High-contrast switching and high-efficiency extracting for spontaneous emission based on tunable gap surface plasmon

Controlling spontaneous emission at optical scale lies in the heart of ultracompact quantum photonic devices, such as on-chip single photon sources, nanolasers and nanophotonic detectors. However, achiving a large modulation of fluorescence intensity and guiding the emitted photons into low-loss nanophotonic structures remain rather challenging issue. Here, using the liquid crystal-tuned gap surface plasmon, we theoretically demonstrate both a high-contrast switching of the spontaneous emission and high-efficiency extraction of the photons with a specially-designed tunable surface plasmon nanostructures. Through varying the refractive index of liquid crystal, the local electromagnetic field of the gap surface plasmon can be greatly modulated, thereby leading to the swithching of the spontaneous emission of the emitter placed at the nanoscale gap. By optimizing the material and geometrical parameters, the total decay rate can be changed from 103γ0 to 8750γ0, [γ0 is the spontaneous emission rate in vacuum] with the contrast ratio of 85. Further more, in the design also enables propagation of the emitted photons along the low-loss phase-matched nanofibers with a collection efficiency of more than 40%. The proposal provides a novel mechanism for simultaneously switching and extracting the spontaneous emitted photons in hybrid photonic nanostructures, propelling the implementation in on-chip tunable quantum devices.


The effect of the size of Ag nanorod on the GSPs and switching SE
The spectral properties of the GSPs depend on not only the material characteristics but also the geometrical factors, such as the size of nanorod, the distance between nanorod and nanofilm [1][2][3] . The properties of the GSPs and the performance of switching SE vary strongly with the radius r. As shown in Fig. S1, when r decreases, the resonance length for each multipole mode shifts to a longer value, in line with the variation tendency of absorption spectra for the Ag nanorod in homogeneus medium 1 . For example, the resonance length for the 16-pole mode changes from 180 nm, 241 nm to 370 nm corresponding to r=10 nm, 20 nm and 30 nm respectively. When the radius is smaller, the higher γ total will be obtained.
For r=10 nm, γ total switches from 184γ 0 to 11886γ 0 [contrast ratio of 64], while γ spp changes from 14γ 0 to 2358γ 0 [contrast ratio of 168]; whereas for r=30 nm, γ total changes from 270γ 0 to 3189γ 0 [contrast ratio of 12], and γ spp changes from 138γ 0 to 2128γ 0 [contrast ratio of 15]. However, such large contrast ratios are accompanied by considerable rise in the nonradiative component γ nr and therefore a lower fraction of γ spp in the total decay rate. When r=10 nm, γ nr changes from 170γ 0 to 8862γ 0 , occupying more than 75% of γ total =11886γ 0 , compared to the case for r=30 nm where the fraction of γ nr (changing from 122γ 0 to 674γ 0 ) in the total decay rate γ total =3189 is less. Therefore, in the discussion presented in the main text, r=20 nm is chosen to balance the enhancement of SE rate and the metallic loss.

The effect of the distance between nanorod and nanofilm on the GSPs and SE modulation
A parameter that produces more dramatic effects on the GSPs and SE modulation is the gap distance d between the nanorod and nanofilm 2,3 . The data shown in Fig. S2 illustrate the trend of absorption spectrum with lengthening the gap size. When the nanorod and the nanofilm are further apart, the resonance length becomes longer due to the weaker interaction between them. For d=5 nm, the 16-pole mode shows a resonance at about a=175 nm, while for d = 40 nm, the resonance length a=340 nm. Besides, owing to the ultra-concentrated field for the small gap size, all decay rates experience the large enhancement, but modest contrast ratio. For example, when d=5 nm, γ total changes from 2923γ 0 to 35846γ 0 with the contrast ratio of only 12, and γ spp changes from 2790γ 0 to 19579γ 0 with the contrast ratio of only 7. When the gap size becomes larger, all decay rates decreases, e.g., when d=40 nm,  direct relationship between the contrast ratio and r or d. There exists however a optimal set of r and d for both large enhancement of SE rate and high-contrast ratio. As shown in the main text, when r=20 nm and d=10 nm, the contrast ratio can reach about 85 with the enhancement of SE rate of 8750γ 0 .

Effects of the wavelength on the GSPs and switching SE
In the main text, we demonstrate both the large enhancement of SE rates and highcontrast ratio of SE switching for a particular wavelength λ=720 nm. These findings are actually also valid across a broad range of emission wavelength 4 . for λ=680 nm or λ=632.8 nm, the resonance length for the 16-pole mode shifts to longer value when ∆n decreases, in line with the results obtained at λ=720 nm (Fig. 3 in the main text). The dependence of the contrast ratio on the ∆n also remains the same as for λ=720 nm (Fig. 5 in the main text), i.e., the contrast ratio becomes higher when ∆n increases.
Besides, under the same parameters, the resonance length for the same order of GSPs at longer wavelength shifts to longer value. For the example of the 16-pole mode at ∆n=0.8, the resonance length a=190 nm for λ=632.8 nm (Fig. S3b) while a=200 nm for λ=680 nm (Fig. S3a). For λ=720 nm, the resonance length increases to a=241 nm (Fig. 5a in the main text). As for the contrast ratio, as λ=632.8 nm, γ total can change from 164γ 0 to 5318γ 0 with the contrast ratio of 32 at ∆n=0.8 (Fig. S3d). For the same ∆n with λ = 680 nm, γ total changes from 115γ 0 to 7280γ 0 with the contrast ratio of 63 (Fig. S3c). Both the maximum decay rate and the contrast ratio increases when the wavelength red shifts,

Influence of double rectangle nanofibers on switching SE
To efficiently collect and guide the emitted photons, we design the symmetrical double dielectric rectangle nanofibers in such a tunable gap plasmon nano-structure. The double nanofibers have little influences on all decay rates since they are made of dielectric material.
As shown in the Fig. S4, we display all decay rates with and without double nanofibers. For γ nr , the two sets of data coincidence with each other very well. For γ spp and γ r , the values obtained with and without nanofibers agree well except near n eff =1.65 and n eff =1.81. In the case of n eff =1.81, γ spp with double nanofibers is larger than the value obtained without the nanofibers. While γ r with the nanofibers is smaller than the values without the nanofibers.
Thus, the values of γ total obtained without and with the nanofibers agree well with each other. In the case of n eff =1.65, the values of γ r are different in the two situations, but the difference has little contribution to γ total since γ r occupies a small fraction of the total.
Therefore, we can conclude that the double rectangle nanofibers have little influences on the decay rates, and serve well as an efficient routing of the emitted photons to the preferred channel.

Collecting photons via different types of nanofibers
In the main text, we choose the nanofibers with rectangle cross section rather than cylindrical nanofiber. This is based on the calculation of the collection efficiencies for both cases. The results are shown in the Table. S1. The collection efficiency for a single nanofiber with circle cross section (with the radius of 350 nm) is 9.8% while it increases to 16.5% for a single rectangle nanofiber with dimension of 800 × 640 nm 2 . Noting that the single nanofiber is not the ideal choice, therefore, we design the symmetrical double nanofibers. In that case, the double circle nanofibers yield a collection efficiency of only 14% whereas the collection efficiency increases to 42% with the double rectangle nanofibers