Abstract

Simultaneously obtaining high photon emission rate and collection efficiency is highly desirable for applications of single photon sources. However, it remains great challenging and is seldom reported before. Here, we demonstrate that highly enhanced radiation of the emitter and efficient collection of the emitted photons can be simultaneously fulfilled in a hybrid photonic-plasmonic cavity which comprises of an Au nanorod dimer and a photonic crystal nanobeam cavity with a collecting waveguide, where the resonance wavelength of nanobeam cavity is red-detuned from that of the Au nanorod dimer. Our calculations show that the spontaneous emission rate of a single emitter can be enhanced by 5060 -folds, correspondingly, the far-field radiation efficiency and collection efficiency into a dielectric waveguide reaches ~97% and ~67%, respectively. The proposed mechanism paves the way towards the practical applications in ultra-bright on-chip single photon sources and plasmon-based nanolasers.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Background

Manipulation and efficient collection of single photon emission is not only important to fundamental science but also vital to many applications such as quantum cryptography [1] and quantum information processing [2–4]. Since the spontaneous emission rate can be greatly enhanced by placing quantum emitters in engineered electromagnetic environments [5], various artificial electromagnetic structures, such as optical microcavities [6–8] and plasmonic nanocavities [9–11], have been extensively explored to enhance spontaneous emission rate of the emitter. However, constrained by the diffraction limit, optical microcavities have relatively large mode volumes Vm compared to the light wavelength [12–14]. In order to enhance the emission rate of the emitter, ultrahigh Q-factors for the optical microcavities are required to compensate for their relatively large mode volumes. Unfortunately, these ultrahigh-Q cavities require good spectral matching between a narrowband emitter and the narrowband cavity resonance, which is still a challenge for nanofabrication and an obstacle to the practical applications. On the other hand, localized surface plasmon resonance originating from the collective oscillation of the conductive electrons in metal can highly confine the electromagnetic fields into a nanoscale space, yielding a ultrasmall mode volume [15–17]. Although large enhancements in the total decay rate have been observed in these plasmonic structures, the nonradiative quenching is dominant owing to the inherent large ohmic losses [18,19]. In addition, in these cavities based techniques, the subsequent coupling of the emitted photons into a single-mode optical fiber or waveguide may reduce the actual collection efficiency. In the view of the ability to directly collect the emitted photons, optical fibers or waveguides would be particularly promising and have been extensively explored [20–23]. However, the maximum enhancement of emission rates in these photonic nanostructures can reach only several ten times.

To overcome these challenges mentioned above, various hybrid structures have been extensively investigated theoretically and experimentally [24–26]. Although the spontaneous emission rate of the emitter placed into these hybrid structures can be enhanced, the ohmic losses of the metal antenna are still large due to the fact that the optical cavity resonances with the metal antenna. For example, Zhang et al. [25] have demonstrated lasing in a plasmonic-photonic crystal coupled nanolaser, but the laser thresholds of hybrid structures are higher than that of the bare photonic crystal cavity without metal antenna due to the large ohmic losses. Furthermore, Doeleman et al. [27] have theoretically demonstrated that the spontaneous emission rate of the emitter can be enhanced in antenna-cavity hybrid system and the collection of the emitted photons into a waveguide can be efficient. However, they have not proposed a specific geometry for the collection of emission, which is necessary for on-chip optical circuits. In the metal nanostructure-nanowire hybrid systems [28–30], the nanowires can play a role for the collection of photons. However, the resonant absorption of the metal reduces the radiation and collection efficiency, which is inevitable in these hybrid systems. In addition, the metal nanowires are not suitable for the transmission of photons [29]. Very recently, manipulation of quench has been demonstrated in nanoantenna-emitter hybrid systems via an external detuned cavities [31], which is significant for improving the collection of emission.

Here, we propose a hybrid photonic-plasmonic cavity consisting of an Au nanorod dimer and a photonic crystal nanobeam cavity with a collecting waveguide. This hybrid cavity simultaneously possesses high Q-factor and ultrasmall Vm, which consequently results in a significantly enhanced spontaneous emission rate of the emitter placed into the gap of the Au nanorod dimer. More importantly, the emitted photons can be efficiently collected and guided by the collecting waveguide. In addition, the emission wavelengths of the emitter in these hybrid cavities are detuned far from the resonant wavelengths of the Au nanorod dimer. Therefore, the nonradiative quenching has been reduced significantly, which leads to improved radiation efficiency and collection efficiency. Our numerical calculations demonstrate that the far-field radiation efficiency and collection efficiency into a dielectric waveguide reach up to ~97% and ~67%, respectively. Simultaneously, the corresponding enhancement of the spontaneous emission rate still remains up to 5060 -folds. These results suggest that the hybrid photonic-plasmonic cavity proposed here is the best candidate for significantly enhancing the spontaneous emission rate of the emitter and simultaneously obtaining large radiation and collection efficiency.

2. Theory and methods

The photonic-plasmonic hybrid cavity proposed here is schematically shown in Fig. 1(a). An Au nanorod dimer is coupled with a Si photonic crystal nanobeam. In addition, a quantum emitter is inserted in the gap formed by the nanorods and the nanobeam, as shown in Fig. 1(b). The nanobeam cavity consists of two mirror sections, a tapering region and a collecting waveguide. Where, the two mirrors have asymmetric structure. Right mirror contains 17 air holes with a fixed radius r=118nm and a fixed lattice constant Λ=394nm. The left mirror contains few air holes with the same radius and lattice constant as the right mirror and the number N of air holes of the left mirror is tunable. The tapering region is made of 12 air holes, such that their radii were linearly decreased from r1=133nm to r6=118nm and the tapering region has the same lattice constant as the mirrors. The Si nanobeam has a width w=460nm and a thickness h=220nm, and lays on a silica semi-infinite substrate. The background dielectric is air. In the calculations, the refractive index of silica is set to be 1.45, the frequency-dependent refractive index of gold and silicon are obtained by interpolating the experimental data [32,33]. Note that when the wavelength is in the range of λ1445nm, the refractive index of silicon is set to be 3.45. All results are calculated by COMSOL Multiphysics except Fig. 1(e) by RSoft. In the simulations using the COMSOL Multiphysics, a cylindrical model with radius of 2μm and length of 16.548μm (42Λ) is configured, and a perfectly matched layer with thickness of 800 nm is introduced to minimize boundary reflections.

 figure: Fig. 1

Fig. 1 (a) Schematic diagram of an Au nanorod dimer coupled with a photonic crystal nanobeam cavity with a collecting waveguide. The nanobeam cavity is composed of a tapering region, two mirror sections and a collecting waveguide. (b), (c) Details of an Au nanorod dimer directly placed on the nanobeam and on a dielectric spacer, respectively. The cross section length s of the Au nanorod is 40 nm and the length l of the Au nanorod and the gap distance d of the Au nanorod dimer is tunable. The two ends of the Au nanorod are ground with a radius of 8 nm. The width ws of the spacer layer in (c) is set to 90nm. (d) The electric field |E|distribution of the eigenmode of the nanobeam cavity. (e) The energy band structure of the nanobeam with the lattice constant Λ=394nm, the width w=460nm and the height h=220nm. The black and red lines denote the cases of the air holes with radius r to be 118 and133nm, respectively. (f) The extinction cross section of the Au nanorod dimer on Si substrate, the parameters d and l are set to be 20nm and 80nm, respectively. The insert shows the electric field distribution around the Au nanorod dimer.

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Figure 1(e) presents the energy band structures of the nanobeam with perfect lattice structure placed on a semi-infinite silica substrate. The black lines represent the energy band structure for the nanobeam with r=118nm, which includes a big bandgap. When the radii of the air holes increase up to r=133nm, as the red lines show, the corresponding energy bands shift. Therefore, by tapering the air holes, a resonant condition with λ1552nm which corresponds to the communication wavelength, is created in the photonic crystal bandgap for the case of N=1. The electric field distribution of eigenmode with λ1552nm in the bare nanobeam cavity is shown in Fig. 1(d). Obviously, the electromagnetic energy is mainly confined into the space of the nanobeam cavity. The electric field is polarized in the x-y plane with the component Ex dominating, which can couple well with the waveguide mode.

The Au nanorod dimer is placed on the nanobeam and between the two central air holes as shown in Fig. 1(b). The cross section length of the nanorod is set to a fixed value of s=40nm, the length l of the nanorod and the gap distance d of the dimer are tunable and strongly influence the performance of the Au nanorod dimer. In order to understand the features of the Au nanorod dimer, we calculated the extinction spectrum of the Au nanorod dimer on Si substrate with l=80nm and d=20nm. As shown in Fig. 1(f), the resonance wavelength of the bare Au nanorod dimer is 1180nm, and the electric field of the eigenmode is significantly confined into the gap domain. The electric field in the dimer gap is mainly polarized along the dimer axis. Therefore, the Au nanorod dimer is placed on the nanobeam with dimer axis along the x-axis in the hybrid system. When a dipole emitter is placed in the dimer gap, it should polarize along the dimer axis.

When an Au nanorod dimer is placed on the nanobeam cavity, the individual modes of the two subsystems become strongly hybridized, generating new eigenmodes. With the coupling between the two subsystems, interference between different scattering paths can largely affect the total spontaneous emission rate of the emitter. Importantly, when the mode of the bare nanobeam cavity is red-detuned from the mode of the bare dimer, the spontaneous emission rate can be boosted, which can outperforms that in the subsystems [27]. The spontaneous emission rate of a quantum dipole emitter placed at some position can be obtained by [34]:

Γ(r0,ω,d)=Γ0Fp(r0,ω,d),
where, Γ0=ω03d2/3πε0c3 is the spontaneous emission rate of the quantum emitter in vacuum and Fp(r0,ω,d) is defined as the Purcell factor, which can be obtained by [35] Fp(r0,ω,d)=ρ(r0,ω,d0)/ρ0(r0,ω), where ρ(r0,ω,d0) is the projected local density of states in the hybrid cavity and ρ0(r0,ω)=ω2/3π2c3is density of state in vacuum, d=dd0, d and d0 are the transition dipole moment and its unit direction vector, respectively. Therefore, when the Purcell factor Fp is determined, the spontaneous emission rate of the quantum emitter can be obtained by Eq. (1).

Large Purcell enhancements have recently been demonstrated in similar hybrid systems [36,37]. However, for practical applications, such as ultra-bright on-chip single photons sources, the collection of emission via a single-mode waveguide is necessary and vital beside large spontaneous emission rate. In our hybrid cavity, we propose the nanobeam cavity with a single-mode waveguide, where the mode in nanobeam cavity is compatible with the waveguide mode. Therefore, the photon emission can be coupled well into the waveguide and collected by the waveguide port (denoted by the red arrow in Fig. 1(a)), which results in large collection efficiency. The collection efficiency ηc is defined as [28]

ηc=ΓcΓ,
and the radiation efficiency ηr is defined as
ηr=ΓrΓ,
where, Γc is decay rate into the waveguide channel of the emitter in the hybrid cavity, Γr is the radiation rate into far-field of the emitter in the hybrid cavity and Γ is the total decay rate of the emitter in the hybrid cavity.

For the simulation, the efficiency ηr and ηc can be obtained by ηr=Wr/Wt and ηc=Wc/Wt, respectively [30], where Wt is the total emitted power, which can be obtained by calculating the surface integration of the nanosphere enveloping the emitter over the energy flows in the hybrid system; Wr is the far-field radiation energy of the emitter obtained by calculating the surface integration of the closed surface enveloping the whole hybrid cavity over the energy flows; Wc is the energy collected by the waveguide from the port denoted by the red arrow in Fig. 1(a).

3. Results and discussion

Guided by the theories discussed above, we calculate the Purcell factor Fp for the quantum emitter placed in the hybrid photonic-plasmonic cavity and in the two corresponding subsystems, where the parameters are set as: l=80nm, d=20nm and N=1. In calculations, the quantum emitter is located in the center of the gap of the Au nanorod dimer in the hybrid cavity or bare Au nanorod dimer, and it’s dipole moment parallels to the Au nanorod as shown in Fig. 1(b). The distances from the emitter to the surface of the nanobeam and Si substrate are the same and set to be 20nm. For the bare nanobeam cavity, the emitter is placed between the central air holes and 20nm above the surface of the nanobeam. The dipole moment of the emitter parallels to the x-axis. Figure 2(a) shows the Purcell factor Fp for the quantum emitter in the two subsystems. The blue line in Fig. 2(a) shows Fp as a function of the emission wavelength for the quantum emitter in the bare Au nanorod dimer. This Au nanorod dimer has a single mode behavior over a wide range of wavelength and the peak appears at λ=1180nm, consistent with the extinction peak, and the maximum Fp reaches up to 652. The magenta and orange lines in the same figure present Fp as a function of emission wavelength for the bare nanobeam. The bare nanobeam has two eigenmodes in the wavelength range of interest, the eigenmode with longer wavelength denoted by symbol a in Fig. 2(a) has a Q-factor of 1936 and a maximum Fp of 249. The eigenmode with shorter wavelength denoted by symbol b in Fig. 2(a) has a Q-factor of 160 and a maximum Fp of 15. In contrast, the hybrid cavity has different behavior from the two subsystems. Figure 2(b) presents Fp of the hybrid eigenmodes. It can be seen that the new hybrid eigenmodes have obvious Fano line shape, manifesting themselves as a broaden resonance and a narrow resonance, respectively [37]. The narrow resonance close to the cavity mode of the nanobeam slightly red-shifts and broadens due to the interaction between the dipole mode of the nanorod dimer and the nanobeam cavity mode [38,39]. As mentioned earlier, when the mode of the bare nanobeam cavity is red-detuned from the mode of the bare dimer, due to constructive interference between different scattering paths, the Fano peak close to the nanobeam cavity resonance can obtain large spontaneous emission enhancement. However, quite the opposite occurs when the mode of the bare nanobeam cavity blue-detuned from the mode of the bare dimer, as the case of the mode B in Fig. 2(b). The calculation results show that the hybrid eigenmode denoted by symbol A in Fig. 2(b) has a large Fp reaching up to 5290, which outperforms that of the Au nanorod dimer at resonance by more than a factor of 8 and that of the nanobeam cavity by more than a factor of 21, respectively. In the remainder of this paper, only the mode A is considered.

 figure: Fig. 2

Fig. 2 Purcell factor Fp of the emitter as a function of emission wavelength. (a) Fp of the emitter placed into the gap of the bare Au nanorod dimer on Si substrate and 20nm above the Si substrate surface (the blue line), and between the two central air holes of the bare nanobeam cavity and 20nm above the surface of the nanobeam cavity (the orange and magenta lines). (b) Fp of the emitter placed into the gap of the Au nanorod dimer in the photonic-plasmonic hybrid cavity and 20 nm above the surface of the nanobeam. The other parameters are set as follows: l=80nm, d=20nm, N=1.

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The reason why the Fano-resonance mode A demonstrates much larger Fp than those of the two bare subsystems is that it inherits the advantages of the two subsystems. In other words, the hybrid eigenmode A has a high Q-factor (having been discussed above) and an ultrasmall mode volume. To further understand the underlying mechanism to enhance the spontaneous emission rate, we can estimate the mode volume of the eigenmode A according to the definition written as:

Veff=vε(r)|E(r)|2dvε(r0)|E(r0)|2,
where, ε(r) and ε(r0) are the relative permittivity at the position rand the emitter location r0, respectively. E(r) and E(r0) are the electric field of the position r and the emitter location r0, respectively. The calculation results show that the hybrid mode A has an ultrasmall Veff0.013(λ3). The result by the Eq. (4) is just an approximation, because the Eq. (4) is not strictly valid for the plasmonic system [40,41]. To validate this result, we also calculate Veff of the eigenmode A using the standard Purcell factor calculation [41,42]. The effective mode volume can be written as
Veff=34π2ε(r0)QFPλ3,
where, ε(r0) are the relative permittivity at the emitter location r0. By extracting the Q-factor and Purcell factor Fp of the eigenmode A from Fig. 2(b), we can obtain Veff0.014(λ3). Obviously, the results obtained via the two methods are consistent. Figure 3 shows the electric field distribution of the hybrid eigenmode A. It can be seen that the electric field is mainly confined in the gap of the Au nanorod dimer, which results in an ultrasmall effective mode volume Veff. Importantly, the electromagnetic energy can effectively couple into the collecting waveguide, as can be seen from Fig. 3(c). The photons can be further guided by the collecting waveguide and used for other applications.

 figure: Fig. 3

Fig. 3 Electric field distribution in hybrid cavity. (a) at y=240nm plane (at the mid-plane of Au nanorod dimer), (b) at y=220nm plane (at the beam surface), (c) at y=110nm plane (in the middle of the photonic crystal nanobeam). Since the field intensity in dimer gap is several orders of magnitude larger than in nanobeam, the logarithmic value scale of lg(|E|) is used to better highlight the spatial distribution of the electric field. The parameters are set as follows: l=80nm, d=20nm, N=1.

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In order to obtain the optimal performance of the hybrid cavity, in the following sections, we would investigate the influence of the geometrical parameters on the performance of the hybrid cavity. Here, a dielectric spacer with lower refractive index is placed between the Au nanorod dimer and nanobeam cavity, as shown in Fig. 1(c). This dielectric spacer can improve the coupling between the Au nanorod dimer and the nanobeam cavity, leading to a better performance of the hybrid cavity. The physical origin is that the dielectric spacer can make the electric fields localized in the nanobeam cavity and the nanorod dimer redistribute, which improves an overlap between the two evanescent electric fields. The width of the spacer layer is set to be a fixed value ws=90nm. The parameter d is set to be 20nm and Nis set to be 1, and their influence on the performance of the hybrid cavity will be discussed later. Note that the emitter is placed in the gap of the nanorod dimer and 30nm and 40nm above the surface of the Si nanobeam for the case with hs=10nm and hs=20nm, respectively. Figure 4(a) shows the influence of the nanorod length l and the thickness hs of the spacer layer on Fp. As the black circle dot line shows, when the Au nanorod dimer is directly placed on the nanobeam, i.e., without spacer layer between the Au nanorod dimer and the nanobeam, the Purcell factor increases first and then decreases with the increase of l. Similar phenomena can also be observed in the presence of a spacer layer (hs=10nm and h=20nm). According to Eq. (5), the Purcell factor is proportional to Q/Veff. When the nanorod length increases, the resonance wavelength of the bare nanorod dimer red-shifts, which leads to the reduced wavelength detuning between the bare nanobeam cavity and the nanorod dimer. With the reduced wavelength detuning, the nanorod can more strongly confine the electric field, resulting in the reduced mode volume. On the other hand, with the reduced wavelength detuning, the Q-factor reduces due to the enhanced ohmic loss and scattering of the nanorod dimer. When the nanorod length is small, the Q-factor reduces slightly as l increases, which results in the enhanced Purcell factor. However, when the nanorod length is large, the Q-factor degrades significantly, which causes the Purcell factor to decrease gradually [27]. With a spacer layer was placed between the Au nanorod dimer and the nanobeam, Fp can reach larger value than that without spacer layer, as can be seen from the magenta hexagon dot line and the cyan rhomboidal dot line.

 figure: Fig. 4

Fig. 4 Purcell factor Fp, radiation efficiency and collection efficiency as a function of l. (a) Purcell factor Fp of the emitter in the hybrid cavity as a function of l. (b) Far-field radiation efficiency as a function of l. (c) Collection efficiency of the photons into the collecting waveguide as a function of l. The black circle dot lines represent the case that there have no spacer between the Au nanorod dimer and the nanobeam. The magenta hexagon dot lines and the cyan rhomboidal dot lines represent the cases of hs=10nm and hs=20nm, respectively. The other parameters are set as follows: d=20nm and N=1.

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Figures 4(b) and 4(c) show the influence of both the nanorod length l and the thickness hs of the spacer layer on the radiation efficiency ηr and collection efficiency ηc, respectively. In our paper, all efficiencies are calculated at the wavelengths of maximum Purcell enhancement. As shown in Fig. 4(b), ηr decrease with the increase of l for the cases with and without spacer layer. The system with hs=20nm has larger ηr than that without spacer layer and with hs=10nm for the same l. Interestingly, when the length of the nanorod is short, specially, l=70nm, the radiation efficiencies ηr are very large and reach ~79%, ~97% and ~98% for the cases without spacer layer, with hs=10nm and hs=20nm, respectively. These large radiation efficiencies, which are much larger than those in many plasmonic nanostructures [18,43], arises from the reduced ohmic losses because that the emission wavelength of the emitter is detuned far from the resonant wavelength of the bare Au nanorod dimer. With the decrease of l, the wavelength detuning between the bare nanorod dimer and the emission wavelength of the emitter increases, which results in enhanced radiation efficiency. The enhanced radiation efficiency can increase the photons that can potentially be collected by the collecting waveguide, which consequently results in enhanced collection efficiency. Figure 4(c) presents ηc as functions of l and hs. ηc reduces as l increases and has largest value for the hybrid cavity with hs=20nm for the same l. It is worth to note that ηc can obtain high value when the nanorod length is short, and the value of ηc is approximately equal for the cases of hs=10nm and hs=20nm. In order to simultaneously obtain large collection efficiency and high spontaneous emission rate, selecting geometrical parameters of l=80nm and hs=20nm is a reasonable consideration.

The gap distance of the Au nanorod dimer can also significantly influence the performance of the hybrid cavity. Here we set the geometrical parameters hs=10nm and l=80nm, which are optimal parameters as discussed above. The parameter N is set to be 1. The influence of N on the performance of the hybrid cavity will be discussed later. As can be seen from Fig. 5(a), the Purcell factor Fp significantly reduces with the increase of the gap distance d. However, the radiation efficiency ηr and collection efficiency ηc change little as d varies, as shown in Fig. 5(b). In d range of interest, ηr and ηc can keep above 94% and 64%, respectively. Therefore, the nanorod dimer with small d prepared experimentally is vital for enhancing the spontaneous emission rate and simultaneously maintaining large radiation and collection efficiency.

 figure: Fig. 5

Fig. 5 Purcell factorFp, radiation and collection efficiency as a function of the gap distance d. (a) Purcell factor Fp of the emitter in the hybrid cavity. (b) Radiation and collection efficiency. The magenta rhomboidal dot line and orange circle dot line in (b) represent the radiation efficiency and collection efficiency, respectively. The geometrical parameters are set as follows: hs=10nm, l=80nm and N=1.

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Figure 6 shows that how the air hole number N of the left mirror influences the performance of the hybrid cavity. In calculations, the parameters of hs and l are set to be 10nm and80nm, respectively, which is optimal parameters as discussed above. The parameter d is set to20nm, which is a moderate and experimentally reasonable value. It can be seen from Fig. 6(a) that as N increases, Fp increases significantly for the hybrid cavity. The increase of Fp arises from the improved Q-factor of the bare nanobeam cavity due to the increase of N and the resultant improved Q-factor of the hybrid cavity. Figure 6(b) presents the radiation efficiency ηr and collection efficiency ηc as a function ofN. As can be seen, ηr and ηc reduce with the increase ofN. This is also attributed to the enhanced Q-factor, because that when the Q-factor increases, although the hybrid mode dissipates more rapidly, the energy guiding through the collecting waveguide becomes less efficient, consequently, a substantial portion of emitted photons is reabsorbed by the Au nanorod dimer. Therefore, for the practical applications, it should select an optimal value of N so that it can compromise between the spontaneous emission rate and collection efficiency.

 figure: Fig. 6

Fig. 6 Purcell factor Fp, radiation and collection efficiency as a function of the air holes number N of left mirror. (a) Purcell factor Fpof the emitter in the hybrid cavity as a function of N. (b) Radiation and collection efficiency as a function of N. The orange circle dot line and the cyan rhomboidal dot line in (b) represent the radiation efficiency and collection efficiency, respectively. The parameters are set as follows: hs=10nm, d=20nm and l=80nm.

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4. Conclusions

In conclusion, by proposing the hybrid photonic-plasmonic cavity composed of an Au nanorod dimer and a Si photonic crystal nanobeam cavity with a collecting waveguide, we have simultaneously obtained high enhancement of the spontaneous emission rate and large collection efficiency. Our numerical calculations show that the collection efficiency of the emitted photons into a dielectric waveguide and the far-field radiation efficiency reach up to ~67% and ~97%, and the corresponding enhancement of the spontaneous emission rate still remains up to 5060 -folds. This phenomenon arises from three facts: The first is that the hybrid photonic-plasmonic cavity proposed here simultaneously possesses the merits of the two subsystems: high Q-factor and ultrasmall mode volume, consequently leading to high Fp. The second is that the collecting waveguide can couple well with the hybrid mode which results in improved ηc. The third is that the nonradiative quenching is significantly reduced because the emission wavelength of the emitter is detuned far from the resonant wavelength of the Au nanorod dimer. The mechanism proposed here is promising for significantly enhancing the spontaneous emission rate of the emitter and simultaneously obtaining large collection efficiency and paves the way towards the applications of the ultra-bright on-chip single photon sources and the plasmon-based nanolasers.

Funding

Ministry of Science and Technology of China (Grant No. 2016YFA0301300), the National Natural Science Foundations of China (Grants No. 11334015, No. 11364001, No. 11504050 and No. 61675237).

Acknowledgments

We thank Dr. J. M. Liu in Guangdong University of Education, Dr. H. X. Jiang in South China Normal University and Dr. Y. C. Yu in Foshan University for fruitful discussions.

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20. J. Bleuse, J. Claudon, M. Creasey, N. S. Malik, J. M. Gérard, I. Maksymov, J. P. Hugonin, and P. Lalanne, “Inhibition, enhancement, and control of spontaneous emission in photonic nanowires,” Phys. Rev. Lett. 106(10), 103601 (2011). [CrossRef]   [PubMed]  

21. R. Yalla, F. Le Kien, M. Morinaga, and K. Hakuta, “Efficient channeling of fluorescence photons from single quantum dots into guided modes of optical nanofiber,” Phys. Rev. Lett. 109(6), 063602 (2012). [CrossRef]   [PubMed]  

22. V. V. Klimov and M. Ducloy, “Spontaneous emission rate of an excited atom placed near a nanofiber,” Phys. Rev. A 69(1), 013812 (2004). [CrossRef]  

23. M. Arcari, I. Söllner, A. Javadi, S. Lindskov Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113(9), 093603 (2014). [CrossRef]   [PubMed]  

24. M. Barth, S. Schietinger, S. Fischer, J. Becker, N. Nüsse, T. Aichele, B. Löchel, C. Sönnichsen, and O. Benson, “Nanoassembled plasmonic-photonic hybrid cavity for tailored light-matter coupling,” Nano Lett. 10(3), 891–895 (2010). [CrossRef]   [PubMed]  

25. T. Zhang, S. Callard, C. Jamois, C. Chevalier, D. Feng, and A. Belarouci, “Plasmonic-photonic crystal coupled nanolaser,” Nanotechnology 25(31), 315201 (2014). [CrossRef]   [PubMed]  

26. A. E. Eter, T. Grosjean, P. Viktorovitch, X. Letartre, T. Benyattou, and F. I. Baida, “Huge light-enhancement by coupling a Bowtie Nano-antenna’s plasmonic resonance to a photonic crystal mode,” Opt. Express 22(12), 14464–14472 (2014). [CrossRef]   [PubMed]  

27. H. M. Doeleman, E. Verhagen, and A. F. Koenderink, “Antenna–Cavity Hybrids: Matching Polar Opposites for Purcell Enhancements at Any Linewidth,” ACS Photonics 3(10), 1943–1951 (2016). [CrossRef]  

28. H. Lian, Y. Gu, J. Ren, F. Zhang, L. Wang, and Q. Gong, “Efficient single photon emission and collection based on excitation of gap surface plasmons,” Phys. Rev. Lett. 114(19), 193002 (2015). [CrossRef]   [PubMed]  

29. K. J. Russell, T.-L. Liu, S. Cui, and E. L. Hu, “Large spontaneous emission enhancement in plasmonic nanocavities,” Nat. Photonics 6(7), 459–462 (2012). [CrossRef]  

30. J. Ren, Y. Gu, D. Zhao, F. Zhang, T. Zhang, and Q. Gong, “Evanescent-vacuum-enhanced photon-exciton coupling and fluorescence collection,” Phys. Rev. Lett. 118(7), 073604 (2017). [CrossRef]   [PubMed]  

31. B. Gurlek, V. Sandoghdar, and D. Martín-Cano, “Manipulation of quenching in nanoantenna–emitter systems enabled by external detuned cavities: a path to enhance strong-coupling,” ACS Photonics 5(2), 456–461 (2018). [CrossRef]  

32. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]  

33. M. A. Green, “Self-consistent optical parameters of intrinsic silicon at 300K including temperature coefficients,” Sol. Energy Mater. Sol. Cells 92(11), 1305–1310 (2008). [CrossRef]  

34. G. Chen, Y.-C. Yu, X.-L. Zhuo, Y.-G. Huang, H. Jiang, J.-F. Liu, C.-J. Jin, and X.-H. Wang, “Ab initiodetermination of local coupling interaction in arbitrary nanostructures: Application to photonic crystal slabs and cavities,” Phys. Rev. B Condens. Matter Mater. Phys. 87(19), 195138 (2013). [CrossRef]  

35. V. Krachmalnicoff, E. Castanié, Y. De Wilde, and R. Carminati, “Fluctuations of the local density of states probe localized surface plasmons on disordered metal films,” Phys. Rev. Lett. 105(18), 183901 (2010). [CrossRef]   [PubMed]  

36. D. Conteduca, C. Reardon, M. G. Scullion, F. Dell’Olio, M. N. Armenise, T. F. Krauss, and C. Ciminelli, “Ultra-high Q/V hybrid cavity for strong light-matter interaction,” APL Photonics 2(8), 086101 (2017). [CrossRef]  

37. M. Kamandar Dezfouli, R. Gordon, and S. Hughes, “Modal theory of modified spontaneous emission of a quantum emitter in a hybrid plasmonic photonic-crystal cavity system,” Phys. Rev. A (Coll. Park) 95(1), 013846 (2017). [CrossRef]  

38. F. I. Baida and T. Grosjean, “Double-way spectral tunability for the control of optical nanocavity resonance,” Sci. Rep. 5(1), 17907 (2016). [CrossRef]   [PubMed]  

39. A. F. Koenderink, M. Kafesaki, B. C. Buchler, and V. Sandoghdar, “Controlling the resonance of a photonic crystal microcavity by a near-field probe,” Phys. Rev. Lett. 95(15), 153904 (2005). [CrossRef]   [PubMed]  

40. A. F. Koenderink, “On the use of Purcell factors for plasmon antennas,” Opt. Lett. 35(24), 4208–4210 (2010). [CrossRef]   [PubMed]  

41. P. T. Kristensen, C. Van Vlack, and S. Hughes, “Generalized effective mode volume for leaky optical cavities,” Opt. Lett. 37(10), 1649–1651 (2012). [CrossRef]   [PubMed]  

42. R. Chikkaraddy, B. de Nijs, F. Benz, S. J. Barrow, O. A. Scherman, E. Rosta, A. Demetriadou, P. Fox, O. Hess, and J. J. Baumberg, “Single-molecule strong coupling at room temperature in plasmonic nanocavities,” Nature 535(7610), 127–130 (2016). [CrossRef]   [PubMed]  

43. A. Delga, J. Feist, J. Bravo-Abad, and F. J. Garcia-Vidal, “Quantum emitters near a metal nanoparticle: strong coupling and quenching,” Phys. Rev. Lett. 112(25), 253601 (2014). [CrossRef]   [PubMed]  

References

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  1. G. R. N. Gisin, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
    [Crossref]
  2. D. E. Chang, V. Vuletić, and M. D. Lukin, “Quantum nonlinear optics — photon by photon,” Nat. Photonics 8(9), 685–694 (2014).
    [Crossref]
  3. T. M. Babinec, B. J. Hausmann, M. Khan, Y. Zhang, J. R. Maze, P. R. Hemmer, and M. Loncar, “A diamond nanowire single-photon source,” Nat. Nanotechnol. 5(3), 195–199 (2010).
    [Crossref] [PubMed]
  4. M. J. Holmes, K. Choi, S. Kako, M. Arita, and Y. Arakawa, “Room-temperature triggered single photon emission from a III-nitride site-controlled nanowire quantum dot,” Nano Lett. 14(2), 982–986 (2014).
    [Crossref] [PubMed]
  5. E. M. Purcell, H. C. Torrey, and R. V. Pound, “Resonance Absorption by Nuclear Magnetic Moments in a Solid,” Phys. Rev. 69(1-2), 37–38 (1946).
    [Crossref]
  6. H. Y. Ryu, M. Notomi, G. H. Kim, and Y. H. Lee, “High quality-factor whispering-gallery mode in the photonic crystal hexagonal disk cavity,” Opt. Express 12(8), 1708–1719 (2004).
    [Crossref] [PubMed]
  7. M. Pelton, C. Santori, J. Vucković, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, “Efficient source of single photons: a single quantum dot in a micropost microcavity,” Phys. Rev. Lett. 89(23), 233602 (2002).
    [Crossref] [PubMed]
  8. P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A Quantum Dot Single-Photon Turnstile Device,” Science 290(5500), 2282–2285 (2000).
    [Crossref] [PubMed]
  9. G. M. Akselrod, C. Argyropoulos, T. B. Hoang, C. Ciracì, C. Fang, J. Huang, D. R. Smith, and M. H. Mikkelsen, “Probing the mechanisms of large Purcell enhancement in plasmonic nanoantennas,” Nat. Photonics 8(11), 835–840 (2014).
    [Crossref]
  10. T. B. Hoang, G. M. Akselrod, and M. H. Mikkelsen, “Ultrafast Room-Temperature Single Photon Emission from Quantum Dots Coupled to Plasmonic Nanocavities,” Nano Lett. 16(1), 270–275 (2016).
    [Crossref] [PubMed]
  11. S.-H. Kwon, “Deep subwavelength plasmonic whispering-gallery-mode cavity,” Opt. Express 20(22), 24918–24924 (2012).
    [Crossref] [PubMed]
  12. Y. Lai, S. Pirotta, G. Urbinati, D. Gerace, M. Minkov, V. Savona, A. Badolato, and M. Galli, “Genetically designed L3 photonic crystal nanocavities with measured quality factor exceeding one million,” Appl. Phys. Lett. 104(24), 241101 (2014).
    [Crossref]
  13. P. Lodahl, S. Mahmoodian, and S. Stobbe, “Interfacing single photons and single quantum dots with photonic nanostructures,” Rev. Mod. Phys. 87(2), 347–400 (2015).
    [Crossref]
  14. K. Nozaki, S. Kita, and T. Baba, “Room temperature continuous wave operation and controlled spontaneous emission in ultrasmall photonic crystal nanolaser,” Opt. Express 15(12), 7506–7514 (2007).
    [Crossref] [PubMed]
  15. K. J. Russell and E. L. Hu, “Gap-mode plasmonic nanocavity,” Appl. Phys. Lett. 97(16), 163115 (2010).
    [Crossref]
  16. J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
    [Crossref] [PubMed]
  17. J.-H. Kang, Y.-S. No, S.-H. Kwon, and H.-G. Park, “Ultrasmall subwavelength nanorod plasmonic cavity,” Opt. Lett. 36(11), 2011–2013 (2011).
    [Crossref] [PubMed]
  18. R. Faggiani, J. Yang, and P. Lalanne, “Quenching, Plasmonic, and Radiative Decays in Nanogap Emitting Devices,” ACS Photonics 2(12), 1739–1744 (2015).
    [Crossref]
  19. J. B. Khurgin, “How to deal with the loss in plasmonics and metamaterials,” Nat. Nanotechnol. 10(1), 2–6 (2015).
    [Crossref] [PubMed]
  20. J. Bleuse, J. Claudon, M. Creasey, N. S. Malik, J. M. Gérard, I. Maksymov, J. P. Hugonin, and P. Lalanne, “Inhibition, enhancement, and control of spontaneous emission in photonic nanowires,” Phys. Rev. Lett. 106(10), 103601 (2011).
    [Crossref] [PubMed]
  21. R. Yalla, F. Le Kien, M. Morinaga, and K. Hakuta, “Efficient channeling of fluorescence photons from single quantum dots into guided modes of optical nanofiber,” Phys. Rev. Lett. 109(6), 063602 (2012).
    [Crossref] [PubMed]
  22. V. V. Klimov and M. Ducloy, “Spontaneous emission rate of an excited atom placed near a nanofiber,” Phys. Rev. A 69(1), 013812 (2004).
    [Crossref]
  23. M. Arcari, I. Söllner, A. Javadi, S. Lindskov Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113(9), 093603 (2014).
    [Crossref] [PubMed]
  24. M. Barth, S. Schietinger, S. Fischer, J. Becker, N. Nüsse, T. Aichele, B. Löchel, C. Sönnichsen, and O. Benson, “Nanoassembled plasmonic-photonic hybrid cavity for tailored light-matter coupling,” Nano Lett. 10(3), 891–895 (2010).
    [Crossref] [PubMed]
  25. T. Zhang, S. Callard, C. Jamois, C. Chevalier, D. Feng, and A. Belarouci, “Plasmonic-photonic crystal coupled nanolaser,” Nanotechnology 25(31), 315201 (2014).
    [Crossref] [PubMed]
  26. A. E. Eter, T. Grosjean, P. Viktorovitch, X. Letartre, T. Benyattou, and F. I. Baida, “Huge light-enhancement by coupling a Bowtie Nano-antenna’s plasmonic resonance to a photonic crystal mode,” Opt. Express 22(12), 14464–14472 (2014).
    [Crossref] [PubMed]
  27. H. M. Doeleman, E. Verhagen, and A. F. Koenderink, “Antenna–Cavity Hybrids: Matching Polar Opposites for Purcell Enhancements at Any Linewidth,” ACS Photonics 3(10), 1943–1951 (2016).
    [Crossref]
  28. H. Lian, Y. Gu, J. Ren, F. Zhang, L. Wang, and Q. Gong, “Efficient single photon emission and collection based on excitation of gap surface plasmons,” Phys. Rev. Lett. 114(19), 193002 (2015).
    [Crossref] [PubMed]
  29. K. J. Russell, T.-L. Liu, S. Cui, and E. L. Hu, “Large spontaneous emission enhancement in plasmonic nanocavities,” Nat. Photonics 6(7), 459–462 (2012).
    [Crossref]
  30. J. Ren, Y. Gu, D. Zhao, F. Zhang, T. Zhang, and Q. Gong, “Evanescent-vacuum-enhanced photon-exciton coupling and fluorescence collection,” Phys. Rev. Lett. 118(7), 073604 (2017).
    [Crossref] [PubMed]
  31. B. Gurlek, V. Sandoghdar, and D. Martín-Cano, “Manipulation of quenching in nanoantenna–emitter systems enabled by external detuned cavities: a path to enhance strong-coupling,” ACS Photonics 5(2), 456–461 (2018).
    [Crossref]
  32. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
    [Crossref]
  33. M. A. Green, “Self-consistent optical parameters of intrinsic silicon at 300K including temperature coefficients,” Sol. Energy Mater. Sol. Cells 92(11), 1305–1310 (2008).
    [Crossref]
  34. G. Chen, Y.-C. Yu, X.-L. Zhuo, Y.-G. Huang, H. Jiang, J.-F. Liu, C.-J. Jin, and X.-H. Wang, “Ab initiodetermination of local coupling interaction in arbitrary nanostructures: Application to photonic crystal slabs and cavities,” Phys. Rev. B Condens. Matter Mater. Phys. 87(19), 195138 (2013).
    [Crossref]
  35. V. Krachmalnicoff, E. Castanié, Y. De Wilde, and R. Carminati, “Fluctuations of the local density of states probe localized surface plasmons on disordered metal films,” Phys. Rev. Lett. 105(18), 183901 (2010).
    [Crossref] [PubMed]
  36. D. Conteduca, C. Reardon, M. G. Scullion, F. Dell’Olio, M. N. Armenise, T. F. Krauss, and C. Ciminelli, “Ultra-high Q/V hybrid cavity for strong light-matter interaction,” APL Photonics 2(8), 086101 (2017).
    [Crossref]
  37. M. Kamandar Dezfouli, R. Gordon, and S. Hughes, “Modal theory of modified spontaneous emission of a quantum emitter in a hybrid plasmonic photonic-crystal cavity system,” Phys. Rev. A (Coll. Park) 95(1), 013846 (2017).
    [Crossref]
  38. F. I. Baida and T. Grosjean, “Double-way spectral tunability for the control of optical nanocavity resonance,” Sci. Rep. 5(1), 17907 (2016).
    [Crossref] [PubMed]
  39. A. F. Koenderink, M. Kafesaki, B. C. Buchler, and V. Sandoghdar, “Controlling the resonance of a photonic crystal microcavity by a near-field probe,” Phys. Rev. Lett. 95(15), 153904 (2005).
    [Crossref] [PubMed]
  40. A. F. Koenderink, “On the use of Purcell factors for plasmon antennas,” Opt. Lett. 35(24), 4208–4210 (2010).
    [Crossref] [PubMed]
  41. P. T. Kristensen, C. Van Vlack, and S. Hughes, “Generalized effective mode volume for leaky optical cavities,” Opt. Lett. 37(10), 1649–1651 (2012).
    [Crossref] [PubMed]
  42. R. Chikkaraddy, B. de Nijs, F. Benz, S. J. Barrow, O. A. Scherman, E. Rosta, A. Demetriadou, P. Fox, O. Hess, and J. J. Baumberg, “Single-molecule strong coupling at room temperature in plasmonic nanocavities,” Nature 535(7610), 127–130 (2016).
    [Crossref] [PubMed]
  43. A. Delga, J. Feist, J. Bravo-Abad, and F. J. Garcia-Vidal, “Quantum emitters near a metal nanoparticle: strong coupling and quenching,” Phys. Rev. Lett. 112(25), 253601 (2014).
    [Crossref] [PubMed]

2018 (1)

B. Gurlek, V. Sandoghdar, and D. Martín-Cano, “Manipulation of quenching in nanoantenna–emitter systems enabled by external detuned cavities: a path to enhance strong-coupling,” ACS Photonics 5(2), 456–461 (2018).
[Crossref]

2017 (3)

J. Ren, Y. Gu, D. Zhao, F. Zhang, T. Zhang, and Q. Gong, “Evanescent-vacuum-enhanced photon-exciton coupling and fluorescence collection,” Phys. Rev. Lett. 118(7), 073604 (2017).
[Crossref] [PubMed]

D. Conteduca, C. Reardon, M. G. Scullion, F. Dell’Olio, M. N. Armenise, T. F. Krauss, and C. Ciminelli, “Ultra-high Q/V hybrid cavity for strong light-matter interaction,” APL Photonics 2(8), 086101 (2017).
[Crossref]

M. Kamandar Dezfouli, R. Gordon, and S. Hughes, “Modal theory of modified spontaneous emission of a quantum emitter in a hybrid plasmonic photonic-crystal cavity system,” Phys. Rev. A (Coll. Park) 95(1), 013846 (2017).
[Crossref]

2016 (4)

F. I. Baida and T. Grosjean, “Double-way spectral tunability for the control of optical nanocavity resonance,” Sci. Rep. 5(1), 17907 (2016).
[Crossref] [PubMed]

R. Chikkaraddy, B. de Nijs, F. Benz, S. J. Barrow, O. A. Scherman, E. Rosta, A. Demetriadou, P. Fox, O. Hess, and J. J. Baumberg, “Single-molecule strong coupling at room temperature in plasmonic nanocavities,” Nature 535(7610), 127–130 (2016).
[Crossref] [PubMed]

H. M. Doeleman, E. Verhagen, and A. F. Koenderink, “Antenna–Cavity Hybrids: Matching Polar Opposites for Purcell Enhancements at Any Linewidth,” ACS Photonics 3(10), 1943–1951 (2016).
[Crossref]

T. B. Hoang, G. M. Akselrod, and M. H. Mikkelsen, “Ultrafast Room-Temperature Single Photon Emission from Quantum Dots Coupled to Plasmonic Nanocavities,” Nano Lett. 16(1), 270–275 (2016).
[Crossref] [PubMed]

2015 (4)

P. Lodahl, S. Mahmoodian, and S. Stobbe, “Interfacing single photons and single quantum dots with photonic nanostructures,” Rev. Mod. Phys. 87(2), 347–400 (2015).
[Crossref]

H. Lian, Y. Gu, J. Ren, F. Zhang, L. Wang, and Q. Gong, “Efficient single photon emission and collection based on excitation of gap surface plasmons,” Phys. Rev. Lett. 114(19), 193002 (2015).
[Crossref] [PubMed]

R. Faggiani, J. Yang, and P. Lalanne, “Quenching, Plasmonic, and Radiative Decays in Nanogap Emitting Devices,” ACS Photonics 2(12), 1739–1744 (2015).
[Crossref]

J. B. Khurgin, “How to deal with the loss in plasmonics and metamaterials,” Nat. Nanotechnol. 10(1), 2–6 (2015).
[Crossref] [PubMed]

2014 (8)

M. Arcari, I. Söllner, A. Javadi, S. Lindskov Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113(9), 093603 (2014).
[Crossref] [PubMed]

T. Zhang, S. Callard, C. Jamois, C. Chevalier, D. Feng, and A. Belarouci, “Plasmonic-photonic crystal coupled nanolaser,” Nanotechnology 25(31), 315201 (2014).
[Crossref] [PubMed]

A. E. Eter, T. Grosjean, P. Viktorovitch, X. Letartre, T. Benyattou, and F. I. Baida, “Huge light-enhancement by coupling a Bowtie Nano-antenna’s plasmonic resonance to a photonic crystal mode,” Opt. Express 22(12), 14464–14472 (2014).
[Crossref] [PubMed]

Y. Lai, S. Pirotta, G. Urbinati, D. Gerace, M. Minkov, V. Savona, A. Badolato, and M. Galli, “Genetically designed L3 photonic crystal nanocavities with measured quality factor exceeding one million,” Appl. Phys. Lett. 104(24), 241101 (2014).
[Crossref]

D. E. Chang, V. Vuletić, and M. D. Lukin, “Quantum nonlinear optics — photon by photon,” Nat. Photonics 8(9), 685–694 (2014).
[Crossref]

M. J. Holmes, K. Choi, S. Kako, M. Arita, and Y. Arakawa, “Room-temperature triggered single photon emission from a III-nitride site-controlled nanowire quantum dot,” Nano Lett. 14(2), 982–986 (2014).
[Crossref] [PubMed]

G. M. Akselrod, C. Argyropoulos, T. B. Hoang, C. Ciracì, C. Fang, J. Huang, D. R. Smith, and M. H. Mikkelsen, “Probing the mechanisms of large Purcell enhancement in plasmonic nanoantennas,” Nat. Photonics 8(11), 835–840 (2014).
[Crossref]

A. Delga, J. Feist, J. Bravo-Abad, and F. J. Garcia-Vidal, “Quantum emitters near a metal nanoparticle: strong coupling and quenching,” Phys. Rev. Lett. 112(25), 253601 (2014).
[Crossref] [PubMed]

2013 (1)

G. Chen, Y.-C. Yu, X.-L. Zhuo, Y.-G. Huang, H. Jiang, J.-F. Liu, C.-J. Jin, and X.-H. Wang, “Ab initiodetermination of local coupling interaction in arbitrary nanostructures: Application to photonic crystal slabs and cavities,” Phys. Rev. B Condens. Matter Mater. Phys. 87(19), 195138 (2013).
[Crossref]

2012 (4)

K. J. Russell, T.-L. Liu, S. Cui, and E. L. Hu, “Large spontaneous emission enhancement in plasmonic nanocavities,” Nat. Photonics 6(7), 459–462 (2012).
[Crossref]

R. Yalla, F. Le Kien, M. Morinaga, and K. Hakuta, “Efficient channeling of fluorescence photons from single quantum dots into guided modes of optical nanofiber,” Phys. Rev. Lett. 109(6), 063602 (2012).
[Crossref] [PubMed]

S.-H. Kwon, “Deep subwavelength plasmonic whispering-gallery-mode cavity,” Opt. Express 20(22), 24918–24924 (2012).
[Crossref] [PubMed]

P. T. Kristensen, C. Van Vlack, and S. Hughes, “Generalized effective mode volume for leaky optical cavities,” Opt. Lett. 37(10), 1649–1651 (2012).
[Crossref] [PubMed]

2011 (2)

J.-H. Kang, Y.-S. No, S.-H. Kwon, and H.-G. Park, “Ultrasmall subwavelength nanorod plasmonic cavity,” Opt. Lett. 36(11), 2011–2013 (2011).
[Crossref] [PubMed]

J. Bleuse, J. Claudon, M. Creasey, N. S. Malik, J. M. Gérard, I. Maksymov, J. P. Hugonin, and P. Lalanne, “Inhibition, enhancement, and control of spontaneous emission in photonic nanowires,” Phys. Rev. Lett. 106(10), 103601 (2011).
[Crossref] [PubMed]

2010 (6)

M. Barth, S. Schietinger, S. Fischer, J. Becker, N. Nüsse, T. Aichele, B. Löchel, C. Sönnichsen, and O. Benson, “Nanoassembled plasmonic-photonic hybrid cavity for tailored light-matter coupling,” Nano Lett. 10(3), 891–895 (2010).
[Crossref] [PubMed]

V. Krachmalnicoff, E. Castanié, Y. De Wilde, and R. Carminati, “Fluctuations of the local density of states probe localized surface plasmons on disordered metal films,” Phys. Rev. Lett. 105(18), 183901 (2010).
[Crossref] [PubMed]

K. J. Russell and E. L. Hu, “Gap-mode plasmonic nanocavity,” Appl. Phys. Lett. 97(16), 163115 (2010).
[Crossref]

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[Crossref] [PubMed]

T. M. Babinec, B. J. Hausmann, M. Khan, Y. Zhang, J. R. Maze, P. R. Hemmer, and M. Loncar, “A diamond nanowire single-photon source,” Nat. Nanotechnol. 5(3), 195–199 (2010).
[Crossref] [PubMed]

A. F. Koenderink, “On the use of Purcell factors for plasmon antennas,” Opt. Lett. 35(24), 4208–4210 (2010).
[Crossref] [PubMed]

2008 (1)

M. A. Green, “Self-consistent optical parameters of intrinsic silicon at 300K including temperature coefficients,” Sol. Energy Mater. Sol. Cells 92(11), 1305–1310 (2008).
[Crossref]

2007 (1)

2005 (1)

A. F. Koenderink, M. Kafesaki, B. C. Buchler, and V. Sandoghdar, “Controlling the resonance of a photonic crystal microcavity by a near-field probe,” Phys. Rev. Lett. 95(15), 153904 (2005).
[Crossref] [PubMed]

2004 (2)

2002 (2)

M. Pelton, C. Santori, J. Vucković, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, “Efficient source of single photons: a single quantum dot in a micropost microcavity,” Phys. Rev. Lett. 89(23), 233602 (2002).
[Crossref] [PubMed]

G. R. N. Gisin, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

2000 (1)

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A Quantum Dot Single-Photon Turnstile Device,” Science 290(5500), 2282–2285 (2000).
[Crossref] [PubMed]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

1946 (1)

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M. J. Holmes, K. Choi, S. Kako, M. Arita, and Y. Arakawa, “Room-temperature triggered single photon emission from a III-nitride site-controlled nanowire quantum dot,” Nano Lett. 14(2), 982–986 (2014).
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J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
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A. F. Koenderink, M. Kafesaki, B. C. Buchler, and V. Sandoghdar, “Controlling the resonance of a photonic crystal microcavity by a near-field probe,” Phys. Rev. Lett. 95(15), 153904 (2005).
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M. J. Holmes, K. Choi, S. Kako, M. Arita, and Y. Arakawa, “Room-temperature triggered single photon emission from a III-nitride site-controlled nanowire quantum dot,” Nano Lett. 14(2), 982–986 (2014).
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Letartre, X.

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A. F. Koenderink, M. Kafesaki, B. C. Buchler, and V. Sandoghdar, “Controlling the resonance of a photonic crystal microcavity by a near-field probe,” Phys. Rev. Lett. 95(15), 153904 (2005).
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P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A Quantum Dot Single-Photon Turnstile Device,” Science 290(5500), 2282–2285 (2000).
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J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
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D. Conteduca, C. Reardon, M. G. Scullion, F. Dell’Olio, M. N. Armenise, T. F. Krauss, and C. Ciminelli, “Ultra-high Q/V hybrid cavity for strong light-matter interaction,” APL Photonics 2(8), 086101 (2017).
[Crossref]

Smith, D. R.

G. M. Akselrod, C. Argyropoulos, T. B. Hoang, C. Ciracì, C. Fang, J. Huang, D. R. Smith, and M. H. Mikkelsen, “Probing the mechanisms of large Purcell enhancement in plasmonic nanoantennas,” Nat. Photonics 8(11), 835–840 (2014).
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M. Arcari, I. Söllner, A. Javadi, S. Lindskov Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113(9), 093603 (2014).
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M. Pelton, C. Santori, J. Vucković, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, “Efficient source of single photons: a single quantum dot in a micropost microcavity,” Phys. Rev. Lett. 89(23), 233602 (2002).
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Song, J. D.

M. Arcari, I. Söllner, A. Javadi, S. Lindskov Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113(9), 093603 (2014).
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M. Barth, S. Schietinger, S. Fischer, J. Becker, N. Nüsse, T. Aichele, B. Löchel, C. Sönnichsen, and O. Benson, “Nanoassembled plasmonic-photonic hybrid cavity for tailored light-matter coupling,” Nano Lett. 10(3), 891–895 (2010).
[Crossref] [PubMed]

Stobbe, S.

P. Lodahl, S. Mahmoodian, and S. Stobbe, “Interfacing single photons and single quantum dots with photonic nanostructures,” Rev. Mod. Phys. 87(2), 347–400 (2015).
[Crossref]

M. Arcari, I. Söllner, A. Javadi, S. Lindskov Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113(9), 093603 (2014).
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Thyrrestrup, H.

M. Arcari, I. Söllner, A. Javadi, S. Lindskov Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113(9), 093603 (2014).
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G. R. N. Gisin, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
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E. M. Purcell, H. C. Torrey, and R. V. Pound, “Resonance Absorption by Nuclear Magnetic Moments in a Solid,” Phys. Rev. 69(1-2), 37–38 (1946).
[Crossref]

Urbinati, G.

Y. Lai, S. Pirotta, G. Urbinati, D. Gerace, M. Minkov, V. Savona, A. Badolato, and M. Galli, “Genetically designed L3 photonic crystal nanocavities with measured quality factor exceeding one million,” Appl. Phys. Lett. 104(24), 241101 (2014).
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Van Vlack, C.

Verhagen, E.

H. M. Doeleman, E. Verhagen, and A. F. Koenderink, “Antenna–Cavity Hybrids: Matching Polar Opposites for Purcell Enhancements at Any Linewidth,” ACS Photonics 3(10), 1943–1951 (2016).
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Vuckovic, J.

M. Pelton, C. Santori, J. Vucković, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, “Efficient source of single photons: a single quantum dot in a micropost microcavity,” Phys. Rev. Lett. 89(23), 233602 (2002).
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Vuletic, V.

D. E. Chang, V. Vuletić, and M. D. Lukin, “Quantum nonlinear optics — photon by photon,” Nat. Photonics 8(9), 685–694 (2014).
[Crossref]

Wang, L.

H. Lian, Y. Gu, J. Ren, F. Zhang, L. Wang, and Q. Gong, “Efficient single photon emission and collection based on excitation of gap surface plasmons,” Phys. Rev. Lett. 114(19), 193002 (2015).
[Crossref] [PubMed]

Wang, X.-H.

G. Chen, Y.-C. Yu, X.-L. Zhuo, Y.-G. Huang, H. Jiang, J.-F. Liu, C.-J. Jin, and X.-H. Wang, “Ab initiodetermination of local coupling interaction in arbitrary nanostructures: Application to photonic crystal slabs and cavities,” Phys. Rev. B Condens. Matter Mater. Phys. 87(19), 195138 (2013).
[Crossref]

White, J. S.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[Crossref] [PubMed]

Yalla, R.

R. Yalla, F. Le Kien, M. Morinaga, and K. Hakuta, “Efficient channeling of fluorescence photons from single quantum dots into guided modes of optical nanofiber,” Phys. Rev. Lett. 109(6), 063602 (2012).
[Crossref] [PubMed]

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M. Pelton, C. Santori, J. Vucković, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, “Efficient source of single photons: a single quantum dot in a micropost microcavity,” Phys. Rev. Lett. 89(23), 233602 (2002).
[Crossref] [PubMed]

Yang, J.

R. Faggiani, J. Yang, and P. Lalanne, “Quenching, Plasmonic, and Radiative Decays in Nanogap Emitting Devices,” ACS Photonics 2(12), 1739–1744 (2015).
[Crossref]

Yu, Y.-C.

G. Chen, Y.-C. Yu, X.-L. Zhuo, Y.-G. Huang, H. Jiang, J.-F. Liu, C.-J. Jin, and X.-H. Wang, “Ab initiodetermination of local coupling interaction in arbitrary nanostructures: Application to photonic crystal slabs and cavities,” Phys. Rev. B Condens. Matter Mater. Phys. 87(19), 195138 (2013).
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Zbinden, H.

G. R. N. Gisin, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
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Zhang, B.

M. Pelton, C. Santori, J. Vucković, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, “Efficient source of single photons: a single quantum dot in a micropost microcavity,” Phys. Rev. Lett. 89(23), 233602 (2002).
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Zhang, F.

J. Ren, Y. Gu, D. Zhao, F. Zhang, T. Zhang, and Q. Gong, “Evanescent-vacuum-enhanced photon-exciton coupling and fluorescence collection,” Phys. Rev. Lett. 118(7), 073604 (2017).
[Crossref] [PubMed]

H. Lian, Y. Gu, J. Ren, F. Zhang, L. Wang, and Q. Gong, “Efficient single photon emission and collection based on excitation of gap surface plasmons,” Phys. Rev. Lett. 114(19), 193002 (2015).
[Crossref] [PubMed]

Zhang, L.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A Quantum Dot Single-Photon Turnstile Device,” Science 290(5500), 2282–2285 (2000).
[Crossref] [PubMed]

Zhang, T.

J. Ren, Y. Gu, D. Zhao, F. Zhang, T. Zhang, and Q. Gong, “Evanescent-vacuum-enhanced photon-exciton coupling and fluorescence collection,” Phys. Rev. Lett. 118(7), 073604 (2017).
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T. Zhang, S. Callard, C. Jamois, C. Chevalier, D. Feng, and A. Belarouci, “Plasmonic-photonic crystal coupled nanolaser,” Nanotechnology 25(31), 315201 (2014).
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T. M. Babinec, B. J. Hausmann, M. Khan, Y. Zhang, J. R. Maze, P. R. Hemmer, and M. Loncar, “A diamond nanowire single-photon source,” Nat. Nanotechnol. 5(3), 195–199 (2010).
[Crossref] [PubMed]

Zhao, D.

J. Ren, Y. Gu, D. Zhao, F. Zhang, T. Zhang, and Q. Gong, “Evanescent-vacuum-enhanced photon-exciton coupling and fluorescence collection,” Phys. Rev. Lett. 118(7), 073604 (2017).
[Crossref] [PubMed]

Zhuo, X.-L.

G. Chen, Y.-C. Yu, X.-L. Zhuo, Y.-G. Huang, H. Jiang, J.-F. Liu, C.-J. Jin, and X.-H. Wang, “Ab initiodetermination of local coupling interaction in arbitrary nanostructures: Application to photonic crystal slabs and cavities,” Phys. Rev. B Condens. Matter Mater. Phys. 87(19), 195138 (2013).
[Crossref]

ACS Photonics (3)

R. Faggiani, J. Yang, and P. Lalanne, “Quenching, Plasmonic, and Radiative Decays in Nanogap Emitting Devices,” ACS Photonics 2(12), 1739–1744 (2015).
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Figures (6)

Fig. 1
Fig. 1 (a) Schematic diagram of an Au nanorod dimer coupled with a photonic crystal nanobeam cavity with a collecting waveguide. The nanobeam cavity is composed of a tapering region, two mirror sections and a collecting waveguide. (b), (c) Details of an Au nanorod dimer directly placed on the nanobeam and on a dielectric spacer, respectively. The cross section length s of the Au nanorod is 40 nm and the length l of the Au nanorod and the gap distance d of the Au nanorod dimer is tunable. The two ends of the Au nanorod are ground with a radius of 8 nm. The width ws of the spacer layer in (c) is set to 90 nm. (d) The electric field | E |distribution of the eigenmode of the nanobeam cavity. (e) The energy band structure of the nanobeam with the lattice constant Λ=394 nm, the width w=460 nm and the height h=220 nm. The black and red lines denote the cases of the air holes with radius r to be 118 and 133 nm, respectively. (f) The extinction cross section of the Au nanorod dimer on Si substrate, the parameters d and l are set to be 20 nm and 80 nm, respectively. The insert shows the electric field distribution around the Au nanorod dimer.
Fig. 2
Fig. 2 Purcell factor F p of the emitter as a function of emission wavelength. (a) F p of the emitter placed into the gap of the bare Au nanorod dimer on Si substrate and 20 nm above the Si substrate surface (the blue line), and between the two central air holes of the bare nanobeam cavity and 20 nm above the surface of the nanobeam cavity (the orange and magenta lines). (b) F p of the emitter placed into the gap of the Au nanorod dimer in the photonic-plasmonic hybrid cavity and 20 nm above the surface of the nanobeam. The other parameters are set as follows: l=80 nm, d=20 nm, N=1.
Fig. 3
Fig. 3 Electric field distribution in hybrid cavity. (a) at y=240 nm plane (at the mid-plane of Au nanorod dimer), (b) at y=220 nm plane (at the beam surface), (c) at y=110 nm plane (in the middle of the photonic crystal nanobeam). Since the field intensity in dimer gap is several orders of magnitude larger than in nanobeam, the logarithmic value scale of lg( | E | ) is used to better highlight the spatial distribution of the electric field. The parameters are set as follows: l=80 nm, d=20 nm, N=1.
Fig. 4
Fig. 4 Purcell factor F p , radiation efficiency and collection efficiency as a function of l. (a) Purcell factor F p of the emitter in the hybrid cavity as a function of l. (b) Far-field radiation efficiency as a function of l. (c) Collection efficiency of the photons into the collecting waveguide as a function of l. The black circle dot lines represent the case that there have no spacer between the Au nanorod dimer and the nanobeam. The magenta hexagon dot lines and the cyan rhomboidal dot lines represent the cases of hs=10 nm and hs=20 nm, respectively. The other parameters are set as follows: d=20 nm and N=1.
Fig. 5
Fig. 5 Purcell factor F p , radiation and collection efficiency as a function of the gap distance d. (a) Purcell factor F p of the emitter in the hybrid cavity. (b) Radiation and collection efficiency. The magenta rhomboidal dot line and orange circle dot line in (b) represent the radiation efficiency and collection efficiency, respectively. The geometrical parameters are set as follows: hs=10 nm, l=80 nm and N=1.
Fig. 6
Fig. 6 Purcell factor F p , radiation and collection efficiency as a function of the air holes number N of left mirror. (a) Purcell factor F p of the emitter in the hybrid cavity as a function of N. (b) Radiation and collection efficiency as a function of N. The orange circle dot line and the cyan rhomboidal dot line in (b) represent the radiation efficiency and collection efficiency, respectively. The parameters are set as follows: hs=10 nm, d=20 nm and l=80 nm.

Equations (5)

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Γ( r 0 ,ω,d)= Γ 0 F p ( r 0 ,ω,d),
η c = Γ c Γ ,
η r = Γ r Γ ,
V eff = v ε(r) | E(r) | 2 dv ε( r 0 ) | E( r 0 ) | 2 ,
V eff = 3 4 π 2 ε( r 0 ) Q F P λ 3 ,

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