High-Q/Veff gap-mode plasmonic FP nanocavity

Houqiang Jiang; Chen Liu; Pei Wang; Douguo Zhang; Yonghua Lu; Hai Ming

doi:10.1364/OE.21.004752

High-Q/Veff gap-mode plasmonic FP nanocavity

Houqiang Jiang, Chen Liu, Pei Wang, Douguo Zhang, Yonghua Lu, and Hai Ming

Optics Express
Vol. 21,
Issue 4,
pp. 4752-4757
(2013)
•https://doi.org/10.1364/OE.21.004752

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Houqiang Jiang, Chen Liu, Pei Wang, Douguo Zhang, Yonghua Lu, and Hai Ming, "High-Q/Veff gap-mode plasmonic FP nanocavity," Opt. Express 21, 4752-4757 (2013)

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Abstract

In this paper, a high-Q/V_eff gap-mode plasmonic Fabry-Perot nanocavity, which is composed of a silver nanowire on a flat silver substrate spaced by patterned dielectric distributed Bragg gratings, is investigated both analytically and numerically. The design parameters and properties of the nanocavity are exploited with the use of generalized Fabry-Perot model. The V_eff ~0.0026 (λ/n)³ and Q/V_eff ~1.4 × 10⁵/μm³ of the nanocavity can be achieved. Such a gap-mode plasmonic Fabry-Perot nanocavity design provides a promising realization for wide novel band filters and spaser.

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S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1(8), 449–458 (2007).
[Crossref]
P. Bianucci, X. Wang, J. G. Veinot, and A. Meldrum, “Silicon nanocrystals on bottle resonators: Mode structure, loss mechanisms and emission dynamics,” Opt. Express 18(8), 8466–8481 (2010).
[Crossref] [PubMed]
K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003).
[Crossref] [PubMed]
A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450(7168), 402–406 (2007).
[Crossref] [PubMed]
R. Kolesov, B. Grotz, G. Balasubramanian, R. J. Stöhr, A. A. L. Nicolet, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Wave–particle duality of single surface plasmon polaritons,” Nat. Phys. 5(7), 470–474 (2009).
[Crossref]
D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97(5), 053002 (2006).
[Crossref] [PubMed]
K. J. Russell and E. L. Hu, “Gap-mode plasmonic nanocavity,” Appl. Phys. Lett. 97(16), 163115 (2010).
[Crossref]
K. J. Russell, T. L. Liu, S. Cui, and E. L. Hu, “Large spontaneous emission enhancement in plasmonic nanocavities,” Nat. Photonics 6(7), 459–462 (2012).
[Crossref]
A. Hohenau, P. Kusar, C. Gruber, and J. R. Krenn, “Analysis of damping-induced phase flips of plasmonic nanowire modes,” Opt. Lett. 37(4), 746–748 (2012).
[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(7264), 629–632 (2009).
[Crossref] [PubMed]
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(22), 226803 (2012).
[Crossref] [PubMed]
M. Yi, D. Zhang, X. Wen, Q. Fu, P. Wang, Y. Lu, and H. Ming, “Fluorescence enhancement caused by plasmonics coupling between silver nano-cubes and silver film,” Plasmonics 6(2), 213–217 (2011).
[Crossref]
X. Wen, M. Yi, D. Zhang, P. Wang, Y. Lu, and H. Ming, “Tunable plasmonic coupling between silver nano-cubes and silver nano-hole arrays,” Nanotechnology 22(8), 085203 (2011).
[Crossref] [PubMed]
C. L. Zou, F. W. Sun, Y. F. Xiao, C. H. Dong, X. D. Chen, J. M. Cui, Q. Gong, Z. F. Han, and G. C. Guo, “Plasmon modes of silver nanowire on a silica substrate,” Appl. Phys. Lett. 97(18), 183102 (2010).
[Crossref]
P. B. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]
R. Ruppin, “Electromagnetic energy density in a dispersive and absorptive material,” Phys. Lett. A 299(2-3), 309–312 (2002).
[Crossref]
Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic Press, 1985).

2012 (3)

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

A. Hohenau, P. Kusar, C. Gruber, and J. R. Krenn, “Analysis of damping-induced phase flips of plasmonic nanowire modes,” Opt. Lett. 37(4), 746–748 (2012).
[Crossref] [PubMed]

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(22), 226803 (2012).
[Crossref] [PubMed]

2011 (2)

M. Yi, D. Zhang, X. Wen, Q. Fu, P. Wang, Y. Lu, and H. Ming, “Fluorescence enhancement caused by plasmonics coupling between silver nano-cubes and silver film,” Plasmonics 6(2), 213–217 (2011).
[Crossref]

X. Wen, M. Yi, D. Zhang, P. Wang, Y. Lu, and H. Ming, “Tunable plasmonic coupling between silver nano-cubes and silver nano-hole arrays,” Nanotechnology 22(8), 085203 (2011).
[Crossref] [PubMed]

2010 (3)

C. L. Zou, F. W. Sun, Y. F. Xiao, C. H. Dong, X. D. Chen, J. M. Cui, Q. Gong, Z. F. Han, and G. C. Guo, “Plasmon modes of silver nanowire on a silica substrate,” Appl. Phys. Lett. 97(18), 183102 (2010).
[Crossref]

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

P. Bianucci, X. Wang, J. G. Veinot, and A. Meldrum, “Silicon nanocrystals on bottle resonators: Mode structure, loss mechanisms and emission dynamics,” Opt. Express 18(8), 8466–8481 (2010).
[Crossref] [PubMed]

2009 (2)

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(7264), 629–632 (2009).
[Crossref] [PubMed]

R. Kolesov, B. Grotz, G. Balasubramanian, R. J. Stöhr, A. A. L. Nicolet, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Wave–particle duality of single surface plasmon polaritons,” Nat. Phys. 5(7), 470–474 (2009).
[Crossref]

2007 (2)

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1(8), 449–458 (2007).
[Crossref]

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450(7168), 402–406 (2007).
[Crossref] [PubMed]

2006 (1)

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97(5), 053002 (2006).
[Crossref] [PubMed]

2003 (1)

K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003).
[Crossref] [PubMed]

2002 (1)

R. Ruppin, “Electromagnetic energy density in a dispersive and absorptive material,” Phys. Lett. A 299(2-3), 309–312 (2002).
[Crossref]

1972 (1)

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

Akimov, A. V.

Asano, T.

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1(8), 449–458 (2007).
[Crossref]

Balasubramanian, G.

Bartal, G.

Bianucci, P.

Chang, D. E.

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97(5), 053002 (2006).
[Crossref] [PubMed]

Chen, X. D.

Christy, R.

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

Cui, J. M.

Cui, S.

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

Dai, L.

de Leon, N. P.

Dong, C. H.

Englund, D. E.

Fu, Q.

Fujita, M.

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1(8), 449–458 (2007).
[Crossref]

Gladden, C.

Gong, Q.

Grotz, B.

Gruber, C.

A. Hohenau, P. Kusar, C. Gruber, and J. R. Krenn, “Analysis of damping-induced phase flips of plasmonic nanowire modes,” Opt. Lett. 37(4), 746–748 (2012).
[Crossref] [PubMed]

Guo, G. C.

Han, Z. F.

Hemmer, P. R.

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97(5), 053002 (2006).
[Crossref] [PubMed]

Hohenau, A.

A. Hohenau, P. Kusar, C. Gruber, and J. R. Krenn, “Analysis of damping-induced phase flips of plasmonic nanowire modes,” Opt. Lett. 37(4), 746–748 (2012).
[Crossref] [PubMed]

Hu, E. L.

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

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

Jelezko, F.

Johnson, P. B.

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

Kolesov, R.

Krenn, J. R.

A. Hohenau, P. Kusar, C. Gruber, and J. R. Krenn, “Analysis of damping-induced phase flips of plasmonic nanowire modes,” Opt. Lett. 37(4), 746–748 (2012).
[Crossref] [PubMed]

Kusar, P.

A. Hohenau, P. Kusar, C. Gruber, and J. R. Krenn, “Analysis of damping-induced phase flips of plasmonic nanowire modes,” Opt. Lett. 37(4), 746–748 (2012).
[Crossref] [PubMed]

Liu, T. L.

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

Lu, Y.

X. Wen, M. Yi, D. Zhang, P. Wang, Y. Lu, and H. Ming, “Tunable plasmonic coupling between silver nano-cubes and silver nano-hole arrays,” Nanotechnology 22(8), 085203 (2011).
[Crossref] [PubMed]

Lukin, M. D.

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97(5), 053002 (2006).
[Crossref] [PubMed]

Ma, R. M.

Meldrum, A.

Ming, H.

X. Wen, M. Yi, D. Zhang, P. Wang, Y. Lu, and H. Ming, “Tunable plasmonic coupling between silver nano-cubes and silver nano-hole arrays,” Nanotechnology 22(8), 085203 (2011).
[Crossref] [PubMed]

Mukherjee, A.

Nicolet, A. A. L.

Noda, S.

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1(8), 449–458 (2007).
[Crossref]

Oulton, R. F.

Park, H.

Ruppin, R.

R. Ruppin, “Electromagnetic energy density in a dispersive and absorptive material,” Phys. Lett. A 299(2-3), 309–312 (2002).
[Crossref]

Russell, K. J.

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

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

Shields, B. J.

Sørensen, A. S.

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97(5), 053002 (2006).
[Crossref] [PubMed]

Sorger, V. J.

Stöhr, R. J.

Sun, F. W.

Vahala, K. J.

K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003).
[Crossref] [PubMed]

Veinot, J. G.

Wang, P.

X. Wen, M. Yi, D. Zhang, P. Wang, Y. Lu, and H. Ming, “Tunable plasmonic coupling between silver nano-cubes and silver nano-hole arrays,” Nanotechnology 22(8), 085203 (2011).
[Crossref] [PubMed]

Wang, X.

Wen, X.

X. Wen, M. Yi, D. Zhang, P. Wang, Y. Lu, and H. Ming, “Tunable plasmonic coupling between silver nano-cubes and silver nano-hole arrays,” Nanotechnology 22(8), 085203 (2011).
[Crossref] [PubMed]

Wrachtrup, J.

Xiao, Y. F.

Yi, M.

X. Wen, M. Yi, D. Zhang, P. Wang, Y. Lu, and H. Ming, “Tunable plasmonic coupling between silver nano-cubes and silver nano-hole arrays,” Nanotechnology 22(8), 085203 (2011).
[Crossref] [PubMed]

Yu, C. L.

Zentgraf, T.

Zhang, D.

X. Wen, M. Yi, D. Zhang, P. Wang, Y. Lu, and H. Ming, “Tunable plasmonic coupling between silver nano-cubes and silver nano-hole arrays,” Nanotechnology 22(8), 085203 (2011).
[Crossref] [PubMed]

Zhang, X.

Zibrov, A. S.

Zou, C. L.

Appl. Phys. Lett. (2)

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

Nanotechnology (1)

X. Wen, M. Yi, D. Zhang, P. Wang, Y. Lu, and H. Ming, “Tunable plasmonic coupling between silver nano-cubes and silver nano-hole arrays,” Nanotechnology 22(8), 085203 (2011).
[Crossref] [PubMed]

Nat. Photonics (2)

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

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1(8), 449–458 (2007).
[Crossref]

Nat. Phys. (1)

Nature (3)

K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003).
[Crossref] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

A. Hohenau, P. Kusar, C. Gruber, and J. R. Krenn, “Analysis of damping-induced phase flips of plasmonic nanowire modes,” Opt. Lett. 37(4), 746–748 (2012).
[Crossref] [PubMed]

Phys. Lett. A (1)

R. Ruppin, “Electromagnetic energy density in a dispersive and absorptive material,” Phys. Lett. A 299(2-3), 309–312 (2002).
[Crossref]

Phys. Rev. B (1)

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

Phys. Rev. Lett. (2)

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97(5), 053002 (2006).
[Crossref] [PubMed]

Plasmonics (1)

Other (1)

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

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Fig. 1

Schematic diagram of the gap-mode plasmonic Fabry-Perot nanocavity.

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Fig. 2

(a)Transmission spectrum of plasmonic nanocavity with different cavity lengths and without cavity (black line). (b), (c), (d) Electric field distributions of the resonance at L = 0.14μm, 0.28μm, and 0.7μm, respectively, in y-z plan which across the centre of the nanowire.

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Fig. 3

Schematic diagram of a generalized Fabry-Perot model.

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Fig. 4

Numerical solutions of (a) the real part and (b) the imaginary part of the SPP–gap mode dispersion relation (k_sp). Inset of (a), energy density distribution on the cross section of this silver nanowires-PMMA-silver film structure, the wavelength used here is λ = 650nm. (c)The normalized transmission spectrum of the DBRs (black line), transmission $| \tilde{t} |$ is approximately set to the red short dash line. (d) The light path shift (generalized wave loss) between the border of the cavity and the nearest maxima of electric field isΔL = −6nm, when cavity length is L = 0.14μm.

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Fig. 5

Theoretical spectra calculated by a generalized Fabry-Perot model.

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Equations (10)

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V_{e f f} = \frac{\int ε {| E |}^{2} d V}{\max (ε {| E |}^{2})} = 0.0026 {(λ / n)}^{3},

U_{-} \tilde{t} + A \tilde{r} = U_{1},

U_{+} = A \tilde{t} + U_{-} \tilde{r},

U_{+} \exp (i k_{s p} L) \times \tilde{t} = U_{2},

U_{-} \exp (- i k_{s p} L) = U_{+} \exp (i k_{s p} L) \times \tilde{r} .

U_{1} = A r \frac{1 - {\tilde{r}}^{2} \exp (2 i k_{s p} L) + {\tilde{t}}^{2} \exp (2 i k_{s p} L)}{1 - {\tilde{r}}^{2} \exp (2 i k_{s p} L)},

U_{2} = \frac{A {\tilde{t}}^{2} \exp (i k_{s p} L)}{1 - {\tilde{r}}^{2} \exp (2 i k_{s p} L)} .

I_{2} = U_{2} U_{2}^{*} = \frac{{| A {\tilde{t}}^{2} \exp (i k_{s p} L) |}^{2}}{{| 1 - {\tilde{r}}^{2} \exp (2 i k_{s p} L) |}^{2}} = \frac{{| A {| \tilde{t} |}^{2} \exp (i k_{s p} L) |}^{2}}{{| 1 - {| \tilde{r} |}^{2} \exp (2 i k_{s p} L + 2 i φ) |}^{2}} .

I_{2} \approx \frac{{| A {| \tilde{t} |}^{2} \exp (i k_{s p} L) |}^{2}}{{| 1 - {| \tilde{r} |}^{2} \exp [2 i k_{s p} (L + Δ L)] |}^{2}} .

| \tilde{t} (λ) | = {\begin{matrix} 0.65, \begin{matrix} λ \leq 600 n m \end{matrix} \begin{matrix}  \end{matrix} \\ \begin{array}{l} 0.20, 600 n m < λ <700nm \\ 0.45, λ \geq 700 n m \end{array} \end{matrix}