Abstract

Modal volumes at the nano-scale, much smaller than the “diffraction-limit”, with appreciable quality factors, are calculated for a dielectric cavity embedded in a space between metal plates. The modal field is bounded between the metal interfaces in one dimension and can be reduced in size almost indefinitely in this dimension. But more surprisingly, due to the “plasmonic” slow wave effect, this reduction is accompanied by a similar in-plane modal size reduction. Another interesting result is that higher order cavity modes exhibit lower radiation loss. The scheme is studied with effective index analysis, and validated by FDTD simulations.

© 2007 Optical Society of America

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  1. K. J. Vahala, "Optical microcavities," Nature 424, 839 (2003).
    [CrossRef] [PubMed]
  2. R. Coccioli, M. Boroditsky, K. W. Kim, Y. Rahmat-Samii, and E. Yablonovitch, "Smallest possible electromagnetic mode volume in a dielectric cavity," IEE Proc.: Optoelectron. 145, 391 (1998).
    [CrossRef]
  3. J. Scheuer, W. M. Green, G. A. DeRose, and A. Yariv, "Lasing from a circular Bragg nanocavity with an ultra small modal volume," Appl. Phys. Lett. 86, 251101 (2005).
    [CrossRef]
  4. M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, "Simultaneous inhibition and redistribution of spontaneous light emission in Photonic Crystals," Science 308, 1296 (2005).
    [CrossRef] [PubMed]
  5. Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944 (2003).
    [CrossRef] [PubMed]
  6. K. Tanaka and M. Tanaka, "Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide," Appl. Phys. Lett. 82, 1158 (2003).
    [CrossRef]
  7. W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824 (2003).
    [CrossRef] [PubMed]
  8. P. Grinberg, E. Feigenbaum, and M. Orenstein, "2D Photonic band gap cavities embedded in a plasmonic gap structure - zero modal volume," LEOS Annual Meeting, Australia (paper TuZ5) (2005).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  14. J. A. Kong, Electromagnetic Waves - Progress In Electromagnetics Research 10, (EMW, Cambridge, 1995).
  15. L. C. Andreani, G. Panzarini, and J. M. Ge´rard, "Strong-coupling regime for quantum boxes in pillar microcavities: Theory," Phys. Rev. B 60, 13276 (1999).
    [CrossRef]

2006 (1)

H. T. Miyazaki0 and Y. Kurokawa, "Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity," Phys. Rev. Lett 96, 097401 (2006).
[CrossRef]

2005 (3)

J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, "Ultra small mode volumes in Dielectric Optical Microcavities," Phys. Rev. Lett. 95, 143901 (2005).
[CrossRef] [PubMed]

J. Scheuer, W. M. Green, G. A. DeRose, and A. Yariv, "Lasing from a circular Bragg nanocavity with an ultra small modal volume," Appl. Phys. Lett. 86, 251101 (2005).
[CrossRef]

M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, "Simultaneous inhibition and redistribution of spontaneous light emission in Photonic Crystals," Science 308, 1296 (2005).
[CrossRef] [PubMed]

2003 (4)

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944 (2003).
[CrossRef] [PubMed]

K. Tanaka and M. Tanaka, "Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide," Appl. Phys. Lett. 82, 1158 (2003).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824 (2003).
[CrossRef] [PubMed]

K. J. Vahala, "Optical microcavities," Nature 424, 839 (2003).
[CrossRef] [PubMed]

1999 (1)

L. C. Andreani, G. Panzarini, and J. M. Ge´rard, "Strong-coupling regime for quantum boxes in pillar microcavities: Theory," Phys. Rev. B 60, 13276 (1999).
[CrossRef]

1998 (1)

R. Coccioli, M. Boroditsky, K. W. Kim, Y. Rahmat-Samii, and E. Yablonovitch, "Smallest possible electromagnetic mode volume in a dielectric cavity," IEE Proc.: Optoelectron. 145, 391 (1998).
[CrossRef]

1997 (1)

1991 (1)

B. Prade, J. Y. Vinet, and A. Mysyrowicz, "Guided optical waves in planar heterostructures with negative dielectric constant," Phys. Rev. B 44, 13556 (1991).
[CrossRef]

1986 (1)

J. J. Burke, G. I. Stegeman, and T. Tamir, "Surface-polariton-like waves guided by thin, lossy metal films," Phys. Rev. B 335186 (1986).
[CrossRef]

Akahane, Y.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944 (2003).
[CrossRef] [PubMed]

Andreani, L. C.

L. C. Andreani, G. Panzarini, and J. M. Ge´rard, "Strong-coupling regime for quantum boxes in pillar microcavities: Theory," Phys. Rev. B 60, 13276 (1999).
[CrossRef]

Asano, T.

M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, "Simultaneous inhibition and redistribution of spontaneous light emission in Photonic Crystals," Science 308, 1296 (2005).
[CrossRef] [PubMed]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944 (2003).
[CrossRef] [PubMed]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824 (2003).
[CrossRef] [PubMed]

Boroditsky, M.

R. Coccioli, M. Boroditsky, K. W. Kim, Y. Rahmat-Samii, and E. Yablonovitch, "Smallest possible electromagnetic mode volume in a dielectric cavity," IEE Proc.: Optoelectron. 145, 391 (1998).
[CrossRef]

Burke, J. J.

J. J. Burke, G. I. Stegeman, and T. Tamir, "Surface-polariton-like waves guided by thin, lossy metal films," Phys. Rev. B 335186 (1986).
[CrossRef]

Chen, L.

J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, "Ultra small mode volumes in Dielectric Optical Microcavities," Phys. Rev. Lett. 95, 143901 (2005).
[CrossRef] [PubMed]

Coccioli, R.

R. Coccioli, M. Boroditsky, K. W. Kim, Y. Rahmat-Samii, and E. Yablonovitch, "Smallest possible electromagnetic mode volume in a dielectric cavity," IEE Proc.: Optoelectron. 145, 391 (1998).
[CrossRef]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824 (2003).
[CrossRef] [PubMed]

DeRose, G. A.

J. Scheuer, W. M. Green, G. A. DeRose, and A. Yariv, "Lasing from a circular Bragg nanocavity with an ultra small modal volume," Appl. Phys. Lett. 86, 251101 (2005).
[CrossRef]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824 (2003).
[CrossRef] [PubMed]

Fujita, M.

M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, "Simultaneous inhibition and redistribution of spontaneous light emission in Photonic Crystals," Science 308, 1296 (2005).
[CrossRef] [PubMed]

Ge´rard, J. M.

L. C. Andreani, G. Panzarini, and J. M. Ge´rard, "Strong-coupling regime for quantum boxes in pillar microcavities: Theory," Phys. Rev. B 60, 13276 (1999).
[CrossRef]

Green, W. M.

J. Scheuer, W. M. Green, G. A. DeRose, and A. Yariv, "Lasing from a circular Bragg nanocavity with an ultra small modal volume," Appl. Phys. Lett. 86, 251101 (2005).
[CrossRef]

Kim, K. W.

R. Coccioli, M. Boroditsky, K. W. Kim, Y. Rahmat-Samii, and E. Yablonovitch, "Smallest possible electromagnetic mode volume in a dielectric cavity," IEE Proc.: Optoelectron. 145, 391 (1998).
[CrossRef]

Kobayashi, T.

Lipson, M.

J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, "Ultra small mode volumes in Dielectric Optical Microcavities," Phys. Rev. Lett. 95, 143901 (2005).
[CrossRef] [PubMed]

Manolatou, C.

J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, "Ultra small mode volumes in Dielectric Optical Microcavities," Phys. Rev. Lett. 95, 143901 (2005).
[CrossRef] [PubMed]

Miyazaki, H. T.

H. T. Miyazaki0 and Y. Kurokawa, "Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity," Phys. Rev. Lett 96, 097401 (2006).
[CrossRef]

Morimoto, A.

Mysyrowicz, A.

B. Prade, J. Y. Vinet, and A. Mysyrowicz, "Guided optical waves in planar heterostructures with negative dielectric constant," Phys. Rev. B 44, 13556 (1991).
[CrossRef]

Noda, S.

M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, "Simultaneous inhibition and redistribution of spontaneous light emission in Photonic Crystals," Science 308, 1296 (2005).
[CrossRef] [PubMed]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944 (2003).
[CrossRef] [PubMed]

Panzarini, G.

L. C. Andreani, G. Panzarini, and J. M. Ge´rard, "Strong-coupling regime for quantum boxes in pillar microcavities: Theory," Phys. Rev. B 60, 13276 (1999).
[CrossRef]

Prade, B.

B. Prade, J. Y. Vinet, and A. Mysyrowicz, "Guided optical waves in planar heterostructures with negative dielectric constant," Phys. Rev. B 44, 13556 (1991).
[CrossRef]

Rahmat-Samii, Y.

R. Coccioli, M. Boroditsky, K. W. Kim, Y. Rahmat-Samii, and E. Yablonovitch, "Smallest possible electromagnetic mode volume in a dielectric cavity," IEE Proc.: Optoelectron. 145, 391 (1998).
[CrossRef]

Robinson, J. T.

J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, "Ultra small mode volumes in Dielectric Optical Microcavities," Phys. Rev. Lett. 95, 143901 (2005).
[CrossRef] [PubMed]

Scheuer, J.

J. Scheuer, W. M. Green, G. A. DeRose, and A. Yariv, "Lasing from a circular Bragg nanocavity with an ultra small modal volume," Appl. Phys. Lett. 86, 251101 (2005).
[CrossRef]

Song, B. S.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944 (2003).
[CrossRef] [PubMed]

Stegeman, G. I.

J. J. Burke, G. I. Stegeman, and T. Tamir, "Surface-polariton-like waves guided by thin, lossy metal films," Phys. Rev. B 335186 (1986).
[CrossRef]

Takahara, J.

Takahashi, S.

M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, "Simultaneous inhibition and redistribution of spontaneous light emission in Photonic Crystals," Science 308, 1296 (2005).
[CrossRef] [PubMed]

Taki, H.

Tamir, T.

J. J. Burke, G. I. Stegeman, and T. Tamir, "Surface-polariton-like waves guided by thin, lossy metal films," Phys. Rev. B 335186 (1986).
[CrossRef]

Tanaka, K.

K. Tanaka and M. Tanaka, "Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide," Appl. Phys. Lett. 82, 1158 (2003).
[CrossRef]

Tanaka, M.

K. Tanaka and M. Tanaka, "Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide," Appl. Phys. Lett. 82, 1158 (2003).
[CrossRef]

Tanaka, Y.

M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, "Simultaneous inhibition and redistribution of spontaneous light emission in Photonic Crystals," Science 308, 1296 (2005).
[CrossRef] [PubMed]

Vahala, K. J.

K. J. Vahala, "Optical microcavities," Nature 424, 839 (2003).
[CrossRef] [PubMed]

Vinet, J. Y.

B. Prade, J. Y. Vinet, and A. Mysyrowicz, "Guided optical waves in planar heterostructures with negative dielectric constant," Phys. Rev. B 44, 13556 (1991).
[CrossRef]

Yablonovitch, E.

R. Coccioli, M. Boroditsky, K. W. Kim, Y. Rahmat-Samii, and E. Yablonovitch, "Smallest possible electromagnetic mode volume in a dielectric cavity," IEE Proc.: Optoelectron. 145, 391 (1998).
[CrossRef]

Yamagishi, S.

Yariv, A.

J. Scheuer, W. M. Green, G. A. DeRose, and A. Yariv, "Lasing from a circular Bragg nanocavity with an ultra small modal volume," Appl. Phys. Lett. 86, 251101 (2005).
[CrossRef]

Appl. Phys. Lett. (2)

J. Scheuer, W. M. Green, G. A. DeRose, and A. Yariv, "Lasing from a circular Bragg nanocavity with an ultra small modal volume," Appl. Phys. Lett. 86, 251101 (2005).
[CrossRef]

K. Tanaka and M. Tanaka, "Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide," Appl. Phys. Lett. 82, 1158 (2003).
[CrossRef]

IEE Proc.: Optoelectron. (1)

R. Coccioli, M. Boroditsky, K. W. Kim, Y. Rahmat-Samii, and E. Yablonovitch, "Smallest possible electromagnetic mode volume in a dielectric cavity," IEE Proc.: Optoelectron. 145, 391 (1998).
[CrossRef]

Nature (3)

K. J. Vahala, "Optical microcavities," Nature 424, 839 (2003).
[CrossRef] [PubMed]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824 (2003).
[CrossRef] [PubMed]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944 (2003).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rev. B (3)

B. Prade, J. Y. Vinet, and A. Mysyrowicz, "Guided optical waves in planar heterostructures with negative dielectric constant," Phys. Rev. B 44, 13556 (1991).
[CrossRef]

J. J. Burke, G. I. Stegeman, and T. Tamir, "Surface-polariton-like waves guided by thin, lossy metal films," Phys. Rev. B 335186 (1986).
[CrossRef]

L. C. Andreani, G. Panzarini, and J. M. Ge´rard, "Strong-coupling regime for quantum boxes in pillar microcavities: Theory," Phys. Rev. B 60, 13276 (1999).
[CrossRef]

Phys. Rev. Lett (1)

H. T. Miyazaki0 and Y. Kurokawa, "Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity," Phys. Rev. Lett 96, 097401 (2006).
[CrossRef]

Phys. Rev. Lett. (1)

J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, "Ultra small mode volumes in Dielectric Optical Microcavities," Phys. Rev. Lett. 95, 143901 (2005).
[CrossRef] [PubMed]

Science (1)

M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, "Simultaneous inhibition and redistribution of spontaneous light emission in Photonic Crystals," Science 308, 1296 (2005).
[CrossRef] [PubMed]

Other (2)

P. Grinberg, E. Feigenbaum, and M. Orenstein, "2D Photonic band gap cavities embedded in a plasmonic gap structure - zero modal volume," LEOS Annual Meeting, Australia (paper TuZ5) (2005).

J. A. Kong, Electromagnetic Waves - Progress In Electromagnetics Research 10, (EMW, Cambridge, 1995).

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Figures (3)

Fig. 1.
Fig. 1.

Analysis results: (a) averaged modal size vs. cylinder height at λ0=700nm, according to both our definition of “uncertainty volume” [Eq. (2)] as well as the Purcell effective volume. (b) Outgoing radial power vs. cylinder radius for 20nm gap. nsi=3.5, n0=1, λplasma=137nm.

Fig. 2.
Fig. 2.

FDTD simulations: Gold thickness: 100nm (practically infinite). Excitation: short x polarized pulse with Gaussian y distribution inside the cavity. In-plane and vertical resolutions are 10nm and 1nm respectively. Major spectral peak is at ~700nm. Hθ distribution: (a) vertical plane at z=0 (result obtained from CW excitation at 700nm for higher resolution). Inset: the field profile along y=20nm. (b) in-plane at x=0 (result obtained from the impulse excitation since CW has poorer visualization due to interference with the continuous source).

Fig. 3.
Fig. 3.

Modal calculations by the effective index method for d=20nm: (a) coherent summation of modes {0,2}{2,1} at λ0=700nm, a=50nm (cylinder boundaries in dashed white). (b) Cylinder radius supporting specific modes vs. the wavelength (λ0). Red dashed line denotes the 50nm radius used in FDTD simulations. The inset shows the |Hθ|2 distributions for the different modes for a=50nm (with respective resonance frequencies) (cylinder boundaries in dashed green).

Equations (2)

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H θ m , l θ r = e jmθ { J m ( k 0 n 1 r ) r a A m , l H m ( 2 ) ( k 0 n 2 r ) r a
h eff = 2 σ I = 2 · VAR { I } = 2 x 2 I ( x ) 2 dx I ( x ) 2 dx ; R eff 2 r 2 I ( r ) 2 rdr I ( r ) 2 rdr

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