Abstract

Three-dimensional scattering matrix method is proposed to investigate mode characteristics for metal-coated nanocavities, with the vertical waveguide structure of an active region confined by upper and lower cladding layers. For a nanocavity with radius of 800 nm, Q factors of well-confined modes with wavelength around 1550 nm first decrease with the increase of the metallic layer thickness due to the metallic absorption and the increase of radiation loss as the metallic layer thickness is less than 10 nm, and then rise with the increase of the metallic layer. However, for a weak confined nanocavity with a radius of 500 nm, the mode Q factor increases with the metallic layer thickness first, reaches a maximum value at an optimal metallic thickness, then decrease with the further increase of the metallic layer. For nanocavities confined by a thick metallic layer, the Q factors approach constants limited by the metallic absorption. However, mode field patterns, including the vertical field distributions, are affected by the metallic layer, which not only influences the metallic layer absorption but also the optical confinement factor in the active region.

© 2013 Optical Society of America

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  1. M. T. Hill, Y. S. 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. H. Kwon, Y. H. Lee, R. Notzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1, 589–594 (2007).
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    [CrossRef]
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2013 (1)

Q. F. Yao, Y. Z. Huang, L. X. Zou, X. M. Lv, J. D. Lin, and Y. D. Yang, “Analysis of mode coupling and threshold gain control for nanocircular resonators confined by isolation and metallic layers,” IEEE J. Lightwave Technol. 31, 786–792 (2013).
[CrossRef]

2012 (1)

K. Ding, Z. C. Liu, L. J. Yin, M. T. Hill, M. J. H. Marell, P. J. van Veldhoven, R. Nöetzel, and C. Z. Ning, “Room-temperature continuous wave lasing in deep-subwavelength metallic cavities under electrical injection,” Phys. Rev. B 85, 041301(R) (2012).
[CrossRef]

2011 (2)

2010 (4)

R. M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nat. Mater. 10, 110–113 (2010).
[CrossRef]

M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics 4, 395–399 (2010).
[CrossRef]

S. H. Kwon, J. H. Kang, C. Seassal, S. K. Kim, P. Regreny, Y. H. Lee, C. M. Lieber, and H. G. Park, “Subwavelength plasmonic lasing from a semiconductor nanodisk with silver nanopan cavity,” Nano Lett. 10, 3679–3683 (2010).
[CrossRef]

J. Huang, S. H. Kim, and A. Scherer, “Design of a surface-emitting, subwavelength metal-clad disk laser in the visible spectrum,” Opt. Express 18, 19581–19591 (2010).
[CrossRef]

2009 (1)

2007 (1)

M. T. Hill, Y. S. 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. H. Kwon, Y. H. Lee, R. Notzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1, 589–594 (2007).
[CrossRef]

2006 (1)

2005 (1)

H. E. Tureci, H. G. L. Schwefel, Ph. Jacquod, and A. D. Stone, “Modes of wave-chaotic dielectric resonators,” Prog. Opt. 47, 75–137 (2005).
[CrossRef]

2004 (1)

2002 (1)

M. Hentschel and K. Richter, “Quantum chaos in optical systems: the annular billard,” Phys. Rev. E 66, 056207(2002).
[CrossRef]

1996 (1)

B. J. Li and P. L. Liu, “Numerical analysis of the whispering gallery modes by the finite-difference time-domain method,” IEEE J. Quantum Electron 32, 1583–1587 (1996).
[CrossRef]

Bartal, G.

R. M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nat. Mater. 10, 110–113 (2010).
[CrossRef]

Bimberg, D.

S. L. Chuang and D. Bimberg, “Metal-cavity nanolasers,” IEEE Photon. J. 3, 288–292 (2011).
[CrossRef]

Bondarenko, O.

M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics 4, 395–399 (2010).
[CrossRef]

Chen, Q.

Chuang, S. L.

De Vries, T.

M. T. Hill, Y. S. 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. H. Kwon, Y. H. Lee, R. Notzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1, 589–594 (2007).
[CrossRef]

De Waardt, H.

M. T. Hill, Y. S. 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. H. Kwon, Y. H. Lee, R. Notzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1, 589–594 (2007).
[CrossRef]

Ding, K.

K. Ding, Z. C. Liu, L. J. Yin, M. T. Hill, M. J. H. Marell, P. J. van Veldhoven, R. Nöetzel, and C. Z. Ning, “Room-temperature continuous wave lasing in deep-subwavelength metallic cavities under electrical injection,” Phys. Rev. B 85, 041301(R) (2012).
[CrossRef]

Eijkemans, T. J.

M. T. Hill, Y. S. 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. H. Kwon, Y. H. Lee, R. Notzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1, 589–594 (2007).
[CrossRef]

Fainman, Y.

M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics 4, 395–399 (2010).
[CrossRef]

Feng, L.

M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics 4, 395–399 (2010).
[CrossRef]

Geluk, E. J.

M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. C. Zhu, M. H. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y. S. Oei, R. Notzel, C. Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17, 11107–11112 (2009).
[CrossRef]

M. T. Hill, Y. S. 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. H. Kwon, Y. H. Lee, R. Notzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1, 589–594 (2007).
[CrossRef]

Guo, W. H.

Hentschel, M.

M. Hentschel and K. Richter, “Quantum chaos in optical systems: the annular billard,” Phys. Rev. E 66, 056207(2002).
[CrossRef]

Hill, M. T.

K. Ding, Z. C. Liu, L. J. Yin, M. T. Hill, M. J. H. Marell, P. J. van Veldhoven, R. Nöetzel, and C. Z. Ning, “Room-temperature continuous wave lasing in deep-subwavelength metallic cavities under electrical injection,” Phys. Rev. B 85, 041301(R) (2012).
[CrossRef]

M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. C. Zhu, M. H. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y. S. Oei, R. Notzel, C. Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17, 11107–11112 (2009).
[CrossRef]

M. T. Hill, Y. S. 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. H. Kwon, Y. H. Lee, R. Notzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1, 589–594 (2007).
[CrossRef]

Huang, J.

Huang, Y. Z.

Q. F. Yao, Y. Z. Huang, L. X. Zou, X. M. Lv, J. D. Lin, and Y. D. Yang, “Analysis of mode coupling and threshold gain control for nanocircular resonators confined by isolation and metallic layers,” IEEE J. Lightwave Technol. 31, 786–792 (2013).
[CrossRef]

X. S. Luo, Y. Z. Huang, W. H. Guo, Q. Chen, M. Q. Wang, and L. J. Yu, “Investigation of mode characteristics for microdisk resonators by S-matrix and three-dimensional finite-difference time-domain technique,” J. Opt. Soc. Am. B 23, 1068–1073 (2006).
[CrossRef]

Jacquod, Ph.

H. E. Tureci, H. G. L. Schwefel, Ph. Jacquod, and A. D. Stone, “Modes of wave-chaotic dielectric resonators,” Prog. Opt. 47, 75–137 (2005).
[CrossRef]

Kang, J. H.

S. H. Kwon, J. H. Kang, C. Seassal, S. K. Kim, P. Regreny, Y. H. Lee, C. M. Lieber, and H. G. Park, “Subwavelength plasmonic lasing from a semiconductor nanodisk with silver nanopan cavity,” Nano Lett. 10, 3679–3683 (2010).
[CrossRef]

Karouta, F.

Kim, S. H.

Kim, S. K.

S. H. Kwon, J. H. Kang, C. Seassal, S. K. Kim, P. Regreny, Y. H. Lee, C. M. Lieber, and H. G. Park, “Subwavelength plasmonic lasing from a semiconductor nanodisk with silver nanopan cavity,” Nano Lett. 10, 3679–3683 (2010).
[CrossRef]

Kwon, S. H.

S. H. Kwon, J. H. Kang, C. Seassal, S. K. Kim, P. Regreny, Y. H. Lee, C. M. Lieber, and H. G. Park, “Subwavelength plasmonic lasing from a semiconductor nanodisk with silver nanopan cavity,” Nano Lett. 10, 3679–3683 (2010).
[CrossRef]

M. T. Hill, Y. S. 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. H. Kwon, Y. H. Lee, R. Notzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1, 589–594 (2007).
[CrossRef]

Lee, Y. H.

S. H. Kwon, J. H. Kang, C. Seassal, S. K. Kim, P. Regreny, Y. H. Lee, C. M. Lieber, and H. G. Park, “Subwavelength plasmonic lasing from a semiconductor nanodisk with silver nanopan cavity,” Nano Lett. 10, 3679–3683 (2010).
[CrossRef]

M. T. Hill, Y. S. 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. H. Kwon, Y. H. Lee, R. Notzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1, 589–594 (2007).
[CrossRef]

Leong, E. S. P.

Li, B. J.

B. J. Li and P. L. Liu, “Numerical analysis of the whispering gallery modes by the finite-difference time-domain method,” IEEE J. Quantum Electron 32, 1583–1587 (1996).
[CrossRef]

Lieber, C. M.

S. H. Kwon, J. H. Kang, C. Seassal, S. K. Kim, P. Regreny, Y. H. Lee, C. M. Lieber, and H. G. Park, “Subwavelength plasmonic lasing from a semiconductor nanodisk with silver nanopan cavity,” Nano Lett. 10, 3679–3683 (2010).
[CrossRef]

Lin, J. D.

Q. F. Yao, Y. Z. Huang, L. X. Zou, X. M. Lv, J. D. Lin, and Y. D. Yang, “Analysis of mode coupling and threshold gain control for nanocircular resonators confined by isolation and metallic layers,” IEEE J. Lightwave Technol. 31, 786–792 (2013).
[CrossRef]

Liu, P. L.

B. J. Li and P. L. Liu, “Numerical analysis of the whispering gallery modes by the finite-difference time-domain method,” IEEE J. Quantum Electron 32, 1583–1587 (1996).
[CrossRef]

Liu, Z. C.

K. Ding, Z. C. Liu, L. J. Yin, M. T. Hill, M. J. H. Marell, P. J. van Veldhoven, R. Nöetzel, and C. Z. Ning, “Room-temperature continuous wave lasing in deep-subwavelength metallic cavities under electrical injection,” Phys. Rev. B 85, 041301(R) (2012).
[CrossRef]

Lomakin, V.

M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics 4, 395–399 (2010).
[CrossRef]

Lu, C. Y.

Luo, X. S.

Lv, X. M.

Q. F. Yao, Y. Z. Huang, L. X. Zou, X. M. Lv, J. D. Lin, and Y. D. Yang, “Analysis of mode coupling and threshold gain control for nanocircular resonators confined by isolation and metallic layers,” IEEE J. Lightwave Technol. 31, 786–792 (2013).
[CrossRef]

Ma, R. M.

R. M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nat. Mater. 10, 110–113 (2010).
[CrossRef]

Marcuse, D.

D. Marcuse, Light Transmission Optics, 2nd ed. (Van Nostrand Reinhold, 1982).

Marell, M.

Marell, M. J. H.

K. Ding, Z. C. Liu, L. J. Yin, M. T. Hill, M. J. H. Marell, P. J. van Veldhoven, R. Nöetzel, and C. Z. Ning, “Room-temperature continuous wave lasing in deep-subwavelength metallic cavities under electrical injection,” Phys. Rev. B 85, 041301(R) (2012).
[CrossRef]

Mizrahi, A.

M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics 4, 395–399 (2010).
[CrossRef]

Nezhad, M. P.

M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics 4, 395–399 (2010).
[CrossRef]

Ning, C. Z.

K. Ding, Z. C. Liu, L. J. Yin, M. T. Hill, M. J. H. Marell, P. J. van Veldhoven, R. Nöetzel, and C. Z. Ning, “Room-temperature continuous wave lasing in deep-subwavelength metallic cavities under electrical injection,” Phys. Rev. B 85, 041301(R) (2012).
[CrossRef]

M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. C. Zhu, M. H. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y. S. Oei, R. Notzel, C. Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17, 11107–11112 (2009).
[CrossRef]

Nöetzel, R.

K. Ding, Z. C. Liu, L. J. Yin, M. T. Hill, M. J. H. Marell, P. J. van Veldhoven, R. Nöetzel, and C. Z. Ning, “Room-temperature continuous wave lasing in deep-subwavelength metallic cavities under electrical injection,” Phys. Rev. B 85, 041301(R) (2012).
[CrossRef]

Notzel, R.

M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. C. Zhu, M. H. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y. S. Oei, R. Notzel, C. Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17, 11107–11112 (2009).
[CrossRef]

M. T. Hill, Y. S. 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. H. Kwon, Y. H. Lee, R. Notzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1, 589–594 (2007).
[CrossRef]

Oei, Y. S.

M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. C. Zhu, M. H. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y. S. Oei, R. Notzel, C. Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17, 11107–11112 (2009).
[CrossRef]

M. T. Hill, Y. S. 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. H. Kwon, Y. H. Lee, R. Notzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1, 589–594 (2007).
[CrossRef]

Oulton, R. F.

R. M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nat. Mater. 10, 110–113 (2010).
[CrossRef]

Park, H. G.

S. H. Kwon, J. H. Kang, C. Seassal, S. K. Kim, P. Regreny, Y. H. Lee, C. M. Lieber, and H. G. Park, “Subwavelength plasmonic lasing from a semiconductor nanodisk with silver nanopan cavity,” Nano Lett. 10, 3679–3683 (2010).
[CrossRef]

Rahachou, A. I.

Regreny, P.

S. H. Kwon, J. H. Kang, C. Seassal, S. K. Kim, P. Regreny, Y. H. Lee, C. M. Lieber, and H. G. Park, “Subwavelength plasmonic lasing from a semiconductor nanodisk with silver nanopan cavity,” Nano Lett. 10, 3679–3683 (2010).
[CrossRef]

Richter, K.

M. Hentschel and K. Richter, “Quantum chaos in optical systems: the annular billard,” Phys. Rev. E 66, 056207(2002).
[CrossRef]

Scherer, A.

Schwefel, H. G. L.

H. E. Tureci, H. G. L. Schwefel, Ph. Jacquod, and A. D. Stone, “Modes of wave-chaotic dielectric resonators,” Prog. Opt. 47, 75–137 (2005).
[CrossRef]

Seassal, C.

S. H. Kwon, J. H. Kang, C. Seassal, S. K. Kim, P. Regreny, Y. H. Lee, C. M. Lieber, and H. G. Park, “Subwavelength plasmonic lasing from a semiconductor nanodisk with silver nanopan cavity,” Nano Lett. 10, 3679–3683 (2010).
[CrossRef]

Simic, A.

M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics 4, 395–399 (2010).
[CrossRef]

Slutsky, B.

M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics 4, 395–399 (2010).
[CrossRef]

Smalbrugge, B.

M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. C. Zhu, M. H. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y. S. Oei, R. Notzel, C. Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17, 11107–11112 (2009).
[CrossRef]

M. T. Hill, Y. S. 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. H. Kwon, Y. H. Lee, R. Notzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1, 589–594 (2007).
[CrossRef]

Smit, M. K.

M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. C. Zhu, M. H. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y. S. Oei, R. Notzel, C. Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17, 11107–11112 (2009).
[CrossRef]

M. T. Hill, Y. S. 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. H. Kwon, Y. H. Lee, R. Notzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1, 589–594 (2007).
[CrossRef]

Sorger, V. J.

R. M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nat. Mater. 10, 110–113 (2010).
[CrossRef]

Stone, A. D.

H. E. Tureci, H. G. L. Schwefel, Ph. Jacquod, and A. D. Stone, “Modes of wave-chaotic dielectric resonators,” Prog. Opt. 47, 75–137 (2005).
[CrossRef]

Sun, M. H.

Tureci, H. E.

H. E. Tureci, H. G. L. Schwefel, Ph. Jacquod, and A. D. Stone, “Modes of wave-chaotic dielectric resonators,” Prog. Opt. 47, 75–137 (2005).
[CrossRef]

Turkiewicz, J. P.

M. T. Hill, Y. S. 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. H. Kwon, Y. H. Lee, R. Notzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1, 589–594 (2007).
[CrossRef]

Van Otten, F. W. M.

M. T. Hill, Y. S. 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. H. Kwon, Y. H. Lee, R. Notzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1, 589–594 (2007).
[CrossRef]

van Veldhoven, P. J.

K. Ding, Z. C. Liu, L. J. Yin, M. T. Hill, M. J. H. Marell, P. J. van Veldhoven, R. Nöetzel, and C. Z. Ning, “Room-temperature continuous wave lasing in deep-subwavelength metallic cavities under electrical injection,” Phys. Rev. B 85, 041301(R) (2012).
[CrossRef]

M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. C. Zhu, M. H. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y. S. Oei, R. Notzel, C. Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17, 11107–11112 (2009).
[CrossRef]

M. T. Hill, Y. S. 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. H. Kwon, Y. H. Lee, R. Notzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1, 589–594 (2007).
[CrossRef]

Wang, M. Q.

Yang, Y. D.

Q. F. Yao, Y. Z. Huang, L. X. Zou, X. M. Lv, J. D. Lin, and Y. D. Yang, “Analysis of mode coupling and threshold gain control for nanocircular resonators confined by isolation and metallic layers,” IEEE J. Lightwave Technol. 31, 786–792 (2013).
[CrossRef]

Yao, Q. F.

Q. F. Yao, Y. Z. Huang, L. X. Zou, X. M. Lv, J. D. Lin, and Y. D. Yang, “Analysis of mode coupling and threshold gain control for nanocircular resonators confined by isolation and metallic layers,” IEEE J. Lightwave Technol. 31, 786–792 (2013).
[CrossRef]

Yin, L. J.

K. Ding, Z. C. Liu, L. J. Yin, M. T. Hill, M. J. H. Marell, P. J. van Veldhoven, R. Nöetzel, and C. Z. Ning, “Room-temperature continuous wave lasing in deep-subwavelength metallic cavities under electrical injection,” Phys. Rev. B 85, 041301(R) (2012).
[CrossRef]

Yu, L. J.

Zhang, X.

R. M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nat. Mater. 10, 110–113 (2010).
[CrossRef]

Zhu, Y.

M. T. Hill, Y. S. 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. H. Kwon, Y. H. Lee, R. Notzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1, 589–594 (2007).
[CrossRef]

Zhu, Y. C.

Zou, L. X.

Q. F. Yao, Y. Z. Huang, L. X. Zou, X. M. Lv, J. D. Lin, and Y. D. Yang, “Analysis of mode coupling and threshold gain control for nanocircular resonators confined by isolation and metallic layers,” IEEE J. Lightwave Technol. 31, 786–792 (2013).
[CrossRef]

Zozoulenko, I. V.

Appl. Opt. (1)

IEEE J. Lightwave Technol. (1)

Q. F. Yao, Y. Z. Huang, L. X. Zou, X. M. Lv, J. D. Lin, and Y. D. Yang, “Analysis of mode coupling and threshold gain control for nanocircular resonators confined by isolation and metallic layers,” IEEE J. Lightwave Technol. 31, 786–792 (2013).
[CrossRef]

IEEE J. Quantum Electron (1)

B. J. Li and P. L. Liu, “Numerical analysis of the whispering gallery modes by the finite-difference time-domain method,” IEEE J. Quantum Electron 32, 1583–1587 (1996).
[CrossRef]

IEEE Photon. J. (1)

S. L. Chuang and D. Bimberg, “Metal-cavity nanolasers,” IEEE Photon. J. 3, 288–292 (2011).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nano Lett. (1)

S. H. Kwon, J. H. Kang, C. Seassal, S. K. Kim, P. Regreny, Y. H. Lee, C. M. Lieber, and H. G. Park, “Subwavelength plasmonic lasing from a semiconductor nanodisk with silver nanopan cavity,” Nano Lett. 10, 3679–3683 (2010).
[CrossRef]

Nat. Mater. (1)

R. M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nat. Mater. 10, 110–113 (2010).
[CrossRef]

Nat. Photonics (2)

M. T. Hill, Y. S. 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. H. Kwon, Y. H. Lee, R. Notzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1, 589–594 (2007).
[CrossRef]

M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics 4, 395–399 (2010).
[CrossRef]

Opt. Express (3)

Phys. Rev. B (1)

K. Ding, Z. C. Liu, L. J. Yin, M. T. Hill, M. J. H. Marell, P. J. van Veldhoven, R. Nöetzel, and C. Z. Ning, “Room-temperature continuous wave lasing in deep-subwavelength metallic cavities under electrical injection,” Phys. Rev. B 85, 041301(R) (2012).
[CrossRef]

Phys. Rev. E (1)

M. Hentschel and K. Richter, “Quantum chaos in optical systems: the annular billard,” Phys. Rev. E 66, 056207(2002).
[CrossRef]

Prog. Opt. (1)

H. E. Tureci, H. G. L. Schwefel, Ph. Jacquod, and A. D. Stone, “Modes of wave-chaotic dielectric resonators,” Prog. Opt. 47, 75–137 (2005).
[CrossRef]

Other (1)

D. Marcuse, Light Transmission Optics, 2nd ed. (Van Nostrand Reinhold, 1982).

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Figures (10)

Fig. 1.
Fig. 1.

(a) 3D schematic diagram and (b) cross section of the metal-coated nanocircular with vertical waveguide consisting of an active region sandwiched by cladding layers. The origin of the coordinate system is located at the center of the active region.

Fig. 2.
Fig. 2.

Spectra of det(S) and Wigner delay time τ for the dielectric nanocavity with R1=800nm without the metallic confinement layer.

Fig. 3.
Fig. 3.

Mode field distribution of (a) Ez(r) at z=0, (b) Ez(z) at r=700nm, and (c) Hz(z) in the z direction at r=700nm obtained by the S-matrix and FDTD methods for the mode at wavelength of 1638 nm in the nanocavity with R1=800nm without the metal confinement layer.

Fig. 4.
Fig. 4.

Spectra of det(S) and det(S1) for the metal-coated nanocavity with R1=800nm and t=5nm.

Fig. 5.
Fig. 5.

Mode wavelength and quality factor of HE7,1 mode versus the metallic layer thickness in the nanocavity with R1=800nm.

Fig. 6.
Fig. 6.

Electric field Ez distributions in the rφ plane at z=0 (upper) and in the rz plane (lower) of HE7,1 mode in the nanocavity with R1=800nm and the metallic layer thickness of (a) 0, (b) 6 nm, and (c) 50 nm.

Fig. 7.
Fig. 7.

Mode wavelength and quality factor of EH7,1 mode versus the metallic thickness in the nanocavity with R1=800nm.

Fig. 8.
Fig. 8.

Magnetic field Hz distributions in the rφ plane at z=0 (upper) and in the rz plane (lower) of EH7,1 mode in the nanocavity with R1=800nm and the metallic layer thickness of (a) 0, (b) 10 nm, and (c) 50 nm.

Fig. 9.
Fig. 9.

Mode wavelength and Q factor of HE3,1 mode versus the thickness of metallic layer in a nanocavity with R1=500nm.

Fig. 10.
Fig. 10.

Electric field Ez distributions in the rφ plane at z=0 (upper) and in the rz plane (lower) of HE3,1 mode in the nanocavity with R1=500nm and the metallic layer thickness of (a) 0, (b) 20 nm, and (c) 50 nm.

Equations (41)

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Ez=Ag(z)Jv(κr)Jv(κR1)rR1,
Hz=Bf(z)Jv(γr)Jv(γR1)rR1,
|m=exp(ipmz)L,pm=2mπL,
|g(z)=m=+gm|m,|f(z)=m=+fm|m.
Ez=m=Ezm|m,Hz=m=Hzm|m.
Ezm={AgmJv(κr)Jv(κR1)0rR1CmimIv(qmmr)Iv(qmmR1)+CmomKv(qmmr)Kv(qmmR1)R1rR2CmioHv1(qmor)Hv1(qmoR2)+CmooHv2(qmor)Hv2(qmoR2)R2r,
Hzm={BfmJv(γr)Jv(γR1)0rR1DmimIv(qmmr)Iv(qmmR1)+DmomKv(qmmr)Kv(qmmR1)R1rR2DmioHv1(qmor)Hv1(qmoR2)+DmooHv2(qmor)Hv2(qmoR2)R2r,
qmm=inm2k2pm2,qmo=no2k2pm2.
Hφm=Aik0Jv(κr)κJv(κR1)sm+Bv(ipmfm)Jv(γr)γ2rJv(γR1)0rR1,
Hφm=ik0nm2qmm[CmimIv(qmmr)Iv(qmmR1)+CmomKv(qmmr)Kv(qmmR1)]+ipmvr(qmm)2[DmimIv(qmmr)Iv(qmmR1)+DmomKv(qmmr)Kv(qmmR1)]R1rR2,
Hφm=ik0no2qmo[CmioHv1(qmor)Hv1(qmoR2)+CmooHv2(qmor)Hv2(qmoR2)]ipmvr(qmo)2[DmioHv1(qmor)Hv1(qmoR2)+DmooHv2(qmor)Hv2(qmoR2)]rR2,
Eφm=Bik0Jv(γr)κJv(γR1)fm+Av(ipmfm)Jv(κr)κ2rJv(κR1)0rR1,
Eφm=ik0qmm[DmimIv(qmmr)Iv(qmmR1)+DmomKv(qmmr)Kv(qmmR1)]+ipmvr(qmm)2[CmimIv(qmmr)Iv(qmmR1)+CmomKv(qmmr)Kv(qmmR1)]R1rR2,
Eφm=ik0qmo[DmioHv1(qmor)Hv1(qmoR2)+DmooHv2(qmor)Hv2(qmoR2)]ipmvr(qmo)2[CmioHv1(qmor)Hv1(qmoR2)+CmooHv2(qmor)Hv2(qmoR2)]rR2,
sm=n=MMm|n2(z)|ngn,
CmimIv(qmmR1)Iv(qmmR2)+CmomKv(qmmR1)Kv(qmmR2)=Cmio+Cmoo,
CmimIv(qmmR1)Iv(qmmR2)=a1mCmio+b1mCmoo+c1m(Dmio+Dmoo),
CmomKv(qmmR1)Kv(qmmR2)=(1a1m)Cmio+(1b1m)Cmooc1m(Dmio+Dmoo),
a1m=sse1[k0no2qmoHv1(qmoR2)Hv1(qmoR2)+k0nm2qmmKv(qmmR2)Kv(qmmR2)],
b1m=sse1[k0no2qmoHv2(qmoR2)Hv2(qmoR2)+k0nm2qmmKv(qmmR2)Kv(qmmR2)],
c1m=sse1pmvR2[1(qmo)2+1(qmm)2],
sse=k0nm2qmm[Iv(qmmR2)Iv(qmmR2)Kv(qmmR2)Kv(qmmR2)].
DmimIv(qmmR1)Iv(qmmR2)+DmomKv(qmmR1)Kv(qmmR2)=Dmio+Dmoo,
DmimIv(qmmR1)Iv(qmmR2)=a2mDmio+b2mDmoo+c2m(Cmio+Cmoo),
DmomKv(qmmR1)Kv(qmmR2)=(1a2m)Dmio+(1b2m)Dmooc2m(Cmio+Cmoo),
a2m=ssh1[k0qmoHv1(qmoR2)Hv1(qmoR2)+k0qmmKv(qmmR2)Kv(qmmR2)],
b2m=ssh1[k0qmoHv2(qmoR2)Hv2(qmoR2)+k0qmmKv(qmmR2)Kv(qmmR2)],
c2m=ssh1pmvR2[1(qmo)2+1(qmm)2],
ssh=k0qmm[Iv(qmmR2)Iv(qmmR2)Kv(qmmR2)Kv(qmmR2)].
Agm=Cmim+Cmom,
Bfm=Dmim+Dmom,
ik0Jv(κr)κJv(κR1)smgmT(Cmim+Cmom)+v(ipmfm)γ2R1fmT(Dmim+Dmom)=diag(ik0nm2qmmCmimIv(qmmR1)Iv(qmmR1))+diag(ik0nm2qmmCmomKv(qmmR1)Kv(qmmR1))+diag(ipmvR1(qmm)2(Dmim+Dmom))
v(ipmgm)κ2R1gmT(Cmim+Cmom)+ik0Jv(γr)γJv(γR1)fmfmT(Dmim+Dmom)=diag(ipmvR1(qmm)2(Cmim+Cmom))+diag(ik0qmmDmimIv(qmmR1)Iv(qmmR1))+diag(ik0qmmDmomKv(qmmR1)Kv(qmmR1))
[L11L12L21L22][CmooDmoo]=[R11R12R21R22][CmioDmio],
[CmooDmoo]=[O11O12O21O22][CmioDmio].
det(S)=exp(iθ).
det(S)=det(S1)+d0,
det(S1)=c0exp(iθ),
τ(k)=2πdθdk.
λ=2πkcentre,Q=kcentreΔk.
[L11L12L21L22][CmooDmoo]=0.

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