Enhanced two-photon photoluminescence assisted by multi-resonant characteristics of a gold nanocylinder

1 Introduction

Two-photon photoluminescence (TPPL) is an emission process which can take place when an emitter absorbs two photons of low energy simultaneously and emits a photon of high energy. TPPL has promising applications in biosensing and bioimaging thanks to the high penetration depth and low photodamaging in bio-tissues due to the infrared illumination [1], [2], [3]. The increasing interest in TPPL is explained also by the importance of achieving solar panels with highly efficient energy conversion of overall solar radiation [4], [5], [6]. Most commonly, silicon-based solar panels are efficient or quasi-efficient in the spectral range of 400–1100 nm according to the crystalline silicon bandgap [7], while the solar radiation covers the spectral range from 280 nm to 2.5 µm for Air Mass 1.5 global [8]. The energy higher than the bandgap is absorbed and thermalized [4], while the lower energy (< 1.1 eV) is transmitted. Therefore, this UV absorption and IR transmission are the losses, which need to be transformed to photons possessing an energy utilizable for an efficient photo-current conversion [5]. Indeed, an emitter with a high two-photon absorption cross-section may absorb two photons simultaneously in the IR spectral range and emit a photon in the visible [9], [10]. Hence, this visible photon can efficiently generate free carriers and through electron-holes recombination release current in the electrical chain of solar cells.

Surface plasmon polaritons or shortly surface plasmons are collective oscillations of the electron cloud at the interface between metals or metal-like materials and dielectrics, driven by an external electromagnetic wave. The frequencies at which the light can resonantly excite surface plasmons in metallic nanostructures that are smaller than the illumination wavelength are called localized surface plasmon resonances (LSPRs) [11], [12]. They lead to high electromagnetic field confinement in a small volume near these nanostructures. Due to their size and shape dependent optical properties, metallic nanoparticles find application in various fields, amongst others plasmon-enhanced photoluminescence (PL) [13]. There are three main mechanisms contributing to the plasmon-enhanced PL [13], [14], [15], [16], [17], [18]. Firstly, a plasmonic nanostructure under resonant excitation exhibits an enhanced electric field at particular spatial positions in its vicinity. An emitter located at these positions shows an increase in the excitation rate. Secondly, the plasmonic nanostructure may act as an optical resonator by increasing the relaxation rates in the emitter at the emission frequency. This leads to a strong modification of the local density of states and of the emission rate due to the plasmon-exciton coupling [19], [20]. Thirdly, a plasmonic nanostructure may also increase the coupling between the far-field and the near-field, giving directionality to the emitted light towards the detector or accumulating incident light in the system depending on the nature of the plasmonic mode [21], [22] .

Many studies of plasmon-enhanced PL focus on the interaction of dipolar resonances (electric dipoles) with excitons. However, depending on its size and geometry, a metallic nanostructure can exhibit multipolar resonances besides the dipolar ones. Also, structures such as cylinders, ellipsoids etc. may exhibit dipolar oscillations excited along different axes at different wavelengths [23], [24]. Based on these properties new approaches to enhance simultaneously the excitation rate and quantum efficiency by different localized surface plasmon resonances were proposed [25], [26], [27]. In one of the pioneering works, Liu et al. used the two localized plasmon resonances of a simple geometry nanoparticle (gold nanorod) in order to enhance the photoluminescence of dye emitters [25]. A gold nanorod exhibits two dipolar modes along the short (transverse dipolar mode) and the long axis (longitudinal dipolar mode), respectively at different wavelengths. Liu et al. proposed to use the transverse dipolar mode to enhance the excitation rate and the longitudinal dipolar mode to increase the emission rate. Besides the spectral position of the LSPRs, it is also important to pay attention to the spatial distribution of the near field around the nanostructures. Indeed, for nanorods, the near fields associated with these two dipolar resonances do not spatially overlap, meaning that some of the emitters experience enhancement at the excitation step; whilst others at the emission process.

Later, this approach was extended to increase the intensity of two-photon photoluminescence. Two theoretical papers proposed to excite emitters using the metallic nanoparticle’s dipolar mode, while the emitted light overlaps with the quadrupolar mode. In this case the fluorophores are excited by simultaneous absorption of two photons of lower energy (longer wavelength) and emit light of higher energy (shorter wavelength). Zhang et al. demonstrated by numerical simulations that the PL enhancement factor of a single emitter (Cy5 dye) in the vicinity of a single gold nanodisk can reach the order of 10⁴ [28]. Liu et al. demonstrated in a similar theoretical study the enhanced upconversion of a single Er³⁺ doped nanocrystal using a nanorod as a multi-resonant simple geometry which can reach an up to 160-fold enhancement factor [29]. Herein, they also used the dipolar mode to enhance the excitation rate and the quadrupolar or transversal dipolar mode, depending on the emission wavelength, to enhance the quantum efficiency. They showed that the enhancement factor of multi-resonant matching systems is much higher than that of single resonant systems. Recently, it was shown experimentally that the enhancement factor for the TPPL of the single quantum dot coupled with the single resonance of a gold nanorod can reach up to 10⁴ [30], [31]. However, for energy applications, large-scale surfaces covered with emitters are preferred.

In this paper, we demonstrate experimentally the double resonant effects produced by single nanocylinders covered with multiple emitters. We perform a comparative study of one-photon PL and two-photon PL (TPPL) for single resonant systems. Also, we propose a method to study the plasmon-enhanced TPPL from double resonant systems and separate the emission rate changes from the total enhancement factor. Additionally, we show and discuss the sensitivity of quadrupolar and dipolar modes due to shape imperfections of the nanocylinders.

2 Methods

We produce gold nanocylinder (GNC) arrays and single GNCs on a glass substrate by using the electron-beam lithography technique. The GNCs’ height is 50 nm and the pitch is fixed at 1 µm for the arrays. The GNCs’ diameters in the arrays were measured to be 110 nm, 130 nm, 150 nm, 170 and 220 nm. The distance between the single GNCs is 5 µm. To prepare for the emitter deposition, the sample was first covered with an 8 nm-thick silica layer using the electron beam evaporation technique (evaporation rate: 0.1 nm/s, pressure: 2 × 10⁻⁶ Torr). The sample, tilted at 45° to the evaporation axis, was rotated during the process to ensure the homogeneity of the silica layer. Subsequently, we cleaned the sample surface by immersing it in piranha solution (a mixture of concentrated sulfuric acid with hydrogen peroxide, ratio of 3:1).

Then core–shell CdSe/ZnS quantum dots (QDs) presenting an emission peak at 610 nm and an average diameter of 8 nm were used as the emitters. A high-density monolayer of QDs is obtained through a silanization process, as the QDs are bound covalently to the silica layer. In detail, the substrate is incubated in 3,3-mercaptopropyl trimethoxysilane (Sigma-Aldrich, 95%) in anhydrous toluene at 0.01 % in weight for 12 h in a glovebox. Next, the substrate is immersed in a solution of QDs dispersed in toluene (0.08 g/L) for 24 h [32].

The angle-resolved extinction spectra are recorded using a home-built optical setup [33]. A broad-band white light source is focused by a long-focal-distance objective (NA = 0.28) onto the sample. The sample can be rotated by a controllable angle up to 50° with respect to the illumination (objective) axis. To collect the extinction spectra, we used an objective (NA = 0.42) coupled to the spectrometer (Ocean Optics QE65000) by a 200 μm core fiber.

One-photon photoluminescence (PL) measurements are performed on a commercial microscope (Eclipse Ti-U from Nikon) equipped with a cooled (−39 °C) spectrograph (Andor Technology). The sample was illuminated by the “Intensilight epi-fluorescence illuminator” Mercury light source. A filter cube (AHF Analysentechnik AG) was inserted, providing a bandpass filter with a center wavelength of 435 nm and bandwidth of 40 nm for the excitation, as well as a dichroic mirror blocking the wavelengths below 510 nm and a longpass filter with an edge wavelength of 515 nm for the detection. A schematic of the experimental setup for measuring PL is illustrated in Figure 1A. We used a pinhole of 50 µm diameter, which corresponds to an area of collection of 833 nm-diameter on the sample surface. The PL microscope is also equipped by a dark-field condenser (NA = 0.8–0.95), which allows us to find a single nanoparticle using the dark-field illumination technique.

Figure 1:

(A) Scheme of the experimental setup for PL measurements. Light from the UV lamp focused through an objective excites the QDs coated on the glass substrate. A bandpass filter with a center wavelength of 435 nm and bandwidth of 40 nm for the excitation is inserted. The same objective is used to collect the PL signal using a dichroic mirror which blocks the illumination wavelengths (below 510 nm) and a longpass filter with an edge wavelength of 515 nm. A pinhole is used to spatially filter the collection zone. (B) Schematic of the experimental setup of the parabolic mirror (PM) assisted confocal microscope. The laser beam is linearly polarized and focused with the PM onto the sample. The signal is collected by the mirror under angles between 28° and 85°. A beam splitter (BS) and a filter (F) separate the signal from the excitation light. Using a flipping mirror (FM) the signal can be directed to either an avalanche photodiode (APD) or a spectrometer (SP) with a cooled CCD-camera. The laser beam polarization can be converted to a radial mode by a home-built mode converter (MC) constructed from zero order lambda half plates.

The two-photon photoluminescence setup equipped with a PM is shown in Figure 1B. The advantages of the PM setup include a high geometrical numerical aperture (N.A. = 0.996) and a chromatic-free focusing [34]. We use a femtosecond erbium fiber pulsed laser beam (774 nm, 120 fs, 89 MHz repetition rate) for the sample excitation. The illumination was either linearly or radially polarized. The laser output power was measured as 42 mW. We used a neutral density filter with an optical density of 1.5, which corresponds to 3.2 % (1.3 mW) transmission of total power. Note that this power is decreased in the focus by about 10 times because of the multiple lenses and the sample holder in case of a Gaussian beam profile. We use this filter to avoid photodamage of the nanoparticle. Furthermore, in this manner we avoid the saturation of the QDs’ excitation. The second-order nature of the two-photon photoluminescence was verified in a power-dependent study (see Supporting Information Figure S1). The laser beam was focused on the sample in reflection mode, and the emitted light from the sample was collected by the PM under angles from 28° to 85°. A short pass filter (Semrock FF01-680/SP) excludes the collection of the excitation wavelength, transmitting wavelengths from 350 to 680 nm to the avalanche photodiode (APD) for photon counting imaging. TPPL spectra are recorded by a thermo-electrically cooled charge-coupled device (CCD) camera coupled to a spectrograph. All spectra were obtained using a spectrometer grating with 150 grooves per mm. The sample displacement was carried out by a piezo stage. The images taken by the APD present an intensity map by scanning the sample through the laser focus pixel by pixel. The scanning speed is fixed to 50 ms per pixel and 64 pixels per line. The laser beam diameter at the focus is ∼ 400 nm (about λ/2) [34]. The electric field distribution in the focus of a PM is calculated using a home-written software [35]. The pulse duration due to the optical elements can be lengthened, although pulses longer than 100 fs have been shown to be stretched only 3.5 fs by travelling in a 20 mm glass lens [36]. Nevertheless, the second order nature of the excitation of QDs shows that probable pulse stretching does not change the non-linear regime of excitation.

Numerical simulations were performed with the help of the commercial software “FDTD solutions” from Lumerical.

3 Results and discussion

In Figure 2A the laser wavelength (vertical red line), absorption (green dashed curve) and emission (red dashed curve) of non-linearly excited QDs are depicted. Additionally, the experimental extinction spectrum of a GNC excited at an angle of 50° by p-polarized light is given (black curve) in order to reveal the higher order plasmon modes which are not excited under normal incidence [33]. At the peak positions we calculated the charge distributions in order to determine the nature of the plasmon modes. The extinction peak at 760 nm results from an in-plane dipolar mode, and the one at 600 nm is a radiative quadrupolar mode due to an asymmetric dipole moments distribution. Furthermore, the one at 525 nm is an out-of-plane dipolar mode (Supporting information, Figure S2). The emission wavelength of the QDs matches the spectral position of the quadrupolar plasmonic mode of the GNC, while the laser excitation wavelength is close to the spectral position of the dipolar plasmonic mode. A schematic of a GNC functionalized by a monolayer of QDs is shown in Figure 2B.

Figure 2:

(A) Schematic of quantum dot non-linear excitation and emission, where the laser excitation wavelength is 774 nm, and the QD emission is centred at 610 nm. The black curve shows the extinction spectrum of a GNC of 170 nm-diameter excited at 50°. The green dashed line shows the linear absorption spectrum of the QDs and the red one shows the emission spectrum. The calculated charge distributions are at 525 nm (out-of-plane dipolar mode), 600 nm (quadrupolar mode), and 760 nm (in-plane dipolar mode). (B) Schematic of GNC with an 8 nm silica spacer layer functionalized by a QD monolayer.

In this manner, we aspire to obtain doubly enhanced photoluminescence of the QDs through the excitation enhancement attributed to the enhanced electric field of the GNCs due to the dipolar mode, and the emission process enhanced due to coupling between the quadrupolar mode and the induced dipole of the QDs, which was predicted by Liu and Zhang [28], [29].

The extinction spectrum of the GNC (Figure 2A) demonstrates far-field characteristics, although the interaction QD-GNC takes place in the near-field regime. It has been shown that near-field and far-field characteristics of plasmon modes can be different [37], [38]. According to the reciprocity theorem the near-field spectrum of a particle under far-field illumination monitored by a dipole positioned in the near-field should be equal to the scattering spectrum of the particle monitored in the far-field when excited from a dipole in the near-field [39], [40].

In order to ensure that the quadrupolar mode of the GNC excited in the near-field at the location of the QDs is spectrally not much shifted compared to the far-field spectrum of the GNC, we calculated the averaged scattering by the GNC excited by a local source (dipole emitter) placed 8 nm from the GNC and compared it with the far-field scattering spectrum (Supporting Information Figure S3). The calculation shows that the GNC quadrupolar mode excited by a local near-field source is only shifted about 9 nm compared to its far-field characteristics. Figure 3 also shows that the near-field of the dipolar mode is red-shifted > 30 nm. Figure 3 may indicate that for the excitation enhancement in the near-field, the dipolar mode may match the 774 nm laser more closely to resonance than expected from the far-field scattering simulation. These spectral shifts therefore become relevant when designing resonant particles.

Figur 3:

(A) Photoluminescence (PL) spectra of a monolayer of QDs on a glass substrate and on single silica-covered GNCs of different diameters, where D is the diameter in nm. (B) Scheme of the overlapping of the PL spectrum of the QDs (red dashed line) and the experimental normalized extinction spectra of single GNCs.

Depending on the interplay between the excitation enhancement, radiative decay rates and also the increase of non-radiative energy transfer to the metal, metallic nanoparticles can either enhance the emission of QDs or quench it [13], [15], [41]. It has been demonstrated that the optimal distance between a plasmonic nanoparticle and an emitter for the highest total enhancement of TPPL varies from 5 to 10 nm depending on the plasmonic mode nature [29]. Therefore the 8 nm silica layer in the present case is expected to be sufficient to avoid the quenching regime.

As a reference for the double resonant systems, the impact of a GNC on the emission rate of QDs needs to be demonstrated. For this purpose, one-photon PL was measured (Figure 3A) and Supporting Information Figure S4). The excitation was performed using a UV lamp and in this spectral region no plasmonic enhancement of the excitation rate by the gold nanoparticles is expected [42]. In the UV to the blue spectral range gold nanoparticles exhibit strong inter-band and intra-band transitions and do not sustain localized plasmon modes. In Figure 3A, the red curve shows the PL intensity of QDs on the glass substrate, the other curves show the PL intensities of QDs coupled to single GNCs of different diameters. For TPPL enhancement, we directly excite the dipolar mode of the GNC with the laser and use the ensuing near-field to enhance the QD excitation. In the PL experiment we directly excite the QDs and use the QD emission to excite the plasmonic mode in the near-field through the spectral overlap. One may note, that with the increase of the GNCs’ diameter the enhancement of the PL intensity decreases. The relative positions of the PL and plasmon resonances are shown in Figure 3B.

In Figure 3A we observe a 2.1-fold, 1.8-fold, 1.7-fold and 1.5-fold PL enhancement on the GNCs of 110 nm, 130 nm, 150 and 170 nm diameters, respectively. It is important to note, that the GNCs increase the surface for the QDs deposition, which can result in an overall signal enhancement. To be sure that the enhancement is not due to the larger number of emitters, we calculated the effective surface for QDs localization with GNC D170 and without GNC. In the case of full filling factor, the effective surface with GNC is only 1.1 times higher than without, although the enhancement factor is 1.7-fold. Therefore, this enhancement factor is attributed mostly to plasmon enhanced PL.

In TPPL the relative position of the laser excitation and plasmon modes is important. We present calculated extinction spectra of D150, D170 and D220 GNCs excited under 50° in Figure 4A. The excitation wavelength is indicated by the vertical red line, and the emission of the QDs by a red dashed line. The 170-nm GNC has a better overlap of the extinction spectrum with the excitation wavelength than the nanocylinders with other diameters. Figure 4B–D display the TPPL scanning APD maps of coupled QDs/GNC systems for different diameters of the GNC D150, D170, and D220, respectively. This comparative study is required to understand the process of double resonant enhancement of QDs emission. Each map presents the TPPL recorded on a set of 4 GNCs designed with the same diameter. We depict the emission spectra of QDs near the 150 nm (D150), 170 nm (D170) and 220 nm-diameters (D220) GNCs in Figures 4E,F and 4G respectively, measured on the different particles shown in Figure 4B–D. D150 GNCs show from 3.5 to 5.3-fold TPPL increase considering the spectra in Figure 4E. When we look at the 170 nm-diameter QDs/GNC system in Figure 4F, we register 10–20-fold enhancement of the TPPL depending on the nanoparticle. The D220 GNCs coupled to QDs show an enhancement factor between 7.5- and 11-fold (Figure 4G). One may note that the system that we outlined in Figure 2 demonstrates the highest enhancement factor (Figure 4F). Further analysis is needed to explain the enhancement factors generated by GNCs of different diameters, as well as the intensity differences of nominally identical GNCs.

Figure 4:

(A) Spectral positions of the calculated extinction spectra of D150, D170 and D220 GNCs compared to the laser excitation wavelength (red vertical line) and QD emission (dashed line). (B), (C), (D) TPPL scanning maps of QDs on GNCs of different diameters: 150 nm, 170 nm, and 220 nm. The intensities of the TPPL maps are normalized by the maximum value of each map. (E), (F), (G) TPPL spectra when the linearly polarized beam is focused on the center of the different GNCs.

A first important point is that the enhancement rate is much higher for the two-photon PL than for the one-photon PL (1.7-fold) due to several reasons. The high enhancement of the excitation rates is gained due to the enhanced electromagnetic field near the GNCs thanks to the dipolar plasmon resonance, as well as due to the quadratic dependence of two-photon absorption on the excitation intensity.

From a geometrical point of view, the D220 GNCs could be expected to show higher enhancement than the D170 GNCs due to their larger surface. D220 GNCs may have more QDs attached in their vicinity than D170 and D150 GNCs. Nevertheless, the D170 GNC leads to higher TPPL enhancement than the other diameters. The highest enhancement factor of QDs emission is expected when the plasmon resonance peak positions overlap with the excitation or emission wavelengths. For D150 GNCs, the image is quite clear, the excitation and the emission wavelengths appear at the right and the left slope of the main plasmon resonance respectively, hence the smallest expected TPPL enhancement is observed (3.5–5.3-fold). The extinction spectra of D170 and D220 GNCs have similar overlap with the emission and excitation of the QDs and thus should be considered more carefully.

Since we deal with a high-density of QDs a complete modelling of the simultaneous interaction of >100 emitters is a complex physical and mathematical problem. We consider a system with the initial quantum efficiency of one (QE = 1) in order to compare the impact of GNCs on the excitation rate, emission rate and the total enhancement. Figure 5A depicts the calculated relative enhancement factors for the GNCs of different diameters in comparison with the experimental data. The black squares in Figure 5A show the calculated relative and normalized enhancement rates of an emitter placed 10 nm away from the GNCs of different diameters. The calculated enhancements are normalized by the minimum value for D150 in order to understand the relative enhancement factors of different diameters. The red squares in Figure 5A show the relative and normalized PL experimental enhancement. We normalized by the PL enhancement factor for D150, which is 1.5 according to Figure 3A. In this manner we obtain the relative enhancement factors of different diameters relative to each other, which allows us to make a comparison with the simulated data. Here, D110 shows 1.95 times higher enhancement in the emission rate than D150, while in the experiment the ratio is 1.4. This can be explained by the fact that the calculation is done for a single emitter. In the PL experiments, we collect the signal from a region of 830 nm-diameter, where many emitters are placed. Not all of the emitters interact with the GNCs, and the total amount of QDs is also different in the case of various diameters. Although the calculated and measured relative enhancement factors do not have the same value, it is important to note that they show similar trends of the enhancement in the emission.

Figure 5:

(A) The black squares show the calculated relative enhancement of the emission rates of an emitter placed 10 nm away from the edge of the GNC for different diameters and normalized by the minimum value. The minimum is observed for D150. The emission rate enhancement is averaged over three orientations of the dipole source (XYZ). The red squares show the experimental relative enhancement factor normalized by the minimum value (D150). The values are calculated from PL measurements (Figure 2A, Figure 4 – Supporting Information). (B) Calculated relative enhancement of the excitation rate (|E|⁴/|E₀|⁴) for different diameters and normalized by the value for D150. The calculated excitation enhancement is integrated over the whole volume occupied by QDs. (C) The black squares show the calculated relative total enhancement obtained by multiplying the excitation and emission enhancements normalized by the value for D150. The red squares show the measured relative total enhancement factor normalized by the value for D150. The values are calculated from the TPPL measurements (Figure 4E–G). No TPPL signal above the background level was observed for D110 and D130. The dashed lines are guides to the eye.

In order to calculate the total enhancement factor, we need to first retrieve the excitation enhancement, since the total enhancement factor is obtained by the multiplication of the excitation and emission enhancement. The electric field maps of GNCs excited at 774 nm are shown in Figure 5 (Supporting Information). One can see that D170 exhibits the highest maximum electric field enhancement (E/E₀ = 26) in comparison with the other diameters. D110 shows the lowest value (E/E₀ = 15). However, the value of the highest electric field enhancement in a “hot spot” does not define the enhancement in the excitation rate, since we work with many emitters in our system. Hence, it is preferable not to calculate the enhancement factor of the excitation rate in a single position of the near-field. Consequently, we present in Figure 5B the calculation of the integrated electric field to the forth power (E⁴/E₀⁴) over the volume occupied by the QDs for different diameters of GNCs [46]. Herein, we normalized the excitation enhancement by the value for D150 in order to obtain the ratio of the enhancement factors for different diameters similarly to the emission rate enhancement calculations. These simulations show that the maximum enhancement in the excitation process may be observed for GNC D170, which is 1.44 times higher than the value for D150 and 1.32 times that for D220. The black squares in Figure 5C depict the calculated relative total enhancement factors for GNCs of different diameters normalized by the enhancement value for D150, while the red squares represent the experimental relative and normalized total enhancement factor. The experimental data is retrieved from the result presented in Figures 4E–4G. The enhancement factor for each diameter is mathematically averaged, then normalized by the value for D150 similarly to the simulations. One may see that the experimental values follow the trend expected from the simulations: D170 ensures a higher enhancement than D220, and D220 leads to a higher enhancement than D150, while D110 and D130 show the lowest enhancement in both simulations and experiments.

As for the TPPL of QDs on D110 and D130 GNCs, no clear signal from these arrays was observed during the scanning process. The APD image for D150 (Figure 4B) already has a low contrast between the GNCs and background. The calculated total enhancement factors for D110 and D130 are two times lower compared to D150 (Figure 5C). We thus suppose that the TPPL signal from the QDs on the nanoparticles of this size is nearly the same as the background signal.

One may notice the fluctuation of the TPPL enhancement on D170 (Figure 4F) which can be explained by the fact that the GNCs are not perfect and not identical, which is also seen in the TPPL map (Figure 4C) and the scanning electron images (Supporting Information Figure S6). The dipolar resonance is very sensitive to the shape symmetry, particularly, to the geometrical changes along the polarization axis, the so-called plasmon length [43], while the quadrupolar mode is less sensitive. If the cylinder has an elliptical base shape, the restoring force on the induced dipole charges changes with the light polarization. For the quadrupolar mode, the total dipole moment is the vectoral sum of two counter dipole moments, which may change only insignificantly due to ellipticity. Figure 6A shows how both the dipolar and quadrupolar modes shift with the modification of one of the axes lengths of the GNC. We calculated the extinction spectra of circular and elliptical GNCs illuminated from the side in order to excite the quadrupolar mode in addition to the dipolar one. We used an averaged refractive index approach in order to perform side illumination in simulations to avoid the possible numerical artifacts in FDTD caused by the injection of the light simultaneously in different media (glass-air). The effective refractive index was taken to be 1.25 [44]. By illumination from the side we can excite the quadrupolar mode by creating a phase variation along the base of the nanocylinder [33], [45]. We fixed the size of one axis of the GNC at 170 nm and the size of the second axis was varied. Figure 6B depicts the calculated and normalized scattering spectra of GNCs of the same dimension as in Figure 6A excited by a dipole source. These scattering spectra show the efficiency of the GNC to scatter the light from the dipole source. Here we observe that the spectral quadrupolar mode peak position is almost invariable under the variation of the axis of the GNC. The dipolar mode shows a sensitivity susceptible to the changes of the diameter of one of the axes similarly as

Figure 6:

(A) Calculated extinction spectra of circular and elliptical nanocylinders, where E is the electric field, and k is the propagation wave-vector. The effective refractive index is set to 1.25. (B) Calculated scattering spectra of circular and elliptical nanocylinders excited by a dipole source. In the inset a schematic of the dipole position relative to the particle is shown. The calculation summarizes the average of the scattering spectra of the GNCs for three orthogonal orientations (x,y,z) of the dipole.

For far-field excitation (Figure 6A). One may conclude that the elliptical shape does not change much the enhancement factor for the emission process through the quadrupolar mode, while the excitation rate can change significantly due to the changes of the dipolar mode’s spectral position, as seen in the TPPL map (Figure 4C) and spectra in Figure 4F.

In order to understand the influence of the emission rate on the total enhancement factor, we study the change of the emission rate of TPPL of QDs near the plasmonic nanoparticles in detail. The peak of the out-of-plane dipolar mode of the 170 nm-diameter and 50 nm-height GNC appears around 525 nm, and the quadrupolar mode occurs near 600 nm (Figures 2, 4A and 6B), which means that the laser (774 nm) does not resonantly excite these modes. Also, it is important to note that the enhancement in the emission process should be only dependent on the plasmonic modes’ coupling to the QDs’ emission dipole (plasmon-exciton interaction). Under a radially polarized beam, which has a strong out-of-plane (vertical) component of the electric field and a weak in-plane component in the focus, mainly out-of-plane modes should be excited, suppressing the main dipolar mode. Accordingly, the use of radial incident polarization should exclude the enhancement of TPPL through the excitation process. In Figure 7A we demonstrate the scanned TPPL map of QDs on D170 GNCs (the same GNCs as in Figure 4B) excited by a radially polarized beam. The map for radially polarized excitation differs significantly from the map for linearly polarized excitation. In order to understand this donut-shaped TPPL signal from the GNCs we need to study the electric field generated in the focus of a radially polarized laser beam. Figure 7B–E presents the out-of-plane (|E_Z|²) and in-plane (|E_X|²+|E_y|²) components of the electric field intensity within the focus on the substrate.

Figure 7:

(A) TPPL map of QDs on GNCs D170 excited by a focused radially polarized laser beam. Calculated and normalized intensity of the electric field distribution for (B) |E_Z|² component and (C) |E_X|²+|E_Y|²components with the GNC centered in the laser focus. (D) |E_Z|² and (E) |E_X|²+|E_Y|² components of the electric field with the GNC shifted away from the center of the laser focus for maximum overlap with the in-plane field [34], [47]. The blue circles show the spatial positions of the GNCs. (F) TPPL spectra for D170 GNCs excited by radially polarized laser beam, focused on the center of the GNCs.

When the GNC is placed at the center of the focus of the radially polarized beam, the GNC (170 nm-diameter) interacts only with the vertical component of the electric field as it is shown in Figures 7B, C. In this manner, when the GNC is placed at the center of the focus no in-plane dipolar or other in-plane plasmonic modes are excited. Moreover, 774 nm is not resonant with the vertical dipolar mode (525 nm), which means that the TPPL excitation process of the QDs is not enhanced anymore, while the emission process is still enhanced by the quadrupolar mode. If we move the GNC slightly away from the focus center, it overlaps with the in-plane component of the electric field (cf. Figures 7D,E) and the dipolar enhancement of the excitation process is present, albeit weaker than for the case of linear polarization. If we look at the enhancement factor in Figure 7F, when the GNC is centered in the focus of the radially polarized laser beam, it varies between 2.2 and 2.7, while within the donut shape, the enhancement factor is 5.1–6.6 (Supporting Information Figure S7). One may note the asymmetry of the donut shape in Figure 7A, which we attribute to the non-perfect alignment of the mode converter (Figure 1B MC). One can also notice that the variations of the enhancement factor in the center of the donut shapes for the particles P1 to P4 are quite small (about ±10% in Figure 7F), while for the doubly enhanced TPPL the variation is significant (> 30% in Figure 4E) depending on the GNC. As demonstrated previously, the quadrupolar mode is less sensitive to the shape changes than the dipolar one, therefore the quadrupolar-only enhancement of TPPL for the GNCs centered in the focus is more homogenous. The linear PL enhancement, which was shown to be 1.7-fold for D170 (Figure 3A), is of the same magnitude as the 2.2-fold TPPL enhancement for radially polarized illumination, even in spite of the quite different geometries of the two experimental setups (Figure 1A and Figure 1B). In both cases the excitation enhancement was suppressed, and only emission enhancement through the quadrupolar mode was experienced by the QDs, in contrast to the 10–20-fold enhancement of the doubly enhanced process.

4 Conclusion

In this study, we showed that the spectral position of the quadrupolar mode is much less sensitive than the dipolar mode under shape changes from circular to elliptical cylinders. We demonstrated experimentally that the TPPL enhancement factor observed for a doubly resonant GNC system was about 10–20, while for the single-resonant systems it was about 2 for both linear and nonlinear excitation. For systems with excitation and emission enhancement, the enhancement factor of the QD emission was thus increased from 5 to 10 times compared to the systems relying only on the emission enhancement. The qualitative enhancement factor of the TPPL or PL demonstrates the superiority of the double-resonant system coupled with fluorophores over the single-resonant coupling.

We show that it is possible to effectively enhance the photoluminescence via coupling with a double-resonant plasmonic nanoparticle with a simple geometry. We also showed a method to separate the emission rate enhancement from the total enhancement for double-resonant systems experimentally by using a radially polarized laser beam.

The double resonant systems obtained by a simple plasmonic geometry may pave the way towards highly efficient solar panels by integrating plasmon enhanced upconversion modules.