Abstract

The rate of single-photon generation by quantum emitters (QEs) can be enhanced by placing a QE inside a resonant structure. This structure can represent an all-dielectric micro-resonator or waveguide and thus be characterized by ultra-low loss and dimensions on the order of wavelength. Or it can be a metal nanostructure supporting localized or propagating surface plasmon-polariton modes that are of subwavelength dimensions, but suffer from strong absorption. In this work, we develop a physically transparent analytical model of single-photon emission in resonant structures and show unambiguously that, notwithstanding the inherently high loss, the external emission rate can be enhanced with plasmonic nanostructures by two orders of magnitude compared to all-dielectric structures. Our analysis provides guidelines for developments of new plasmonic configurations and materials to be exploited in quantum plasmonics.

© 2016 Optical Society of America

Efficient and bright single-photon sources, which enable the generation of single photons with high repetition rates, are crucial components for quantum communication and computation systems [1,2]. The common approach to the realization of single-photon sources is to make use of spontaneous emission (SE) from two-level systems emitting one photon at a time—so-called quantum emitters (QEs) that can be selected from various atomic or molecular structures, such as dye molecules, quantum dots, and color centers in crystals.

The intrinsic radiative lifetime τ of a QE placed within an unconstrained dielectric is of the order of 10 ns in the visible or near-IR spectral range, which is certainly too long to ensure high repetition rates of single-photon emission. The SE rate can, however, be increased by placing a QE in a suitable photonic environment with an increased electromagnetic local density of states [3]. Thus, for a non-absorbing cavity characterized by the quality factor Q and volume V and containing a properly located and oriented QE and being in resonance with the QE radiative transition at the wavelength λ, the ratio between the modified γSE and free-space γ0=1/τ SE rates, the Purcell factor F, is given by [4]

F=γSEγ0=6π2(λ2n)3QV,
where n is the medium refractive index inside the cavity.

It is clear from Eq. (1) that the SE rate can be enhanced by using an optical cavity having either a small volume or a high finesse or, preferably, both. In recent years, following intensive investigations (see a recent review [2]) two classes of nanostructures have emerged as the candidates for use in SE control and enhancement. The first class is all-dielectric micro-cavities [Fig. 1(a)], including those formed by photonic crystals, in which extremely high quality factors (Q104) can be achieved, while the volume remains relatively large, on the order of (λ/2n)3 [5,6]. The second class includes “plasmonic nanocavities” incorporating metals [Fig. 1(b)], in which volumes are much smaller than (λ/2n)3 [7], but the Q-factor is typically small (Q100) due to large loss in metals [8]. Despite the large volume of work, it is still not clear which route (all-dielectric or plasmonic) can lead to the highest SE rate enhancement. Nor is it apparent whether fundamental limits of SE modification can be found in these configurations. The goal of this Letter is to provide the answers to these questions.

 figure: Fig. 1.

Fig. 1. (a) Dielectric cavity with a QE placed inside. (b) Plasmonic nanostructure with a QE located within a tightly confined LSP field. (c) Normalized out-of-cavity QE emission rate for different ratios between the cavity emission rate and Rabi frequency.

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To do so we consider theoretically QE coupling to localized surface plasmons (LSPs) and dielectric micro-cavities from the viewpoint of assessing fundamental factors limiting the achievable SE rates in these configurations. We then compare the QE coupling to propagating surface plasmon-polariton (SPP) modes and to dielectric waveguide modes, arguing that the usage of plasmonic configurations is advantageous in both cases.

For dielectric, i.e., diffraction-limited and lossless, cavities, one can obtain [Eq. (1)] the following upper limit for the Purcell factor:

V(λ2n)3F6π2Q.
The fundamental issue with this configuration is related to the fact that an increase in Q is strictly connected with the corresponding decrease in the cavity emission rate: γcav=ω/Q, where ω is the cavity resonant frequency. This decrease will inevitably limit an increase in the SE rate out of the cavity, since it cannot exceed the cavity emission rate. Intuitively, the optimum coupling is achieved when the two rates are equal, γSEγcav; i.e., each photon emitted into the cavity leaves it before the next one appears and no “bottleneck” is formed. This condition also happens to define the boundary when the QE-cavity coupling enters the strong-coupling regime with energy oscillating coherently between the QE and the cavity in the process of Rabi oscillations [2]. Using the above condition, one can evaluate the optimum quality factor Qopt ensuring the highest out-of-cavity SE rate and, consequently, the fundamental limit for the SE emission rate enhanced by a dielectric cavity (see Supplement 1):
Qoptπω6γ0,andγSEmax6ωγ0π.

The above condition was obtained by considering the SE modification as described with the Purcell factor [Eq. (1)], which is valid only in the weak-coupling approximation, when γSEγcav. It is instructive to show that a similar relation can be found using a more rigorous approach that considers vacuum Rabi oscillations. Introducing the cavity emission into coupled equations describing vacuum Rabi oscillations, one can arrive at the following expression for the out-of-cavity emission rate (see Supplement 1):

r(t)=4γcavΩ2·|s1s2s2s1[es1tes2t]|2,
where Ω=6γ0ω/π is the vacuum Rabi frequency in the diffraction-limited cavity, i.e., with the volume V=(λ/2n)3, noting that the vacuum Rabi frequency is exactly equal to the maximum SE rate in Eq. (3), and
s1,2=γcav4(γcav4)2Ω24.

Considering the relations obtained, one realizes that the most important parameter determining the emission temporal behavior is the ratio R=γcav/Ω [Fig. 1(c)]. Well-developed Rabi oscillations are observed for R1. In this case, the out-of-cavity emission rate oscillates accordingly, and the emission process stretches over long time periods. In the opposite limit, R1, there is a long non-oscillatory response, and it is found that the emission rate is reaching maximum values and the emission takes the shortest time, when Ropt1.1 (see Supplement 1)—roughly the critical coupling condition, with the optimum cavity quality factor given by

Qopt=ωRoptΩπ1.1ω6γ0=π1.1πν3γ0.
Here, we introduced the frequency ν=ω/2π in order to facilitate example calculations. The above relation is practically the same as that derived within the weak-coupling approximation [Eq. (3)], and we conclude that the time required for a photon to leave the optimum cavity is T2π/Ω, and thus the maximum rate of photons is
BmaxΩ2π=6γ0ω2π2=3πγ0νπ2.
The above relation represents the fundamental diffraction-determined limit for the photon rate out of dielectric cavities.

Considering, for example, a QE with the lifetime of 10 ns, i.e., with γ0=108s1, and the SE being centered at the wavelength of 1 μm, i.e., ν3·1014s1, one obtains from Eq. (6) that the optimum quality factor (for the diffraction-limited cavity) should be 5100, which would ensure the maximum rate of single photons of 54GHz [Eq. (7)]. Note that, for larger cavities, both of these values should be proportionally modified: the cavity (optimum) quality factor should be larger, resulting, consequently, in a lower (out-of-cavity) emission rate [see Eq. (3)]. From the viewpoint of Rabi oscillations, larger cavities imply weaker vacuum fields and thus smaller Rabi frequencies, which in turn require smaller optimum cavity emission rates and larger quality factors [see Eq. (6)]. At any rate, this level of cavity quality factors has already been realized and even exceeded, bringing QE-cavity systems in the strong-coupling regime [5,6].

Let us now consider the QE coupling to a generic LSP sustained by a plasmonic nanostructure [7]. The fundamental issue with this configuration is related to the fact that the LSP quality factor is relatively low and principally limited (in the electrostatic approximation [8]) by the electron collision frequency γm1014s1 in metals, when adopting the Drude model for describing the metal dielectric function [9]. One should also take into account the radiation channel of the LSP dissipation (characterized by the emission rate γrad). When a QE interacts efficiently with an LSP field, i.e., when the QE is sufficiently close to the corresponding plasmonic nanostructure, photons are emitted primarily via the LSP radiation [10]. The SE rate of the QE–LSP system can therefore be written in the weak-coupling approximation as follows:

γSE=Fγradγm+γradγ0=34π2(λn)3ωγradVLSP(γm+γrad)2γ0.
Here, the LSP volume VLSP should be understood as an effective volume occupied by the LSP field, whose calculation is, in general, a complicated issue due to energy dissipation [11], but whose value (for strongly confined modes) is typically of the same order of magnitude as the nanostructure volume itself. Also the Purcell factor should be used with care when considering plasmonic nanostructures [12].

The LSP emission rate can be estimated by considering the LSP being due to an electrical dipole resonance [13], with free electrons in metal oscillating (without dissipation) and generating the corresponding dipole moment (see Supplement 1). Introducing the effective nanostructure volume,

Veff=|E(r)d3r|2/E2(r)d3r,
we can link the dipole magnitude and the LSP mode energy and find the emission rate using the classical formula for the radiating dipole:
γrad=43π2ωVeffλλp2,
with λp=2πc/ωp and the validity domain being Veffλλp2.

Relating the LSP mode volume VLSP associated with the Purcell factor [Eq. (8)] and the effective nanostructure volume Veff, which for a spherical nanoparticle is simply equal to the particle volume, is a challenging issue that can hardly be dealt with in a simple and general way. Since these volumes are of the same order of magnitude for highly confined modes that we are interested in, we assume hereafter that VLSPVeff. Combining Eqs. (8) and (10), we obtain a key result—the fundamental loss-determined limit for LSP-enhanced photon rates:

γSE=(λn)3ω2λλp2(γm+γrad)2γ01n3·ωp2γm2γ0=γSEmax,
with the validity domain (γSEγm) imposed by the weak-coupling approximation. It should be understood that the upper limit cannot be physically reached as it requires the zero LSP volume and placing the QE on the metal surface (of a metal nanostructure sustaining the corresponding LSP). Considering a realistic case when the LSP radiative decay equals its absorption decay, γrad=γm, one obtains a (realistic) limit decay rate:
γSErl=0.251n3·ωp2γm2γ0.

Considering the same QE as above, n=1 and a silver (gold)-based LSP nanostructure characterized by ωp9.6(8.55)eV and γm22.8(18.4)meV5.5(4.4)·1012s1 [14], one obtains from Eq. (12) the maximum SE rate γSErl4.43(5.4)·1012s1γm, setting thus the maximum rate of single photons at 4.4(5.4)THz, which is two orders of magnitude larger than that obtained above for dielectric cavities. One can also use Eq. (10) to deduce that this SE rate requires the LSP volume corresponding to a 10nm-radius spherical nanoparticle. Recently, ultrafast (γSE113·1012s) single-photon SE was demonstrated with quantum dots coupled to gap-plasmon-based nanocavities [15], and large SE enhancements in metal nanostructures (found using the antenna RLC-circuit approach) were suggested for improving the performance of light-emitting diodes [16]. It should further be noted that the difference in the limits obtained for these two classes would, for a given metal, increase for QEs with shorter lifetimes radiating at longer wavelengths, since γSErl/Bmaxγ0/ω [cf. Eqs. (7) and (12)]. Finally, the estimated SE rate is seen just at the limit of the weak-coupling approximation, indicating that the strong-coupling regime (γSEγ0) is within reach for strongly confined QE–LSP configurations as indeed was very recently demonstrated [17].

Let us now turn our attention to the SE enhancement for QEs located in waveguides, starting with the dielectric case [Fig. 2(a)]. If a waveguide mode is strongly confined, e.g., in high dielectric contrast ridge, nanowire, and photonic crystal waveguides, the SE occurs mainly into the propagating waveguide modes with rate enhancement that can be described by the Purcell factor for waveguides [18]:

Fw1π(λ2n)2ngAwmγSEFwγ0,
where ng is the mode group index and Awm is the mode size, i.e., the mode cross-sectional area whose definition is a somewhat complicated issue [18]. Under the condition of diffraction-limited performance, one obtains the upper limit for the Purcell factor:
Awm(λ2n)2Fwngπ.
The only possibility to significantly increase the SE rate into diffraction-limited waveguide modes is therefore to make use of slow-down effects that can conveniently be realized with photonic crystal waveguides (ensuring also tight mode confinement) near the band edge [19]. The fundamental issue with this configuration is related to the fact that the slow-down effect is of a very narrow bandwidth, also causing a drastic increase in the propagation losses, so that even an optimistic estimate would be ng100 [19,20]. Consequently, this implies that the Purcell factor is at best limited by 30 with the maximum rate of photons estimated (for the same QE) to be <3GHz.

 figure: Fig. 2.

Fig. 2. Schematic configurations of (a) dielectric waveguide with a QE inside and (b) tapered gap SPP waveguide configuration providing a strong mode confinement at the place where a QE is located. Possible realizations of the corresponding two-dimensional waveguides are illustrated to the right, depicting cross sections perpendicular to the propagation direction and the locations of the supported mode fields.

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We now turn our attention to the plasmonic waveguides supporting the propagation of SPP modes, laterally confined far beyond the diffraction limit [18,21]. The fundamental issue with this configuration is related to the fact that the propagation loss in SPP-based waveguides increases drastically for strongly confined modes. This problem, known since the very inception of research in quantum plasmonics, can be mitigated by coupling a strongly confined SPP waveguide to a low-loss (dielectric) waveguide before the SPP energy is dissipated in the metal [22]. Typically, one would first adiabatically taper out a very narrow lossy SPP waveguide to a relatively wider and lower loss SPP waveguide, as discussed in [23] in relation to nanofocusing and subsequently couple to a dielectric, e.g., Si-based, waveguide [Fig. 2(b)] as has already been successfully and efficiently realized in gap SPP (GSP) waveguides [24]. Taking into account the propagation loss incurred in the narrowest part of a plasmonic waveguide while neglecting the power loss elsewhere (i.e., to absorption and radiation out of the waveguide as well as during propagation in adiabatic tapers and coupling to lossless photonic waveguides), the SE rate can be written by modifying Eq. (13) as follows:

γSE=Fwγ0exp(L/LSPP),
where L is the length of the narrowest part of a plasmonic waveguide [Fig. 2(b)] with the SPP mode being characterized by the wavelength λSPP and the propagation length LSPP.

Let us consider a tapered configuration supporting GSP modes [25], leaving its coupling to a wider GSP waveguide [Fig. 2(b)] and further to a dielectric waveguide out of analysis. Another similar configuration is a V-groove, or indeed any trench waveguide, with the width w being in this case an averaged trench width. Using the limiting case of very small gap width (wλ) for approximating the GSP wavelength [21] one can estimate the corresponding Purcell factor with the help of Eq. (13) as follows:

FwλGSPπ|εm||wεd;AwmwλGSP2εdπ3·λpλ(λpw)3.
Here εm| is the real part of the metal permittivity, εd=n2, and the mode area is approximated by AGSP0.5λGSPw. The 1/w3 scaling in [Eq. (16)] is similar to 1/R3 scaling found for metal nanowires [22], signifying the fact that very large Purcell factors can be achieved with plasmonic waveguides.

Considering the same system parameters as in the above case of QE–LSP coupling and the GSP configuration with a challenging but reasonable gap of 4 nm (e.g., a 0.9-nm-wide gap was realized in the recent experiments [17]), one obtains λp130(145)nm and, consequently, Fw144(223). The latter values are significantly larger than the best estimate for photonic crystal waveguides, and the 1/w3 scaling indicates that even much larger values of the Purcell factor are within the reach. The presence of the exponential loss factor in the expression for the enhanced SE rate [Eq. (15)] emphasizes the importance of a proper choice of the narrow gap length L. It seems reasonable to suggest that this length should be close to the mode wavelength, LλSPP (this length is sufficient to transform the QE radiated field into the mode field [26]), so that the role of the loss factor can be neglected (for silver and gold, LGSP/λGSPω/(4πγm)>1), at least in the present estimations.

Plasmonics offers unique possibilities for the manipulation of light at the nanoscale resulting in extreme light concentration and giant local field enhancements, phenomena that can be advantageously exploited in many fundamental and applied disciplines, including quantum optics. The field of quantum plasmonics is still relatively new [7], and its case is yet to be presented and tried, given the inevitable dissipation found in any plasmonic configuration [13]. In this Letter, we attempted to analyze the “pros” and “cons” for a particular problem in quantum optics, viz., the realization of efficient and bright single-photon sources that would enable the generation of single photons with high repetition rates. We have considered QE coupling to dielectric cavities (waveguides) and localized (propagating) SPPs assessing fundamental factors that limit the achievable SE rates in these configurations. It has been found that the latter allows one to obtain the SE rate larger by almost two orders of magnitude than the former one. It is worthwhile to note (see Supplement 1) that the optimized metal structure with today’s lossy metals offers SE rate enhancements that are just a few times below the theoretical maximum attainable in the hypothetical [27] limit of lossless plasmonic structures. It is our view that QE enhancement, where the rate rather than the overall external efficiency (as in the case of LED) of emission is the ultimate measure of performance, is one of the few application niches where plasmonics can shine despite the inherent metal loss. We believe that the present analysis will also be of great help when looking for new plasmonic configurations and materials to be exploited in quantum plasmonics.

Funding

European Research Council (ERC) (341054); Army Research Office (ARO) (W911NF-15-1-0629).

 

See Supplement 1 for supporting content.

REFERENCES

1. J. L. O’Brien, Science 318, 1567 (2007). [CrossRef]  

2. M. Pelton, Nat. Photonics 9, 427 (2015). [CrossRef]  

3. L. Novotny and B. Hecht, Principles of Nano-Optics, 2nd ed. (Cambridge University, 2012).

4. M. Fox, Quantum Optics: An Introduction (Oxford University, 2006).

5. J. P. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, Nature 432, 197 (2004).

6. T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).

7. M. S. Tame, K. R. McEnery, Ş. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, Nat. Phys. 9, 329 (2013).

8. F. Wang and Y. R. Shen, Phys. Rev. Lett. 97, 206806 (2006). [CrossRef]  

9. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

10. A. Trügler and U. Hohenester, Phys. Rev. B 77, 115403 (2008).

11. C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, Phys. Rev. Lett. 110, 237401 (2013). [CrossRef]  

12. A. F. Koenderink, Opt. Lett. 35, 4208 (2010). [CrossRef]  

13. G. Sun, J. B. Khurgin, and R. A. Soref, J. Opt. Soc. Am. B 25, 1748 (2008). [CrossRef]  

14. M. G. Blaber, M. D. Arnold, and M. J. Ford, J. Phys. Chem. C 113, 3041 (2009). [CrossRef]  

15. T. B. Hoang, G. M. Akselrod, and M. H. Mikkelsen, Nano Lett. 16, 270 (2016). [CrossRef]  

16. K. L. Tsakmakidis, R. W. Boyd, E. Yablonovitch, and X. Zhang, Opt. Express 24, 17916 (2016). [CrossRef]  

17. 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, Nature 535, 127 (2016).

18. R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, New J. Phys. 10, 105018 (2008). [CrossRef]  

19. T. Baba, Nat. Photonics 2, 465 (2008). [CrossRef]  

20. H. C. Nguyen, S. Hashimoto, M. Shinkawa, and T. Baba, Opt. Express 20, 22465 (2012). [CrossRef]  

21. Z. Han and S. I. Bozhevolnyi, Rep. Prog. Phys. 76, 016402 (2013). [CrossRef]  

22. D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, Phys. Rev. Lett. 97, 053002 (2006). [CrossRef]  

23. D. K. Gramotnev and S. I. Bozhevolnyi, Nat. Photonics 8, 13 (2013). [CrossRef]  

24. J. Tian, S. Yu, W. Yan, and M. Qiu, Appl. Phys. Lett. 95, 013504 (2009). [CrossRef]  

25. D. F. P. Pile and D. K. Gramotnev, Appl. Phys. Lett. 89, 041111 (2006). [CrossRef]  

26. E. Bermúdez-Ureña, C. Gonzalez-Ballestero, M. Geiselmann, R. Marty, I. P. Radko, T. Holmgaard, Y. Alaverdyan, E. Moreno, F. J. García-Vidal, S. I. Bozhevolnyi, and R. Quidant, Nat. Commun. 6, 7883 (2015). [CrossRef]  

27. J. B. Khurgin, Nat. Nanotechnol. 10, 2 (2015). [CrossRef]  

References

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  1. J. L. O’Brien, Science 318, 1567 (2007).
    [Crossref]
  2. M. Pelton, Nat. Photonics 9, 427 (2015).
    [Crossref]
  3. L. Novotny and B. Hecht, Principles of Nano-Optics, 2nd ed. (Cambridge University, 2012).
  4. M. Fox, Quantum Optics: An Introduction (Oxford University, 2006).
  5. J. P. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, Nature 432, 197 (2004).
  6. T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
  7. M. S. Tame, K. R. McEnery, Ş. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, Nat. Phys. 9, 329 (2013).
  8. F. Wang and Y. R. Shen, Phys. Rev. Lett. 97, 206806 (2006).
    [Crossref]
  9. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
  10. A. Trügler and U. Hohenester, Phys. Rev. B 77, 115403 (2008).
  11. C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, Phys. Rev. Lett. 110, 237401 (2013).
    [Crossref]
  12. A. F. Koenderink, Opt. Lett. 35, 4208 (2010).
    [Crossref]
  13. G. Sun, J. B. Khurgin, and R. A. Soref, J. Opt. Soc. Am. B 25, 1748 (2008).
    [Crossref]
  14. M. G. Blaber, M. D. Arnold, and M. J. Ford, J. Phys. Chem. C 113, 3041 (2009).
    [Crossref]
  15. T. B. Hoang, G. M. Akselrod, and M. H. Mikkelsen, Nano Lett. 16, 270 (2016).
    [Crossref]
  16. K. L. Tsakmakidis, R. W. Boyd, E. Yablonovitch, and X. Zhang, Opt. Express 24, 17916 (2016).
    [Crossref]
  17. 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, Nature 535, 127 (2016).
  18. R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, New J. Phys. 10, 105018 (2008).
    [Crossref]
  19. T. Baba, Nat. Photonics 2, 465 (2008).
    [Crossref]
  20. H. C. Nguyen, S. Hashimoto, M. Shinkawa, and T. Baba, Opt. Express 20, 22465 (2012).
    [Crossref]
  21. Z. Han and S. I. Bozhevolnyi, Rep. Prog. Phys. 76, 016402 (2013).
    [Crossref]
  22. D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, Phys. Rev. Lett. 97, 053002 (2006).
    [Crossref]
  23. D. K. Gramotnev and S. I. Bozhevolnyi, Nat. Photonics 8, 13 (2013).
    [Crossref]
  24. J. Tian, S. Yu, W. Yan, and M. Qiu, Appl. Phys. Lett. 95, 013504 (2009).
    [Crossref]
  25. D. F. P. Pile and D. K. Gramotnev, Appl. Phys. Lett. 89, 041111 (2006).
    [Crossref]
  26. E. Bermúdez-Ureña, C. Gonzalez-Ballestero, M. Geiselmann, R. Marty, I. P. Radko, T. Holmgaard, Y. Alaverdyan, E. Moreno, F. J. García-Vidal, S. I. Bozhevolnyi, and R. Quidant, Nat. Commun. 6, 7883 (2015).
    [Crossref]
  27. J. B. Khurgin, Nat. Nanotechnol. 10, 2 (2015).
    [Crossref]

2016 (3)

T. B. Hoang, G. M. Akselrod, and M. H. Mikkelsen, Nano Lett. 16, 270 (2016).
[Crossref]

K. L. Tsakmakidis, R. W. Boyd, E. Yablonovitch, and X. Zhang, Opt. Express 24, 17916 (2016).
[Crossref]

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, Nature 535, 127 (2016).

2015 (3)

M. Pelton, Nat. Photonics 9, 427 (2015).
[Crossref]

E. Bermúdez-Ureña, C. Gonzalez-Ballestero, M. Geiselmann, R. Marty, I. P. Radko, T. Holmgaard, Y. Alaverdyan, E. Moreno, F. J. García-Vidal, S. I. Bozhevolnyi, and R. Quidant, Nat. Commun. 6, 7883 (2015).
[Crossref]

J. B. Khurgin, Nat. Nanotechnol. 10, 2 (2015).
[Crossref]

2013 (4)

D. K. Gramotnev and S. I. Bozhevolnyi, Nat. Photonics 8, 13 (2013).
[Crossref]

M. S. Tame, K. R. McEnery, Ş. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, Nat. Phys. 9, 329 (2013).

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, Phys. Rev. Lett. 110, 237401 (2013).
[Crossref]

Z. Han and S. I. Bozhevolnyi, Rep. Prog. Phys. 76, 016402 (2013).
[Crossref]

2012 (1)

2010 (1)

2009 (2)

M. G. Blaber, M. D. Arnold, and M. J. Ford, J. Phys. Chem. C 113, 3041 (2009).
[Crossref]

J. Tian, S. Yu, W. Yan, and M. Qiu, Appl. Phys. Lett. 95, 013504 (2009).
[Crossref]

2008 (4)

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, New J. Phys. 10, 105018 (2008).
[Crossref]

T. Baba, Nat. Photonics 2, 465 (2008).
[Crossref]

G. Sun, J. B. Khurgin, and R. A. Soref, J. Opt. Soc. Am. B 25, 1748 (2008).
[Crossref]

A. Trügler and U. Hohenester, Phys. Rev. B 77, 115403 (2008).

2007 (1)

J. L. O’Brien, Science 318, 1567 (2007).
[Crossref]

2006 (3)

F. Wang and Y. R. Shen, Phys. Rev. Lett. 97, 206806 (2006).
[Crossref]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, Phys. Rev. Lett. 97, 053002 (2006).
[Crossref]

D. F. P. Pile and D. K. Gramotnev, Appl. Phys. Lett. 89, 041111 (2006).
[Crossref]

2004 (2)

J. P. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, Nature 432, 197 (2004).

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).

Akselrod, G. M.

T. B. Hoang, G. M. Akselrod, and M. H. Mikkelsen, Nano Lett. 16, 270 (2016).
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Alaverdyan, Y.

E. Bermúdez-Ureña, C. Gonzalez-Ballestero, M. Geiselmann, R. Marty, I. P. Radko, T. Holmgaard, Y. Alaverdyan, E. Moreno, F. J. García-Vidal, S. I. Bozhevolnyi, and R. Quidant, Nat. Commun. 6, 7883 (2015).
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Arnold, M. D.

M. G. Blaber, M. D. Arnold, and M. J. Ford, J. Phys. Chem. C 113, 3041 (2009).
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Baba, T.

Barrow, S. J.

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, Nature 535, 127 (2016).

Bartal, G.

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, New J. Phys. 10, 105018 (2008).
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Baumberg, J. J.

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, Nature 535, 127 (2016).

Benz, F.

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, Nature 535, 127 (2016).

Bermúdez-Ureña, E.

E. Bermúdez-Ureña, C. Gonzalez-Ballestero, M. Geiselmann, R. Marty, I. P. Radko, T. Holmgaard, Y. Alaverdyan, E. Moreno, F. J. García-Vidal, S. I. Bozhevolnyi, and R. Quidant, Nat. Commun. 6, 7883 (2015).
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Blaber, M. G.

M. G. Blaber, M. D. Arnold, and M. J. Ford, J. Phys. Chem. C 113, 3041 (2009).
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Boyd, R. W.

Bozhevolnyi, S. I.

E. Bermúdez-Ureña, C. Gonzalez-Ballestero, M. Geiselmann, R. Marty, I. P. Radko, T. Holmgaard, Y. Alaverdyan, E. Moreno, F. J. García-Vidal, S. I. Bozhevolnyi, and R. Quidant, Nat. Commun. 6, 7883 (2015).
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Z. Han and S. I. Bozhevolnyi, Rep. Prog. Phys. 76, 016402 (2013).
[Crossref]

D. K. Gramotnev and S. I. Bozhevolnyi, Nat. Photonics 8, 13 (2013).
[Crossref]

Chang, D. E.

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, Phys. Rev. Lett. 97, 053002 (2006).
[Crossref]

Chikkaraddy, R.

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, Nature 535, 127 (2016).

de Nijs, B.

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, Nature 535, 127 (2016).

Demetriadou, A.

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, Nature 535, 127 (2016).

Deppe, D. G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).

Ell, C.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).

Forchel, A.

J. P. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, Nature 432, 197 (2004).

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M. G. Blaber, M. D. Arnold, and M. J. Ford, J. Phys. Chem. C 113, 3041 (2009).
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Fox, M.

M. Fox, Quantum Optics: An Introduction (Oxford University, 2006).

Fox, P.

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, Nature 535, 127 (2016).

García-Vidal, F. J.

E. Bermúdez-Ureña, C. Gonzalez-Ballestero, M. Geiselmann, R. Marty, I. P. Radko, T. Holmgaard, Y. Alaverdyan, E. Moreno, F. J. García-Vidal, S. I. Bozhevolnyi, and R. Quidant, Nat. Commun. 6, 7883 (2015).
[Crossref]

Geiselmann, M.

E. Bermúdez-Ureña, C. Gonzalez-Ballestero, M. Geiselmann, R. Marty, I. P. Radko, T. Holmgaard, Y. Alaverdyan, E. Moreno, F. J. García-Vidal, S. I. Bozhevolnyi, and R. Quidant, Nat. Commun. 6, 7883 (2015).
[Crossref]

Gibbs, H. M.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).

Gonzalez-Ballestero, C.

E. Bermúdez-Ureña, C. Gonzalez-Ballestero, M. Geiselmann, R. Marty, I. P. Radko, T. Holmgaard, Y. Alaverdyan, E. Moreno, F. J. García-Vidal, S. I. Bozhevolnyi, and R. Quidant, Nat. Commun. 6, 7883 (2015).
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Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, Nat. Photonics 8, 13 (2013).
[Crossref]

D. F. P. Pile and D. K. Gramotnev, Appl. Phys. Lett. 89, 041111 (2006).
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Han, Z.

Z. Han and S. I. Bozhevolnyi, Rep. Prog. Phys. 76, 016402 (2013).
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Hashimoto, S.

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics, 2nd ed. (Cambridge University, 2012).

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D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, Phys. Rev. Lett. 97, 053002 (2006).
[Crossref]

Hendrickson, J.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).

Hess, O.

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, Nature 535, 127 (2016).

Hoang, T. B.

T. B. Hoang, G. M. Akselrod, and M. H. Mikkelsen, Nano Lett. 16, 270 (2016).
[Crossref]

Hofmann, C.

J. P. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, Nature 432, 197 (2004).

Hohenester, U.

A. Trügler and U. Hohenester, Phys. Rev. B 77, 115403 (2008).

Holmgaard, T.

E. Bermúdez-Ureña, C. Gonzalez-Ballestero, M. Geiselmann, R. Marty, I. P. Radko, T. Holmgaard, Y. Alaverdyan, E. Moreno, F. J. García-Vidal, S. I. Bozhevolnyi, and R. Quidant, Nat. Commun. 6, 7883 (2015).
[Crossref]

Hugonin, J. P.

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, Phys. Rev. Lett. 110, 237401 (2013).
[Crossref]

Keldysh, L. V.

J. P. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, Nature 432, 197 (2004).

Khitrova, G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).

Khurgin, J. B.

Kim, M. S.

M. S. Tame, K. R. McEnery, Ş. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, Nat. Phys. 9, 329 (2013).

Koenderink, A. F.

Kuhn, S.

J. P. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, Nature 432, 197 (2004).

Kulakovskii, V. D.

J. P. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, Nature 432, 197 (2004).

Lalanne, P.

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, Phys. Rev. Lett. 110, 237401 (2013).
[Crossref]

Lee, J.

M. S. Tame, K. R. McEnery, Ş. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, Nat. Phys. 9, 329 (2013).

Löffler, A.

J. P. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, Nature 432, 197 (2004).

Lukin, M. D.

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, Phys. Rev. Lett. 97, 053002 (2006).
[Crossref]

Maier, S. A.

M. S. Tame, K. R. McEnery, Ş. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, Nat. Phys. 9, 329 (2013).

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

Maksymov, I. S.

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, Phys. Rev. Lett. 110, 237401 (2013).
[Crossref]

Marty, R.

E. Bermúdez-Ureña, C. Gonzalez-Ballestero, M. Geiselmann, R. Marty, I. P. Radko, T. Holmgaard, Y. Alaverdyan, E. Moreno, F. J. García-Vidal, S. I. Bozhevolnyi, and R. Quidant, Nat. Commun. 6, 7883 (2015).
[Crossref]

McEnery, K. R.

M. S. Tame, K. R. McEnery, Ş. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, Nat. Phys. 9, 329 (2013).

Mikkelsen, M. H.

T. B. Hoang, G. M. Akselrod, and M. H. Mikkelsen, Nano Lett. 16, 270 (2016).
[Crossref]

Moreno, E.

E. Bermúdez-Ureña, C. Gonzalez-Ballestero, M. Geiselmann, R. Marty, I. P. Radko, T. Holmgaard, Y. Alaverdyan, E. Moreno, F. J. García-Vidal, S. I. Bozhevolnyi, and R. Quidant, Nat. Commun. 6, 7883 (2015).
[Crossref]

Nguyen, H. C.

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-Optics, 2nd ed. (Cambridge University, 2012).

O’Brien, J. L.

J. L. O’Brien, Science 318, 1567 (2007).
[Crossref]

Oulton, R. F.

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, New J. Phys. 10, 105018 (2008).
[Crossref]

Özdemir, S. K.

M. S. Tame, K. R. McEnery, Ş. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, Nat. Phys. 9, 329 (2013).

Pelton, M.

M. Pelton, Nat. Photonics 9, 427 (2015).
[Crossref]

Pile, D. F. P.

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, New J. Phys. 10, 105018 (2008).
[Crossref]

D. F. P. Pile and D. K. Gramotnev, Appl. Phys. Lett. 89, 041111 (2006).
[Crossref]

Qiu, M.

J. Tian, S. Yu, W. Yan, and M. Qiu, Appl. Phys. Lett. 95, 013504 (2009).
[Crossref]

Quidant, R.

E. Bermúdez-Ureña, C. Gonzalez-Ballestero, M. Geiselmann, R. Marty, I. P. Radko, T. Holmgaard, Y. Alaverdyan, E. Moreno, F. J. García-Vidal, S. I. Bozhevolnyi, and R. Quidant, Nat. Commun. 6, 7883 (2015).
[Crossref]

Radko, I. P.

E. Bermúdez-Ureña, C. Gonzalez-Ballestero, M. Geiselmann, R. Marty, I. P. Radko, T. Holmgaard, Y. Alaverdyan, E. Moreno, F. J. García-Vidal, S. I. Bozhevolnyi, and R. Quidant, Nat. Commun. 6, 7883 (2015).
[Crossref]

Reinecke, T. L.

J. P. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, Nature 432, 197 (2004).

Reithmaier, J. P.

J. P. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, Nature 432, 197 (2004).

Reitzenstein, S.

J. P. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, Nature 432, 197 (2004).

Rosta, E.

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, Nature 535, 127 (2016).

Rupper, G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).

Sauvan, C.

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, Phys. Rev. Lett. 110, 237401 (2013).
[Crossref]

Scherer, A.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).

Scherman, O. A.

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, Nature 535, 127 (2016).

Sek, G.

J. P. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, Nature 432, 197 (2004).

Shchekin, O. B.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).

Shen, Y. R.

F. Wang and Y. R. Shen, Phys. Rev. Lett. 97, 206806 (2006).
[Crossref]

Shinkawa, M.

Soref, R. A.

Sørensen, A. S.

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, Phys. Rev. Lett. 97, 053002 (2006).
[Crossref]

Sun, G.

Tame, M. S.

M. S. Tame, K. R. McEnery, Ş. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, Nat. Phys. 9, 329 (2013).

Tian, J.

J. Tian, S. Yu, W. Yan, and M. Qiu, Appl. Phys. Lett. 95, 013504 (2009).
[Crossref]

Trügler, A.

A. Trügler and U. Hohenester, Phys. Rev. B 77, 115403 (2008).

Tsakmakidis, K. L.

Wang, F.

F. Wang and Y. R. Shen, Phys. Rev. Lett. 97, 206806 (2006).
[Crossref]

Yablonovitch, E.

Yan, W.

J. Tian, S. Yu, W. Yan, and M. Qiu, Appl. Phys. Lett. 95, 013504 (2009).
[Crossref]

Yoshie, T.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).

Yu, S.

J. Tian, S. Yu, W. Yan, and M. Qiu, Appl. Phys. Lett. 95, 013504 (2009).
[Crossref]

Zhang, X.

K. L. Tsakmakidis, R. W. Boyd, E. Yablonovitch, and X. Zhang, Opt. Express 24, 17916 (2016).
[Crossref]

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, New J. Phys. 10, 105018 (2008).
[Crossref]

Appl. Phys. Lett. (2)

J. Tian, S. Yu, W. Yan, and M. Qiu, Appl. Phys. Lett. 95, 013504 (2009).
[Crossref]

D. F. P. Pile and D. K. Gramotnev, Appl. Phys. Lett. 89, 041111 (2006).
[Crossref]

J. Opt. Soc. Am. B (1)

J. Phys. Chem. C (1)

M. G. Blaber, M. D. Arnold, and M. J. Ford, J. Phys. Chem. C 113, 3041 (2009).
[Crossref]

Nano Lett. (1)

T. B. Hoang, G. M. Akselrod, and M. H. Mikkelsen, Nano Lett. 16, 270 (2016).
[Crossref]

Nat. Commun. (1)

E. Bermúdez-Ureña, C. Gonzalez-Ballestero, M. Geiselmann, R. Marty, I. P. Radko, T. Holmgaard, Y. Alaverdyan, E. Moreno, F. J. García-Vidal, S. I. Bozhevolnyi, and R. Quidant, Nat. Commun. 6, 7883 (2015).
[Crossref]

Nat. Nanotechnol. (1)

J. B. Khurgin, Nat. Nanotechnol. 10, 2 (2015).
[Crossref]

Nat. Photonics (3)

T. Baba, Nat. Photonics 2, 465 (2008).
[Crossref]

D. K. Gramotnev and S. I. Bozhevolnyi, Nat. Photonics 8, 13 (2013).
[Crossref]

M. Pelton, Nat. Photonics 9, 427 (2015).
[Crossref]

Nat. Phys. (1)

M. S. Tame, K. R. McEnery, Ş. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, Nat. Phys. 9, 329 (2013).

Nature (3)

J. P. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, Nature 432, 197 (2004).

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).

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, Nature 535, 127 (2016).

New J. Phys. (1)

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, New J. Phys. 10, 105018 (2008).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. B (1)

A. Trügler and U. Hohenester, Phys. Rev. B 77, 115403 (2008).

Phys. Rev. Lett. (3)

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, Phys. Rev. Lett. 110, 237401 (2013).
[Crossref]

F. Wang and Y. R. Shen, Phys. Rev. Lett. 97, 206806 (2006).
[Crossref]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, Phys. Rev. Lett. 97, 053002 (2006).
[Crossref]

Rep. Prog. Phys. (1)

Z. Han and S. I. Bozhevolnyi, Rep. Prog. Phys. 76, 016402 (2013).
[Crossref]

Science (1)

J. L. O’Brien, Science 318, 1567 (2007).
[Crossref]

Other (3)

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

L. Novotny and B. Hecht, Principles of Nano-Optics, 2nd ed. (Cambridge University, 2012).

M. Fox, Quantum Optics: An Introduction (Oxford University, 2006).

Supplementary Material (1)

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Figures (2)

Fig. 1.
Fig. 1. (a) Dielectric cavity with a QE placed inside. (b) Plasmonic nanostructure with a QE located within a tightly confined LSP field. (c) Normalized out-of-cavity QE emission rate for different ratios between the cavity emission rate and Rabi frequency.
Fig. 2.
Fig. 2. Schematic configurations of (a) dielectric waveguide with a QE inside and (b) tapered gap SPP waveguide configuration providing a strong mode confinement at the place where a QE is located. Possible realizations of the corresponding two-dimensional waveguides are illustrated to the right, depicting cross sections perpendicular to the propagation direction and the locations of the supported mode fields.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

F = γ SE γ 0 = 6 π 2 ( λ 2 n ) 3 Q V ,
V ( λ 2 n ) 3 F 6 π 2 Q .
Q opt π ω 6 γ 0 , and γ SE max 6 ω γ 0 π .
r ( t ) = 4 γ cav Ω 2 · | s 1 s 2 s 2 s 1 [ e s 1 t e s 2 t ] | 2 ,
s 1,2 = γ cav 4 ( γ cav 4 ) 2 Ω 2 4 .
Q opt = ω R opt Ω π 1.1 ω 6 γ 0 = π 1.1 π ν 3 γ 0 .
B max Ω 2 π = 6 γ 0 ω 2 π 2 = 3 π γ 0 ν π 2 .
γ SE = F γ rad γ m + γ rad γ 0 = 3 4 π 2 ( λ n ) 3 ω γ rad V LSP ( γ m + γ rad ) 2 γ 0 .
V eff = | E ( r ) d 3 r | 2 / E 2 ( r ) d 3 r ,
γ rad = 4 3 π 2 ω V eff λ λ p 2 ,
γ SE = ( λ n ) 3 ω 2 λ λ p 2 ( γ m + γ rad ) 2 γ 0 1 n 3 · ω p 2 γ m 2 γ 0 = γ SE max ,
γ SE r l = 0.25 1 n 3 · ω p 2 γ m 2 γ 0 .
F w 1 π ( λ 2 n ) 2 n g A w m γ SE F w γ 0 ,
A w m ( λ 2 n ) 2 F w n g π .
γ SE = F w γ 0 exp ( L / L SPP ) ,
F w λ GSP π | ε m | | w ε d ; A w m w λ GSP 2 ε d π 3 · λ p λ ( λ p w ) 3 .

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