1. Introduction

Optical antennas are efficient devices to generate strong electromagnetic fields and control the light emission in nanoscale volumes, with major applications in molecular sensing, light-emitting devices, and photovoltaics [1]. One of the most important features of an optical antenna relates to its amplification of the local excitation intensity [2]. Enhancement factors are generally estimated from fluorescence spectroscopy [3], Raman scattering [4], or nonlinear photoluminescence measurements [5]. However, all these techniques quantify the overall response of the coupled emitter-antenna system, merging excitation and emission processes into a single output. For the given example of fluorescence spectroscopy, the signal enhancement near the antenna is a complex combination of modifications on excitation intensity, fluorescence quantum yield, and collection efficiency [3, 6]. In some configurations, the quenching phenomenon may prevent detecting enhanced fluorescence although the excitation intensity is locally enhanced by the antenna.

Here, we present a novel approach to quantify the electromagnetic amplification on aperture antennas by taking advantage of the intrinsic non linear property of the fluorescence process. Our approach relies on the fact that the fluorescence signal is a nonlinear function of the excitation intensity, while it linearly depends on the number of emitters, their quantum yield, and the microscope collection efficiency. This technique builds on a method that we developed recently to quantify separately the local excitation intensity from the number of emitters [7], which also relates to saturated excitation fluorescence microscopy (SAX) [8,9]. For the first time, we apply this extended method to quantify the excitation intensity enhancement on plasmonic aperture antennas. The use of incoherent detection via fluorescent molecules as a probe also improves the detection accuracy by eliminating the effects from local refractive index change.

The technique can be summarized as follows: to probe the nonlinear fluorescence response induced by laser excitation, we modulate the excitation intensity at a given fundamental frequency f = 5 kHz, and demodulate the fluorescence signal at the first and second harmonic frequencies f and 2f (Fig. 1(a)). The main source for the second harmonic generation of fluorescence upon excitation modulation relates to the intrinsic non-linear dependence of the fluorescence signal on the excitation intensity, which is a natural consequence of the fluorescence saturation and finite lifetime [7–9]. As we will demonstrate below, the ratio ρ = F_2f/F_f between the fluorescence amplitudes F_f, F_2f at the fundamental and second harmonic frequencies forms a metric only sensitive to the local excitation intensity. This ratio is used as a direct probe of the electromagnetic intensity enhancement brought by single and corrugated metallic nanoapertures (Fig. 1(b)). Such aperture antennas have been the topic of intensive studies for the last decade [10, 11], and several studies have been performed to enhance and control the fluorescence emission of emitters located inside the central aperture [12–14]. An exhaustive exploration of the design parameters defining the corrugated aperture is now at hand for the optical transmission process [15]. This makes aperture antennas an ideal platform to validate the saturated excitation fluorescence spectroscopy technique.

 

Fig. 1 (a) Principle of saturated excitation of fluorescence: upon excitation intensity modulation at a frequency f, the deformed fluorescence signal contains the fundamental frequency f and also harmonics at higher frequencies (2f, 3f ...) which are recorded by lock-in detection. (b) Scanning electron microscope images of single aperture and corrugated aperture with five grooves of 440 nm period.

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2. Characterization procedure by saturated excitation of fluorescence

To detect the nonlinear components in the fluorescence emission signal of molecules, we consider an incident laser excitation temporally modulated at the fundamental frequency f with a modulation amplitude α. Under these conditions, the temporal dependence of the excitation intensity I_e(t) is given by:

Equation (5) demonstrate that at low excitation intensities, the fundamental frequency amplitude F_f grows linearly with Ī_e, while the second harmonic F_2f grows quadratically. Moreover, every harmonic amplitude depends linearly on the number of fluorescent emitters N and the emission rate κk_r. Hence it is possible to separate the contributions of excitation and emission from the fluorescence signal. To quantify the local excitation intensity independently on the emission properties, we introduce the ratio ρ of the first and second harmonic amplitudes:

To quantify the excitation intensity enhancement η_exc = Ī_e–ant/Ī_e–sol brought by an optical antenna, we compare the ratio ρ found in the vicinity of an antenna to a free solution case in the regime below fluorescence saturation:

Concerning the emission properties, the ratio $F_f^2/F_{2f}$ reduces to 2Nκk_r in the excitation regime below saturation (Ī_e ≪ I_sat). Therefore, this ratio quantifies the product of the number of emitters times their radiative rate and collection efficiency. This is a limit of the method, which does not provide direct access to the antenna’s influence on the emission properties κk_r independently on the number of emitters. To solve this issue, some assumptions have to be made to set the quantity N. For such task, fluorescence correlation spectroscopy (FCS) [12] appears a more relevant method, as it characterizes directly the number of emitters. Hereafter, we rather focus on the main interest of the modulation technique, which is quantify the excitation intensity enhancement brought by the antenna.

3. Results and discussion

To validate the method we investigate single apertures milled in 200 nm thick gold film with 135 nm diameter. Some apertures are decorated with a set of five shallow concentric grooves of 65 nm depth and 440 nm period, as in reference [12]. The experimental setup is based on a confocal microscope with a NA= 1.2 water-immersion objective. Temporal modulation of the incident excitation laser beam (CW HeNe linearly polarized operating at 633 nm) is performed with an acousto-optic modulator (AA Optoelectronic, MT200-A0.2-VIS) driven at f = 5 kHz. Alexa Fluor 647 molecules (A647, Invitrogen, Carlsbad CA, absorption / emission peaks respectively at 650 and 672 nm) diluted in a standard water-based phosphate buffered saline (PBS) solution are used as fluorescent probes. Fluorescence emission is detected within the 670±20 nm spectral range by a photomultiplier tube (Hamamatsu, H10721-20), and the fundamental and second harmonic amplitudes are extracted through a lock-in amplifier (Signal Recovery, 7280-DSP).

First, we calibrate the experiment for the open solution case (no aperture). Figure 2(a) displays the evolution of the fundamental F_f and the second harmonic F_2f fluorescence amplitudes while increasing the average excitation power. As expected from Eq. (5), F_f and F_2f grow respectively linearly and quadratically with average excitation power in the low excitation regime. The good agreement between our model based on fluorescence saturation and the experimental data confirms fluorescence saturation is the main source for the second harmonic of fluorescence (Fig. 2). The evolution of F_f and F_2f versus the excitation power are respectively presented in Fig. 2(b) and 2(c) for the single and corrugated apertures. In both cases, the second harmonic amplitude F_2f can be detected at lower excitation powers as compared to the open solution, which is a direct consequence of the excitation enhancement inside the apertures.

 

Fig. 2 Demodulated fluorescence amplitudes at f = 5 kHz and 2 f = 10 kHz versus average excitation power for (a) the open solution, (b) a single 135 nm aperture and (c) a single aperture with a set of five circular corrugations. Lines are numerical fits based on Eq. (5).

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To quantify the excitation intensity enhancement, we compute the ratio ρ = F_2f/F_f for each sample. The results versus the excitation power are presented on Fig. 3(a) along with numerical interpolation according to Eq. (6). The slopes near origin for the three cases of reference solution, single aperture and corrugated aperture amount to 0.022, 0.080, and 0.146 μW⁻¹ respectively, while the saturation intensities equal 215, 228 and 252 μW. These figures are used to compute the ratios η_ρ = ρ_ant/ρ_sol and η_Isat = I_sat−ant/I_sat−sol, and finally to quantify the excitation intensity enhancement η_exc = η_ρ η_Isat. Results for the excitation intensity enhancement are presented in Fig. 3(b) and compared to the values probed with fluorescence correlation spectroscopy found previously in reference [12]. Satisfactory correspondence is shown between the different methods, well within the error margins which appear of similar magnitude for both saturated excitation fluorescence and correlation spectroscopy.

 

Fig. 3 (a) Fluorescence amplitudes ratio ρ = F_2f/F_f for the different samples. (b) Excitation intensity enhancement deduced from the data set in (a) (filled bars), and compared to the results using fluorescence correlation spectroscopy (FCS, hatched bars) [12].

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4. Conclusion

Using fluorescent molecules to probe the excitation intensity enhancement near an optical antenna is a challenging task as the detected fluorescence signal mixes information from excitation and emission. Previous methods to solve this challenge combined fluorescence correlation spectroscopy (FCS) and lifetime measurements [12], or monitored the complex emission dynamics of quantum dots [16]. These approaches are restricted by complex experimental analysis and/or non-commercial quantum dots probes. Here we describe a new method to directly quantify the antenna enhancement on the excitation intensity independently on the emission process. By temporally modulating the laser excitation, we record the fundamental and the second harmonic amplitudes of the fluorescence signal, whose ratio is validated as a local probe of the excitation intensity, independently on the number of emitters and their emission properties. As for the FCS approach, an intrinsic limitation of the method stands in that all results are for spatial averaged over all possible molecular orientations and positions inside the sampled volume. Hence, we point out that the estimated enhancement factor may be lower than that of the peak in the sampled volume, which can be derived separately from surface sensitive emission processes such as surface-enhanced Raman scattering (SERS) [17].