Abstract

The control and enhancement of the spontaneous emission (SE) of emitters embedded in subwavelength structures are fundamentally interesting and of practical interest. For example, in plasmonic lasers and on-chip single photon sources, a large SE rate and the active modulation of SE over a very broad spectral band are highly desired functionalities. In this paper, we demonstrate by an explicit theoretical calculation that a plasmonic waveguide cladded with liquid crystals (LCs) and low-index metamaterials can give rise to an enhancement in the intrinsic SE rate γ0 of more than two orders of magnitude. Furthermore, by varying the refractive index of the LC cladding, thereby changing the density of states of the surface plasmons, the enhanced SE rate can be modulated over a very large range, e.g., from 131γ0 to 327γ0. In general, the modulation range increases with the anisotropy in the refractive index of the LC, while for a fixed range of modulation, the SE rate is larger with lower cladding indices. These results for active modulation and enhanced SE may find application in enabling low-threshold plasmonic nanolasers and tunable on-chip single photon sources.

© 2017 Optical Society of America

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References

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2015 (2)

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, 193002 (2015).
[Crossref] [PubMed]

A. Yang, T. B. Hoang, M. Dridi, C. Deeb, M. H. Mikkelsen, G. C. Schatz, and T. W. Odom, “Real-time tunable lasing from plasmonic nanocavity arrays,” Nat. Commum. 66939 (2015).
[Crossref]

2014 (2)

A. Rose, T. B. Hoang, F. Mcguire, J. J. Mock, C. Ciraci, D. R. Smith, and M. H. Mikkelsen, “Control of radiative processes using tunable plasmonic nanopatch antennas,” Nano Lett. 14, 4797–4802 (2014).
[Crossref] [PubMed]

L. Shi, X. Yuan, Y. Zhang, T. Hakala, S. Yin, D. Han, X. Zhu, B. Zhang, X. Liu, P. Torma, W. Lu, and J. Zi, “Coherent fluorescence emission by using hybrid photonic?plasmonic crystals,” Laser Photonics Rev. 8, 717–725 (2014).
[Crossref]

2013 (4)

R.-M. Ma, R. F. Oulton, V. J. Sorger, and X. Zhang, “Plasmon lasers: coherent light source at molecular scales,” Laser Photonics Rev. 7, 1–21 (2013).
[Crossref]

R. Luo, Y. Gu, X. Li, L. Wang, I. C. Khoo, and Q. Gong, “Mode recombination and alternation of surface plasmons in anisotropic mediums,” Appl. Phys. Lett. 102, 0111117 (2013).
[Crossref]

S. Kang, S. Nakajima, Y. Arakawa, G. Konishi, and J. Watanabe, “Large extraordinary refractive index in highly birefringent nematic liquid crystals of dinaphthyldiacetylene-based materials,” J. Mater. Chem. C 1,4222 (2013).
[Crossref]

J. Mertens, A. L. Eiden, D. O. Sigle, F. Huang, A. Lombardo, Z. Sun, R. S. Sundaram, A. Colli, C. Tserkezis, J. Aizpurua, S. Milana, A. C. Ferrari, and J. J. Baumberg, “Controlling subnanometer gaps in plasmonic dimers using graphene,” Nano Lett. 13, 5033–5038 (2013).
[Crossref] [PubMed]

2012 (4)

Y. Arakawa, S. Nakajima, S. M. Kang, M. Shigeta, G. Konishi, and J. Watanabe, “Design of an extremely high birefringence nematic liquid crystal based on a dinaphthyl-diacetylene mesogen,” J. Mater. Chem. 22, 13908–13910 (2012).
[Crossref]

X. Shan, I. D. Perez, L. Wang, Y. Gu, L. Zhang, W. Wang, J. Lu, S. Wang, and Q. Gong, “Imaging the electrocatalytic activity of single nanoparticles,” Nat. Nanotechnol. 7, 668–672 (2012).
[Crossref] [PubMed]

J. Bleuse, J. Claudon, M. Creasey, and K. Hakuta, “Efficient channeling of fluorescence photons from single quantum dots into guided modes of optical nanofiber,” Phys. Rev. Lett. 109, 063602 (2012).
[Crossref]

A. Moreau, C. Ciraci, J. J. Mock, R. T. Hill, Q. Wang, B. J. Wiley, A. Chilkoti, and D. V. Smith, “Controlled-reflectance surfaces with film-coupled colloidal nanoantennas,” Nature 492, 86–89 (2012).
[Crossref] [PubMed]

2011 (2)

P. Lodahl, A. F. Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Inhibited spontaneous emission of quantum dots observed in a 3D photonic band gap,” Phys. Rev. Lett. 107, 193903 (2011).
[Crossref]

C. T. Chen, C. C. Liu, C. H. Wang, C. W. Chen, and Y. F. Chen, “Tunable coupling between excitation and surface plasmon in liquid crystal devices consisting of Au nanoparticles and Cdse quantum dots,” Appl. Phys. Lett. 98, 261918 (2011).
[Crossref]

2010 (4)

I. C. Khoo, A. Diaz, J. Liou, M. V. Stinger, J. Huang, and Y. Ma, “Liquid crystals tunable optical metamaterials,” IEEE J. Sel. Top. Quant. 16, 410–417 (2010).
[Crossref]

P. Yao, V. S. Rao, and S. Hunges, “On-chip single photon sources using planar photonic crystals and single quantum dots,” Laser Photonics Rev. 4, 499–516 (2010).
[Crossref]

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. Photon. 4, 174–177 (2010).

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]

2009 (4)

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photonics 3, 654–657 (2009).
[Crossref]

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Winesner, “Demonstration of a spacer-based nanolaser,” Nature 460, 1110 (2009).
[Crossref] [PubMed]

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[Crossref] [PubMed]

I. C. Khoo, “Nonlinear optics of liquid crystalline materials,” Phys. Rep. 471, 221–267 (2009).
[Crossref]

2008 (5)

R. Li, C. Cheng, F. Ren, J. Chen, Y. Fan, J. Ding, and H. Wang, “Hybridized surface plasmon polaritons at an interface between a metal and a uniaxial crystal,” Appl. Phys. Lett. 92, 141115 (2008).
[Crossref]

V. K. Hsiao, Y. B. Zheng, B. K. Juluri, and T. J. Huang, “Light-driven plasmonic switches based on Au nanodisk arrays and photoresponsive liquid crystal,” Adv. Mater. 20, 3520–3532 (2008).

J. J. Mock, R. T. Hill, A. Degiron, S. Zauscher, A. Chilkoti, and D. R. Smith, “Distance-dependent plasmon resonant coupling between a gold nanoparticle and gold film,” Nano Lett. 8, 2245 (2008).
[Crossref] [PubMed]

J. Valentine, S. Zhang, T. Zentgraf, E. U. Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455, 376 (2008).
[Crossref] [PubMed]

J. A. Bossard, X. Liang, L. Li, S. Yun, D. H. Werner, B. Weiner, T. S. Mayer, P. F. Cristman, A. Diza, and I. C. Khoo, “Tunable frequency selective surfaces and negative-zero-positive index metamaterials based on liquid crystals,” IEEE Trans. Antenn. Propag. 56, 1308–1320 (2008).
[Crossref]

2007 (3)

X. Wang, D.-H. Kwon, D. H. Werner, and I. C. Khoo, “Tunable optical negative-index metamaterials employing anisotropic liquid crystals,” Appl. Phys. Lett. 91, 143122 (2007).
[Crossref]

A. Minovich, J. Faarnell, D. N. Neshev, I. McKerracher, F. Karouta, J. Tian, D. A. Powell, I. V. Shadrivov, H. H. Tan, C. Jagadish, and Y. S. Kivshar, “Liquid crystal based nonlinear fishnet metamaterials,” Appl. Phys. Lett. 100, 121113 (2007).
[Crossref]

D. H. Werner, D. H. Kwon, I. C. Khoo, A. V. Kildeshev, and V. M. Shalaev, “Liquid crystal-clad near-infrared metamaterials with tunable negative-zero-positive refractive indices,” Opt. Express 15, 3342–3347 (2007).
[Crossref] [PubMed]

2006 (1)

K. Okano, O. Tsutsumi, A. Shishido, and T. Ikeda, “Azotolane liquid-crystalline polymers: huge change in birefringence by photoinduced alignment change,” J. Am. Chem. Soc. 128, 15368–15269 (2006).
[Crossref] [PubMed]

2005 (1)

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

2004 (1)

P. Lodahl, A. F. Driel, I. S. Nokolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430654–657 (2004).
[Crossref] [PubMed]

2001 (2)

J. R. Lakowicz, “Radiative decay engineering: biophysical and biomedical applications,” Anal. Biochem. 298, 1–24 (2001).
[Crossref] [PubMed]

Y. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mork, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81, 125431 (2001).
[Crossref]

2000 (1)

K. Ichimura, “Photoalignment of liquid-crystal systems,” Chem. Rev. 100, 1847 (2000).
[Crossref]

1988 (1)

1946 (1)

E. M. Purcell and H. C. Torrey, “Proceedings of the American Physical Society,” Phys. Rev. 69, 37–38 (1946).
[Crossref]

Aizpurua, J.

J. Mertens, A. L. Eiden, D. O. Sigle, F. Huang, A. Lombardo, Z. Sun, R. S. Sundaram, A. Colli, C. Tserkezis, J. Aizpurua, S. Milana, A. C. Ferrari, and J. J. Baumberg, “Controlling subnanometer gaps in plasmonic dimers using graphene,” Nano Lett. 13, 5033–5038 (2013).
[Crossref] [PubMed]

Arakawa, Y.

S. Kang, S. Nakajima, Y. Arakawa, G. Konishi, and J. Watanabe, “Large extraordinary refractive index in highly birefringent nematic liquid crystals of dinaphthyldiacetylene-based materials,” J. Mater. Chem. C 1,4222 (2013).
[Crossref]

Y. Arakawa, S. Nakajima, S. M. Kang, M. Shigeta, G. Konishi, and J. Watanabe, “Design of an extremely high birefringence nematic liquid crystal based on a dinaphthyl-diacetylene mesogen,” J. Mater. Chem. 22, 13908–13910 (2012).
[Crossref]

Arendt, P.

Avila, E. U.

J. Valentine, S. Zhang, T. Zentgraf, E. U. Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455, 376 (2008).
[Crossref] [PubMed]

Avlasevich, Y.

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photonics 3, 654–657 (2009).
[Crossref]

Bakker, R.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Winesner, “Demonstration of a spacer-based nanolaser,” Nature 460, 1110 (2009).
[Crossref] [PubMed]

Bartal, G.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[Crossref] [PubMed]

J. Valentine, S. Zhang, T. Zentgraf, E. U. Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455, 376 (2008).
[Crossref] [PubMed]

Baumberg, J. J.

J. Mertens, A. L. Eiden, D. O. Sigle, F. Huang, A. Lombardo, Z. Sun, R. S. Sundaram, A. Colli, C. Tserkezis, J. Aizpurua, S. Milana, A. C. Ferrari, and J. J. Baumberg, “Controlling subnanometer gaps in plasmonic dimers using graphene,” Nano Lett. 13, 5033–5038 (2013).
[Crossref] [PubMed]

Bazin, M.

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. Photon. 4, 174–177 (2010).

Belgrave, A. M.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Winesner, “Demonstration of a spacer-based nanolaser,” Nature 460, 1110 (2009).
[Crossref] [PubMed]

Bleuse, J.

J. Bleuse, J. Claudon, M. Creasey, and K. Hakuta, “Efficient channeling of fluorescence photons from single quantum dots into guided modes of optical nanofiber,” Phys. Rev. Lett. 109, 063602 (2012).
[Crossref]

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. Photon. 4, 174–177 (2010).

Bossard, J. A.

J. A. Bossard, X. Liang, L. Li, S. Yun, D. H. Werner, B. Weiner, T. S. Mayer, P. F. Cristman, A. Diza, and I. C. Khoo, “Tunable frequency selective surfaces and negative-zero-positive index metamaterials based on liquid crystals,” IEEE Trans. Antenn. Propag. 56, 1308–1320 (2008).
[Crossref]

Cash, W. C.

Chen, C. T.

C. T. Chen, C. C. Liu, C. H. Wang, C. W. Chen, and Y. F. Chen, “Tunable coupling between excitation and surface plasmon in liquid crystal devices consisting of Au nanoparticles and Cdse quantum dots,” Appl. Phys. Lett. 98, 261918 (2011).
[Crossref]

Chen, C. W.

C. T. Chen, C. C. Liu, C. H. Wang, C. W. Chen, and Y. F. Chen, “Tunable coupling between excitation and surface plasmon in liquid crystal devices consisting of Au nanoparticles and Cdse quantum dots,” Appl. Phys. Lett. 98, 261918 (2011).
[Crossref]

Chen, J.

R. Li, C. Cheng, F. Ren, J. Chen, Y. Fan, J. Ding, and H. Wang, “Hybridized surface plasmon polaritons at an interface between a metal and a uniaxial crystal,” Appl. Phys. Lett. 92, 141115 (2008).
[Crossref]

Chen, Y.

Y. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mork, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81, 125431 (2001).
[Crossref]

Chen, Y. F.

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Figures (7)

Fig. 1
Fig. 1 Schematic of the LC-Au-LIM subwavelength plasmonic waveguide. Here, the thickness of Au film is 50 nm and the dipole emitter is embedded in the LC layer.
Fig. 2
Fig. 2 Mechanism of modulating spontaneous emission. (a) Modulation of normalized spontaneous emission rates for a dipole emitter oriented parallel along the Y-axis with d=5 nm above the Au film. (b) The normalized propagation constant, propagation length and (c) penetration depths of SPP as a function of θ. (d) Electric field intensity distributions at three specific θ. When θ increases, the permittivity tensor of LC is changed. This leads to a decreasement of penetration depths Δ, which means electric field is more concentrated. As a result, the total decay rate γtotal can be changed from 131γ0 to 327γ0.
Fig. 3
Fig. 3 Effect of LC’s refractive index anisotropy and LIM’s refractive index on spontaneous emission modulation. (a) Normalized total decay rates γmax/γ0 (θ = 90), γmin/γ0 (θ = 0°) and (b) modulation range γmax/γmin as a function of Δn. Other parameters are the same as those in Fig. 2. The modulation range increases with Δn as a linear relationship, γmax/γmin=1.91Δn+0.98. (c) Normalized total decay rate γtotal/γ0 and (d) penetration depths into LIM ΔLIM for different refractive index nd as a function of θ. The enhancement of total decay rate is larger for smaller nd due to the more concentrated SPP, but the modulation range remains almost constant.
Fig. 4
Fig. 4 (a) Normalized total decay rate γmax/γ0 (θ = 90°), γmin/γ0 (θ = 0) and (b) modulation range γmax/γmin as a function of wavelength. The parameters are the same as those in Fig. 2. With red shift of wavelength, the γmax/γ0 and γmin/γ0 decrease within visible spectrum while increase within infrared spectrum, but γmax/γmin remains almost constant 2.5 over a broad spectrum region.
Fig. 5
Fig. 5 Modulation of normalized spontaneous emission rates for a dipole emitter placed at (a) d=2 nm, (b) d=3 nm, (c) d=10 nm and (d)=15 nm. The enhancement of spontaneous emission rate is large when dipole is close to the Au film while it is small when dipole is away from the Au film, but the modulation range nearly unchanged.
Fig. 6
Fig. 6 Schematic and validity of modelling in COMSOL. (a) dimensions of model, the dark blue area is the upper and lower integral surfaces for computing Pr. (b) integral sphere for computing total radiative power Ptotal. (c) integral volume for computing metal loss Pnr.(d) The method in the main text (denoted as Method I in black curve) and energy flux method (denoted as Method II in dotted curve) of computing SPP channel normalized decay rates γspp/γ0
Fig. 7
Fig. 7 Modulation of spontaneous emission rates when OA lies in the X-Y plane for (a) and dipole embedded in LIM for (b). The parameters are the same as those in Fig. 2(a) of main text.

Tables (1)

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Table 1 Radiative power of a dipole with different polarizatioin

Equations (4)

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ε ^ = [ ε o 0 0 0 ε e c o s 2 θ + ε o s i n 2 θ ( ε 0 ε e ) s i n θ c o s θ 0 ( ε 0 ε e ) s i n θ c o s θ ε o c o s 2 θ + ε e s i n 2 θ ]
P = ω 4 | p | 2 12 π ε 0 c 3
γ spp γ 0 = P t o t a l P m P r P 0
γ spp γ 0 = P x + P y P r P 0

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