Abstract

This paper proposes a layered metal-dielectric waveguide consisting of a stack of alternating metal and dielectric films which enables an ultracompact mode confinement. The properties of whispering gallery modes supported by disk resonators based on such waveguides are investigated for achieving a large Purcell factor. We show that by stacking three layers of 10 nm thick silver with two layers of 50 nm dielectric layers (of refractive index n) in sequence, the disk radius can be as small as 61 nm λ0/(7n) and the mode volume is only 0.0175(λ0/(2n))3. When operating at 40 K, the cavity’s Q-factor can be ~670; Purcell factor can be as large as 2.3×104, which is more than five times larger than that achievable in a metal-dielectric-metal disk cavity in the same condition. When more dielectric layers with smaller thicknesses are used, even more compact confinement can be achieved. For example, the radius of a cavity consisting of seven dielectric-layer waveguide can be shrunk down to λ0/(13.5n), corresponding to a mode volume of 0.005λ0/(2n))3, and Purcell factor can be enhanced to 7.3×104 at 40 K. The influence of parameters like thicknesses of dielectric and metal films, cavity size, and number of dielectric layers is also comprehensively studied. The proposed waveguide and nanodisk cavity provide an alternative for ultracompact light confinement, and can find applications where a strong light-matter interaction is necessary.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
  4. H. Y. Ryu, M. Notomi, Y. H. Lee, “High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities,” Appl. Phys. Lett. 83(21), 4294–4296 (2003).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  18. H. T. Miyazaki, Y. Kurokawa, “Squeezing Visible Light Waves into a 3-nm-Thick and 55-nm-Long Plasmon Cavity,” Phys. Rev. Lett. 96(9), 097401 (2006).
    [CrossRef] [PubMed]
  19. R. Zia, M. D. Selker, P. B. Catrysse, M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. A 21(12), 2442–2446 (2004).
    [CrossRef] [PubMed]
  20. J. A. Dionne, L. A. Sweatlock, H. A. Atwater, A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
    [CrossRef]
  21. S.-H. Kwon, “Deep subwavelength plasmonic whispering gallery-mode cavity,” Opt. Express 20, 918–924 (2012).
  22. M. Yan, L. Thylén, M. Qiu, “Layered metal-dielectric waveguide: subwavelength guidance, leveraged modulation sensitivity in mode index, and reversed mode ordering,” Opt. Express 19(4), 3818–3824 (2011).
    [CrossRef] [PubMed]
  23. Y. He, S. He, J. Gao, X. Yang, “Nanoscale metamaterial optical waveguides with ultrahigh refractive indices,” J. Opt. Soc. Am. B 29(9), 2559–2566 (2012).
    [CrossRef]
  24. Y. He, L. Sun, S. He, X. Yang, “Deep subwavelength beam propagation in extremely loss-anisotropic metamaterials,” J. Opt. 15(5), 055105 (2013).
    [CrossRef]
  25. X. Yang, J. Yao, J. Rho, X. Yin, X. Zhang, “Experimental realization of three-dimensional indefinite cavities at the nanoscale with anomalous scaling laws,” Nat. Photonics 6(7), 450–454 (2012).
    [CrossRef]
  26. H. N. S. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, V. M. Menon, “Topological Transitions in Metamaterials,” Science 336(6078), 205–209 (2012).
    [CrossRef] [PubMed]
  27. P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
    [CrossRef]
  28. Y. Francescato, V. Giannini, S. A. Maier, “Strongly confined gap plasmon modes in graphene sandwiches and graphene-on-silicon,” New J. Phys. 15(6), 063020 (2013).
    [CrossRef]
  29. Q. Wang, H. Zhao, X. Du, W. Zhang, M. Qiu, Q. Li, “Hybrid photonic-plasmonic molecule based on metal/Si disks,” Opt. Express 21(9), 11037–11047 (2013).
    [CrossRef] [PubMed]
  30. W. Chen, M. D. Thoreson, S. Ishii, A. V. Kildishev, V. M. Shalaev, “Ultra-thin ultra-smooth and low-loss silver films on a germanium wetting layer,” Opt. Express 18(5), 5124–5134 (2010).
    [CrossRef] [PubMed]
  31. D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, J. Vucković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95(1), 013904 (2005).
    [CrossRef] [PubMed]
  32. J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
    [CrossRef] [PubMed]

2013

Y. He, L. Sun, S. He, X. Yang, “Deep subwavelength beam propagation in extremely loss-anisotropic metamaterials,” J. Opt. 15(5), 055105 (2013).
[CrossRef]

Y. Francescato, V. Giannini, S. A. Maier, “Strongly confined gap plasmon modes in graphene sandwiches and graphene-on-silicon,” New J. Phys. 15(6), 063020 (2013).
[CrossRef]

Q. Wang, H. Zhao, X. Du, W. Zhang, M. Qiu, Q. Li, “Hybrid photonic-plasmonic molecule based on metal/Si disks,” Opt. Express 21(9), 11037–11047 (2013).
[CrossRef] [PubMed]

F. Lou, D. Dai, L. Thylen, L. Wosinski, “Design and analysis of ultra-compact EO polymer modulators based on hybrid plasmonic microring resonators,” Opt. Express 21(17), 20041–20051 (2013).
[CrossRef] [PubMed]

2012

S.-H. Kwon, “Deep subwavelength plasmonic whispering gallery-mode cavity,” Opt. Express 20, 918–924 (2012).

Y. He, S. He, J. Gao, X. Yang, “Nanoscale metamaterial optical waveguides with ultrahigh refractive indices,” J. Opt. Soc. Am. B 29(9), 2559–2566 (2012).
[CrossRef]

X. Yang, J. Yao, J. Rho, X. Yin, X. Zhang, “Experimental realization of three-dimensional indefinite cavities at the nanoscale with anomalous scaling laws,” Nat. Photonics 6(7), 450–454 (2012).
[CrossRef]

H. N. S. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, V. M. Menon, “Topological Transitions in Metamaterials,” Science 336(6078), 205–209 (2012).
[CrossRef] [PubMed]

M. Khajavikhan, A. Simic, M. Katz, J. H. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482(7384), 204–207 (2012).
[CrossRef] [PubMed]

2011

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nat. Mater. 10(2), 110–113 (2011).
[CrossRef] [PubMed]

Y. Song, J. Wang, M. Yan, M. Qiu, “Subwavelength hybrid plasmonic nanodisk with high Q factor and Purcell factor,” J. Opt. 13(7), 075001 (2011).
[CrossRef]

M. Yan, L. Thylén, M. Qiu, “Layered metal-dielectric waveguide: subwavelength guidance, leveraged modulation sensitivity in mode index, and reversed mode ordering,” Opt. Express 19(4), 3818–3824 (2011).
[CrossRef] [PubMed]

A. V. Krasavin, S. Randhawa, J.-S. Bouillard, J. Renger, R. Quidant, A. V. Zayats, “Optically-programmable nonlinear photonic component for dielectric-loaded plasmonic circuitry,” Opt. Express 19(25), 25222–25229 (2011).
[CrossRef] [PubMed]

2010

W. Chen, M. D. Thoreson, S. Ishii, A. V. Kildishev, V. M. Shalaev, “Ultra-thin ultra-smooth and low-loss silver films on a germanium wetting layer,” Opt. Express 18(5), 5124–5134 (2010).
[CrossRef] [PubMed]

R. M. Briggs, J. Grandidier, S. P. Burgos, E. Feigenbaum, H. A. Atwater, “Efficient coupling between dielectric-loaded plasmonic and silicon photonic waveguides,” Nano Lett. 10(12), 4851–4857 (2010).
[CrossRef] [PubMed]

D. K. Gramotnev, S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[CrossRef]

S.-H. Kwon, J.-H. Kang, C. Seassal, S.-K. Kim, P. Regreny, Y.-H. Lee, C. M. Lieber, H.-G. Park, “Subwavelength plasmonic lasing from a semiconductor nanodisk with silver nanopan cavity,” Nano Lett. 10(9), 3679–3683 (2010).
[CrossRef] [PubMed]

M. Kuttge, F. J. García de Abajo, A. Polman, “Ultrasmall mode volume plasmonic nanodisk resonators,” Nano Lett. 10(5), 1537–1541 (2010).
[CrossRef] [PubMed]

2009

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature 457(7228), 455–458 (2009).
[CrossRef] [PubMed]

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

2008

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

2007

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, M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

2006

H. T. Miyazaki, Y. Kurokawa, “Squeezing Visible Light Waves into a 3-nm-Thick and 55-nm-Long Plasmon Cavity,” Phys. Rev. Lett. 96(9), 097401 (2006).
[CrossRef] [PubMed]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[CrossRef]

K. Srinivasan, M. Borselli, O. Painter, A. Stintz, S. Krishna, “Cavity Q, mode volume, and lasing threshold in small diameter AlGaAs microdisks with embedded quantum dots,” Opt. Express 14(3), 1094–1105 (2006).
[CrossRef] [PubMed]

2005

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, J. Vucković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95(1), 013904 (2005).
[CrossRef] [PubMed]

2004

T. J. Kippenberg, S. M. Spillane, K. J. Vahala, “Demonstration of ultra-high-Q small mode volume toroid microcavities on a chip,” Appl. Phys. Lett. 85(25), 6113–6115 (2004).
[CrossRef]

R. Zia, M. D. Selker, P. B. Catrysse, M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. A 21(12), 2442–2446 (2004).
[CrossRef] [PubMed]

2003

H. Y. Ryu, M. Notomi, Y. H. Lee, “High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities,” Appl. Phys. Lett. 83(21), 4294–4296 (2003).
[CrossRef]

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

1972

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

Arakawa, Y.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, J. Vucković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95(1), 013904 (2005).
[CrossRef] [PubMed]

Atwater, H. A.

R. M. Briggs, J. Grandidier, S. P. Burgos, E. Feigenbaum, H. A. Atwater, “Efficient coupling between dielectric-loaded plasmonic and silicon photonic waveguides,” Nano Lett. 10(12), 4851–4857 (2010).
[CrossRef] [PubMed]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[CrossRef]

Bartal, G.

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nat. Mater. 10(2), 110–113 (2011).
[CrossRef] [PubMed]

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Borselli, M.

Bouillard, J.-S.

Bozhevolnyi, S. I.

D. K. Gramotnev, S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[CrossRef]

Briggs, R. M.

R. M. Briggs, J. Grandidier, S. P. Burgos, E. Feigenbaum, H. A. Atwater, “Efficient coupling between dielectric-loaded plasmonic and silicon photonic waveguides,” Nano Lett. 10(12), 4851–4857 (2010).
[CrossRef] [PubMed]

Brongersma, M. L.

Burgos, S. P.

R. M. Briggs, J. Grandidier, S. P. Burgos, E. Feigenbaum, H. A. Atwater, “Efficient coupling between dielectric-loaded plasmonic and silicon photonic waveguides,” Nano Lett. 10(12), 4851–4857 (2010).
[CrossRef] [PubMed]

Catrysse, P. B.

Chen, W.

Christy, R. W.

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

Dai, D.

Dai, L.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

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, M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 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, M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

Dionne, J. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[CrossRef]

Du, X.

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, M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

Englund, D.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, J. Vucković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95(1), 013904 (2005).
[CrossRef] [PubMed]

Fainman, Y.

M. Khajavikhan, A. Simic, M. Katz, J. H. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482(7384), 204–207 (2012).
[CrossRef] [PubMed]

Fattal, D.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, J. Vucković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95(1), 013904 (2005).
[CrossRef] [PubMed]

Feigenbaum, E.

R. M. Briggs, J. Grandidier, S. P. Burgos, E. Feigenbaum, H. A. Atwater, “Efficient coupling between dielectric-loaded plasmonic and silicon photonic waveguides,” Nano Lett. 10(12), 4851–4857 (2010).
[CrossRef] [PubMed]

Francescato, Y.

Y. Francescato, V. Giannini, S. A. Maier, “Strongly confined gap plasmon modes in graphene sandwiches and graphene-on-silicon,” New J. Phys. 15(6), 063020 (2013).
[CrossRef]

Gao, J.

García de Abajo, F. J.

M. Kuttge, F. J. García de Abajo, A. Polman, “Ultrasmall mode volume plasmonic nanodisk resonators,” Nano Lett. 10(5), 1537–1541 (2010).
[CrossRef] [PubMed]

Geluk, E. 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, M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

Genov, D. A.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Giannini, V.

Y. Francescato, V. Giannini, S. A. Maier, “Strongly confined gap plasmon modes in graphene sandwiches and graphene-on-silicon,” New J. Phys. 15(6), 063020 (2013).
[CrossRef]

Gladden, C.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

Gramotnev, D. K.

D. K. Gramotnev, S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[CrossRef]

Grandidier, J.

R. M. Briggs, J. Grandidier, S. P. Burgos, E. Feigenbaum, H. A. Atwater, “Efficient coupling between dielectric-loaded plasmonic and silicon photonic waveguides,” Nano Lett. 10(12), 4851–4857 (2010).
[CrossRef] [PubMed]

He, S.

Y. He, L. Sun, S. He, X. Yang, “Deep subwavelength beam propagation in extremely loss-anisotropic metamaterials,” J. Opt. 15(5), 055105 (2013).
[CrossRef]

Y. He, S. He, J. Gao, X. Yang, “Nanoscale metamaterial optical waveguides with ultrahigh refractive indices,” J. Opt. Soc. Am. B 29(9), 2559–2566 (2012).
[CrossRef]

He, Y.

Y. He, L. Sun, S. He, X. Yang, “Deep subwavelength beam propagation in extremely loss-anisotropic metamaterials,” J. Opt. 15(5), 055105 (2013).
[CrossRef]

Y. He, S. He, J. Gao, X. Yang, “Nanoscale metamaterial optical waveguides with ultrahigh refractive indices,” J. Opt. Soc. Am. B 29(9), 2559–2566 (2012).
[CrossRef]

Hill, M. 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, M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

Ishii, S.

Jacob, Z.

H. N. S. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, V. M. Menon, “Topological Transitions in Metamaterials,” Science 336(6078), 205–209 (2012).
[CrossRef] [PubMed]

Johnson, P. B.

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

Kang, J.-H.

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Figures (7)

Fig. 1
Fig. 1

(a) Schematic diagram of a 1D LMD2 waveguide. The propagation direction is along x + . (b) Field distributions of the even (TM1) mode supported in the 1D LMD2 waveguide. (c) Field distributions of the odd (TM2) mode supported in the 1D LMD2 waveguide.

Fig. 2
Fig. 2

Influence of metal and dielectric thicknesses on the effective refractive indices and propagation lengths of the concerned modes. Standard parameters are h M =10 nm and h 2 =50 nm . (a) and (b) are variation of effective indices and propagation lengths when changing h M , respectively. (c) and (d) are variation of effective indices and propagation lengths when changing h 2 , respectively.

Fig. 3
Fig. 3

(a) 3-D schematic diagram of a whispering gallery mode cavity based on the LMD2 waveguide. (b) and (c) are the Ez field distributions of TM1 resonant mode with an azimuthal number m = 3 along ϕr and zr planes, and R = 203 nm. (d) and (e) are the Ez field distributions of TM2 resonant mode with m = 3 along ϕr and zr planes, and R = 142 nm.

Fig. 4
Fig. 4

(a) Ez field distributions of the whispering gallery modes of MDM, TM1 and TM2 LMD2 nanodisks along zr cross-sectional half plane (r + ). Here, the azimuthal number is m = 2. (b) Q and V of MDM disk as functions of m. (c) Q and V of TM1 and TM2 LMD2 disks as functions of m. (d) Purcell factors F as functions of m.

Fig. 5
Fig. 5

(a) 2D colormap of the resonant wavelength as a function of silver height hM and the disk radius. The unit of colorbar is nm. Black markers represent resonant conditions around 1550 nm. (b) Effective index of the whispering gallery mode as a function of hM. (c) Q-factors and normalized mode volume as functions of hM; here, Q, Qrad and Qabs are the cavity’s intrinsic Q, radiation-related and absorption related Q-factors, respectively. (d) Purcell factor as a function of hM.

Fig. 6
Fig. 6

(a) 2D colormap of the resonant wavelength as a function of dielectric height h2 and disk radius. The unit of colorbar is nm. Black markers represent resonant conditions around 1550 nm. (b) Effective index of the WGM and radiation-related Q-factor Qabs as functions of h2. (c) Cavity Q-factor Q, absorption related Qabs and normalized mode volume V as functions of h2. (d) Purcell factor as a function of h2.

Fig. 7
Fig. 7

(a) Ez field distributions of WGM disks based on LMD waveguide with N = 3, 4… 7. (b) Selected radius and the corresponding effective mode index as functions of N. (c) Q-factors and normalized mode volume as functions of N. (d) Purcell factor as a function of N.

Tables (1)

Tables Icon

Table 1 Selected Radii for mth Azimuthal Order Resonance within 1550 ± 20 nm (Unit: nm)

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