1. Introduction

In nanophotonics, single emitters including QDs [1], dye molecules, or other quantum emitters, have been widely investigated in the fields of solar cells, biologic labeling [2], quantum information [3,4], etc. Experimentalists have spared no effort to control their properties and to improve the signal collection efficiency and spatial resolution, both of which require strong light-matter interaction [5]. Traditionally, people study the quantum emitters by collecting the fluorescence at far-field with lens, but the spatial resolution is diffraction limited. Along with the development of fiber- and integrated-optics [6], integrated photon source, as well as its near-field manipulation and detection, are possible by incorporating the single emitters with integrated photonic structures. More importantly, due to the strong light confinement in waveguides or cavities, the emission of quantum emitters can be efficiently collected and directly utilized for the followed processing.

Recently, the coupling between quantum emitters and dielectric waveguides have been demonstrated [7,8]. Schemes aiming to increase the collection efficiency by placing the emitters at the waveguide end facet have been proposed as well, for example, a theoretical calculation with fiber taper [9], and a movable diamond single photon source [10]. However, in all these studies on which dielectric waveguide is based, the density of state is small and the mode area is limited by the diffraction of light, resulting in the low collection efficiency and poor spatial resolution. Even though the weak interaction can be compensated by slowing down the group velocity of light via strong dispersive photonic crystal waveguide [11], the widely spread mode area (usually micrometer scale) makes the local control over quantum emitter beyond the optical diffraction limit quite difficult. Near-field collection method with metal-coated optical probe may break the diffraction limit, but the efficiency is very low (usually only about $0.1\%$ or even lower with 200nm spatial resolution for visible light).

Fortunately, plasmonic nanostructure has natural advantages in addressing such problems. Compared to the optical mode in dielectric waveguide, plasmonic mode has much higher mode density, leading to stronger coupling between quantum emitters and photons [12]. And the smaller plasmonic mode area also makes the local operation of quantum emitters possible. Such stronger coupling doesn’t rely on a cavity with ultra-high quality factor, and the enhancement of surface plasmon is broadband. Experimentally, the coupling of quantum emitters, including QDs, nitrogen-vacancy centers, 2D materials with metallic waveguide and nanocavity has been investigated [13–19]. Recently, even the strong coupling of quantum emitters and plasmonic modes were observed [20,21], pushing the application of plasmonics in the field of quantum information processing a great step forward. People have also demonstrated that the quantum statistical features of the emitted photons, the distinguishability of single plasmons emitted by different QDs near a plasmonic waveguide [22] and the quantum states can be preserved by surface plasmon polariton [23–25]. These researches have encouraged the development of quantum plasmonics [26,27]. Owing to the enhanced interaction strength, the spatial and polarization property of the radiation fields from quantum emitters [28] are strongly modulated by the plasmonic structures. Plasmonic antennas that support resonant modes can convert the emitter radiation into highly direction emission, increasing the collection efficiency with objective lens [29] and photonic-plasmonic cavity [30]. Gap surface plasmons also shows its potential advantange to enhance both the emission and collection of single photons [31,32]. For propagating plasmonic modes, it is possible to obtain near-unity collection efficiency [33] and long-range energy transfer [34] by coupling quantum emitters with plasmonic waveguides.

In this work, we develop a new method to collect the fluorescence of $ZnS$ coated colloidal $CdSe$ QDs efficiently with a fiber-integrated plasmonic probe. Among various plasmonic waveguides, AgNWs [35–37] have been widely implemented in nanophotonics due to its low loss, uniformity and easy preparation process. Here, we integrate the AgNW together with a fiber taper to collect the fluorescence of the QDs. The probe can transport light beyond the diffraction limit (200nm here) with high efficiency (at the same level with objective lens collection method), which outperforms the traditional metal-coated dielectric tips. We conduct a detailed analysis on the efficiency of the probe, and characterize the performances of different plasmonic modes during the coupling process by measuring the lifetime of the QDs. The large decrease of the lifetime reflects the strong coupling strength between the QDs and the AgNW. Our plasmonic probe can be a promising candidate for both high-efficiency and high-spatial resolution collection of quantum emitters fluorescence.

2. Experiment and results

The experimental setup is shown in Fig. 1a. The $CdSe$ QDs are spin-coated onto a silica substrate with a uniform distribution. A $532nm$ continuous-wave laser or a $395nm$ ps-pulsed laser is used to excite the QD ensemble by an objective lens. Unlike the previous experiment [38], which also uses objective lens to collect the fluorescence, here we use a fiber-integrated plasmonic probe to collect the signal. Our fiber-integrated plasmonic probe consists of a fiber taper and a AgNW as shown in Fig. 1b. In our experiment, the fiber taper was fabricated by heating a single mode fiber while stretching it from opposite ends. The cone angle of the fiber taper was dependent on the stretching force. The silver nanowire was synthesized using a chemical reaction between silver nitrate (AgNO3) and ethylene glycol in the presence of polyvinyl pyrrolidone (PVP). After purifying the silver nanowires from the reaction product and performing a dilution process, we dripped the solution onto an edge area of a side-polished substrate. A fiber taper was used to move the nanowire to the edge with half of the nanowire free-standing in air. We then used a three-dimensional stage to control another fiber taper and moved it close to the nanowire. Due to the Van de Waals forces between the fiber taper and the nanowire, the silver nanowire adhered onto the surface of the fiber taper and was quite stable in several hours. The stability is further improved by attaching the nanowire to the fiber taper with epoxy resin glue. Adiabatic coupling between the dielectric modes in the fiber taper and the plasmonic modes in AgNW ensures the highly efficient transport of light [39,40], thus makes the detection of single emitters possible. A three-dimensional piezo-stage is used to control the distance between the hybrid probe and the excited QDs. After adjusting the probe to an appropriate position, the signal from the fiber output is analyzed after passing through a $561nm$ long-pass filter. In the measurement, we used low pump power (under 10 $\mu W$) to excite the QD ensemble, thus the fluorescence counts are quite stable.

 

Fig. 1. Experimental setup. (a) A $532nm$ continuous-wave laser or a $395nm$ ps-pulsed laser is used to excite the QD ensemble by an objective lens. PBS and HWP are used to control the polarization of the laser. The fluorescence is collected by the AgNW-fiber probe and filtered with a $561nm$ long pass filter to block the excitation laser before detection. The fluorescence can also be collected by the same objective lens. We use a single photon detector or a spectrometer to record the single photons emitted by the QDs. A multichannel analyzer is used to record the time interval between the laser pulse and the fluorescence photon, thus giving the lifetime of the fluorescence. PBS, polarization beamsplitter; HWP, half waveplate; BS, beamsplitter. (b) CCD image of the hybrid probe with laser light launched from the fiber. Magenta circles show the scattering laser light from the fiber taper end and the AgNW end. Inset: SEM (scanning electron microscope) image of the hybrid probe. Scalar bar: $10\mu m$. (c) Eigenmodes of the AgNW. The AgNW can support three eigenmodes, $TEM_{0}$ and two degenerate modes, $TE_{1}$ and $TM_{1}$. Here, we give the electric field distributions of $TEM_{0}$ (left panel) and $TM_{1}$ (right panel).

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First of all, we guided the collected signal into the spectrometer. For comparison, we collected the QDs emission with both objective lens ($N.A.=0.8$) and AgNW-fiber probe, and the measured spectra are shown in Fig. 2. The spectra are centered at $655nm$, which is consistent with the fluorescence spectrum of $CdSe$ QD. This clearly demonstrates that we can collect the fluorescence of quantum emitters with such a probe. With a fixed excitation laser power, the counts collected by the probe and the objective lens ($N.A.=0.8$) are $3.67 \times 10^{5}/s$ and $9.75 \times 10^{5}/s,$ respectively. In consideration that the collection area of the probe is smaller than the objective lens, the collection efficiency of the plasmonic probe is at least in the same order with that of the objective lens.

 

Fig. 2. Normalized fluorescence spectra of $CdSe$ quantum dots. Red line: Fluorescence of QDs on the substrate collected by the objective lens. Blue line: Fluorescence collected by the AgNW-fiber probe. The spectra are displaced vertically for comparison.

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A strong evidence for the strong near-field coupling strength is the decrease of the QD lifetime. According to the Fermi’s golden rule, the spontaneous emission rate of a dipole to mode $i$ is proportional to the square of the coupling strength and the density of state. The lifetime of the dipole is defined as the inverse of the spontaneous emission rate. So the lifetime $\tau$ has a inverse relation with the mode density and the coupling strength. If we put a probe near the quantum emitter, the dipole not only interacts with the continuum vacuum field in free space, but also interacts with the plasmonic modes supported by the probe. The additional channel causes the increase of the spontaneous emission rate and the decrease of the lifetime of the florescence signal. In our experiment, we measured the lifetime of the QD ensemble in different situation: (1) QDs on silica substrate, with objective lens collection. (2) QDs on silica substrate, with plasmonic probe collection. (3) QDs attached on fiber taper, with fiber taper collection.

First we measured the averaged lifetime of $CdSe$ QD ensemble on the silica substrate with the objective lens. The data are perfectly fitted with a single exponential function $f_{1}=I_{0}+Ae^{-t/\tau _{0}}$, and the fitted lifetime is $15.25 \pm 0.10ns$ (See Fig. 3a). Then we moved our plasmonic probe towards the excited QDs and maximized the collection efficiency. Different from the above case, the data can not be effectively fitted with a single exponential function, which results in an averaged lifetime of $8.61 \pm 0.35ns$ (see Fig. 3b, black dash line). It means that the collected photons are a mixture of photons with different lifetimes. So we used the sum of two exponential functions to fit the experimental data (see Fig. 3b, blue solid line). The function is $f_{2}=I_{0}+A_{1}e^{-t/\tau _{1}}+A_{2}e^{-t/\tau _{2}}$, where $\tau _{1}$ and $\tau _{2}$ are the lifetimes of QDs in different environments respectively, and $A_{1}$ and $A_{2}$ are the weight of the collected photons from the corresponding QDs (Here, $A_{1}/A_{2}=1.17$). The fitted $\tau _{1}$ and $\tau _{2}$ are $2.21 \pm 0.07ns$ and $19.25 \pm 0.68ns$ respectively. The shorter lifetime $\tau _{1}$ may correspond to photons from QDs near the probe, while the longer lifetime $\tau _{2}$ corresponds to those relatively far from the probe, as described in detail later. From this result, we concluded that the probe has a strong effect on the emission of the QDs.

 

Fig. 3. Lifetime of the collected fluorescence. (a) QDs on silica substrate, with objective lens collection. Intensity-time relation is fitted with a single exponential function $f_{1}$. Fitted lifetime is $\tau _{0}=15.25 \pm 0.10\:ns$. (b) QDs on silica subsrate, with plasmonic probe collection. Solid line is fitted with the sum of two exponential functions $f_{2}$. $\tau _{1}=2.21 \pm 0.07\:ns$, $\tau _{2}=19.25 \pm 0.68\:ns$. Dashed line is fitted with a single exponential function $f_{1}$ with $\tau _{0}=8.61 \pm 0.35ns$. The large disagreement between the data and the fitted curve using $f_{1}$ implies that the collected photons come from at least two coupling processes with significant different lifetimes. (c) Intensity-time relation for fluorescence collected by fiber taper. The data is fitted with function $f_{1}$ with $\tau _{0}=19.02 \pm 0.26\:ns$. In the experiment, the data acquisition time is different for different cases.

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As a comparison, a similar measurement was done for a fiber taper without AgNW. We pasted some QDs on the tip of a fiber taper and excited the QDs with objective lens. The fluorescence is detected from the output of the fiber. In this case, the experimental data (see Fig. 3c) can be nicely fitted with $f_{1}$. The fitted lifetime is $19.02 \pm 0.26ns$, which is much larger than that with plasmonic probe collection. This is because the surface plasmon mode has a stronger field confinement, resulting in larger coupling strength with QDs.

3. Influence of different plasmonic modes

In this section, we discuss in detail how the plasmonic modes influence the lifetime of the QDs. In previous works, people have theoretically studied the effect of the coupling between electric dipoles and different waveguide modes [41], and experimentally measured the mode distribution around nanowire with single NV center [42]. Here the effect of each eigenmode in a multimode AgNW waveguide was experimentally investigated. For a AgNW, there should exist three stationary modes, $TEM_{0}$, $TE_{1}$ and $TM_{1}$ (See Fig. 1c). Since the later two higher-order modes are degenerate, here we take $TE_{1}$ as an illustration. The fundamental mode $TEM_{0}$ is strongly confined and symmetrically distributed near the nanowire surface. Its effective mode area scales as $r^{2}$, where $r$ is the radius of the nanowire. The higher-order modes have larger effective mode area compared to the fundamental mode. As shown in Fig. 4a, the effective mode areas of the fundamental mode $TEM_{0}$ and the higher-order mode $TE_{1}$ are calculated. The $TE_{1}$ mode is always larger than the $TEM_{0}$ mode when $r<100\:nm$. Since the three modes have different electric field distributions, they couple with different QDs on the substrate. For AgNWs with $r<100\:nm$, the $TEM_{0}$ mode can only interact with QDs very close to the nanowire surface, while the $TE_{1}$ and $TM_{1}$ modes can interact with QDs several hundred nanometers away.

 

Fig. 4. Numerical simulation. (a) Effective mode area of the plasmonic modes. The inset is the schematic diagram of the plasmonic mode on AgNW. (b) Relation between the collection efficiency of the AgNW and its radius. The efficiency can even exceed $90\%$ when $r<30\:nm$. It should be noted that the efficiency is the probability the photon directly radiated into the surface plasmonic modes, and does not include the propagation loss of the silver nanowire. (c) yz cut plane image of the 3D simulation. The radius of the nanowire is $100nm$ and the angle between the probe and the substrate is $10^\circ$.

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In our experiment, the probe is placed near the substrate. For QDs near the surface of the AgNW, it can interact with both $TEM_{0}$ and higher-order modes. As a result, the lifetime we detected is greatly decreased. For QDs far from the AgNW, they only interact with $TE_{1}$ and $TM_{1}$ modes with weak coupling strength, so the lifetime is relatively large. Our measured signal is a mixture of photons from QDs near and far from the AgNW surface. $A_{1}$ and $A_{2}$ are the weights of these two processes, which is relevant to the coupling strength, the number of QDs and the efficiency of the hybrid probe. In the experiment above, the ratio of $A_{1}$ to $A_{2}$ is $1.17$. Taken into consideration of the low transmittance of the fundamental mode, the value of $A_{1}/A_{2}$ should be larger. We also changed the distribution of QDs by pasting some QDs on the AgNW surface and moving the plasmonic probe away from the substrate. In this free standing case, all QDs are near the nanowire surface, and $A_{1}/A_{2}$ reached $3.93$, which proves that the fundamental $TEM_{0}$ mode dominates in the coupling process.

Theoretically, the coupling strength $g$ between a two level quantum emitter and an optical mode can be expressed as:

4. Efficiency of the plasmonic probe

In the following, we will give a discussion about the collection efficiency of our plasmonic probe with a single QD. There are two processes that determine the collection efficiency of the probe: the coupling between the QD and the AgNW, and the transmittance of light from the AgNW to the fiber taper including the propagation loss and the coupling loss. The efficiency of the first process mainly depends on the Purcell factor [43] of the waveguide, while the later process depends on the structure of the hybrid probe. Here we mainly focus on the first process.

The QD is treated as an electric dipole, and the coupling between an electric dipole and the plasmonic probe is simulated to characterize the efficiency of the probe. In our simulation, the dipole is placed $5\:nm$ away from the surface of the AgNW, and orientation is set normal to the surface. By integrating the total energy flow inside the simulation box and the energy flow along two directions of the AgNW, the collection efficiency of the $100\:nm$-radius AgNW is estimated to be $47.9\%$. Because the fluorescence propagates towards two directions, only half of the fluorescence is guided to the fiber taper. This directional energy loss can be avoided by putting the QD at the end of the probe, which results in a simulated efficiency of $56.3\%$. As the radius of the AgNW becomes smaller, the Purcell factor of the $TEM_{0}$ mode increases rapidly, thus the collection efficiency of the probe will increase significantly. When $r<30nm$, the collection efficiency of the AgNW can reach $90\%$. Figure 4b gives the relation between the collection efficiency and the nanowire radius. It should be noted that the efficiency is the probability the photon directly radiated into the surface plasmonic modes, and does not include the propagation loss of the silver nanowire. In fact, the propagation loss will increase quickly with the decrease of AgNW diameter.

In our case, the total collection efficiency of the probe is $8.79\%$ according to the numerical simulation results. Here, the angle between the probe and the substrate is $10^\circ$. The relatively low efficiency in our experiment mainly originates from the absorption on the AgNW and the coupling between the AgNW and the fiber taper. Both losses can be reduced by carefully designing the structure of the hybrid probe. This efficiency can be as high as $17.76\%$ if we put the QD at the end of the probe. According to the simulation and analysis above, we confirm that the probe can be a promising candidate to collect fluorescence of quantum emitters with high efficiency.

5. Discussions and conclusions

In our experiment, we have realized the near-field collection of fluorescence from quantum emitters with a high-efficiency fiber-integrated plasmonic probe. The dramatic decrease of lifetime from $15.25ns$ to $2.21ns$ unambiguously demonstrated the strong near-field interaction between the QDs and the plasmonic modes. We also experimentally investigated the influence of each plasmonic mode on a multimode plasmonic waveguide. Our analysis on the lifetime of the fluorescence clarified the mechanisms of the coupling between the QDs and different surface plasmon modes. Theoretical simulation verifies the high collection efficiency of the probe. The collection efficiency and the coupling strength can be further increased by reducing the diameter of the metallic nanowire or designing other structures with resonance [44–46]. An alternative way is to replace the nanowire by a metallic tapered tip [33]. By carefully designing the coupling between nanowire and fiber, and accurately controlling the position of the probe, we expect to realize highly efficient coupling between the plasmonic probe and single quantum emitters, which is promising to build a transistor in the single photon level [47].

Due to the high confinement of the plasmonic mode, the probe only interacts with emitters localized near the nanowire, which can increase the signal to noise ratio. It is also promising to construct a nanoscope and realize local optical operation of quantum emitters in nanometer scale. A possible application is to image luminous emitters beyond the diffraction limit. The probe can also be used to locally excite quantum emitters in nanoscale.

There are several benefits from the fiber-integrated plasmonic probe: (1) The movable fiber-integrated plasmonic nano-probe gives a new way to collect photons from nano-emitters and can avoid complexity of using bulk optical components. (2) It is promising for near-field quantum probes, photonic endoscopes [48,49] or movable single photon source. (3) The probe is broadband, with a very wide wavelength range. (4) The thermal property of silica fiber and AgNW also makes the probe’s application at cryogenic temperature possible. At low temperature, the decrease of the loss of AgNW may even improve the performance of the probe.

In summary, the fiber-integrated plasmonic probe can both transport light forward and backward with high efficiency beyond the diffraction limit, and can be used to transport quantum states and realize strong light-matter interaction, which mays be useful in the area of nanophotonics and be promising for quantum information devices. Our study encourages further investigations of quantum plasmonics and promotes the applications of surface plasmons in quantum optics field.