Abstract

The confinement of light within nanometer-scale regions may result in the significant enhancement of light–matter interactions. However, light confinement to nanometers is hindered by the diffraction limit of a dielectric material. For a dielectric cavity, if the material loss is negligible, reducing the cavity size usually causes a significantly increase in radiation loss. Surface plasmons show great promise for potential subwavelength light confinement. However, in most circumstances, light confinement by dissipative metallic materials can cause ohmic losses at optical frequencies. In such cases, the realization of light confinement with deep subwavelength mode sizes results in great losses and thus has low quality factors. In the present study, a three-dimensional light confinement with deep subwavelength mode sizes is achieved using dielectric spheres in metal cavities. Contrary to other mechanisms for subwavelength light confinement that are based on the use of dielectric or metal cavities, the nanometer-scale regions ensure that most of the light energy is confined away from the metal-dielectric interfaces, thereby decreasing light absorption in the metal cavity. In turn, the metal cavity decreases the radiation loss of light. Thus, high quality factors ranging from 2×102 to 6×102 can be obtained at room temperature. An effective electrical mode volume ranging from 7×105λ03 to 2×104λ03 (where λ0 is the resonant wavelength in a vacuum) can be achieved. Therefore, this method of three-dimensional light confinement with deep subwavelength mode sizes using dielectric spheres in metal cavities may have potential applications in the design of nanolasers, nanophoton detectors, nonlinear optical switches, and so on.

© 2012 Optical Society of America

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  1. M. T. Hill, Y. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S. Kwon, Y. Lee, R. Notzel, and M. K. Smit, Nat. Photonics 1, 589 (2007).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  4. R. Oulton, V. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
    [CrossRef]
  5. M. K. Seo, S. H. Kwon, H. S. Ee, and H. G. Park, Nano Lett. 9, 4078 (2009).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  10. E. M. Purcell, Phys. Rev. 69, 681 (1946).
    [CrossRef]

2012 (1)

2011 (1)

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, Nat. Mater. 10, 110 (2011).
[CrossRef]

2010 (3)

D. K. Gramotnev and S. I. Bozhevolnyi, Nat. Photonics 4, 83 (2010).
[CrossRef]

Z. H. Zhu, H. Liu, S. M. Wang, W. M. Ye, X. D. Yuan, and S. N. Zhu, Opt. Lett. 35, 754 (2010).
[CrossRef]

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

2009 (2)

R. Oulton, V. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef]

M. K. Seo, S. H. Kwon, H. S. Ee, and H. G. Park, Nano Lett. 9, 4078 (2009).
[CrossRef]

2007 (1)

M. T. Hill, Y. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S. Kwon, Y. Lee, R. Notzel, and M. K. Smit, Nat. Photonics 1, 589 (2007).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

1946 (1)

E. M. Purcell, Phys. Rev. 69, 681 (1946).
[CrossRef]

Bartal, G.

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, Nat. Mater. 10, 110 (2011).
[CrossRef]

R. Oulton, V. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Bozhevolnyi, S. I.

D. K. Gramotnev and S. I. Bozhevolnyi, Nat. Photonics 4, 83 (2010).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Dai, L.

R. Oulton, V. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef]

de Vries, T.

M. T. Hill, Y. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S. Kwon, Y. Lee, R. Notzel, and M. K. Smit, Nat. Photonics 1, 589 (2007).
[CrossRef]

de Waardt, H.

M. T. Hill, Y. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S. Kwon, Y. Lee, R. Notzel, and M. K. Smit, Nat. Photonics 1, 589 (2007).
[CrossRef]

Ee, H. S.

M. K. Seo, S. H. Kwon, H. S. Ee, and H. G. Park, Nano Lett. 9, 4078 (2009).
[CrossRef]

Eijkemans, T. J.

M. T. Hill, Y. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S. Kwon, Y. Lee, R. Notzel, and M. K. Smit, Nat. Photonics 1, 589 (2007).
[CrossRef]

Geluk, E. J.

M. T. Hill, Y. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S. Kwon, Y. Lee, R. Notzel, and M. K. Smit, Nat. Photonics 1, 589 (2007).
[CrossRef]

Gladden, C.

R. Oulton, V. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef]

Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, Nat. Photonics 4, 83 (2010).
[CrossRef]

Hill, M. T.

M. T. Hill, Y. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S. Kwon, Y. Lee, R. Notzel, and M. K. Smit, Nat. Photonics 1, 589 (2007).
[CrossRef]

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Joannopoulos, J.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Kwon, S.

M. T. Hill, Y. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S. Kwon, Y. Lee, R. Notzel, and M. K. Smit, Nat. Photonics 1, 589 (2007).
[CrossRef]

Kwon, S. H.

M. K. Seo, S. H. Kwon, H. S. Ee, and H. G. Park, Nano Lett. 9, 4078 (2009).
[CrossRef]

Lee, Y.

M. T. Hill, Y. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S. Kwon, Y. Lee, R. Notzel, and M. K. Smit, Nat. Photonics 1, 589 (2007).
[CrossRef]

Liu, H.

Liu, K.

Ma, R.

R. Oulton, V. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef]

Ma, R.-M.

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, Nat. Mater. 10, 110 (2011).
[CrossRef]

Notzel, R.

M. T. Hill, Y. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S. Kwon, Y. Lee, R. Notzel, and M. K. Smit, Nat. Photonics 1, 589 (2007).
[CrossRef]

Oei, Y.

M. T. Hill, Y. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S. Kwon, Y. Lee, R. Notzel, and M. K. Smit, Nat. Photonics 1, 589 (2007).
[CrossRef]

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Oulton, R.

R. Oulton, V. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef]

Oulton, R. F.

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, Nat. Mater. 10, 110 (2011).
[CrossRef]

Park, H. G.

M. K. Seo, S. H. Kwon, H. S. Ee, and H. G. Park, Nano Lett. 9, 4078 (2009).
[CrossRef]

Purcell, E. M.

E. M. Purcell, Phys. Rev. 69, 681 (1946).
[CrossRef]

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Seo, M. K.

M. K. Seo, S. H. Kwon, H. S. Ee, and H. G. Park, Nano Lett. 9, 4078 (2009).
[CrossRef]

Smalbrugge, B.

M. T. Hill, Y. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S. Kwon, Y. Lee, R. Notzel, and M. K. Smit, Nat. Photonics 1, 589 (2007).
[CrossRef]

Smit, M. K.

M. T. Hill, Y. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S. Kwon, Y. Lee, R. Notzel, and M. K. Smit, Nat. Photonics 1, 589 (2007).
[CrossRef]

Sorger, V.

R. Oulton, V. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef]

Sorger, V. J.

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, Nat. Mater. 10, 110 (2011).
[CrossRef]

Turkiewicz, J. P.

M. T. Hill, Y. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S. Kwon, Y. Lee, R. Notzel, and M. K. Smit, Nat. Photonics 1, 589 (2007).
[CrossRef]

van Otten, F. W. M.

M. T. Hill, Y. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S. Kwon, Y. Lee, R. Notzel, and M. K. Smit, Nat. Photonics 1, 589 (2007).
[CrossRef]

van Veldhoven, P. J.

M. T. Hill, Y. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S. Kwon, Y. Lee, R. Notzel, and M. K. Smit, Nat. Photonics 1, 589 (2007).
[CrossRef]

Wang, S. M.

Xu, W.

Ye, W. M.

Yuan, X. D.

Zeng, C.

Zentgraf, T.

R. Oulton, V. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef]

Zhang, X.

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, Nat. Mater. 10, 110 (2011).
[CrossRef]

R. Oulton, V. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef]

Zhu, S. N.

Zhu, Y.

M. T. Hill, Y. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S. Kwon, Y. Lee, R. Notzel, and M. K. Smit, Nat. Photonics 1, 589 (2007).
[CrossRef]

Zhu, Z. H.

Comput. Phys. Commun. (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Nano Lett. (1)

M. K. Seo, S. H. Kwon, H. S. Ee, and H. G. Park, Nano Lett. 9, 4078 (2009).
[CrossRef]

Nat. Mater. (1)

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, Nat. Mater. 10, 110 (2011).
[CrossRef]

Nat. Photonics (2)

M. T. Hill, Y. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S. Kwon, Y. Lee, R. Notzel, and M. K. Smit, Nat. Photonics 1, 589 (2007).
[CrossRef]

D. K. Gramotnev and S. I. Bozhevolnyi, Nat. Photonics 4, 83 (2010).
[CrossRef]

Nature (1)

R. Oulton, V. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. (1)

E. M. Purcell, Phys. Rev. 69, 681 (1946).
[CrossRef]

Phys. Rev. B (1)

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Schematic of the three-dimensional subwavelength confinement structure. Circular air holes with diameter dm are drilled in a metal layer. The metal layer with permittivity εm and thickness hm is then deposited onto an insulator (or a metal) clad with permittivity εdl (or εm). A low-index insulator layer with permittivity εdl is deposited onto the bottom with thickness hl and along the side walls of the holes. Then, the diameter of the hole changes to ddh. The thickness T of the low index side wall satisfy T=(dmddh)/2. Two dielectric spheres with radius rd and permittivity εdh are placed in the hole. The radius of the spheres rd satisfies ddh=2×rd, hl satisfies hl+ddh=hm/2. dm=300nm, εdl=2.56, εdh=11.56.

Fig. 2.
Fig. 2.

Cross-sectional views of the electrical field and electrical energy density distributions in the silver hole cavities with hm=800nm, rd=120nm for the first-order TM-like mode. The resonant wavelength is 974 nm.

Fig. 3.
Fig. 3.

Quality factor Q (a), resonant wavelength (b), and Veff (c) of the first-order resonant TM-like mode in the cavity compared with rd.

Fig. 4.
Fig. 4.

Cross-sectional view of the electrical field and electrical energy density distributions in the silver hole cavities of the first-order TE like mode. (a) Parameters are the same as those shown in Fig. 2, with a resonant wavelength of 782 nm. (b) Metal hole structure is the same as that shown in Fig. 1, except that the three dielectric spheres are horizontally placed within the metal cavity, with hm=400nm, dm=400nm, ddh=320nm, and rd=74.3nm. The resonant wavelength λ0=622nm.

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