Abstract

Ultracompact Cu-capped Si hybrid plasmonic waveguide-ring resonators (WRRs) with ring radii of 1.09–2.59 μm are fabricated on silicon on insulator substrates using standard complementary metal-oxide-semiconductor technology and characterized over the telecom wavelength range of 1.52–1.62 μm. The dependence of the spectral characteristics on the key structural parameters such as the Si core width, the ring radius, the separation gap between the ring and bus waveguides, and the ring configuration is systematically studied. A WRR with 2.59-μm radius and 0.250-μm nominal gap exhibits good performances such as normalized insertion loss of ~0.1 dB, extinction ratio of ~12.8 dB, free spectral range of ~47 nm, and quality factor of ~275. The resonance wavelength is redshifted by ~4.6 nm and an extinction ratio of ~7.5 dB is achieved with temperature increasing from 27 to 82°C. The corresponding effective thermo-optical coefficient (dng/dT) is estimated to be ~1.6 × 10−4 K−1, which is contributed by the thermo-optical effect of both the Si core and the Cu cap, as revealed by numerical simulations. Combined with the compact size and the high thermal conductivity of Cu, various effective thermo-optical devices based on these Cu-capped plasmonic WRRs could be realized for seamless integration in existing Si electronic-photonic integrated circuits.

© 2012 OSA

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    [CrossRef] [PubMed]
  3. S. Y. Zhu, T. Y. Liow, G. Q. Lo, and D. L. Kwong, “Fully complementary metal-oxide-semiconductor compatible nanoplasmonic slot waveguides for silicon electronic photonic integrated circuits,” Appl. Phys. Lett.98(2), 021107 (2011).
    [CrossRef]
  4. T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguide,” Phys. Rev. B75(24), 245405 (2007).
    [CrossRef]
  5. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008).
    [CrossRef]
  6. R. Salvador, A. Martinez, C. Garcia-Meca, R. Ortuno, and J. Marti, “Analysis of hybrid dielectric plasmonic waveguides,” IEEE J. Sel. Top.Quant. Electron.14, 1496–1501 (2008).
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  10. M. Wu, Z. Han, and V. Van, “Conductor-gap-silicon plasmonic waveguides and passive components as subwavelength scale,” Opt. Express18(11), 11728–11736 (2010).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  17. H. Hassan, J.-C. Weeber, L. Markey, and A. Dereux, “Thermo-optical control of dielectric loaded plasmonic racetrack resonators,” J. Appl. Phys.110(2), 023106 (2011).
    [CrossRef]
  18. B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature457(7228), 455–458 (2009).
    [CrossRef] [PubMed]
  19. S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Experimental demonstration of horizontal nanoplasmonic slot waveguide-ring resonators with submicron radius,” IEEE Photon. Technol. Lett.23(24), 1896–1898 (2011).
    [CrossRef]
  20. S. Y. Zhu, Q. Fang, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Propagation losses in undoped and n-doped polycrystalline silicon wire waveguides,” Opt. Express17(23), 20891–20899 (2009).
    [CrossRef] [PubMed]
  21. S. Roberts, “Optical properties of copper,” Phys. Rev.118(6), 1509–1518 (1960).
    [CrossRef]
  22. A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett.36(4), 321–322 (2000).
    [CrossRef]
  23. S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Theoretical investigation of silicon MOS-type plasmonic slot waveguide based MZI modulators,” Opt. Express18(26), 27802–27819 (2010).
    [CrossRef] [PubMed]
  24. S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Components for silicon plasmonic nanocircuits based on horizontal Cu-SiO2-Si-SiO2-Cu nanoplasmonic waveguides,” Opt. Express20(6), 5867–5881 (2012).
    [CrossRef] [PubMed]
  25. S. Y. Seo, J. Lee, J. H. Shin, E. S. Kang, and B. S. Bae, “The thermo-optic effect of Si nanocrystals in silicon-rich silicon oxide thin films,” Appl. Phys. Lett.85(13), 2526–2528 (2004).
    [CrossRef]

2012

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev.6(1), 47–73 (2012).
[CrossRef]

S. Randhawa, S. Lachèze, J. Renger, A. Bouhelier, R. E. de Lamaestre, A. Dereux, and R. Quidant, “Performance of electro-optical plasmonic ring resonators at telecom wavelengths,” Opt. Express20(3), 2354–2362 (2012).
[CrossRef] [PubMed]

S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Components for silicon plasmonic nanocircuits based on horizontal Cu-SiO2-Si-SiO2-Cu nanoplasmonic waveguides,” Opt. Express20(6), 5867–5881 (2012).
[CrossRef] [PubMed]

2011

S. Y. Zhu, T. Y. Liow, G. Q. Lo, and D. L. Kwong, “Silicon-based horizontal nanoplasmonic slot waveguides for on-chip integration,” Opt. Express19(9), 8888–8902 (2011).
[CrossRef] [PubMed]

H. S. Chu, Y. A. Akimov, P. Bai, and E. P. Li, “Hybrid dielectric-loaded plasmonic waveguide and wavelength selective components for efficiently controlling light at subwavelength scale,” J. Opt. Soc. Am. B28(12), 2895–2901 (2011).
[CrossRef]

H. Hassan, J.-C. Weeber, L. Markey, and A. Dereux, “Thermo-optical control of dielectric loaded plasmonic racetrack resonators,” J. Appl. Phys.110(2), 023106 (2011).
[CrossRef]

S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Experimental demonstration of horizontal nanoplasmonic slot waveguide-ring resonators with submicron radius,” IEEE Photon. Technol. Lett.23(24), 1896–1898 (2011).
[CrossRef]

S. Y. Zhu, T. Y. Liow, G. Q. Lo, and D. L. Kwong, “Fully complementary metal-oxide-semiconductor compatible nanoplasmonic slot waveguides for silicon electronic photonic integrated circuits,” Appl. Phys. Lett.98(2), 021107 (2011).
[CrossRef]

2010

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4(2), 83–91 (2010).
[CrossRef]

H. S. Chu, E. P. Li, P. Bai, and R. Hegde, “Optical performance of single-mode hybrid dielectric-loaded plasmonic waveguide-based components,” Appl. Phys. Lett.96(22), 221103 (2010).
[CrossRef]

M. Wu, Z. Han, and V. Van, “Conductor-gap-silicon plasmonic waveguides and passive components as subwavelength scale,” Opt. Express18(11), 11728–11736 (2010).
[CrossRef] [PubMed]

I. Goykhman, B. Desiatov, and B. Levy, “Experimental demonstration of locally oxidized hybrid silicon-plasmonic waveguide,” Appl. Phys. Lett.97(14), 141106 (2010).
[CrossRef]

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

S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Theoretical investigation of silicon MOS-type plasmonic slot waveguide based MZI modulators,” Opt. Express18(26), 27802–27819 (2010).
[CrossRef] [PubMed]

2009

S. Y. Zhu, Q. Fang, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Propagation losses in undoped and n-doped polycrystalline silicon wire waveguides,” Opt. Express17(23), 20891–20899 (2009).
[CrossRef] [PubMed]

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature457(7228), 455–458 (2009).
[CrossRef] [PubMed]

D. Dai and S. He, “A silicon-based hybrid plasmonic waveguide with a metal cap for a nano-scale light confinement,” Opt. Express17(19), 16646–16653 (2009).
[CrossRef] [PubMed]

2008

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008).
[CrossRef]

R. Salvador, A. Martinez, C. Garcia-Meca, R. Ortuno, and J. Marti, “Analysis of hybrid dielectric plasmonic waveguides,” IEEE J. Sel. Top.Quant. Electron.14, 1496–1501 (2008).

2007

T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguide,” Phys. Rev. B75(24), 245405 (2007).
[CrossRef]

2006

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature440(7083), 508–511 (2006).
[CrossRef] [PubMed]

2004

S. Y. Seo, J. Lee, J. H. Shin, E. S. Kang, and B. S. Bae, “The thermo-optic effect of Si nanocrystals in silicon-rich silicon oxide thin films,” Appl. Phys. Lett.85(13), 2526–2528 (2004).
[CrossRef]

2000

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett.36(4), 321–322 (2000).
[CrossRef]

1960

S. Roberts, “Optical properties of copper,” Phys. Rev.118(6), 1509–1518 (1960).
[CrossRef]

Akimov, Y. A.

H. S. Chu, Y. A. Akimov, P. Bai, and E. P. Li, “Hybrid dielectric-loaded plasmonic waveguide and wavelength selective components for efficiently controlling light at subwavelength scale,” J. Opt. Soc. Am. B28(12), 2895–2901 (2011).
[CrossRef]

Atwater, H. A.

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

Bae, B. S.

S. Y. Seo, J. Lee, J. H. Shin, E. S. Kang, and B. S. Bae, “The thermo-optic effect of Si nanocrystals in silicon-rich silicon oxide thin films,” Appl. Phys. Lett.85(13), 2526–2528 (2004).
[CrossRef]

Baets, R.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev.6(1), 47–73 (2012).
[CrossRef]

Bai, P.

H. S. Chu, Y. A. Akimov, P. Bai, and E. P. Li, “Hybrid dielectric-loaded plasmonic waveguide and wavelength selective components for efficiently controlling light at subwavelength scale,” J. Opt. Soc. Am. B28(12), 2895–2901 (2011).
[CrossRef]

H. S. Chu, E. P. Li, P. Bai, and R. Hegde, “Optical performance of single-mode hybrid dielectric-loaded plasmonic waveguide-based components,” Appl. Phys. Lett.96(22), 221103 (2010).
[CrossRef]

Bienstman, P.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev.6(1), 47–73 (2012).
[CrossRef]

Bogaerts, W.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev.6(1), 47–73 (2012).
[CrossRef]

Bouhelier, A.

S. Randhawa, S. Lachèze, J. Renger, A. Bouhelier, R. E. de Lamaestre, A. Dereux, and R. Quidant, “Performance of electro-optical plasmonic ring resonators at telecom wavelengths,” Opt. Express20(3), 2354–2362 (2012).
[CrossRef] [PubMed]

Bozhevolnyi, S. I.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4(2), 83–91 (2010).
[CrossRef]

T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguide,” Phys. Rev. B75(24), 245405 (2007).
[CrossRef]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature440(7083), 508–511 (2006).
[CrossRef] [PubMed]

Briggs, R. M.

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

Burgos, S. P.

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

Chu, H. S.

H. S. Chu, Y. A. Akimov, P. Bai, and E. P. Li, “Hybrid dielectric-loaded plasmonic waveguide and wavelength selective components for efficiently controlling light at subwavelength scale,” J. Opt. Soc. Am. B28(12), 2895–2901 (2011).
[CrossRef]

H. S. Chu, E. P. Li, P. Bai, and R. Hegde, “Optical performance of single-mode hybrid dielectric-loaded plasmonic waveguide-based components,” Appl. Phys. Lett.96(22), 221103 (2010).
[CrossRef]

Claes, T.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev.6(1), 47–73 (2012).
[CrossRef]

Dai, D.

D. Dai and S. He, “A silicon-based hybrid plasmonic waveguide with a metal cap for a nano-scale light confinement,” Opt. Express17(19), 16646–16653 (2009).
[CrossRef] [PubMed]

De Heyn, P.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev.6(1), 47–73 (2012).
[CrossRef]

de Lamaestre, R. E.

S. Randhawa, S. Lachèze, J. Renger, A. Bouhelier, R. E. de Lamaestre, A. Dereux, and R. Quidant, “Performance of electro-optical plasmonic ring resonators at telecom wavelengths,” Opt. Express20(3), 2354–2362 (2012).
[CrossRef] [PubMed]

De Vos, K.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev.6(1), 47–73 (2012).
[CrossRef]

Dereux, A.

S. Randhawa, S. Lachèze, J. Renger, A. Bouhelier, R. E. de Lamaestre, A. Dereux, and R. Quidant, “Performance of electro-optical plasmonic ring resonators at telecom wavelengths,” Opt. Express20(3), 2354–2362 (2012).
[CrossRef] [PubMed]

H. Hassan, J.-C. Weeber, L. Markey, and A. Dereux, “Thermo-optical control of dielectric loaded plasmonic racetrack resonators,” J. Appl. Phys.110(2), 023106 (2011).
[CrossRef]

Desiatov, B.

I. Goykhman, B. Desiatov, and B. Levy, “Experimental demonstration of locally oxidized hybrid silicon-plasmonic waveguide,” Appl. Phys. Lett.97(14), 141106 (2010).
[CrossRef]

Devaux, E.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature440(7083), 508–511 (2006).
[CrossRef] [PubMed]

Dumon, P.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev.6(1), 47–73 (2012).
[CrossRef]

Ebbesen, T. W.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature440(7083), 508–511 (2006).
[CrossRef] [PubMed]

Fang, Q.

S. Y. Zhu, Q. Fang, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Propagation losses in undoped and n-doped polycrystalline silicon wire waveguides,” Opt. Express17(23), 20891–20899 (2009).
[CrossRef] [PubMed]

Feigenbaum, E.

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

Garcia-Meca, C.

R. Salvador, A. Martinez, C. Garcia-Meca, R. Ortuno, and J. Marti, “Analysis of hybrid dielectric plasmonic waveguides,” IEEE J. Sel. Top.Quant. Electron.14, 1496–1501 (2008).

Genov, D. A.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008).
[CrossRef]

Goykhman, I.

I. Goykhman, B. Desiatov, and B. Levy, “Experimental demonstration of locally oxidized hybrid silicon-plasmonic waveguide,” Appl. Phys. Lett.97(14), 141106 (2010).
[CrossRef]

Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4(2), 83–91 (2010).
[CrossRef]

Grandidier, J.

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

Han, Z.

M. Wu, Z. Han, and V. Van, “Conductor-gap-silicon plasmonic waveguides and passive components as subwavelength scale,” Opt. Express18(11), 11728–11736 (2010).
[CrossRef] [PubMed]

Hassan, H.

H. Hassan, J.-C. Weeber, L. Markey, and A. Dereux, “Thermo-optical control of dielectric loaded plasmonic racetrack resonators,” J. Appl. Phys.110(2), 023106 (2011).
[CrossRef]

He, S.

D. Dai and S. He, “A silicon-based hybrid plasmonic waveguide with a metal cap for a nano-scale light confinement,” Opt. Express17(19), 16646–16653 (2009).
[CrossRef] [PubMed]

Hegde, R.

H. S. Chu, E. P. Li, P. Bai, and R. Hegde, “Optical performance of single-mode hybrid dielectric-loaded plasmonic waveguide-based components,” Appl. Phys. Lett.96(22), 221103 (2010).
[CrossRef]

Holmgaard, T.

T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguide,” Phys. Rev. B75(24), 245405 (2007).
[CrossRef]

Kang, E. S.

S. Y. Seo, J. Lee, J. H. Shin, E. S. Kang, and B. S. Bae, “The thermo-optic effect of Si nanocrystals in silicon-rich silicon oxide thin films,” Appl. Phys. Lett.85(13), 2526–2528 (2004).
[CrossRef]

Kumar Selvaraja, S.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev.6(1), 47–73 (2012).
[CrossRef]

Kwong, D. L.

S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Components for silicon plasmonic nanocircuits based on horizontal Cu-SiO2-Si-SiO2-Cu nanoplasmonic waveguides,” Opt. Express20(6), 5867–5881 (2012).
[CrossRef] [PubMed]

S. Y. Zhu, T. Y. Liow, G. Q. Lo, and D. L. Kwong, “Fully complementary metal-oxide-semiconductor compatible nanoplasmonic slot waveguides for silicon electronic photonic integrated circuits,” Appl. Phys. Lett.98(2), 021107 (2011).
[CrossRef]

S. Y. Zhu, T. Y. Liow, G. Q. Lo, and D. L. Kwong, “Silicon-based horizontal nanoplasmonic slot waveguides for on-chip integration,” Opt. Express19(9), 8888–8902 (2011).
[CrossRef] [PubMed]

S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Experimental demonstration of horizontal nanoplasmonic slot waveguide-ring resonators with submicron radius,” IEEE Photon. Technol. Lett.23(24), 1896–1898 (2011).
[CrossRef]

S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Theoretical investigation of silicon MOS-type plasmonic slot waveguide based MZI modulators,” Opt. Express18(26), 27802–27819 (2010).
[CrossRef] [PubMed]

S. Y. Zhu, Q. Fang, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Propagation losses in undoped and n-doped polycrystalline silicon wire waveguides,” Opt. Express17(23), 20891–20899 (2009).
[CrossRef] [PubMed]

S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Monolithic integration of hybrid plasmonic waveguide components into a fully CMOS-compatible SOI platform,” IEEE Photon. Technol. Lett. (Accepted).

Lachèze, S.

S. Randhawa, S. Lachèze, J. Renger, A. Bouhelier, R. E. de Lamaestre, A. Dereux, and R. Quidant, “Performance of electro-optical plasmonic ring resonators at telecom wavelengths,” Opt. Express20(3), 2354–2362 (2012).
[CrossRef] [PubMed]

Laluet, J. Y.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature440(7083), 508–511 (2006).
[CrossRef] [PubMed]

Lee, J.

S. Y. Seo, J. Lee, J. H. Shin, E. S. Kang, and B. S. Bae, “The thermo-optic effect of Si nanocrystals in silicon-rich silicon oxide thin films,” Appl. Phys. Lett.85(13), 2526–2528 (2004).
[CrossRef]

Levy, B.

I. Goykhman, B. Desiatov, and B. Levy, “Experimental demonstration of locally oxidized hybrid silicon-plasmonic waveguide,” Appl. Phys. Lett.97(14), 141106 (2010).
[CrossRef]

Li, E. P.

H. S. Chu, Y. A. Akimov, P. Bai, and E. P. Li, “Hybrid dielectric-loaded plasmonic waveguide and wavelength selective components for efficiently controlling light at subwavelength scale,” J. Opt. Soc. Am. B28(12), 2895–2901 (2011).
[CrossRef]

H. S. Chu, E. P. Li, P. Bai, and R. Hegde, “Optical performance of single-mode hybrid dielectric-loaded plasmonic waveguide-based components,” Appl. Phys. Lett.96(22), 221103 (2010).
[CrossRef]

Liow, T. Y.

S. Y. Zhu, T. Y. Liow, G. Q. Lo, and D. L. Kwong, “Silicon-based horizontal nanoplasmonic slot waveguides for on-chip integration,” Opt. Express19(9), 8888–8902 (2011).
[CrossRef] [PubMed]

S. Y. Zhu, T. Y. Liow, G. Q. Lo, and D. L. Kwong, “Fully complementary metal-oxide-semiconductor compatible nanoplasmonic slot waveguides for silicon electronic photonic integrated circuits,” Appl. Phys. Lett.98(2), 021107 (2011).
[CrossRef]

Lo, G. Q.

S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Components for silicon plasmonic nanocircuits based on horizontal Cu-SiO2-Si-SiO2-Cu nanoplasmonic waveguides,” Opt. Express20(6), 5867–5881 (2012).
[CrossRef] [PubMed]

S. Y. Zhu, T. Y. Liow, G. Q. Lo, and D. L. Kwong, “Fully complementary metal-oxide-semiconductor compatible nanoplasmonic slot waveguides for silicon electronic photonic integrated circuits,” Appl. Phys. Lett.98(2), 021107 (2011).
[CrossRef]

S. Y. Zhu, T. Y. Liow, G. Q. Lo, and D. L. Kwong, “Silicon-based horizontal nanoplasmonic slot waveguides for on-chip integration,” Opt. Express19(9), 8888–8902 (2011).
[CrossRef] [PubMed]

S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Experimental demonstration of horizontal nanoplasmonic slot waveguide-ring resonators with submicron radius,” IEEE Photon. Technol. Lett.23(24), 1896–1898 (2011).
[CrossRef]

S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Theoretical investigation of silicon MOS-type plasmonic slot waveguide based MZI modulators,” Opt. Express18(26), 27802–27819 (2010).
[CrossRef] [PubMed]

S. Y. Zhu, Q. Fang, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Propagation losses in undoped and n-doped polycrystalline silicon wire waveguides,” Opt. Express17(23), 20891–20899 (2009).
[CrossRef] [PubMed]

S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Monolithic integration of hybrid plasmonic waveguide components into a fully CMOS-compatible SOI platform,” IEEE Photon. Technol. Lett. (Accepted).

Markey, L.

H. Hassan, J.-C. Weeber, L. Markey, and A. Dereux, “Thermo-optical control of dielectric loaded plasmonic racetrack resonators,” J. Appl. Phys.110(2), 023106 (2011).
[CrossRef]

Marti, J.

R. Salvador, A. Martinez, C. Garcia-Meca, R. Ortuno, and J. Marti, “Analysis of hybrid dielectric plasmonic waveguides,” IEEE J. Sel. Top.Quant. Electron.14, 1496–1501 (2008).

Martinez, A.

R. Salvador, A. Martinez, C. Garcia-Meca, R. Ortuno, and J. Marti, “Analysis of hybrid dielectric plasmonic waveguides,” IEEE J. Sel. Top.Quant. Electron.14, 1496–1501 (2008).

Min, B.

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature457(7228), 455–458 (2009).
[CrossRef] [PubMed]

Ortuno, R.

R. Salvador, A. Martinez, C. Garcia-Meca, R. Ortuno, and J. Marti, “Analysis of hybrid dielectric plasmonic waveguides,” IEEE J. Sel. Top.Quant. Electron.14, 1496–1501 (2008).

Ostby, E.

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature457(7228), 455–458 (2009).
[CrossRef] [PubMed]

Oulton, R. F.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008).
[CrossRef]

Pile, D. F. P.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008).
[CrossRef]

Quidant, R.

S. Randhawa, S. Lachèze, J. Renger, A. Bouhelier, R. E. de Lamaestre, A. Dereux, and R. Quidant, “Performance of electro-optical plasmonic ring resonators at telecom wavelengths,” Opt. Express20(3), 2354–2362 (2012).
[CrossRef] [PubMed]

Randhawa, S.

S. Randhawa, S. Lachèze, J. Renger, A. Bouhelier, R. E. de Lamaestre, A. Dereux, and R. Quidant, “Performance of electro-optical plasmonic ring resonators at telecom wavelengths,” Opt. Express20(3), 2354–2362 (2012).
[CrossRef] [PubMed]

Renger, J.

S. Randhawa, S. Lachèze, J. Renger, A. Bouhelier, R. E. de Lamaestre, A. Dereux, and R. Quidant, “Performance of electro-optical plasmonic ring resonators at telecom wavelengths,” Opt. Express20(3), 2354–2362 (2012).
[CrossRef] [PubMed]

Roberts, S.

S. Roberts, “Optical properties of copper,” Phys. Rev.118(6), 1509–1518 (1960).
[CrossRef]

Salvador, R.

R. Salvador, A. Martinez, C. Garcia-Meca, R. Ortuno, and J. Marti, “Analysis of hybrid dielectric plasmonic waveguides,” IEEE J. Sel. Top.Quant. Electron.14, 1496–1501 (2008).

Seo, S. Y.

S. Y. Seo, J. Lee, J. H. Shin, E. S. Kang, and B. S. Bae, “The thermo-optic effect of Si nanocrystals in silicon-rich silicon oxide thin films,” Appl. Phys. Lett.85(13), 2526–2528 (2004).
[CrossRef]

Shin, J. H.

S. Y. Seo, J. Lee, J. H. Shin, E. S. Kang, and B. S. Bae, “The thermo-optic effect of Si nanocrystals in silicon-rich silicon oxide thin films,” Appl. Phys. Lett.85(13), 2526–2528 (2004).
[CrossRef]

Sorger, V.

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature457(7228), 455–458 (2009).
[CrossRef] [PubMed]

Sorger, V. J.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008).
[CrossRef]

Ulin-Avila, E.

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature457(7228), 455–458 (2009).
[CrossRef] [PubMed]

Vahala, K.

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature457(7228), 455–458 (2009).
[CrossRef] [PubMed]

Van, V.

M. Wu, Z. Han, and V. Van, “Conductor-gap-silicon plasmonic waveguides and passive components as subwavelength scale,” Opt. Express18(11), 11728–11736 (2010).
[CrossRef] [PubMed]

Van Thourhout, D.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev.6(1), 47–73 (2012).
[CrossRef]

Van Vaerenbergh, T.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev.6(1), 47–73 (2012).
[CrossRef]

Volkov, V. S.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature440(7083), 508–511 (2006).
[CrossRef] [PubMed]

Weeber, J.-C.

H. Hassan, J.-C. Weeber, L. Markey, and A. Dereux, “Thermo-optical control of dielectric loaded plasmonic racetrack resonators,” J. Appl. Phys.110(2), 023106 (2011).
[CrossRef]

Wu, M.

M. Wu, Z. Han, and V. Van, “Conductor-gap-silicon plasmonic waveguides and passive components as subwavelength scale,” Opt. Express18(11), 11728–11736 (2010).
[CrossRef] [PubMed]

Yang, L.

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature457(7228), 455–458 (2009).
[CrossRef] [PubMed]

Yariv, A.

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett.36(4), 321–322 (2000).
[CrossRef]

Yu, M. B.

S. Y. Zhu, Q. Fang, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Propagation losses in undoped and n-doped polycrystalline silicon wire waveguides,” Opt. Express17(23), 20891–20899 (2009).
[CrossRef] [PubMed]

Zhang, X.

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature457(7228), 455–458 (2009).
[CrossRef] [PubMed]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008).
[CrossRef]

Zhu, S. Y.

S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Components for silicon plasmonic nanocircuits based on horizontal Cu-SiO2-Si-SiO2-Cu nanoplasmonic waveguides,” Opt. Express20(6), 5867–5881 (2012).
[CrossRef] [PubMed]

S. Y. Zhu, T. Y. Liow, G. Q. Lo, and D. L. Kwong, “Fully complementary metal-oxide-semiconductor compatible nanoplasmonic slot waveguides for silicon electronic photonic integrated circuits,” Appl. Phys. Lett.98(2), 021107 (2011).
[CrossRef]

S. Y. Zhu, T. Y. Liow, G. Q. Lo, and D. L. Kwong, “Silicon-based horizontal nanoplasmonic slot waveguides for on-chip integration,” Opt. Express19(9), 8888–8902 (2011).
[CrossRef] [PubMed]

S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Experimental demonstration of horizontal nanoplasmonic slot waveguide-ring resonators with submicron radius,” IEEE Photon. Technol. Lett.23(24), 1896–1898 (2011).
[CrossRef]

S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Theoretical investigation of silicon MOS-type plasmonic slot waveguide based MZI modulators,” Opt. Express18(26), 27802–27819 (2010).
[CrossRef] [PubMed]

S. Y. Zhu, Q. Fang, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Propagation losses in undoped and n-doped polycrystalline silicon wire waveguides,” Opt. Express17(23), 20891–20899 (2009).
[CrossRef] [PubMed]

S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Monolithic integration of hybrid plasmonic waveguide components into a fully CMOS-compatible SOI platform,” IEEE Photon. Technol. Lett. (Accepted).

Appl. Phys. Lett.

S. Y. Zhu, T. Y. Liow, G. Q. Lo, and D. L. Kwong, “Fully complementary metal-oxide-semiconductor compatible nanoplasmonic slot waveguides for silicon electronic photonic integrated circuits,” Appl. Phys. Lett.98(2), 021107 (2011).
[CrossRef]

H. S. Chu, E. P. Li, P. Bai, and R. Hegde, “Optical performance of single-mode hybrid dielectric-loaded plasmonic waveguide-based components,” Appl. Phys. Lett.96(22), 221103 (2010).
[CrossRef]

I. Goykhman, B. Desiatov, and B. Levy, “Experimental demonstration of locally oxidized hybrid silicon-plasmonic waveguide,” Appl. Phys. Lett.97(14), 141106 (2010).
[CrossRef]

S. Y. Seo, J. Lee, J. H. Shin, E. S. Kang, and B. S. Bae, “The thermo-optic effect of Si nanocrystals in silicon-rich silicon oxide thin films,” Appl. Phys. Lett.85(13), 2526–2528 (2004).
[CrossRef]

Electron. Lett.

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett.36(4), 321–322 (2000).
[CrossRef]

IEEE J. Sel. Top.Quant. Electron.

R. Salvador, A. Martinez, C. Garcia-Meca, R. Ortuno, and J. Marti, “Analysis of hybrid dielectric plasmonic waveguides,” IEEE J. Sel. Top.Quant. Electron.14, 1496–1501 (2008).

IEEE Photon. Technol. Lett.

S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Monolithic integration of hybrid plasmonic waveguide components into a fully CMOS-compatible SOI platform,” IEEE Photon. Technol. Lett. (Accepted).

S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Experimental demonstration of horizontal nanoplasmonic slot waveguide-ring resonators with submicron radius,” IEEE Photon. Technol. Lett.23(24), 1896–1898 (2011).
[CrossRef]

J. Appl. Phys.

H. Hassan, J.-C. Weeber, L. Markey, and A. Dereux, “Thermo-optical control of dielectric loaded plasmonic racetrack resonators,” J. Appl. Phys.110(2), 023106 (2011).
[CrossRef]

J. Opt. Soc. Am. B

H. S. Chu, Y. A. Akimov, P. Bai, and E. P. Li, “Hybrid dielectric-loaded plasmonic waveguide and wavelength selective components for efficiently controlling light at subwavelength scale,” J. Opt. Soc. Am. B28(12), 2895–2901 (2011).
[CrossRef]

Laser Photonics Rev.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev.6(1), 47–73 (2012).
[CrossRef]

Nano Lett.

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

Nat. Photonics

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008).
[CrossRef]

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4(2), 83–91 (2010).
[CrossRef]

Nature

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature440(7083), 508–511 (2006).
[CrossRef] [PubMed]

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature457(7228), 455–458 (2009).
[CrossRef] [PubMed]

Opt. Express

S. Randhawa, S. Lachèze, J. Renger, A. Bouhelier, R. E. de Lamaestre, A. Dereux, and R. Quidant, “Performance of electro-optical plasmonic ring resonators at telecom wavelengths,” Opt. Express20(3), 2354–2362 (2012).
[CrossRef] [PubMed]

S. Y. Zhu, T. Y. Liow, G. Q. Lo, and D. L. Kwong, “Silicon-based horizontal nanoplasmonic slot waveguides for on-chip integration,” Opt. Express19(9), 8888–8902 (2011).
[CrossRef] [PubMed]

M. Wu, Z. Han, and V. Van, “Conductor-gap-silicon plasmonic waveguides and passive components as subwavelength scale,” Opt. Express18(11), 11728–11736 (2010).
[CrossRef] [PubMed]

D. Dai and S. He, “A silicon-based hybrid plasmonic waveguide with a metal cap for a nano-scale light confinement,” Opt. Express17(19), 16646–16653 (2009).
[CrossRef] [PubMed]

S. Y. Zhu, Q. Fang, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Propagation losses in undoped and n-doped polycrystalline silicon wire waveguides,” Opt. Express17(23), 20891–20899 (2009).
[CrossRef] [PubMed]

S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Theoretical investigation of silicon MOS-type plasmonic slot waveguide based MZI modulators,” Opt. Express18(26), 27802–27819 (2010).
[CrossRef] [PubMed]

S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Components for silicon plasmonic nanocircuits based on horizontal Cu-SiO2-Si-SiO2-Cu nanoplasmonic waveguides,” Opt. Express20(6), 5867–5881 (2012).
[CrossRef] [PubMed]

Phys. Rev.

S. Roberts, “Optical properties of copper,” Phys. Rev.118(6), 1509–1518 (1960).
[CrossRef]

Phys. Rev. B

T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguide,” Phys. Rev. B75(24), 245405 (2007).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Vertical Cu-SiO2-Si hybrid plasmonic waveguide-based WRRs fabricated in this paper. (a) Schematic layout, (b) Cross section, and (c) SEM image of the patterned Si core of a typical WRR with R of 2.59 μm. The parameters in the layout are WP = 0.18 μm, R = 1.09, 1.59, 2.09, or 2.59 μm, and gap = 0.2 or 0.25 μm. The parameters which are determined by fabrication are hSi = ~340 nm and tSiO2 = ~17 nm.

Fig. 2
Fig. 2

XTEM images of vertical Cu-SiO2-Si hybrid plasmonic waveguides with different Si core widths, which are caused by the different expose conditions during UV lithography. A thin Si3N4 layer between Si and SiO2 in the bottom Si core region is for the fabrication process control, not for the function. The Si core height is ~300 nm and the thermal SiO2 layer between the Si core and the Cu cap is ~17 nm. These four kinds of plasmonic WRRs are referred as S1, S2, S3, and S4, respectively.

Fig. 3
Fig. 3

Transmitted powers measured on straight Cu-SiO2-Si hybrid plasmonic waveguides with different Si core widths, normalized by that measured on the corresponding reference waveguide (i.e., the Si strip waveguide without the plasmonic area). Each data point is averaged from three identical waveguides and the standard deviation is indicated as the error bar. From the linearly fitting, the propagation losses are extracted, as indicated.

Fig. 4
Fig. 4

Power transmission spectra for plasmonic WRRs with the same nominal gap of 200 nm but with different Si core widths (S1, S2, S3, and S4) and different ring radii (R = 1.09, 1.59, 2.09, and 2.59 μm). The experimental curves (in black) are normalized by the transmission spectrum of the corresponding 7-μm-long straight plasmonic waveguide. The fitting curves (in red) are based on Eq. (1). The fitting parameters of neff, α b , |t|, and θ are indicated for each plasmonic WRR.

Fig. 5
Fig. 5

Power transmission spectra for plasmonic WRRs with the same nominal gap of 250 nm but with different Si core widths (S1, S2, S3, and S4) and different ring radii (R = 1.09, 1.59, 2.09, and 2.59 μm). The experimental curves (in black) are normalized by the transmission spectrum of the corresponding 7-μm-long straight plasmonic waveguide. The fitting curves (in red) are based on Eq. (1). The fitting parameters of neff, α b , |t|, and θ are indicated for each plasmonic WRR.

Fig. 6
Fig. 6

Plasmonic WRRs with a dual-ring configuration. (a) Schematic layout and (b) SEM image of the patterned Si core of a plasmonic WRR with 2.59-μm R. The structural parameters are as before.

Fig. 7
Fig. 7

Power transmission spectra for dual-ring plasmonic WRRs with the same nominal gap of 0.20 μm but with different Si core widths (S1 and S2) and different ring radii (R = 1.09, 1.59, 2.09, and 2.59 μm). The experimental curves (in black) are normalized by the transmission spectrum of the corresponding 7-μm-long straight plasmonic waveguide. The fitting curves (in red) are based on Eq. (1). The fitting parameters of neff, α b , t, and θ are indicated for each plasmonic WRR.

Fig. 8
Fig. 8

(a) Electrical field |Ey| distribution of the fundamental quasi-TM mode in the Cu-SiO2-Si hybrid plasmonic waveguide; (b) Real effective index of straight waveguides with different Si core widths versus wavelength, obtained by the 3-D FDTD numerical simulation.

Fig. 9
Fig. 9

Transmission spectra of the S1 single-ring WRR with 2.59-μm R and 250-nm nominal gap measured at temperature of 27, 50, 82, and 101°C, respectively.

Fig. 10
Fig. 10

(a) Two resonant wavelengths,λr, read from Fig. 9 versus temperature, the thermo-optical coefficient dλr/dT is extracted from linearly fitting; (b) Group index ng of the plasmonic WRR versus temperature, ng is obtained by fitting the spectra in Fig. 9 using Eq. (1), the thermo-optical coefficient dng/dT is then extracted from linearly fitting.

Fig. 11
Fig. 11

Thermo-optical coefficients (dng/dT) extracted from different plasmonic WRRs studied in this work, which are extracted from linearly fitting the data points of ng versus temperature, as shown in Fig. 10(b). The standard deviation of the linear fitting is indicated as the error bar.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

T(λ)= α 2 + t 2 2αtcosθ 1+ α 2 t 2 2αtcosθ
FSR= λ 2 2πR n eff
n g = n eff λ d n eff dλ

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