Hybrid plasmonic waveguide coupling of photons from a single molecule

We demonstrate the emission of photons from a single molecule into a hybrid gap plasmon waveguide (HGPW). Crystals of anthracene, doped with dibenzoterrylene (DBT), are grown on top of the waveguides. We investigate a single DBT molecule coupled to the plasmonic region of one of the guides, and determine its in-plane orientation, excited state lifetime and saturation intensity. The molecule emits light into the guide, which is remotely out-coupled by a grating. The second-order auto-correlation and cross-correlation functions show that the emitter is a single molecule and that the light emerging from the grating comes from that molecule. The coupling efficiency is found to be $\beta_{WG}=11.6(1.5)\%$. This type of structure is promising for building new functionality into quantum-photonic circuits, where localised regions of strong emitter-guide coupling can be interconnected by low-loss dielectric guides.


I. INTRODUCTION
Despite great advances over the last decade, the wider uptake of quantum technology has been inhibited by the lack of an efficient single photon source. Among several candidates 1 , single molecules are promising as a way to deliver narrow-band photons rapidly and on demand [2][3][4][5] . A variety of molecules are photostable and several wavelengths are available by choosing suitable combinations of dopant and host 6 . While fulfilling most of the requirements for quantum technologies, 7 molecules naturally emit light into a range of directions, as do most emitters 1 , and therefore collection of the photons requires some attention. The use of micro-pillars has been a very successful approach 8-10 , but is not naturally suited to building optical circuits as the photons are extracted perpendicular to the chip. Dielectric waveguides can encourage emission into the plane of the chip 4,11-13 but good coupling requires the emitters to be placed inside the guide [14][15][16] , which is a challenge, and even then the coupling is limited by the transverse mode area of the guide. Plasmonic waveguides can have much smaller mode areas, but are compromised by absorption losses and non-radiative decay of the emitter 17,18 . Plasmonic antennas can help by concentrating the field at the site of the emitter into a much smaller volume, and can redirect the emission into a well-controlled direction.
Indeed, this idea was demonstrated with a Yagi-Uda antenna 19,20 , but did not direct the light into a single optical mode and, like the micropillar, is not naturally compatible with a planar integrated architecture. Here we have taken a hybrid dielectric-metal approach 21 , using a planar hybrid gap plasmon waveguide (HGPW). The propagating hybrid optical mode switches from mostly dielectric to mostly plasmonic and back to mostly dielectric, coupling to a single molecule of dibenzoterrylene (DBT) in the plasmonic region. There, the small transverse mode area enhances photon emission into the waveguide, after which the photon moves into the low-loss dielectric region. This structure can provide both high coupling and low loss, making it suitable for an optical network, where single emitters interact with the waveguide field in selected "hot spots", while low-loss propagation interconnects them.

II. HGPW DESIGN, FABRICATION, AND FUNCTIONALISATION
Our HGPW is based on a design introduced by Lafone et al. 21 and first fabricated and studied by Nielsen et al. 22,23 . The design was modified to operate at the ∼785 nm emission propagates between the gold islands predominantly as a TE mode. As the gold islands taper to form a smaller gap the mode becomes increasingly hybridised with the plasmon mode on the edges of the gold. Figure 1(a) and (b) show the distribution of electric field energy density calculated in COMSOL for channels of two different gap widths, and considering a layer of anthracene of 60 nm placed over the structure. In Fig. 1(a) the gold edges are separated by 1000 nm and the energy is mostly in the TiO 2 layer. In Fig. 1(b), where the gap is 200 nm, most of the intensity is concentrated on the edges of the gold. There is no dielectric confinement of the mode in the lateral direction, as the TiO 2 layer covers the entire substrate and is shared by all the fabricated devices. However, the field is prevented from spreading in the plane by its coupling to the plasmon. This requires careful adjustment of the thickness of the SiO 2 spacer layer. By controlling the hybridisation in this way, it is possible to benefit from the field confinement, while still retaining a long enough propagation length that the field can emerge from the structure and be coupled out the other side. This tradeoff is shown in panels (c) and (d) of Fig. 1, where the energy distribution across the device and the propagation length as a function of channel gap width are plotted. It is possible to see that for gap widths smaller than 300 nm the field is extracted from the TiO 2 layer and is progressively concentrated in the gap region. This is accompanied by a decrease in propagation length, as the mode area is reduced. The confocal microscope used to study the waveguides is presented in Fig. 2 Fluo, 100x, 0.9 NA). A telecentric system of lenses and a set of two galvo mirrors allowed raster scanning of the focussed laser spot across the sample. The resulting fluorescence was separated from the pump light by a dichroic mirror (Semrock), and further filtered by two 800 nm long-pass filters before being detected. A pellicle beam splitter was placed before the objective to add two additional beam paths, directing light to or from the gratings on the waveguide.

III. RESULTS AND DISCUSSION
The HGPW of interest, shown in Fig. 3(a), is 200 nm wide at the centre of the tapered region. We chose to work with this short HGPW as it has the lowest propagation loss.
For coupling to longer HGPWs with higher loss, see Supplementary Materials. Figure 3   light while monitoring the detected photon rate, as reported in Fig. 3(c). This showed that the optical dipole was only 6 ± 2 • away from the optimum, that being perpendicular to the direction of propagation. We then varied the intensity of the excitation light while collecting fluorescence, both from the site of the molecule and from the grating to the left in Fig. 3(a).
In both collection arms the fluorescence rate saturates, as shown in Fig. 3(d). The data 6 points are well modelled by the saturation function where R ∞ is the asymptotic rate at high intensity and S = I/I sat , with I being the peak intensity of the excitation light incident on the sample and I sat being the saturation intensity.
These two fits gave saturation intensities I dir sat = 90(8) kW/cm 2 and I grat sat = 104(10) kW/cm 2 for the direct and grating collection respectively, which are in good agreement with each other. The maximum photon rates were different, with values of R dir ∞ = 160(6) kcounts/s and R grat ∞ = 96(3) kcounts/s, because of the differing collection efficiencies. The grating coupler on the right gave a count rate ten times lower. We do not think this was due to a fabrication imperfection because the throughput of this device was similar to that of the others on the same substrate, and we have simulated different molecule positions on the device and found no asymmetry in emission. The more likely explanation is that the surface patterning of the gold, or imperfections in the anthracene crystal, favoured emission into one direction over the other. The pulsed laser at 781 nm was then used to determine the decay time of the excited molecule. The semi-log plot in Fig. 3(e) shows the measured probability distribution of delay times t between excitation of the molecule and detection of a photon, after correcting for the background count rate. A fit using the function A e −t/τ gave the lifetime of the excited state of the molecule as τ = 2.74(2) ns. This is slightly shorter than the expected 3-6 ns for DBT in anthracene 2,3,12,26-28 . This could be because the decay rate of the molecule is enhanced by its coupling to the waveguide (see Supplementary Materials), or possibly that the non-radiative decay rate was increased.
To confirm that this was indeed a single molecule we measured the second-order correlation function g (2) (τ ) for the emitted light, while exciting the molecule at a saturation level S ≈ 1. As a single molecule can only emit one photon at a time, we expect that g (2) (0) = 0 in the ideal case 29 . To determine g (2) (τ ) for the fluorescence collected directly from the molecule, a 50:50 multi-mode fibre splitter (Fig. 2(c)) divided the light between two avalanche photodiodes, and a time correlating card recorded the histogram of start-stop intervals in the standard way. The upper panel of Fig. 4 shows the data points, together with a fit to the function 28 where B = 1 − g (2) (0) was the only free parameter. This g (2) (τ ) exhibits clear anti-bunching, g (2) (τ) g (2) (τ) (a) (b) g (2) (0) = 0.25 (6) g (2) (0) = 0.24 (6)  with the fit giving g (2) (0) = 0.25 (6). Next, we removed the fibre splitter and instead measured the time correlation between the light from the molecule and that collected from the grating. This gave the g (2) (τ ) in the lower panel of Fig. 4, where g (2) (0) = 0.24 (6). The two values of g (2) (0) agree. The fact that g (2) (0) < 0.5 without any correction (e.g. for background counts, dark counts or possible nearby emitters), signifies that we were indeed collecting fluorescence predominantly from a single molecule in both cases. After convolving Eq. (2) with the Gaussian instrument response function due to detector timing jitter (standard deviation of 455 ps), both data sets gave g (2) (0) = 0.20 (2), a value that is consistent with the signal-to-background ratio found in each case.

IV. DEDUCING THE COUPLING EFFICIENCY
We use the detected fluorescence rate to estimate the coupling factor β, defined as the fraction of photons coupled into the waveguide: where Γ wg is the rate at which the molecule emits photons into the waveguide and Γ tot is its total emission rate. The rate at which photons are detected from the grating is R grat = Γ wg η grat , where η grat is the efficiency for coupling light out from the waveguide, collecting it, and detecting it using the APD. We can further write R grat = R grat ∞ S/(1 + S), where R grat ∞ is the fully saturated rate detected from the grating. Similarly, the total emission rate can be written as Γ tot = α Γ 1 S/(1 + S), where Γ 1 = 1/τ . In the limit of large S, this tends to αΓ 1 , where α lies between 0.5 and 1, depending on the excitation scheme 30 . Thus the coupling factor β is given by We have measured τ and R grat ∞ (see above), and for room-temperature DBT excited at 780 nm, we know 30 that α = 0.555 (10). That leaves us needing to assess η grat .
At room temperature the DBT molecule emits photons over a ∼ 20 THz wide frequency range 30 . This is broad enough that η grat has to be determined by convolving the emission spectrum with the frequency-dependent outcoupling/collection/detection efficiency. In separate experiments (see Supplementary Materials), we have measured the frequency-dependent output coupling from the waveguide through the grating. With a peak value of 10% at 800 nm, dropping to 2% at 765 nm and 830 nm, this is the main loss-factor contributing to

V. SUMMARY AND FUTURE PROSPECTS
We have observed the coupling of a single DBT molecule to a HGPW made from a multilayer dielectric slab patterned with gold structures. Measurements on the molecule itself gave values for the in-plane orientation, excited state lifetime and saturation intensity, and confirmed through the second-order correlation function g (2) (τ ) of the emitted light that this was a single molecule. We also detected the light coupled out of the waveguide by a grating, and measured the cross-correlation of this light with that observed at the molecule.
This showed that the light at the grating was indeed emitted by the molecule. The photon count rate detected at the grating was used to infer the efficiency β with which the molecule radiated photons into the guide. These measurements were made at room temperature, where phonon-induced dephasing of the optical dipole 28,30 makes the photons spectrally broad. Such photons can be useful for communication and imaging, but not for applications that require quantum interference such as linear optical quantum computing or quantum simulation. In the future we will look for molecules coupled to HGPW at liquid helium temperatures, where decoherence should be minimized so the spectrum should exhibit a Fourier-limited spectral width.
These measurements were made on a single device with a gold gap width of 200 nm, which is not expected to give a large enhancement of the photon emission rate. We plan to look for molecules coupled to guides with smaller gap sizes where the coupling should be strongly enhanced. One of the main limitations in our device was the low contrast of refractive index between the titanium dioxide and the silica substrate. To improve on this, we have simulated the case of gallium phosphide (GaP) on silica, as it presents a refractive index comparable to silicon and shows low losses in the near infrared 32 . Modifying our structure 22 with a thinner spacing layer to retain mode hybridisation, we have found that a total coupling efficiency higher than 50% can be achieved by placing a DBT molecule in a 500 nm long waveguide with a gap width of 100 nm.
Finally, in the future it should be possible to use similar plasmonic structures to shift the waveguide mode adiabatically in and out of low-loss dielectric ridge waveguides, creating regions of strong light-matter interaction at precise locations in a low-loss integrated photonic network.