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Abstract
We experimentally study the radiation direction and relaxation rate of quantum emitters (QEs) coupled with a plasmonic waveguide integrated with a V-shaped traveling wave antenna. The plasmonic waveguide couples the excitation energy of the nearby QEs into surface plasmons and the connected V-shaped traveling wave antenna converts them into highly directional radiation. The directivity of the radiation depends on the shape of the antenna. The half-power beam widths of the radiation with respect to the azimuthal and polar angles are as small as 15.1° and 13.1°, respectively, when the antenna has a 144° intersection angle. The relaxation rates of the QEs are enhanced up to 33.04 times relative to the intrinsic emission rate. The method to control the fluorescence of QEs is of great significance for optical devices, nanoscale light sources, and integrated optics.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The spontaneous emission of quantum emitters (QEs) plays an important role in determining the performance of many optoelectronic devices, such as lightings, displays, lasers, optical amplifiers, and solar cells [1]. In nano-optics, the control of the spontaneous emission of QEs, including enhancing the emission rate and controlling the emission direction, is an appealing topic due to the wide range of applications [2], such as the efficient detection of molecules [3–5], photonic devices for quantum-information processing [6,7], the incoherent nanoscale light sources, and nano-lasers [8,9]. To date, two kinds of well-performing resonators have been developed to control the spontaneous emission of QEs via Purcell effect: the photonic crystal microcavities and plasmonic metal nanostructures [1,10–13]. The former can significantly enhance the emission rate by confining light with periodic dielectric structures, but are limited by the diffraction limit and require a large intrinsic volume. The latter have shown great confinement of the electromagnetic field and are not subject to the diffraction limit because they confine light by coupling to electron oscillations or plasmons in the metal [14,15]. Various plasmonic metal nanostructures have been used to modify the spontaneous emission rate, such as the plasmonic nano-disk resonators [16], plasmonic nanocavities [17–21], bowtie nano-apertures [11], plasmonic nanoantennas [22–24], and film-coupled metallic nano-cubes [25]. Furthermore, plasmonic metal nanostructures hold great promise for the control of the direction of the spontaneous emission. The emission of a single QE has been directed by coupling to the resonance modes of a metal nanowire (NW) [26] or a V-antenna [27]. The directivity can be effectively enhanced by constructing phased array of plasmonic resonances elements. For instance, the Yagi-Uda antennas have shown significant ability to direct the emission of a single quantum dot (QD) or GaAs NW in the vicinity of the resonant feed element [6,28]. Other ways of using periodic shallow grooves [29–32], nanoaperture arrays [33], or metallic nano-slit array [34,35] to direct the emissions of the nearby QEs have also been reported. While most of the antennas are based on nanoscale resonators or plasmonic resonance element arrays. They are not easy to be integrated with nanoscale waveguides and used in integrated optics. In addition, their areas to interact with the QEs are small in general, thereby limiting the ability to control QEs. Recently, we proposed optical V-shaped traveling wave antennas (VTWAs) integrated with plasmonic NW waveguide, which present a way to control the radiation properties of QEs [36].
In this work, we experimentally study the radiation directions and relaxation rates of QEs coupled with Ag NW plasmonic waveguides integrated with VTWAs. The QEs in the vicinity of the waveguide are excited by surface plasmons (SPs) traveling along the waveguide. Then the excitation energy of the QEs relaxes to SPs and radiates through the VTWA. The radiation of the QEs through the VTWA is significantly directed, and the half-power beam width (HPBW) of the radiation depends on the intersection angle of the VTWA. The HPBWs with respect to the azimuthal and polar angles were 15.1° and 13.1°, respectively, for a VTWA with a 144° intersection angle. The relaxation rate of the QEs was enhanced up to 33.04 times relative to the intrinsic emission rate. The method to control the spontaneous emission of QEs has important applications in many fields, such as integrated incoherent light sources, light-harvesting and emission devices, and transfer of quantum information technology.
2. Experimental method
In the experiment, the Ag NWs with an average diameter of 252 nm were synthesized using a modified wet chemistry method [36]. Figure 1(a) shows a scanning electron microscope (SEM) image of the Ag NW. The V-shaped part of the Ag NW with an intersection angle α acts as an optical VTWA. Here the QEs were commercial CdSe/ZnS QDs with a diameter of approximately 8 nm. As illustrated in Fig. 1(b), some Ag NWs were placed on a coverslip with an aera of ∼18 × 18 mm2. Then, we dropped 10 µL of the QD solution (concentration of 0.32 µM) on the coverslip and spread it by covering another coverslip. After the solvent volatilized, a part of the QDs were coated on the Ag NWs. Then the upper coverslip was removed. Considering the loss of the QDs in these steps, including the QDs squeezed out by the upper coverslip and the QDs adhered to the upper coverslip, the average density of the QDs on the substrate was about 2000 QDs/µm2. Then the coverslip was covered by another coverslip, and the space between them was filled with index-matching oil with a refractive index of 1.52. A pulsed laser beam (vacuum wavelength λ0 = 532 nm, pulse width ∼10 ps, repetition rate = 48 MHz) was focused on the left terminal of the Ag NW by an oil-immersed objective (100×, NA = 1.4) to launch SPs (here called laser SPs) propagating along the Ag NW. The diameter of the focused laser beam was approximately 1.8 µm. The angle between the polarization of the incident laser beam and the x-axis is β. Parallel and perpendicular polarizations, i.e., β = 0° and 90°, were used in the experiment. As the launched SPs propagate along the plasmonic waveguide, the adjacent QDs were excited and a part of the excitation energy relaxed into SPs propagating along the Ag NW (here called fluorescence SPs). The fluorescence SPs radiated into free space through the optical VTWA. A rectangular coordinate system is defined based on the Ag NW, whose xy plane is parallel to the substrate and the x-axis is collinear with the symmetrical axis of the Ag NW, to quantify the angular distribution of the radiation. A spherical coordinate frame with polar angle θ and azimuth angle φ is also defined.
Fig. 1. (a) SEM image of a Ag NW. Inset: a magnified SEM image of the intersection. The scale bar of the inset is 400 nm. (b) Schematic diagram of the plasmonic waveguide and the radiation of the VTWA. (c) Schematic diagram of the experimental setup. Lens1 and Lens2 have the same focal length represented by f. (d) Optical image of the V-shaped Ag NW. (e) Spectra of the radiations from boxes A and B in (d), as well as that of the spontaneous emission of QDs in the absence of the Ag NW.
Figure 1(c) illustrates the experimental setup. The green pulsed laser beam was focused on the left end of the Ag NW by a beam splitter (BS1) and an oil-immersion objective to launch the laser SPs, and the radiations of the QDs through the VTWA were collected by the same objective. A lens (Lens1) and a beam splitter (BS2) were used to image the back focal plane of the objective on a charge-coupled device (CCD) (CCD1) to obtain the angular distributions of the radiations. Between BS1 and Lens1, a 600-nm long-pass optical filter was used to block the scattering light of the incident laser. A pinhole with a diameter of 350 µm was mounted at the back focal plane of Lens1, which served as a spatial filter. The image of the Ag NW was obtained using a lens (Lens2), a beam splitter (BS3) and a CCD (CCD2). A spectrograph (HORIBA Jobin Yvon, iHR320) or a time-correlated single-photon counting module (Picoharp 300, PicoQuant Inc.) was used to measure the spectrum or lifetime of the radiations, respectively.
When the laser beam with a parallel polarization was focused on the left end of the Ag NW, SPs were launched by the laser and the QDs coated on the Ag NW were excited. Figure 1(d) depicts the optical image of a V-shaped Ag NW with an intersection angle α of 144°. The bright line in box A originates from the fluorescence of the QDs and the weak spot in box B is the radiation of the fluorescence SPs from the VTWA. Figure 1(e) shows the spectra of the radiations in boxes A and B and that of the fluorescence of independent QDs immersed in index-matching oil. The spectra are in accordance with each other with a peak wavelength of 620 nm, which means that the Ag NW and the VTWA do not change the spectrum of the QDs.
When the parallelly polarized laser beam was focused on the Ag NW, the observed radiation intensity of the fluorescence SPs Ir, that is, the intensity of the spot in box B in Fig. 1(d), with respect to the position of the laser beam focus on the x-axis is illustrated in Fig. 2(a) (black dots). Here ΔL represents the distance between the focus spot and the left end of the Ag NW, whose negative value means that the focus spot was on the left side of the Ag NW. It is seen that when ΔL = 0 µm, i.e., the laser beam was focused on the left end of the Ag NW, a peak appears, which indicates that laser SPs were launched and excited QDs. Although the laser SPs were launched by the laser beam, the laser beam is not indispensable if an SP source is available in an on-chip system. Thus, this method to excite QDs is of great significance for the optical system miniaturization and integrated optics.
Fig. 2. (a) Observed radiation intensity of the fluorescence SPs through the VTWA versus the position of the incident laser beam focus. The black and red lines are exponential fittings. (b) Theoretical effective refractive indexes of the five modes (TM00, HE1±1, and HE2±2) versus the vacuum wavelength. The insets illustrate the normalized transverse electric field amplitude distributions of the modes, in which the white arrows denote the directions of the instant electric fields.
When ΔL > 1 µm, the radiation intensity Ir exponentially increases due to the decrease of the propagation loss of the fluorescence SPs. For the parallelly and perpendicularly polarized laser beam cases, the intensities of ΔL > 1 µm were fitted with an exponential function, from which the propagation lengths of the fluorescence SPs are obtained as 5.27 and 5.76 µm, respectively, as shown in Fig. 2(a). The radiation intensity Ir of the perpendicularly polarized laser beam case is larger than the parallelly polarized laser beam case. That is because SPs and local SPs (LSPs) were launched, and the later enhanced the excitation of the QDs. We calculated the theoretical propagation lengths of the fluorescence SP modes by solving the Helmholtz equation in the model of a cylindrical Ag waveguide immersed in a dielectric medium with a refractive index of 1.52. The diameter of the Ag waveguide was set as 252 nm and the refractive index of Ag was obtained by interpolation of the data measured by Johnson and Christy [37]. There are five modes, TM00, HE11, HE1-1, HE22, and HE2-2 modes, in which HE11 and HE1-1 ones are degenerated modes, including HE22 and HE2-2 modes. Figure 2(b) shows the effective refractive indexes of the modes neff and the electric field distributions. The HE22 and HE2-2 modes of the fluorescence SPs are cut off. The theoretical propagation lengths of the TM00, HE11, and HE1-1 modes at a fluorescence wavelength of 620 nm are 7.12, 8.69, and 8.69 µm, respectively, which are larger than the experimental results. The differences may originate from the additional loss induced by the scattering or reabsorption of the fluorescence SPs by the QDs. The high-refractive-index QDs around the waveguide and the mismatch of theorical and experimental silver permittivity may result the different propagation lengths as well.
3. Radiation directivity
Based on the experimental setup shown in Fig. 1(c), (a) Fourier imaging method was used to measure the radiation directions of the fluorescence from the VTWA. The angular intensity distribution of the radiations from the VTWAs was extracted from the Fourier images [36,38]. Figure 3(a) illustrates the Fourier image of the radiation of the VTWA shown in Fig. 1(d) when the laser beam with parallel polarization was focused upon the left end of the Ag NW. Only the radiation in the scope 0° ≤θ≤ 67° can be measured due to the limiting NA of the objective. The green circle represents the maximum polar angle θ of 67° that the objective can collect. Figure 3(b) shows the corresponding result of the perpendicular polarization case. The Fourier images of the two different polarization cases are almost the same. Their maximum intensities appear at φ = 14.9° and θ = 60.6° in Figs. 3(a) and (b). Figures 3(c) and (d) depict the corresponding intensity distributions with respect to the azimuthal angle φ (for θ = 60.6°) and the polar angle θ (for φ = 14.9°). The HPBWs Δφ and Δθ are 35.2° and 13.5°, respectively. However, the results in Fig. 3(d) cannot show the real distribution with respect to the polar angle θ due to the limit NA of the objective. We measured the angular intensity distributions of the radiations of VTWAs with a different intersection angle α. Figure 3(e) shows the corresponding Fourier image of another VTWA with an intersection angle of α = 160.8° when β = 0°. Compared with the case shown in Fig. 3(a), that of Fig. 3(e) has a larger intersection angle α but a smaller Δφ = 31.2°. The Fig. 3(f) shows the HPBWs Δφ of these VTWAs when β = 0° with respect to the intersection angle. The increasing α results a decreasing Δφ in principle. A nearly linear relationship between Δφ and α can be fitted by a line of Δφ = −1.49α + 271.13°, which can be used to design the antenna.
Fig. 3. (a)–(b) Fourier images of the light radiated by the antenna for β = (a) 0° and (b) 90°. (c)–(d) Intensity distributions in (a) and (b) versus (c) φ (for θ = 60.6°) and (d) θ (for φ = 14.9°). (e) Fourier image of an antenna with α = 160.8°. (f) Variation of experimental Δφ of the Fourier images for θ = 65° versus α.
We calculated the angular distributions of the radiation of QDs through the VTWAs and Ag NWs to obtain the complete radiation pattern. The diameter and length of the Ag NW were set to 252 nm and 9 µm, respectively, and the intersection angle α was 144°. The QDs were represented by dipoles with a wavelength of 620 nm. The amplitudes of dipole moments were proportional to the electric field amplitudes of the laser SPs launched by the laser beam with β = 0°, which were simulated by a finite-difference time-domain (FDTD) method. The fluorescence SPs launched by a dipole were expanded as the superposition of the TM00, HE11, and HE1-1 modes. The corresponding expansion coefficients depended on the position and orientation of the dipole with respect to the Ag NW and were obtained by the FDTD method. The radiation patterns of the VTWA when fed by the three modes independently were calculated using the FDTD method. Then the corresponding radiation pattern of the dipole can be obtained. The radiation pattern of the VTWA excited by numerous dipoles was obtained as an incoherent superposition of all the radiation patterns of the dipoles. Figures 4(a) and (b) show the calculated angular distributions of the radiations when the VTWA was excited by numerous dipoles, which are corresponding to the radiations to the positive and negative directions of x-axis, respectively. The grids represent the angular coordinates θ and φ. The maximum intensity of the radiations to the negative direction of x-axis is far less than the positive direction case. To give a good demonstration of the angular distributions, the maximum intensity of the color bar in Fig. 4(a) is 250 times larger than that of Fig. 4(b). The radiation is highly directional. The maximum intensity locates at φ = 9.0° and θ = 90.2°. To compare with the experimental results, Fig. 4(c) shows the calculated intensity with respect to φ for θ = 60.6°. Here, the HPBW is 34.3°, which is close to the experimental result 35.2°. The maximum intensity is located at φ = 10.8°, which is smaller than the experimental result 14.9°. The difference may originate from the imperfect shape of the Ag NW in the experiment. Figures 4(c) and (d) show the calculated intensities with respect to φ (for θ = 90.2°) and θ (for φ = 9.0°), respectively. The HPBWs are obtained as Δφ = 15.1° and Δθ = 13.1°. The corresponding results when β = 90° were also calculated, with no distinct difference compared with the results of the case β = 0°. Therefore, a Ag NW combined with a VTWA can effectively control the radiation direction of QEs.
Fig. 4. (a)–(b) Calculated angular distributions of the radiation to the (a) positive and (b) negative direction of the x-axis radiated by the VTWA. The maximum intensity of the color bar in panel (a) is 250 times larger than that of panel (b). The corresponding α and β are 144° and 0°, respectively. (c) Calculated intensities versus φ for θ = 60.6° (blue line) and 90.2° (red line). (d) Calculated intensity versus θ for φ = 9.0°.
The simulation results indicate that the maximum emission occurs at θ = 90° since we set the V-shaped Ag nanowire immersed in index-matching oil. We chose to set the V-shaped Ag NW in homogeneous refractive index surroundings is owing to the application of the VTWAs in integrated optics, such as to communicate between two elements of an on-chip optical circuit.
4. Decay rate enhancement
For the QDs around the Ag NW, the emission properties of the QDs can be modified by the proximity of the Ag NW through three decay channels: the optical emission into free-space modes modified by the metallic surface of the Ag NW, the non-radiative quenching of the QDs to the Ag NW, and the decay of the QDs by exciting guided SP modes on the Ag NW waveguide [1,7]. We measured the decay rates of the radiation of the QDs through the VTWA when the parallelly or perpendicularly polarized laser beam was focus onto the left end of the same Ag NW. The results are shown in Fig. 5(a). The 1/e lifetimes τ, that is, the time required for the normalized counts decreases to 1/e, are obtained as 1.21 and 0.75 ns for the parallel and perpendicular polarization cases, respectively. The slopes of the two curves vary continuously in the logarithmic coordinate, which means that the radiations are multi-exponential decay processes. The shortest and longest lifetimes τ can be obtained according to the dashed lines in Fig. 5(a), which are 1.10 and 12.40 ns for the parallel polarization (β = 0°) and 0.69 and 14.46 ns for the perpendicular polarization (β = 90°), respectively. For comparison, we also measured the decay rate of independent QDs in the absence of Ag NW, which is a typical monoexponential decay with a lifetime of τ0 = 22.80 ns. The decay rate enhancement factor can be calculated as F = τ0/τ. As a result, the longest lifetimes for the parallel and perpendicular polarizations of the laser beam corresponding to the decay rate enhancement factors of 1.84 and 1.58, respectively. The corresponding decay rate enhancement factors of the shortest lifetime cases are 20.72 and 33.04, respectively. Here the QDs can be approached to the Ag NW surface with a distance as small as 4 nm. As Anger et al. and Ratchford et al. have pointed out that the decay rate enhancement is dominated by the channel of non-radiative quenching for such a distance [39,40]. For the QDs with a larger distance to the Ag NW surface, the enhancement of non-radiative quenching is weaker and the proportion of the decay rate enhanced by the channels of free-space emission and exciting guided SP modes on the Ag NW is larger, and then, a smaller decay rate enhancement is resulted. Thus, the multi-exponential decay process should originate from the different orientations of the QDs and the different distances between the QDs and the Ag NW surface. Otherwise, the perpendicularly polarized incident laser beam launched LSPs, which were tightly confined on the Ag NW surface, as shown in Figs. 5(b) and (c). The LSPs excited more QDs in close proximity to the Ag NW surface compared to the parallel polarization case. As a result, the lifetime of the perpendicular polarization case is shorter than that of the parallel polarization case.
Fig. 5. (a) Fluorescence decay histograms for β = 0° (red dots), 90° (blue triangles), and independent QDs in the absence of Ag NW (black squares). Straight dashed lines present the shortest and longest lifetimes. (b)–(c) Normalized transverse electric field amplitude distributions when a laser beam (vacuum wavelength is 532 nm) is focused onto the Ag NW. The laser beam is injected from the top with a polarization angle of β = 0° (b) and β = 90° (c). Both of them correspond to the same scale bar and color bar.
In the experiment, although the QEs were excited by the incident laser beam or by the laser SPs, the laser beam is not indispensable if an SP source is available, which can be used to excite the QEs directly. The manipulations, including exciting QEs, harvesting their energy into SPs, and converting the SPs into directional radiations, can be implemented in an on-chip system using the VTWA integrated with plasmonic NW waveguide, which is of great significance for the optical system miniaturization and integrated optics. Besides, the waveguide can provide a large area to interact with QEs, which is helpful to increase the intensity of the radiation from the VTWA by increasing the number of the QEs coupled with the NW waveguide. Moreover, the method can also be used to control the spontaneous emission of a single QE by controlling the distance between the Ag NW and the QE or sense the orientation of a single QE based on the relationship between the QE orientation and the lifetime.
5. Conclusions
We have demonstrated the radiation directions and relaxation rates of the QEs coupled with a plasmonic NW waveguide integrated with a VTWA. The QEs are excited by SPs traveling along the NW waveguide. The excitation energy of the QEs launches SPs that propagate along the same NW waveguide and radiate via the VTWA. The radiations of the QEs through the VTWA are highly directional. The HPBWs of the radiations decreased with the increase of the intersection angles of the VTWAs. The decay rates of the QEs have been enhanced by a factor of 1.58–33.04 due to the coupling between the NW waveguide and QEs. The large range of the enhancement factor is attributed to the different orientations and locations of the QEs with respect to the NW waveguide. The method to control the radiation direction and relaxation rates of QEs using plasmonic waveguides and optical antennas has important applications in incoherent light sources and integrated optics.
Funding
Ministry of Science and Technology of the People's Republic of China (2016YFA0301300); National Natural Science Foundation of China (91850104).
Disclosures
The authors declare no conflicts of interest.
See Supplement 1 for supporting content.
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