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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 3 — Feb. 10, 2014
  • pp: 2337–2347
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Design of highly efficient metallo-dielectric patch antennas for single-photon emission

F. Bigourdan, F. Marquier, J.-P. Hugonin, and J.-J. Greffet  »View Author Affiliations


Optics Express, Vol. 22, Issue 3, pp. 2337-2347 (2014)
http://dx.doi.org/10.1364/OE.22.002337


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Abstract

Quantum emitters such as NV-centers or quantum dots can be used as single-photon sources. To improve their performance, they can be coupled to microcavities or nano-antennas. Plasmonic antennas offer an appealing solution as they can be used with broadband emitters. When properly designed, these antennas funnel light into useful modes, increasing the emission rate and the collection of single-photons. Yet, their inherent metallic losses are responsible for very low radiative efficiencies. Here, we introduce a new design of directional, metallo-dielectric, optical antennas with a Purcell factor of 150, a total efficiency of 74% and a collection efficiency of emitted photons of 99%.

© 2014 Optical Society of America

1. Introduction

Since the pioneering proposal of Dieter Pohl [1

1. D. W. Pohl, “Near-field optics: comeback of light in microscopy,” Solid State Phenomena , 63–64, 251–256 (1998). [CrossRef]

3

3. P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005). [CrossRef] [PubMed]

], there have been several works using the concept of antennas in the optical range. Indeed, this concept holds great promises to improve the efficiency of both light-emitting (single-photon sources, LED) and light-absorbing devices (photovoltaics, spectroscopy, photodetection) [3

3. P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005). [CrossRef] [PubMed]

8

8. P. Biagioni, J.-S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys. 75, 024402 (2012). [CrossRef] [PubMed]

]. A review of the applications of single-photon sources can be found in [9

9. B. Lounis and M. Orrit, “Single-photon sources,” Rep. Prog. Phys. 68, 1129 (2005). [CrossRef]

]. Coupling them to nano-antennas allows increasing their performance: i) by controlling the emission direction in order to increase the collection efficiency, ii) by reducing the decay time in order to increase the repetition rate of a source of single-photons on demand. The spectral bandwidth of the antenna is an important property. If indistinguishable photons are needed, the antenna should serve as a monochromatic filter. By contrast, when dealing with broadband emitters such as nitrogen-vacancy (NV) centers or quantum dots at ambient temperature, broadband antennas are desirable. Regarding applications to single-photon sources, plasmonic nanoantennas have been introduced by many groups as a way to efficiently couple quantum emitters with propagating modes, in terms of excitation enhancement [10

10. T. Feichtner, O. Selig, M. Kiunke, and B. Hecht, “Evolutionary optimization of optical antennas,” Phys. Rev. Lett. 109, 127701 (2012). [CrossRef] [PubMed]

, 11

11. A. Devilez, B. Stout, and N. Bonod, “Compact metallo-dielectric optical antenna for ultra directional and enhanced radiative emission,” ACS Nano 4, 3390–3396 (2010). [CrossRef] [PubMed]

], emitted power [11

11. A. Devilez, B. Stout, and N. Bonod, “Compact metallo-dielectric optical antenna for ultra directional and enhanced radiative emission,” ACS Nano 4, 3390–3396 (2010). [CrossRef] [PubMed]

21

21. C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J.-P. Hugonin, S. Michaelis de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J.-J. Greffet, P. Senellart, and A. Maitre, “Controlling spontaneous emission with plasmonic optical patch antennas,” Nano Lett. 13, 1516–1521 (2013). [PubMed]

] and directivity [11

11. A. Devilez, B. Stout, and N. Bonod, “Compact metallo-dielectric optical antenna for ultra directional and enhanced radiative emission,” ACS Nano 4, 3390–3396 (2010). [CrossRef] [PubMed]

,19

19. A. F. Koenderink, “Plasmon nanoparticle array waveguides for single-photon and single-plasmon sources,” Nano Lett. 9, 4228–4233 (2009). [CrossRef] [PubMed]

30

30. B. Rolly, B. Stout, and N. Bonod, “Boosting the directivity of optical antennas with magnetic and electric dipolar resonant particles,” Opt. Express 20, 20376–20386 (2012). [CrossRef] [PubMed]

]. Recent advances with NV centers have been reported [31

31. J. T. Choy, B. J. M. Hausmann, T. M. Babinec, I. Burlu, M. Khan, P. Maletinsky, A. Yacoby, and M. Loncar, “Enhanced single-photon emission from a diamond silver aperture,” Nat. Photonics 5, 738–743 (2011). [CrossRef]

]. In order to reduce the decay time, the local density of optical states (LDOS) has to be increased. It has been shown some time ago that metal-insulator-metal (MIM) structures are very efficient for this purpose [32

32. G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195 (1984). [CrossRef]

, 33

33. Y. C. Jun, R. D. Kekatpure, J. S. White, and M. L. Brongersma, “Nonresonant enhancement of spontaneous emission in metal-dielectric-metal plasmon waveguide structures,” Phys. Rev. B 78, 153111 (2008). [CrossRef]

]. Yet, metals introduce losses so that the total efficiency of the antenna is significantly reduced.

Plasmonic patch antennas (see Fig. 1(a)) were designed to take advantage of the large LDOS of MIM structures. They have been investigated both theoretically and experimentally [20

20. R. Esteban, T. V. Teperik, and J.-J. Greffet, “Optical patch antennas for single photon emission using surface plasmon resonances,” Phys. Rev. Lett. 104, 026802 (2010). [CrossRef] [PubMed]

, 21

21. C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J.-P. Hugonin, S. Michaelis de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J.-J. Greffet, P. Senellart, and A. Maitre, “Controlling spontaneous emission with plasmonic optical patch antennas,” Nano Lett. 13, 1516–1521 (2013). [PubMed]

]. The size of the metallic disk controls the radiation pattern, and thus the directivity. This allows for an increase in the collection efficiency of radiated photons. Due to their highly confined plasmonic modes, MIM cavities have been shown to produce spontaneous emission acceleration on the order of 100, with broadband operations [33

33. Y. C. Jun, R. D. Kekatpure, J. S. White, and M. L. Brongersma, “Nonresonant enhancement of spontaneous emission in metal-dielectric-metal plasmon waveguide structures,” Phys. Rev. B 78, 153111 (2008). [CrossRef]

, 34

34. Y. C. Jun, R. Pala, and M. L. Brongersma, “Strong modification of quantum dot spontaneous emission via gap plasmon coupling in metal nanoslits,” J. Phys. Chem. C 114, 7269–7273 (2010). [CrossRef]

]. This acceleration factor is given by the ratio of LDOS with and without the antenna. Here we refer to it as the Purcell factor [35

35. E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

37

37. C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013). [CrossRef]

]. By choosing a proper dielectric thickness, the quantum emitter can simultaneously access those high Purcell factors and avoid quenching [7

7. N. P. de Leon, M. D. Lukin, and H. Park, “Quantum plasmonics circuits,” IEEE J. Sel. Top. Quantum Electron. 18, 1781–1791 (2012). [CrossRef]

, 21

21. C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J.-P. Hugonin, S. Michaelis de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J.-J. Greffet, P. Senellart, and A. Maitre, “Controlling spontaneous emission with plasmonic optical patch antennas,” Nano Lett. 13, 1516–1521 (2013). [PubMed]

]. Hence, one can convert almost all quantum emitter excitations into the plasmonic modes of the antenna with high efficiency. The major drawback of the plasmonic patch antenna is that more than 90% of the energy of the plasmonic modes is then converted into heat instead of being radiated. Let us summarize the efficiency issue. The emission process by a quantum emitter in the presence of a plasmonic nanoantenna consists in two steps: decay of the quantum emitter into plasmonic antenna modes and (radiative) decay of the antenna modes into photons. The efficiency of the first step can be reduced due to competition with two other processes: either a non-unity internal quantum efficiency or quenching which is a non-radiative coupling into losses in the metal. The former will not be considered here. The latter can also be viewed as Joule losses induced by the 1/r3 near-field component of the electric field produced by the quantum emitter. This quenching can be virtually suppressed by keeping the emitter at a distance larger than 10 nm from the surface [21

21. C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J.-P. Hugonin, S. Michaelis de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J.-J. Greffet, P. Senellart, and A. Maitre, “Controlling spontaneous emission with plasmonic optical patch antennas,” Nano Lett. 13, 1516–1521 (2013). [PubMed]

]. Finally, the plasmonic antenna modes can either radiate photons or decay into heat in the antenna. We define the antenna radiative efficiency as the radiated power normalized by the sum of the absorbed and radiated power. In this paper, we introduce a novel design that allows increasing the radiative efficiency of optical patch antennas by more than one order of magnitude.

Fig. 1 Schematics of the systems discussed. (a) Metallic patch antenna: a dipole source (red arrow) is embedded in the middle of a thin silica layer, sandwiched between a gold substrate and a centered, thin gold disk. The whole system is located in vacuum. The dipole is linearly polarized perpendicularly to the patch. (b) Metallic patch - dielectric resonator antenna: a high-refractive-index cylinder is added on top of the metallic patch antenna to increase the radiation efficiency.

By using an in-situ optical lithography technique, C. Belacel et al. [21

21. C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J.-P. Hugonin, S. Michaelis de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J.-J. Greffet, P. Senellart, and A. Maitre, “Controlling spontaneous emission with plasmonic optical patch antennas,” Nano Lett. 13, 1516–1521 (2013). [PubMed]

] fabricated patch antennas of diameters ranging from 1.46 μm to 2.1 μm coupled with CdSe/CdS quantum dots emitting at 630 nm. The antennas were shown to have the expected properties of a high, broadband Purcell factor as well as directivity. However, the radiative efficiency was reported to be on the order of a few percent. Indeed, once the plasmonic mode of the antenna is excited by the quantum emitter, most of its energy is absorbed in the metal instead of being radiated by the patch. The purpose of this paper is to analyze the origin of this low radiative efficiency and introduce new ideas to overcome this limitation.

2. Small metallic patches : a plasmonic strategy

The dependence on the diameter of the metallic disk is reported in Figs. 2(a) and 2(b). It is seen that there is an optimum value of the disk diameter which maximizes both the Purcell factor and the radiative efficiency. At an emission wavelength of 1.55 μm, this optimum value is approximately half this wavelength. It corresponds to the dipolar plasmonic resonance of the antenna. The existence of a joint optimum is due to the fact that the effective wavelength of the main plasmonic mode only differs from the emission wavelength by a few percent. Hence, the patch cavity is both a resonant cavity for the plasmonic mode, ensuring a large Purcell factor, as well as a half-wavelength antenna regarding the coupling with propagating plane waves. Purcell factors as high as 500 can be obtained while the radiative efficiency reaches 24%. Figure 2(b) shows that this efficiency is twice as good as the maximum of the radiative efficiency reachable at a wavelength of 0.63 μm. This confirms the advantage of working in the near-infrared range.

Fig. 2 Numerical results for a patch antenna (see Fig. 1(a)) with a 30 nm-thick silica layer and a 38 nm-thick gold disk of varying diameter. The dipole is polarized perpendicularly to the patch. (a) Decay rate of a dipole coupled with the patch antenna normalized by the decay rate of a dipole in bulk silica. Results are calculated at an emission wavelength of 1.55 μm. (b) Radiative efficiency of a dipole coupled with the patch antenna at an emission wavelength of 1.55 μm (blue) and 0.63 μm (red).

For larger patches, multipolar plasmonic resonances appear. Due to the finite propagation length of lossy plasmonic modes, their quality factor tends to decrease when the patch diameter increases as seen in Fig. 2(a). Hence, at an emission wavelength of 1.55 μm the global optimum value corresponds to the dipolar plasmonic resonance.

3. High-refractive-index medium : a dielectric strategy

It is well known [41

41. W. Lukosz and R. E. Kunz, “Light emission by magnetic and electric dipoles close to a plane interface. I. total radiated power,” J. Opt. Soc. Am. A 67, 1607–1615 (1977).

] that locating a dipole close to a high-index medium has two effects: the power emitted increases and most of the power is radiated into the high refractive medium. This property has been used to enhance the collection of light for sensitive detection of fluorophores [42

42. H. Choumane, N. Ha, C. Nelep, A. Chardon, G. O. Reymond, C. Goutel, G. Cerovic, F. Vallet, C. Weisbuch, and H. Benisty, “Double interference fluorescence enhancement from reflective slides: application to bicolor microarrays,” Appl. Phys. Lett. 87, 031102 (2005). [CrossRef]

] and to increase the efficiency of light emitting devices [43

43. A. C. Hryciw, Y. C. Jun, and M. L. Brongersma, “Plasmon enhanced emission from optically-doped MOS light sources,” Opt. Express 17, 185–192 (2009). [CrossRef] [PubMed]

, 44

44. Y. C. Jun, R. M. Briggs, H. A. Atwater, and M. L. Brongersma, “Broadband enhancement of light emission in silicon slot waveguides,” Opt. Express 17, 7479–7490 (2009). [CrossRef] [PubMed]

]. This idea has been revisited and optimized recently to obtain almost unity collection efficiency [27

27. K. G. Lee, X. W. Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, “A planar dielectric antenna for directional single-photon emission and near-unity collection efficiency,” Nat. Photonics 5, 166–169 (2010). [CrossRef]

, 28

28. X.-W. Chen, S. Götzinger, and V. Sandoghdar, “99% Efficiency in collecting photons from a single emitter,” Opt. Lett. 36, 3545–3547 (2011). [CrossRef] [PubMed]

]. Here, we illustrate this idea by considering a dipole source in the middle of a 30 nm-thick silica layer on a gold substrate and covered by a high-index material as shown in Fig. 3(a). Here again, the silica layer is used as a spacer to prevent quenching. We have studied the changes in the Purcell factor and the radiative efficiency of the antenna when varying the superstrate refractive index. We consider a dipole perpendicularly polarized to the stratified system. We use a plane wave expansion to derive an explicit form of the radiative and total decay rate [33

33. Y. C. Jun, R. D. Kekatpure, J. S. White, and M. L. Brongersma, “Nonresonant enhancement of spontaneous emission in metal-dielectric-metal plasmon waveguide structures,” Phys. Rev. B 78, 153111 (2008). [CrossRef]

, 45

45. R. R. Chance, A. H. Miller, A. Prock, and R. Silbey, “Fluorescence and energy transfer near interfaces: the complete and quantitative description of the Eu+3/mirror systems,” J. Chem. Phys. 63, 1589–1595 (1975). [CrossRef]

, 46

46. J. E. Sipe, “New green-function formalism for surface optics,” J. Opt. Soc. Am. B 4, 481–489 (1987). [CrossRef]

]. Numerical results are given in Figs. 3(b) and 3(c).

Fig. 3 Effect of a high refractive index. A dipole polarized along the normal is located in the middle of the 30 nm-thick silica layer. (a) The silica layer is covered with a dielectric half-space. (d) The silica layer is covered with a 38 nm-thick gold film and a dielectric half-space. (b),(e) Decay rate of a dipole in a stratified system normalized by the decay rate of a dipole in a bulk of silica. (c),(f) Radiative efficiency of the dipole.

It is seen that both the Purcell factor and the radiative efficiency increase when increasing the superstrate refractive index. The onset of this phenomenon is when the refractive index becomes higher than the silica refractive index (nSiO2 = 1.45). Here, the increase of radiation is a near-field effect. It is due to the coupling of evanescent modes of the dipolar field into propagating modes in the dielectric. The higher the refractive index of the superstrate, the more evanescent modes of the source can couple with propagating modes of the superstrate by optical tunneling [41

41. W. Lukosz and R. E. Kunz, “Light emission by magnetic and electric dipoles close to a plane interface. I. total radiated power,” J. Opt. Soc. Am. A 67, 1607–1615 (1977).

, 47

47. L. Novotny, “Allowed and forbidden light in near-field optics. I. A single dipolar light source,” J. Opt. Soc. Am. A 14, 91–104 (1997). [CrossRef]

]. This phenomenon takes place only if the superstrate refractive index is larger than the silica refractive index. As a result, the power radiated increases with an increase in the refractive index of the superstrate. Thus, the total decay rate of the source and the radiative efficiency of the antenna follow the same trend, as shown in Figs. 3(b) and 3(c).

4. The metallic patch - dielectric resonator antenna: best of both worlds

From the results of the last section, it can be construed that inserting a patch antenna in a highly refractive medium drastically improves its radiative efficiency into the high index material. We are facing now the problem of extracting light from the high index material. To address this issue, we use a small dielectric cylinder as a dielectric resonator antenna (DRA [48

48. R. K. Mongia and P. Bhartia, “Dielectric resonator antennas - A review and general design relations for resonant frequency and bandwidth,” Int. J. Microwave Mill. 4, 230–247 (1994).

]). By tailoring a high-refractive-index dielectric resonator antenna added on top of the patch antenna, the coupling between patch plasmonic modes and DRA modes can be optimized. Note that the DRA does not absorb, but radiates light. If the characteristic lengths of the DRA are of the order of a multiple of half the emission wavelength, the excited eigenmodes of the DRA and propagating modes of the free space can couple efficiently. As a result, the coupled system Metallic Patch - Dielectric Resonator Antenna (MP-DRA, see Fig. 1(b)) may have a better efficiency than the MP alone, while keeping a large Purcell factor due to the confinement of the mode in the metal-dielectric-metal. Regarding directivity, radiation is mostly due to the DRA, so that the DRA diameter is the relevant parameter. One can thus make the most of the radiation properties of a resonant dipolar metallic patch and use a DRA in order to improve the radiative efficiency, while collecting most of the emitted single-photons into a microscope objective.

The concept of DRA is standard in microwaves. DRAs working in the optical range have recently been studied theoretically [49

49. G. N. Malheiros-Silveira, G. S. Wiederhecker, and H. E. Hernandez-Figueroa, “Dielectric resonator antenna for applications in nanophotonics,” Opt. Express 21, 1234–1239 (2013). [CrossRef] [PubMed]

] and experimentally [50

50. L. Zou, W. Withayachumnankul, C. M. Shah, A. Mitchell, M. Bhaskaran, S. Sriram, and C. Fumeaux, “Dielectric resonator nanoantennas at visible frequencies,” Opt. Express 21, 1344–1352 (2013). [CrossRef] [PubMed]

]. For our simulations, we chose to work with a refractive index of 2.58 for the DRA, which is the value corresponding to amorphous SiC at 1.55 μm [40

40. E. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

]. The thickness of the silica layer is again chosen to be 30 nm. Four parameters are left unknown : the thicknesses and diameters of both the metallic disk and the DRA. Using a genetic algorithm [38

38. J. H. Holland, Adaptation in Natural and Artificial Systems (The University of Michigan, 1975).

] as a global optimization scheme, these parameters were optimized to get the highest total efficiency of the antenna and the highest Purcell factor possible. The total efficiency is defined in this article as the product of the radiative efficiency and the collection efficiency in a standard microscope objective of numerical aperture 0.85. The a-FMM was used to perform the numerical simulations of the system.

The result of the optimization is shown in Fig. 4 where we have plotted the intensity (square modulus of the electric field) in the structure. The resulting optimized MP-DRA is composed of a 38 nm-thick metallic disk of 764 nm in diameter and a 738 nm-thick DRA of 2447 nm in diameter. For a centered dipole source polarized perpendicularly to the patch, results of the numerical simulations give a Purcell factor of 150 with a 74% total efficiency. The total efficiency is composed of a collection efficiency of 99% and a radiative efficiency of 75%. This is to be compared with a centered dipole source polarized in the plane of the patch, for which numerical results give a Purcell factor of 2.5 with a total efficiency below 0.1%. These latter results ensure that the radiation properties from a randomly oriented dipole source is governed by the vertical component of this dipole. The key to understanding the physical mechanism of the increased efficiency lies in the field distribution plotted in Fig. 4. It is clearly observed that a hybrid mode of the metallo-dielectric structure is excited. This hybrid mode is composed of a resonantly excited plasmonic mode in the metal-silica-metal region and a resonantly excited mode in the dielectric cylinder. As the spatial extension of the mode is much larger in the dielectric, a large part of the hybrid-mode energy is in a non-lossy region so that the nonradiative damping is reduced. Conversely, the large spatial extension of the resonator gives rise to an increase of radiation losses: the DRA is a better radiator than the patch antenna. Both factors are responsible for the increased efficiency of the antenna. An important factor for enhancing the radiation is the resonant character of the excitation of the DRA. In order to assess the role of the large index of the dielectric versus the role of the resonance in the DRA, we have optimized the total efficiency with a silica cylinder instead of a SiC cylinder (not shown here). Interestingly, we found that it is possible to obtain 60% efficiency without using a large index material.

Fig. 4 Calculated vertical cross-section of the intensity of the total electric field inside the optimized Metallic Patch - Dielectric Resonator Antenna (see Fig. 1(c)). The calculation is performed at an emission wavelength of 1.55 μm. The white-dashed lines depict each stages of the antenna. The intensity is saturated and normalized by the maximum obtained.

An important issue for fabrication is the sensitivity of the antenna performances on the geometrical parameters. As shown in Figs. 5(a) and 5(b), the enhancement of the spontaneous emission rate and the total efficiency of the optimized MP-DRA are relatively insensitive to the lateral off-centering of the dipole source. We note that the in-situ optical lithography technique used to fabricate patch antennas [21

21. C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J.-P. Hugonin, S. Michaelis de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J.-J. Greffet, P. Senellart, and A. Maitre, “Controlling spontaneous emission with plasmonic optical patch antennas,” Nano Lett. 13, 1516–1521 (2013). [PubMed]

] has an accuracy of 25 nm in the dipole centering so that virtually no degradation is expected from an alignement error. We have also checked that the performances are not strongly dependent on the heights and diameters of the dielectric cylinder and the metallic disk. Indeed, a variation over a 10% range on either the optimized heights or diameters leads to a total efficiency varying from 64% to 74%. This is not surprising as resonators with low quality factor (on the order of 10) are not expected to be very sensitive to their size dimensions. Furthermore, we have checked that the air gap between the DRA and the silica layer is not crucial. We have optimized the total efficiency for a metallic disk embedded in the DRA and found that it is possible to obtain more than 65% total efficiency with acceleration factor of the spontaneous emission rate on the order of 100. Hence, even without this air gap, the metallo-dielectric antenna shows good performances.

Fig. 5 Numerical results for the optimized Metallic Patch - Dielectric Resonator Antenna (MP-DRA, see 1(c)) with respect to the off-centering of the dipole. Calculations are performed at an emission wavelength of 1.55 μm. (a) Decay rate of a dipole coupled with the MP-DRA normalized by the decay rate of a dipole in a bulk of silica. (b) Total efficiency of a dipole coupled with the MP-DRA for a collection with a numerical aperture of 0.85.

Figures 6(a) and 6(b) show the radiation pattern of the MP-DRA for a centered dipole and for a 140 nm-laterally-off-centered one. Numerical results indicate that 99% of the emitted photons can be collected in a microscope objective of numerical aperture 0.85. Those results ensure that almost all the single-photons emitted can be collected. Finally, one key feature of plasmonic antennas is their large bandwidth. We have seen that the dielectric antenna reduces the ohmic losses but increases the radiation losses. Numerical results (see Figs. 7(a) and 7(b)) show that the optimized MP-DRA preserves the broadband behavior. Purcell factors ranging from 75 to 160 and total efficiencies ranging from 60% to 74% can be obtained over a 100 nm bandwitdth.

Fig. 6 Calculations are performed at λ = 1.55 μm. (a) (Dark blue) Calculated radiation pattern of the optimized MP-DRA with a centered dipole, normalized by its maximum value. The fair blue-dashed lines correspond to the angle of collection for an objective with NA=0.85. (b) Calculated radiation pattern of the MP-DRA with a 140 nm-laterally-off-centered dipole, in the off-centering plane (dark blue) and in the plane perpendicular to the off-centering plane (pink). Values are normalized by the maximum of the whole radiation pattern. The fair blue-dashed lines correspond to the angle of collection for an objective with NA=0.85.
Fig. 7 Numerical results for the optimized MP-DRA with respect to the emission wavelength. (a) Decay rate of a dipole coupled with the MP-DRA normalized by the decay rate of a dipole in a bulk of silica. (b) Total efficiency of a dipole coupled with the MP-DRA for a collection with a numerical aperture of 0.85.

5. Conclusion

In summary, we have introduced a metallo-dielectric patch antenna for single-photon emission. This new design combines the large Purcell factor due to the confinement of the field in the metal-dielectric-metal structure with a large collection efficiency and large emission efficiency which is characteristic of dielectric antenna resonators. An important feature of this design is that it is based on relatively simple technological steps for fabrication. It is fully compatible with the in-situ lithography technique already used for fabricating patch antennas [21

21. C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J.-P. Hugonin, S. Michaelis de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J.-J. Greffet, P. Senellart, and A. Maitre, “Controlling spontaneous emission with plasmonic optical patch antennas,” Nano Lett. 13, 1516–1521 (2013). [PubMed]

]. We anticipate Purcell factors above 100, a collection efficiency of 99% with a numerical aperture of 0.85 and an overall efficiency exceeding 70%. This type of hybrid antennas should be useful for many applications.

Acknowledgments

F. Bigourdan acknowledges the support of the french Direction Generale de l’Armement. The authors thank C. Sauvan for fruitful discussions.

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S. Kühn, U. Hakanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97, 017402 (2006). [CrossRef] [PubMed]

13.

J. P. Hoogenboom, G. Sanchez-Mosteiro, G. Colas des Francs, D. Heinis, G. Legay, A. Dereux, and N. F. van Hulst, “The single molecule probe: nanoscale vectorial mapping of photonic mode density in a metal nanocavity,” Nano Lett. 9, 1189–1195 (2009). [CrossRef] [PubMed]

14.

I. S. Maksymov, M. Besbes, J.-P. Hugonin, J. Yang, A. Beveratos, I. Sagnes, I. Robert-Philip, and P. Lalanne, “Metal-coated nanocylinder cavity for broadband nonclassical light emission,” Phys. Rev. Lett. 105, 180502 (2010). [CrossRef]

15.

S. Derom, R. Vincent, A. Bouhelier, and G. Colas des Francs, “Resonance quality, radiative/ohmic losses and modal volume of Mie plasmons,” Europhys. Lett. 98, 47008 (2012). [CrossRef]

16.

N. P. de Leon, B. J. Shields, C. L. Yu, D. E. Englund, A. V. Akimov, M. D. Lukin, and H. Park, “Tailoring light-matter interaction with a nanoscale plasmon resonator,” Phys. Rev. Lett. 108, 226803 (2012). [CrossRef] [PubMed]

17.

X.-W. Chen, M. Agio, and V. Sandoghdar, “Metallodielectric hybrid antennas for ultrastrong enhancement of spontaneous emission,” Phys. Rev. Lett. 108, 233001 (2012). [CrossRef] [PubMed]

18.

M. P. Busson, B. Rolly, B. Stout, N. Bonod, and S. Bidault, “Accelerated single-photon emission from dye molecule-driven nanoantennas assembled on DNA,” Nat. Commun. 3, 962 (2012). [CrossRef]

19.

A. F. Koenderink, “Plasmon nanoparticle array waveguides for single-photon and single-plasmon sources,” Nano Lett. 9, 4228–4233 (2009). [CrossRef] [PubMed]

20.

R. Esteban, T. V. Teperik, and J.-J. Greffet, “Optical patch antennas for single photon emission using surface plasmon resonances,” Phys. Rev. Lett. 104, 026802 (2010). [CrossRef] [PubMed]

21.

C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J.-P. Hugonin, S. Michaelis de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J.-J. Greffet, P. Senellart, and A. Maitre, “Controlling spontaneous emission with plasmonic optical patch antennas,” Nano Lett. 13, 1516–1521 (2013). [PubMed]

22.

J. Li, A. Salandrino, and N. Engheta, “Shaping light beams in the nanometer scale: a Yagi-Uda nanoantenna in the optical domain,” Phys. Rev. B 76, 245403 (2007). [CrossRef]

23.

T. H. Taminiau, F. D. Stefani, F. B. Segerink, and N. F. van Hulst, “Optical antennas direct single-molecule emission,” Nat. Photonics 2, 234–237 (2008). [CrossRef]

24.

T. H. Taminiau, F. D. Stefani, and N. F. van Hulst, “Single emitters coupled to plasmonic nano-antennas: angular emission and collection efficiency,” New J. Phys. 10, 105005 (2008). [CrossRef]

25.

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329, 930–933 (2010). [CrossRef] [PubMed]

26.

J. Claudon, J. Bleuse, N. S. Malik, M. Bazin, P. Jaffrennou, N. Gregersen, C. Sauvan, P. Lalanne, and J.-M. Gerard, “A highly efficient single-photon source based on a quantum dot in a photonic nanowire,” Nat. Photonics 4, 174–177 (2010). [CrossRef]

27.

K. G. Lee, X. W. Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, “A planar dielectric antenna for directional single-photon emission and near-unity collection efficiency,” Nat. Photonics 5, 166–169 (2010). [CrossRef]

28.

X.-W. Chen, S. Götzinger, and V. Sandoghdar, “99% Efficiency in collecting photons from a single emitter,” Opt. Lett. 36, 3545–3547 (2011). [CrossRef] [PubMed]

29.

T. Shegai, V. D. Miljkovic, K. Bao, H. Xu, P. Nordlander, P. Johansson, and M. Kall, “Unidirectional broadband light emission from supported plasmonic nanowires,” Nano Lett. 11, 706–711 (2011). [CrossRef] [PubMed]

30.

B. Rolly, B. Stout, and N. Bonod, “Boosting the directivity of optical antennas with magnetic and electric dipolar resonant particles,” Opt. Express 20, 20376–20386 (2012). [CrossRef] [PubMed]

31.

J. T. Choy, B. J. M. Hausmann, T. M. Babinec, I. Burlu, M. Khan, P. Maletinsky, A. Yacoby, and M. Loncar, “Enhanced single-photon emission from a diamond silver aperture,” Nat. Photonics 5, 738–743 (2011). [CrossRef]

32.

G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195 (1984). [CrossRef]

33.

Y. C. Jun, R. D. Kekatpure, J. S. White, and M. L. Brongersma, “Nonresonant enhancement of spontaneous emission in metal-dielectric-metal plasmon waveguide structures,” Phys. Rev. B 78, 153111 (2008). [CrossRef]

34.

Y. C. Jun, R. Pala, and M. L. Brongersma, “Strong modification of quantum dot spontaneous emission via gap plasmon coupling in metal nanoslits,” J. Phys. Chem. C 114, 7269–7273 (2010). [CrossRef]

35.

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

36.

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

37.

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013). [CrossRef]

38.

J. H. Holland, Adaptation in Natural and Artificial Systems (The University of Michigan, 1975).

39.

A. Armaroli, A. Morand, P. Benech, G. Bellanca, and S. Trillo, “Three-dimensional analysis of cylindrical microresonators based on the aperiodic Fourier modal method,” J. Opt. Soc. Am. A 25, 667–675 (2008). [CrossRef]

40.

E. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

41.

W. Lukosz and R. E. Kunz, “Light emission by magnetic and electric dipoles close to a plane interface. I. total radiated power,” J. Opt. Soc. Am. A 67, 1607–1615 (1977).

42.

H. Choumane, N. Ha, C. Nelep, A. Chardon, G. O. Reymond, C. Goutel, G. Cerovic, F. Vallet, C. Weisbuch, and H. Benisty, “Double interference fluorescence enhancement from reflective slides: application to bicolor microarrays,” Appl. Phys. Lett. 87, 031102 (2005). [CrossRef]

43.

A. C. Hryciw, Y. C. Jun, and M. L. Brongersma, “Plasmon enhanced emission from optically-doped MOS light sources,” Opt. Express 17, 185–192 (2009). [CrossRef] [PubMed]

44.

Y. C. Jun, R. M. Briggs, H. A. Atwater, and M. L. Brongersma, “Broadband enhancement of light emission in silicon slot waveguides,” Opt. Express 17, 7479–7490 (2009). [CrossRef] [PubMed]

45.

R. R. Chance, A. H. Miller, A. Prock, and R. Silbey, “Fluorescence and energy transfer near interfaces: the complete and quantitative description of the Eu+3/mirror systems,” J. Chem. Phys. 63, 1589–1595 (1975). [CrossRef]

46.

J. E. Sipe, “New green-function formalism for surface optics,” J. Opt. Soc. Am. B 4, 481–489 (1987). [CrossRef]

47.

L. Novotny, “Allowed and forbidden light in near-field optics. I. A single dipolar light source,” J. Opt. Soc. Am. A 14, 91–104 (1997). [CrossRef]

48.

R. K. Mongia and P. Bhartia, “Dielectric resonator antennas - A review and general design relations for resonant frequency and bandwidth,” Int. J. Microwave Mill. 4, 230–247 (1994).

49.

G. N. Malheiros-Silveira, G. S. Wiederhecker, and H. E. Hernandez-Figueroa, “Dielectric resonator antenna for applications in nanophotonics,” Opt. Express 21, 1234–1239 (2013). [CrossRef] [PubMed]

50.

L. Zou, W. Withayachumnankul, C. M. Shah, A. Mitchell, M. Bhaskaran, S. Sriram, and C. Fumeaux, “Dielectric resonator nanoantennas at visible frequencies,” Opt. Express 21, 1344–1352 (2013). [CrossRef] [PubMed]

OCIS Codes
(140.4780) Lasers and laser optics : Optical resonators
(270.0270) Quantum optics : Quantum optics
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Plasmonics

History
Original Manuscript: October 28, 2013
Revised Manuscript: December 23, 2013
Manuscript Accepted: January 2, 2014
Published: January 28, 2014

Citation
F. Bigourdan, F. Marquier, J.-P. Hugonin, and J.-J. Greffet, "Design of highly efficient metallo-dielectric patch antennas for single-photon emission," Opt. Express 22, 2337-2347 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-3-2337


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References

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  13. J. P. Hoogenboom, G. Sanchez-Mosteiro, G. Colas des Francs, D. Heinis, G. Legay, A. Dereux, N. F. van Hulst, “The single molecule probe: nanoscale vectorial mapping of photonic mode density in a metal nanocavity,” Nano Lett. 9, 1189–1195 (2009). [CrossRef] [PubMed]
  14. I. S. Maksymov, M. Besbes, J.-P. Hugonin, J. Yang, A. Beveratos, I. Sagnes, I. Robert-Philip, P. Lalanne, “Metal-coated nanocylinder cavity for broadband nonclassical light emission,” Phys. Rev. Lett. 105, 180502 (2010). [CrossRef]
  15. S. Derom, R. Vincent, A. Bouhelier, G. Colas des Francs, “Resonance quality, radiative/ohmic losses and modal volume of Mie plasmons,” Europhys. Lett. 98, 47008 (2012). [CrossRef]
  16. N. P. de Leon, B. J. Shields, C. L. Yu, D. E. Englund, A. V. Akimov, M. D. Lukin, H. Park, “Tailoring light-matter interaction with a nanoscale plasmon resonator,” Phys. Rev. Lett. 108, 226803 (2012). [CrossRef] [PubMed]
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  18. M. P. Busson, B. Rolly, B. Stout, N. Bonod, S. Bidault, “Accelerated single-photon emission from dye molecule-driven nanoantennas assembled on DNA,” Nat. Commun. 3, 962 (2012). [CrossRef]
  19. A. F. Koenderink, “Plasmon nanoparticle array waveguides for single-photon and single-plasmon sources,” Nano Lett. 9, 4228–4233 (2009). [CrossRef] [PubMed]
  20. R. Esteban, T. V. Teperik, J.-J. Greffet, “Optical patch antennas for single photon emission using surface plasmon resonances,” Phys. Rev. Lett. 104, 026802 (2010). [CrossRef] [PubMed]
  21. C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J.-P. Hugonin, S. Michaelis de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J.-J. Greffet, P. Senellart, A. Maitre, “Controlling spontaneous emission with plasmonic optical patch antennas,” Nano Lett. 13, 1516–1521 (2013). [PubMed]
  22. J. Li, A. Salandrino, N. Engheta, “Shaping light beams in the nanometer scale: a Yagi-Uda nanoantenna in the optical domain,” Phys. Rev. B 76, 245403 (2007). [CrossRef]
  23. T. H. Taminiau, F. D. Stefani, F. B. Segerink, N. F. van Hulst, “Optical antennas direct single-molecule emission,” Nat. Photonics 2, 234–237 (2008). [CrossRef]
  24. T. H. Taminiau, F. D. Stefani, N. F. van Hulst, “Single emitters coupled to plasmonic nano-antennas: angular emission and collection efficiency,” New J. Phys. 10, 105005 (2008). [CrossRef]
  25. A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329, 930–933 (2010). [CrossRef] [PubMed]
  26. J. Claudon, J. Bleuse, N. S. Malik, M. Bazin, P. Jaffrennou, N. Gregersen, C. Sauvan, P. Lalanne, J.-M. Gerard, “A highly efficient single-photon source based on a quantum dot in a photonic nanowire,” Nat. Photonics 4, 174–177 (2010). [CrossRef]
  27. K. G. Lee, X. W. Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, S. Götzinger, “A planar dielectric antenna for directional single-photon emission and near-unity collection efficiency,” Nat. Photonics 5, 166–169 (2010). [CrossRef]
  28. X.-W. Chen, S. Götzinger, V. Sandoghdar, “99% Efficiency in collecting photons from a single emitter,” Opt. Lett. 36, 3545–3547 (2011). [CrossRef] [PubMed]
  29. T. Shegai, V. D. Miljkovic, K. Bao, H. Xu, P. Nordlander, P. Johansson, M. Kall, “Unidirectional broadband light emission from supported plasmonic nanowires,” Nano Lett. 11, 706–711 (2011). [CrossRef] [PubMed]
  30. B. Rolly, B. Stout, N. Bonod, “Boosting the directivity of optical antennas with magnetic and electric dipolar resonant particles,” Opt. Express 20, 20376–20386 (2012). [CrossRef] [PubMed]
  31. J. T. Choy, B. J. M. Hausmann, T. M. Babinec, I. Burlu, M. Khan, P. Maletinsky, A. Yacoby, M. Loncar, “Enhanced single-photon emission from a diamond silver aperture,” Nat. Photonics 5, 738–743 (2011). [CrossRef]
  32. G. W. Ford, W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195 (1984). [CrossRef]
  33. Y. C. Jun, R. D. Kekatpure, J. S. White, M. L. Brongersma, “Nonresonant enhancement of spontaneous emission in metal-dielectric-metal plasmon waveguide structures,” Phys. Rev. B 78, 153111 (2008). [CrossRef]
  34. Y. C. Jun, R. Pala, M. L. Brongersma, “Strong modification of quantum dot spontaneous emission via gap plasmon coupling in metal nanoslits,” J. Phys. Chem. C 114, 7269–7273 (2010). [CrossRef]
  35. E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).
  36. A. F. Koenderink, “On the use of purcell factors for plasmon antennas,” Opt. Lett. 35, 4208–4210 (2010). [CrossRef] [PubMed]
  37. C. Sauvan, J. P. Hugonin, I. S. Maksymov, P. Lalanne, “Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013). [CrossRef]
  38. J. H. Holland, Adaptation in Natural and Artificial Systems (The University of Michigan, 1975).
  39. A. Armaroli, A. Morand, P. Benech, G. Bellanca, S. Trillo, “Three-dimensional analysis of cylindrical microresonators based on the aperiodic Fourier modal method,” J. Opt. Soc. Am. A 25, 667–675 (2008). [CrossRef]
  40. E. Palik, Handbook of Optical Constants of Solids (Academic, 1985).
  41. W. Lukosz, R. E. Kunz, “Light emission by magnetic and electric dipoles close to a plane interface. I. total radiated power,” J. Opt. Soc. Am. A 67, 1607–1615 (1977).
  42. H. Choumane, N. Ha, C. Nelep, A. Chardon, G. O. Reymond, C. Goutel, G. Cerovic, F. Vallet, C. Weisbuch, H. Benisty, “Double interference fluorescence enhancement from reflective slides: application to bicolor microarrays,” Appl. Phys. Lett. 87, 031102 (2005). [CrossRef]
  43. A. C. Hryciw, Y. C. Jun, M. L. Brongersma, “Plasmon enhanced emission from optically-doped MOS light sources,” Opt. Express 17, 185–192 (2009). [CrossRef] [PubMed]
  44. Y. C. Jun, R. M. Briggs, H. A. Atwater, M. L. Brongersma, “Broadband enhancement of light emission in silicon slot waveguides,” Opt. Express 17, 7479–7490 (2009). [CrossRef] [PubMed]
  45. R. R. Chance, A. H. Miller, A. Prock, R. Silbey, “Fluorescence and energy transfer near interfaces: the complete and quantitative description of the Eu+3/mirror systems,” J. Chem. Phys. 63, 1589–1595 (1975). [CrossRef]
  46. J. E. Sipe, “New green-function formalism for surface optics,” J. Opt. Soc. Am. B 4, 481–489 (1987). [CrossRef]
  47. L. Novotny, “Allowed and forbidden light in near-field optics. I. A single dipolar light source,” J. Opt. Soc. Am. A 14, 91–104 (1997). [CrossRef]
  48. R. K. Mongia, P. Bhartia, “Dielectric resonator antennas - A review and general design relations for resonant frequency and bandwidth,” Int. J. Microwave Mill. 4, 230–247 (1994).
  49. G. N. Malheiros-Silveira, G. S. Wiederhecker, H. E. Hernandez-Figueroa, “Dielectric resonator antenna for applications in nanophotonics,” Opt. Express 21, 1234–1239 (2013). [CrossRef] [PubMed]
  50. L. Zou, W. Withayachumnankul, C. M. Shah, A. Mitchell, M. Bhaskaran, S. Sriram, C. Fumeaux, “Dielectric resonator nanoantennas at visible frequencies,” Opt. Express 21, 1344–1352 (2013). [CrossRef] [PubMed]

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