modes, we placed an E_x dipole source at the center of the nano-gap and set its wavelength to the first or third mode. The emission from the dipole source is coupled to the first mode and transmitted to free-space with a unique far-field radiation pattern via the nano-antenna, depending on the local density of states of the antenna mode, position and orientation of the dipole source, and so on [17]. The conventional near-to-far-field (NTFF) method used for calculating surface equivalent current density [21] has been only valid when the antenna and dipole source were surrounded by a homogeneous medium. In order to correctly account for inhomogeneous media, such as the substrate, we employed a novel method of NTFF transformation based on the reciprocity theorem [30] and the transfer matrix method [31]. Figure 4(a) shows the geometry and coordinates used in the far-field calculation, where the polar angle (θ) and azimuthal angle (ϕ) specify the direction of radiation. In order to represent the far-field radiation pattern conveniently, we employed a simple mapping defined by (x, y) = (θ cosϕ, θ sinϕ). The far-field radiations toward the water and glass substrate are represented in the northern and southern hemispheres, respectively.

 

Fig. 4 (a) Mapping scheme of the far-field radiation pattern from the hemispherical domain (3D) to the polar domain (2D). (b) Far-field radiation distribution of the first mode. We also plot angular distributions over the meridional paths for ϕ = 0° (red) and ϕ = 90° (blue). The far-field patterns on the left side are shown using a logarithmic scale and the angular distributions are shown using a linear scale. The far-field distribution was normalized by the maximum radiation intensity. The green solid line in the angular distribution indicates the TIR critical angle of ~66.5° at the glass-water interface. (c) Far-field radiation pattern of the third mode. The angular plot for the meridional path for ϕ = 34°, where the maximum radiation intensity of the third mode appears, is also included. The white dashed line in the far-field pattern corresponds to the meridional path for ϕ = 34°. The antenna structure and the resonant wavelengths of the modes are identical to those in Fig. 2.

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Figures 4(b) and 4(c) show the far-field radiation patterns of the first and third mode, excited by the monochromatic dipole source. Each pattern was normalized to the maximum radiation intensity. The far-field pattern of the first mode is highly similar to that of a single dipole source on the glass-water interface, as shown in Fig. 4(b). This is a natural result since the dipole term is dominant in the multipole decomposition of the first mode with a fundamental charge distribution [32]. Due to its dipole-like radiation, the first mode emits most of the radiation energy in the upward and downward directions. Thus, it provides advantages such as allowing the probing of the fluorescence emission with a high collection efficiency using conventional objective lenses. The first mode respectively delivers ~29% and ~35% of the total radiation energy in the upward and downward directions within the collecting angle of ± 60°. The radiation pattern of the glass substrate exhibits not only the central lobe, but also the narrow peak at the TIR critical angle. The narrow peak disappears at the meridian of ϕ = 0° due to the boundary condition at the glass-water interface for the electric field polarized along the x-axis.

The far-field pattern of the third mode exhibits several radiation lobes related to the higher-order terms in the expression for multipole decomposition [33]. The maximum radiation intensity is in the direction of the TIR critical angle at the meridian of ϕ = 34°, as shown in Fig. 4(c). The primary radiation lobe extends beyond the TIR critical angle with a dominant intensity. This indicates that the third mode is very efficient for capturing the excitation light coming from the specific direction, thus satisfying the TIR condition and accomplishing a strong enhancement of the TIR evanescent field at the central nano-gap. The far-field radiation pattern directly represents the field enhancement tendency according to the incident light direction. We elaborate on the strong correlation in the next section.

6. Deep subwavelength concentration of the TIR incidence light

Reciprocity in electromagnetic wave propagation refers to the invariance under the interchange between the source in the near-field and the detector in the far-field. The far-field radiation pattern of a dipole source coupled to an antenna is equivalent to the incident angle-dependent distribution of local field intensity enhancement of the incident light by the antenna [31]. As shown in Fig. 5(a), a plane wave with the wavelength of the third mode was injected into the antenna from the glass substrate, at a polar angle of θ. The azimuthal angle was fixed at 34°, where the maximum radiation occurred. The excitation field enhancement was defined as the ratio between the electric field intensity at the antenna center and the incident light intensity. Note that the point dipole source for the far-field calculation in the previous section was positioned at the antenna center. Figure 5(b) clearly shows that the enhancement tendency according to the incident direction completely follows the far-field radiation pattern of the third mode, as we predicted in the previous section. A 370-fold intensity enhancement is achieved at the incident angle of 66.5°, which corresponds to the TIR critical angle. It is notable that strong field enhancement with a factor >300 is supported even at a 70° angle, which is sufficiently larger than the critical angle. Indeed, the third resonant mode of the modified bow-tie antenna provides an ideal platform for concentrating the excitation light and enhancing its evanescent field under TIR conditions.

 

Fig. 5 (a) Schematic of the angled plane wave incident on the modified bow-tie nano-antenna. The incident azimuthal angle ϕ was fixed at 34°, where the maximum intensity of far-field radiation appears. (b) Angular plot of electric field intensity enhancement of the excitation light as a function of the incident polar angle θ. Both the field intensity enhancement of the incident excitation light and the far-field radiation intensity of the antenna mode are plotted. The enhancement was calculated at the center of the nano-gap, 10 nm above the substrate, where the dipole source was positioned for the far-field calculation whose result is shown in Fig. 3. (c) Electric field intensity enhancement profiles at different incident polar angles (logarithmic scale). The antenna structure and the resonant wavelength of the modes are identical to those shown in Figs. 2 and 3.

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Figure 5(c) shows the electric field intensity distributions at various incident angles of the excitation light. It is clearly observed that most of the excitation field is concentrated at the central nano-gap, and strong field enhancement is achieved near the TIR critical angle. For the TIR critical angle incidence, the average enhancement factor is ~390 over the area of 30 × 30 nm² near the antenna center. In fact, this value is larger than the enhancement factor at the nano-gap center, since the electric field becomes stronger as it approaches to the metal surface. The confinement within the deep subwavelength area can reduce the size of the TIR evanescent illumination significantly, thus yielding a highly precise spatial resolution with the TIRF microscope. Of course, under TIR conditions, the rest of the incident light, which is not coupled with the nano-antenna is completely reflected back to the substrate. In addition, the maximum electric field appears at the sharp apex of the antenna tip instead of at the nano-gap center, yielding a field enhancement factor of ~4000. This indicates that better performance in excitation or emission is achieved by positioning a fluorescence emitter closer to the apex rather than at the nano-gap center.

7. The Purcell enhancement of spontaneous fluorescence emission

The Purcell enhancement of dipole emission process corresponds to the enhancement of |E_{emission mode}|² at the position of dipole. For a point dipole source located at the antenna center, we calculated the Purcell enhancement, the ratio of its total emission power with and without an antenna. Here, the dipole source was set to be polarized along the x-axis and the maximum values of the Purcell enhancement were achieved. If the dipole is polarized with an angle of θ to the x-axis, the Purcell enhancement is reduced by a factor of cos²θ. The Purcell enhancement by the first mode is plotted with a varying antenna length, as shown in Fig. 6(a), and the gap size, as shown in Fig. 6(b). It is clearly observed that the values and spectra of the Purcell enhancement well match the enhancement spectra shown in Fig. 3. This result has been predicted by theoretical studies on the correlation between the local density of state of a resonant mode and the Purcell enhancement. The Purcell enhancement is maximized at the resonance wavelength of the first mode, and the maximum value changes from ~140 to ~200 as the antenna length is increased from 350 to 500 nm. The broad bandwidth and easy tunability support high Purcell enhancements >100 over the entire NIR range. This indicates that the modified bow-tie antenna enables flexible and feasible enhancement of the fluorescence emission at different wavelengths, originating from diverse fluorophores. The Purcell enhancement also depends on the gap size. The narrower the gap, the higher the Purcell enhancement.

 

Fig. 6 Spectra of the Purcell enhancement of the first mode depending on the antenna geometry: (a) length and (b) gap size. A single electric dipole source was located at the center of nano-gap 10 nm above the substrate, where the field intensity enhancement was calculated. The ratio of the total emission power of the dipole source with and without the nano-antenna was calculated to obtain the Purcell enhancement. The overlapping solid lines are the field enhancement spectra that match those shown in Fig. 3. The antenna structure parameters are identical to those for Figs. 3(a) and 3(b).

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Figure 6. Spectra of the Purcell enhancement of the first mode depending on the antenna geometry: (a) length and (b) gap size. A single electric dipole source was located at the center of nano-gap 10 nm above the substrate, where the field intensity enhancement was calculated. The ratio of the total emission power of the dipole source with and without the nano-antenna was calculated to obtain the Purcell enhancement. The overlapping solid lines are the field enhancement spectra that match those shown in Fig. 3. The antenna structure parameters are identical to those for Figs. 3(a) and 3(b).

8. Conclusions

We have shown that the modified bow-tie plasmonic nano-antenna can efficiently concentrate the TIR evanescent illumination at the deep subwavelength scale and strongly enhance the fluorescence excitation and emission processes simultaneously. The strong correlation between the enhancement in the incident excitation light intensity and the far-field pattern of the antenna radiation was also confirmed. The proposed plasmonic antenna is expected to improve the detection sensitivity and precision of TIRF microscopy significantly and to provide low-noise, high-quality fluorescence signals for biophysical measurement, chemical sensing, and bioimaging application.