Abstract

A novel three-dimensional (3D) metal-nanocavity (or nano-coin) semiconductor laser suitable for electrical injection is proposed and analyzed. Our design uses metals as both the cavity sidewall and the top/bottom reflectors (i. e., a fully metal encapsulated nanolaser) and maintains the surface-emitting nature. As a result of the large permittivity contrast between the dielectric and metal, the optical energy can be well-confined inside the metal nanocavity. With a proper design and the choice of the HE111 mode, which has the best top surface radiation pattern, a laser with a physical size smaller than 0.01λ0 3 is achievable at 1.55 μm wavelength with a reasonable semiconductor gain at room temperature. We provide a detailed theoretical model starting from the waveguide analysis to full 3D structure simulations by taking into account both geometry and metal dispersion. We show a systematic procedure for analyzing this class of 3D metal-cavity (or nano-coin) lasers with discussions on the optimization of the performance such as light output power, threshold reduction, and output beam shaping.

© 2011 OSA

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2011

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(2), 110–113 (2011).
[CrossRef] [PubMed]

C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, U. W. Pohl, and D. Bimberg, “CW substrate-free metal-cavity surface microemitters at 300 K,” Semicond. Sci. Technol. 26(1), 014012 (2011).
[CrossRef]

2010

C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, and D. Bimberg, “Metal-cavity surface emitting microlaser at room temperature,” Appl. Phys. Lett. 96(25), 251101 (2010).
[CrossRef]

R. Safaisini, J. R. Joseph, and K. L. Lear, “Scalable high-CW-power high-speed 980-nm VCSEL arrays,” IEEE J. Quantum Electron. 46(11), 1590–1596 (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(9), 3679–3683 (2010).
[CrossRef] [PubMed]

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(6), 395–399 (2010).
[CrossRef]

K. Yu, A. Lakhani, and M. C. Wu, “Subwavelength metal-optic semiconductor nanopatch lasers,” Opt. Express 18(9), 8790–8799 (2010).
[CrossRef] [PubMed]

S. W. Chang, T. R. Lin, and S. L. Chuang, “Theory of plasmonic fabry-perot nanolasers,” Opt. Express 18(14), 15039–15053 (2010).
[CrossRef] [PubMed]

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(19), 19581–19591 (2010).
[CrossRef] [PubMed]

2009

M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y. S. Oei, R. Nötzel, C. Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17(13), 11107–11112 (2009).
[CrossRef] [PubMed]

S. W. Chang and S. L. Chuang, “Fundamental formulation for plasmonic nanolasers,” IEEE J. Quantum Electron. 45(8), 1014–1023 (2009).
[CrossRef]

M. Motoyoshi, “Through silicon via (TSV),” Proc. IEEE 97(1), 43–48 (2009).
[CrossRef]

2008

C. Manolatou and F. Rana, “Subwavelength nanopatch cavities for semiconductor plasmon lasers,” IEEE J. Quantum Electron. 44(5), 435–447 (2008).
[CrossRef]

A. Mizrahi, V. Lomakin, B. A. Slutsky, M. P. Nezhad, L. Feng, and Y. Fainman, “Low threshold gain metal coated laser nanoresonators,” Opt. Lett. 33(11), 1261–1263 (2008).
[CrossRef] [PubMed]

2007

K. Nozaki, S. Kita, and T. Baba, “Room temperature continuous wave operation and controlled spontaneous emission in ultrasmall photonic crystal nanolaser,” Opt. Express 15(12), 7506–7514 (2007).
[CrossRef] [PubMed]

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

2004

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305(5689), 1444–1447 (2004).
[CrossRef] [PubMed]

2000

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures,” Phys. Rev. B 61(15), 10484–10503 (2000).
[CrossRef]

1994

L. Novotny and C. Hafner, “Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 50(5), 4094–4106 (1994).
[CrossRef] [PubMed]

1993

Y. Zou, J. S. Osinski, P. Grodzinski, P. Dapkus, W. C. Rideout, W. F. Sharfin, J. Schlafer, and F. D. Crawford, “Experimental study of Auger recombination, gain, and temperature sensitivity of 1.5 μm compressively strained semiconductor lasers,” IEEE J. Quantum Electron. 29(6), 1565–1575 (1993).
[CrossRef]

1992

E. Yablonovitch, R. Bhat, C. E. Zah, T. J. Gmitter, and M. A. Koza, “Nearly ideal InP/In0.53Ga0.47As heterojunction regrowth on chemically prepared In0.53Ga0.47As surfaces,” Appl. Phys. Lett. 60(3), 371–373 (1992).
[CrossRef]

1990

J. L. Jewell, N. A. Olsson, A. Scherer, S. L. McCall, J. P. Harbison, L. T. Florez, and Y. H. Lee, “Surface-emitting microlasers for photonic switching and interchip connections,” Opt. Eng. 29(3), 210–214 (1990).
[CrossRef]

1987

S. L. Chuang, “A coupled-mode formulation by reciprocity and a variational principle,” J. Lightwave Technol. 5(1), 5–15 (1987).
[CrossRef]

1986

S. W. Lee, S. L. Chuang, and C. S. Lee, “Normal modes in an overmoded circular waveguide coated with lossy material,” IEEE Trans. Microw. Theory Tech. 34(7), 773–785 (1986).
[CrossRef]

1982

S. Adachi, “Refractive indices of III-V compounds: key properties of InGaAsP relevant to device design,” J. Appl. Phys. 53(8), 5863–5869 (1982).
[CrossRef]

1972

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

Adachi, S.

S. Adachi, “Refractive indices of III-V compounds: key properties of InGaAsP relevant to device design,” J. Appl. Phys. 53(8), 5863–5869 (1982).
[CrossRef]

Baba, T.

Baek, J. H.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305(5689), 1444–1447 (2004).
[CrossRef] [PubMed]

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(2), 110–113 (2011).
[CrossRef] [PubMed]

Berini, P.

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures,” Phys. Rev. B 61(15), 10484–10503 (2000).
[CrossRef]

Bhat, R.

E. Yablonovitch, R. Bhat, C. E. Zah, T. J. Gmitter, and M. A. Koza, “Nearly ideal InP/In0.53Ga0.47As heterojunction regrowth on chemically prepared In0.53Ga0.47As surfaces,” Appl. Phys. Lett. 60(3), 371–373 (1992).
[CrossRef]

Bimberg, D.

C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, U. W. Pohl, and D. Bimberg, “CW substrate-free metal-cavity surface microemitters at 300 K,” Semicond. Sci. Technol. 26(1), 014012 (2011).
[CrossRef]

C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, and D. Bimberg, “Metal-cavity surface emitting microlaser at room temperature,” Appl. Phys. Lett. 96(25), 251101 (2010).
[CrossRef]

S. W. Chang, C. Y. Lu, S. L. Chuang, T. D. Germann, U. W. Pohl, and D. Bimberg, “Theory of metal-cavity surface-emitting microlasers and comparison with experiment,” IEEE J. Sel. Top. Quantum Electron. (in press).

C. Y. Lu, S. L. Chuang, A. Mutig, and D. Bimberg, “Metal-cavity surface-emitting microlasers with hybrid metal-DBR reflectors,” Opt. Lett. (in press).
[PubMed]

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(6), 395–399 (2010).
[CrossRef]

Chang, S. W.

C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, U. W. Pohl, and D. Bimberg, “CW substrate-free metal-cavity surface microemitters at 300 K,” Semicond. Sci. Technol. 26(1), 014012 (2011).
[CrossRef]

S. W. Chang, T. R. Lin, and S. L. Chuang, “Theory of plasmonic fabry-perot nanolasers,” Opt. Express 18(14), 15039–15053 (2010).
[CrossRef] [PubMed]

C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, and D. Bimberg, “Metal-cavity surface emitting microlaser at room temperature,” Appl. Phys. Lett. 96(25), 251101 (2010).
[CrossRef]

S. W. Chang and S. L. Chuang, “Fundamental formulation for plasmonic nanolasers,” IEEE J. Quantum Electron. 45(8), 1014–1023 (2009).
[CrossRef]

S. W. Chang, C. Y. Lu, S. L. Chuang, T. D. Germann, U. W. Pohl, and D. Bimberg, “Theory of metal-cavity surface-emitting microlasers and comparison with experiment,” IEEE J. Sel. Top. Quantum Electron. (in press).

Christy, R. W.

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

Chuang, S. L.

C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, U. W. Pohl, and D. Bimberg, “CW substrate-free metal-cavity surface microemitters at 300 K,” Semicond. Sci. Technol. 26(1), 014012 (2011).
[CrossRef]

S. W. Chang, T. R. Lin, and S. L. Chuang, “Theory of plasmonic fabry-perot nanolasers,” Opt. Express 18(14), 15039–15053 (2010).
[CrossRef] [PubMed]

C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, and D. Bimberg, “Metal-cavity surface emitting microlaser at room temperature,” Appl. Phys. Lett. 96(25), 251101 (2010).
[CrossRef]

S. W. Chang and S. L. Chuang, “Fundamental formulation for plasmonic nanolasers,” IEEE J. Quantum Electron. 45(8), 1014–1023 (2009).
[CrossRef]

S. L. Chuang, “A coupled-mode formulation by reciprocity and a variational principle,” J. Lightwave Technol. 5(1), 5–15 (1987).
[CrossRef]

S. W. Lee, S. L. Chuang, and C. S. Lee, “Normal modes in an overmoded circular waveguide coated with lossy material,” IEEE Trans. Microw. Theory Tech. 34(7), 773–785 (1986).
[CrossRef]

C. Y. Lu, S. L. Chuang, A. Mutig, and D. Bimberg, “Metal-cavity surface-emitting microlasers with hybrid metal-DBR reflectors,” Opt. Lett. (in press).
[PubMed]

S. W. Chang, C. Y. Lu, S. L. Chuang, T. D. Germann, U. W. Pohl, and D. Bimberg, “Theory of metal-cavity surface-emitting microlasers and comparison with experiment,” IEEE J. Sel. Top. Quantum Electron. (in press).

Crawford, F. D.

Y. Zou, J. S. Osinski, P. Grodzinski, P. Dapkus, W. C. Rideout, W. F. Sharfin, J. Schlafer, and F. D. Crawford, “Experimental study of Auger recombination, gain, and temperature sensitivity of 1.5 μm compressively strained semiconductor lasers,” IEEE J. Quantum Electron. 29(6), 1565–1575 (1993).
[CrossRef]

Dapkus, P.

Y. Zou, J. S. Osinski, P. Grodzinski, P. Dapkus, W. C. Rideout, W. F. Sharfin, J. Schlafer, and F. D. Crawford, “Experimental study of Auger recombination, gain, and temperature sensitivity of 1.5 μm compressively strained semiconductor lasers,” IEEE J. Quantum Electron. 29(6), 1565–1575 (1993).
[CrossRef]

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. Nötzel, and 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. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[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. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 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(6), 395–399 (2010).
[CrossRef]

A. Mizrahi, V. Lomakin, B. A. Slutsky, M. P. Nezhad, L. Feng, and Y. Fainman, “Low threshold gain metal coated laser nanoresonators,” Opt. Lett. 33(11), 1261–1263 (2008).
[CrossRef] [PubMed]

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(6), 395–399 (2010).
[CrossRef]

A. Mizrahi, V. Lomakin, B. A. Slutsky, M. P. Nezhad, L. Feng, and Y. Fainman, “Low threshold gain metal coated laser nanoresonators,” Opt. Lett. 33(11), 1261–1263 (2008).
[CrossRef] [PubMed]

Florez, L. T.

J. L. Jewell, N. A. Olsson, A. Scherer, S. L. McCall, J. P. Harbison, L. T. Florez, and Y. H. Lee, “Surface-emitting microlasers for photonic switching and interchip connections,” Opt. Eng. 29(3), 210–214 (1990).
[CrossRef]

Geluk, E. J.

M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y. S. Oei, R. Nötzel, C. Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17(13), 11107–11112 (2009).
[CrossRef] [PubMed]

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

Germann, T. D.

C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, U. W. Pohl, and D. Bimberg, “CW substrate-free metal-cavity surface microemitters at 300 K,” Semicond. Sci. Technol. 26(1), 014012 (2011).
[CrossRef]

C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, and D. Bimberg, “Metal-cavity surface emitting microlaser at room temperature,” Appl. Phys. Lett. 96(25), 251101 (2010).
[CrossRef]

S. W. Chang, C. Y. Lu, S. L. Chuang, T. D. Germann, U. W. Pohl, and D. Bimberg, “Theory of metal-cavity surface-emitting microlasers and comparison with experiment,” IEEE J. Sel. Top. Quantum Electron. (in press).

Gmitter, T. J.

E. Yablonovitch, R. Bhat, C. E. Zah, T. J. Gmitter, and M. A. Koza, “Nearly ideal InP/In0.53Ga0.47As heterojunction regrowth on chemically prepared In0.53Ga0.47As surfaces,” Appl. Phys. Lett. 60(3), 371–373 (1992).
[CrossRef]

Grodzinski, P.

Y. Zou, J. S. Osinski, P. Grodzinski, P. Dapkus, W. C. Rideout, W. F. Sharfin, J. Schlafer, and F. D. Crawford, “Experimental study of Auger recombination, gain, and temperature sensitivity of 1.5 μm compressively strained semiconductor lasers,” IEEE J. Quantum Electron. 29(6), 1565–1575 (1993).
[CrossRef]

Hafner, C.

L. Novotny and C. Hafner, “Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 50(5), 4094–4106 (1994).
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J. L. Jewell, N. A. Olsson, A. Scherer, S. L. McCall, J. P. Harbison, L. T. Florez, and Y. H. Lee, “Surface-emitting microlasers for photonic switching and interchip connections,” Opt. Eng. 29(3), 210–214 (1990).
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M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y. S. Oei, R. Nötzel, C. Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17(13), 11107–11112 (2009).
[CrossRef] [PubMed]

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

Huang, J.

Jewell, J. L.

J. L. Jewell, N. A. Olsson, A. Scherer, S. L. McCall, J. P. Harbison, L. T. Florez, and Y. H. Lee, “Surface-emitting microlasers for photonic switching and interchip connections,” Opt. Eng. 29(3), 210–214 (1990).
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R. Safaisini, J. R. Joseph, and K. L. Lear, “Scalable high-CW-power high-speed 980-nm VCSEL arrays,” IEEE J. Quantum Electron. 46(11), 1590–1596 (2010).
[CrossRef]

Ju, Y. G.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305(5689), 1444–1447 (2004).
[CrossRef] [PubMed]

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(9), 3679–3683 (2010).
[CrossRef] [PubMed]

Karouta, F.

Kim, S. B.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305(5689), 1444–1447 (2004).
[CrossRef] [PubMed]

Kim, S. H.

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(19), 19581–19591 (2010).
[CrossRef] [PubMed]

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305(5689), 1444–1447 (2004).
[CrossRef] [PubMed]

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(9), 3679–3683 (2010).
[CrossRef] [PubMed]

Kita, S.

Koza, M. A.

E. Yablonovitch, R. Bhat, C. E. Zah, T. J. Gmitter, and M. A. Koza, “Nearly ideal InP/In0.53Ga0.47As heterojunction regrowth on chemically prepared In0.53Ga0.47As surfaces,” Appl. Phys. Lett. 60(3), 371–373 (1992).
[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(9), 3679–3683 (2010).
[CrossRef] [PubMed]

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305(5689), 1444–1447 (2004).
[CrossRef] [PubMed]

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

Lakhani, A.

Lear, K. L.

R. Safaisini, J. R. Joseph, and K. L. Lear, “Scalable high-CW-power high-speed 980-nm VCSEL arrays,” IEEE J. Quantum Electron. 46(11), 1590–1596 (2010).
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Lee, C. S.

S. W. Lee, S. L. Chuang, and C. S. Lee, “Normal modes in an overmoded circular waveguide coated with lossy material,” IEEE Trans. Microw. Theory Tech. 34(7), 773–785 (1986).
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Lee, S. W.

S. W. Lee, S. L. Chuang, and C. S. Lee, “Normal modes in an overmoded circular waveguide coated with lossy material,” IEEE Trans. Microw. Theory Tech. 34(7), 773–785 (1986).
[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(9), 3679–3683 (2010).
[CrossRef] [PubMed]

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305(5689), 1444–1447 (2004).
[CrossRef] [PubMed]

J. L. Jewell, N. A. Olsson, A. Scherer, S. L. McCall, J. P. Harbison, L. T. Florez, and Y. H. Lee, “Surface-emitting microlasers for photonic switching and interchip connections,” Opt. Eng. 29(3), 210–214 (1990).
[CrossRef]

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

Leong, E. S. P.

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(9), 3679–3683 (2010).
[CrossRef] [PubMed]

Lin, T. R.

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(6), 395–399 (2010).
[CrossRef]

A. Mizrahi, V. Lomakin, B. A. Slutsky, M. P. Nezhad, L. Feng, and Y. Fainman, “Low threshold gain metal coated laser nanoresonators,” Opt. Lett. 33(11), 1261–1263 (2008).
[CrossRef] [PubMed]

Lu, C. Y.

C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, U. W. Pohl, and D. Bimberg, “CW substrate-free metal-cavity surface microemitters at 300 K,” Semicond. Sci. Technol. 26(1), 014012 (2011).
[CrossRef]

C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, and D. Bimberg, “Metal-cavity surface emitting microlaser at room temperature,” Appl. Phys. Lett. 96(25), 251101 (2010).
[CrossRef]

S. W. Chang, C. Y. Lu, S. L. Chuang, T. D. Germann, U. W. Pohl, and D. Bimberg, “Theory of metal-cavity surface-emitting microlasers and comparison with experiment,” IEEE J. Sel. Top. Quantum Electron. (in press).

C. Y. Lu, S. L. Chuang, A. Mutig, and D. Bimberg, “Metal-cavity surface-emitting microlasers with hybrid metal-DBR reflectors,” Opt. Lett. (in press).
[PubMed]

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(2), 110–113 (2011).
[CrossRef] [PubMed]

Manolatou, C.

C. Manolatou and F. Rana, “Subwavelength nanopatch cavities for semiconductor plasmon lasers,” IEEE J. Quantum Electron. 44(5), 435–447 (2008).
[CrossRef]

Marell, M.

McCall, S. L.

J. L. Jewell, N. A. Olsson, A. Scherer, S. L. McCall, J. P. Harbison, L. T. Florez, and Y. H. Lee, “Surface-emitting microlasers for photonic switching and interchip connections,” Opt. Eng. 29(3), 210–214 (1990).
[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(6), 395–399 (2010).
[CrossRef]

A. Mizrahi, V. Lomakin, B. A. Slutsky, M. P. Nezhad, L. Feng, and Y. Fainman, “Low threshold gain metal coated laser nanoresonators,” Opt. Lett. 33(11), 1261–1263 (2008).
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Motoyoshi, M.

M. Motoyoshi, “Through silicon via (TSV),” Proc. IEEE 97(1), 43–48 (2009).
[CrossRef]

Mutig, A.

C. Y. Lu, S. L. Chuang, A. Mutig, and D. Bimberg, “Metal-cavity surface-emitting microlasers with hybrid metal-DBR reflectors,” Opt. Lett. (in press).
[PubMed]

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(6), 395–399 (2010).
[CrossRef]

A. Mizrahi, V. Lomakin, B. A. Slutsky, M. P. Nezhad, L. Feng, and Y. Fainman, “Low threshold gain metal coated laser nanoresonators,” Opt. Lett. 33(11), 1261–1263 (2008).
[CrossRef] [PubMed]

Ning, C. Z.

Nötzel, R.

M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y. S. Oei, R. Nötzel, C. Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17(13), 11107–11112 (2009).
[CrossRef] [PubMed]

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

Novotny, L.

L. Novotny and C. Hafner, “Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 50(5), 4094–4106 (1994).
[CrossRef] [PubMed]

Nozaki, K.

Oei, Y. S.

Oei, Y.-S.

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

Olsson, N. A.

J. L. Jewell, N. A. Olsson, A. Scherer, S. L. McCall, J. P. Harbison, L. T. Florez, and Y. H. Lee, “Surface-emitting microlasers for photonic switching and interchip connections,” Opt. Eng. 29(3), 210–214 (1990).
[CrossRef]

Osinski, J. S.

Y. Zou, J. S. Osinski, P. Grodzinski, P. Dapkus, W. C. Rideout, W. F. Sharfin, J. Schlafer, and F. D. Crawford, “Experimental study of Auger recombination, gain, and temperature sensitivity of 1.5 μm compressively strained semiconductor lasers,” IEEE J. Quantum Electron. 29(6), 1565–1575 (1993).
[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(2), 110–113 (2011).
[CrossRef] [PubMed]

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(9), 3679–3683 (2010).
[CrossRef] [PubMed]

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305(5689), 1444–1447 (2004).
[CrossRef] [PubMed]

Pohl, U. W.

C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, U. W. Pohl, and D. Bimberg, “CW substrate-free metal-cavity surface microemitters at 300 K,” Semicond. Sci. Technol. 26(1), 014012 (2011).
[CrossRef]

S. W. Chang, C. Y. Lu, S. L. Chuang, T. D. Germann, U. W. Pohl, and D. Bimberg, “Theory of metal-cavity surface-emitting microlasers and comparison with experiment,” IEEE J. Sel. Top. Quantum Electron. (in press).

Rana, F.

C. Manolatou and F. Rana, “Subwavelength nanopatch cavities for semiconductor plasmon lasers,” IEEE J. Quantum Electron. 44(5), 435–447 (2008).
[CrossRef]

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(9), 3679–3683 (2010).
[CrossRef] [PubMed]

Rideout, W. C.

Y. Zou, J. S. Osinski, P. Grodzinski, P. Dapkus, W. C. Rideout, W. F. Sharfin, J. Schlafer, and F. D. Crawford, “Experimental study of Auger recombination, gain, and temperature sensitivity of 1.5 μm compressively strained semiconductor lasers,” IEEE J. Quantum Electron. 29(6), 1565–1575 (1993).
[CrossRef]

Safaisini, R.

R. Safaisini, J. R. Joseph, and K. L. Lear, “Scalable high-CW-power high-speed 980-nm VCSEL arrays,” IEEE J. Quantum Electron. 46(11), 1590–1596 (2010).
[CrossRef]

Scherer, A.

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(19), 19581–19591 (2010).
[CrossRef] [PubMed]

J. L. Jewell, N. A. Olsson, A. Scherer, S. L. McCall, J. P. Harbison, L. T. Florez, and Y. H. Lee, “Surface-emitting microlasers for photonic switching and interchip connections,” Opt. Eng. 29(3), 210–214 (1990).
[CrossRef]

Schlafer, J.

Y. Zou, J. S. Osinski, P. Grodzinski, P. Dapkus, W. C. Rideout, W. F. Sharfin, J. Schlafer, and F. D. Crawford, “Experimental study of Auger recombination, gain, and temperature sensitivity of 1.5 μm compressively strained semiconductor lasers,” IEEE J. Quantum Electron. 29(6), 1565–1575 (1993).
[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(9), 3679–3683 (2010).
[CrossRef] [PubMed]

Sharfin, W. F.

Y. Zou, J. S. Osinski, P. Grodzinski, P. Dapkus, W. C. Rideout, W. F. Sharfin, J. Schlafer, and F. D. Crawford, “Experimental study of Auger recombination, gain, and temperature sensitivity of 1.5 μm compressively strained semiconductor lasers,” IEEE J. Quantum Electron. 29(6), 1565–1575 (1993).
[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(6), 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(6), 395–399 (2010).
[CrossRef]

Slutsky, B. A.

Smalbrugge, B.

M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y. S. Oei, R. Nötzel, C. Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17(13), 11107–11112 (2009).
[CrossRef] [PubMed]

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

Smit, M. K.

M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y. S. Oei, R. Nötzel, C. Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17(13), 11107–11112 (2009).
[CrossRef] [PubMed]

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. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 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(2), 110–113 (2011).
[CrossRef] [PubMed]

Sun, M.

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

van Veldhoven, P. J.

M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y. S. Oei, R. Nötzel, C. Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17(13), 11107–11112 (2009).
[CrossRef] [PubMed]

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

Wu, M. C.

Yablonovitch, E.

E. Yablonovitch, R. Bhat, C. E. Zah, T. J. Gmitter, and M. A. Koza, “Nearly ideal InP/In0.53Ga0.47As heterojunction regrowth on chemically prepared In0.53Ga0.47As surfaces,” Appl. Phys. Lett. 60(3), 371–373 (1992).
[CrossRef]

Yang, J. K.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305(5689), 1444–1447 (2004).
[CrossRef] [PubMed]

Yu, K.

Zah, C. E.

E. Yablonovitch, R. Bhat, C. E. Zah, T. J. Gmitter, and M. A. Koza, “Nearly ideal InP/In0.53Ga0.47As heterojunction regrowth on chemically prepared In0.53Ga0.47As surfaces,” Appl. Phys. Lett. 60(3), 371–373 (1992).
[CrossRef]

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(2), 110–113 (2011).
[CrossRef] [PubMed]

Zhu, Y.

M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y. S. Oei, R. Nötzel, C. Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17(13), 11107–11112 (2009).
[CrossRef] [PubMed]

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

Zou, Y.

Y. Zou, J. S. Osinski, P. Grodzinski, P. Dapkus, W. C. Rideout, W. F. Sharfin, J. Schlafer, and F. D. Crawford, “Experimental study of Auger recombination, gain, and temperature sensitivity of 1.5 μm compressively strained semiconductor lasers,” IEEE J. Quantum Electron. 29(6), 1565–1575 (1993).
[CrossRef]

Appl. Phys. Lett.

C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, and D. Bimberg, “Metal-cavity surface emitting microlaser at room temperature,” Appl. Phys. Lett. 96(25), 251101 (2010).
[CrossRef]

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Figures (19)

Fig. 1
Fig. 1

Our proposed surface-emitting three-dimensional (3D) metal-nanocavity (nano-coin) laser. The active region is composed of a bulk In0.53Ga0.47As with a height h in the active region height and a in radius. InP is used as both electron and hole injectors. An InGaAsP layer serves as a contact layer for n-contact. The whole device is encapsulated in silver with SiN x as a current blocker. (a) A 3D view and (b) a cross sectional view of the structure.

Fig. 2
Fig. 2

Mode patterns of a circular metallic waveguide with a core-shell structure inside, calculated by the finite element method (FEM). (Top left:) the cross-sectional view of the waveguide layered structure. Silver is used to surround the circular waveguide with an In0.53Ga0.47As core of radius a = 250 nm and a thin SiN x shell layer of thickness s = 50 nm. Five lowest order mode patterns (|(E)|, |(H)|, and Pz) are plotted correspondingly. Power nodes at the waveguide center are observed in TM01, HE21, and TE01 modes.

Fig. 3
Fig. 3

(a) Cutoff wavelengths of different modes as a function of core radius. The fundamental mode HE11 has the longest cutoff frequency among all the other modes and can be used to design a cavity of a minimal radial dimension. (b) χ mn λ c/2πn core(b + Δ) as function of core radius. χ mn is the root of Bessel functions or their derivatives (HE11: 1.84, TM01: 2.405, HE21: 3.05, TE01: 3.83, and EH11: 3.83). The dashed line represents the prediction by the use of homogeneous waveguide with a receded PEC wall by a skin depth Δ. The actual cutoff wavelength will be close to the prediction when the wavelengths are long enough such that the thin cladding layer becomes negligible.

Fig. 4
Fig. 4

(a) The effective index as a function of core radius a and the guiding wavelength of the HE11 mode of a silver-coated circular waveguide with an In0.53Ga0.47As core and a SiN x shell (50 nm) as shown in Fig. 2. (b) The guiding wavelength as a function of core radius a and effective index. The wavelength is plotted only in the window of 1000-2000 nm. The white line represents the cutoff wavelength of the HE11 mode, on which the effective index and the propagation constant Re(kz ) equal zero. To have a mode guiding inside the core region, the effective index has to be larger than the refractive index of SiN x (~2.0: dashed line in (a)). This also regulates the choice of cavity radius to be larger than ~70 nm.

Fig. 5
Fig. 5

(a) The cross-section of a core-shell waveguide with perfect electrical conductor (PEC) surroundings. (b) A cavity formed of shorting both ends of a waveguide in (a) with a cavity length of L.

Fig. 6
Fig. 6

Calculated resonance wavelengths of the higher order modes by a full 3D structure FDTD simulation. (a) The resonance wavelengths as a function of the core radius a of the six lowest order modes. (b) Mode chart of the structure curves with the same slope corresponding to the same longitudinal mode number (p/2nop )2.

Fig. 7
Fig. 7

The cavity resonance wavelength as a function of the core radius a of various cavity heights L from 180 to 320 nm. The SiN x shell thickness is fixed at 50 nm. The resonance wavelength with a solid curve is the core (dielectric) mode with n eff > n shell. Fields concentrate inside the core region. The resonance wavelength with a dashed curve is the shell mode with n eff < n shell. Fields leak out of the core region and the wave can propagate inside the shell region. Lines of waveguide cutoff and transition from core mode to shell mode (n eff = n shell = 2.0) are plotted. A PEC model (Section 3) with the metal wall receding by a skin-depth is used in these calculations.

Fig. 8
Fig. 8

(a) Top view of z component of electric and magnetic fields of HE111 mode. (b) Side view of all field components inside the cavity. Note the azimuthal dependence for (b) has been suppressed for simplicity.

Fig. 9
Fig. 9

(a) Calculated resonance wavelengths of various cavity heights as a function of radius a using the FDTD method (solid curves) for the real structure (including the complex permittivity of the metal) compared with those using the PEC model (dashed curves) presented in Section 3. (b) Calculated cavity quality factors as a function of radius. The maximum quality factor is around 275 for all cavity heights.

Fig. 10
Fig. 10

(a) The radiation quality factor Qrad of cavities as a function of the core radius a for various heights L = 220 to 300 nm. The peaks represent the coupling to a resonance structure. (b) The material quality factor Qmat as a function of radius. The material quality factor has only a minimum change among different cavity heights and radii. A sharp drop at around R = 100 nm depicts the transition from core modes to shell modes.

Fig. 11
Fig. 11

The energy confinement factor (a) and extraction efficiency (b) of the cavity as a function of the core radius a with different cavity heights (220 nm – 300 nm). In the inner mode region, ΓE is above 0.6.

Fig. 12
Fig. 12

(a) The physical cavity volume and (b) the threshold material gain for different cavity heights L = 220 to 300 nm. The cavity volume approaches the diffraction limit ~(λ 0/2n)3. The threshold can be as low as 600 cm−1 for a≥ 250 nm and cavity heights L≥ 240 nm.

Fig. 13
Fig. 13

The physical properties for different SiN x shell thicknesses s = 20 to 80 nm. (a) The resonance wavelength. (b) The quality factor of the cavity Q. (c) The computed radiation quality factor Qrad . (d) The material quality factor Qmat . (e) The energy confinement factor ΓE. (f) The threshold material gain gth .

Fig. 14
Fig. 14

The cavity properties with different metal reflector thicknesses from 20 nm to 80 nm. (a) The resonance wavelength. (b) The quality factor of the cavity Q. (c) The computed radiation quality factor Qrad . (d) The material quality factor Qmat . (e) The energy confinement factor ΓE. (f) The threshold material gain gth .

Fig. 15
Fig. 15

Computed far field radiation pattern of Hz and Eρ components. Note the azimuthal dependence (e ± ) has been suppressed.

Fig. 16
Fig. 16

Far-field radiation patterns of cavity with different radii, a, from 130 to 370 nm. The azimuthal dependence has been assumed to be e ± . The radiation pattern narrows as the aperture size (radius) increases.

Fig. 17
Fig. 17

Material gain spectra of bulk In0.53Ga0.47As at different injected carrier densities at room temperature.

Fig. 18
Fig. 18

(a) The L-I curve at room temperature of a device with a = 190 nm, SiN x shell thickness = 50 nm, b = 240 nm, metal reflector thickness = 50 nm, and cavity height = 240 nm. (b) The transition rates of the corresponding device. The stimulated emission rate starts to take over after 0.12 mA. (Inset) The turning point from stimulated absorption to stimulated emission (red).

Fig. 19
Fig. 19

The light output power as a function of the injected current (L-I curves) of devices with different metal reflector thicknesses from 30 nm to 80 nm. A transition point when the stimulated emission rate equals the non-radiative recombination rate is plotted as the green symbols. Also, the transition point when the stimulated emission rate equals the spontaneous emission is plotted as the orange symbols.

Equations (48)

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k ρ 2 + k z 2 = ω 2 μ ε c o r e = ( 2 π λ 0 n core ) 2 ,
( 2 π λ c n core ) = k ρ = χ m n b .
Ε m n p ( ρ , φ , z ) = Ε m n + ( ρ , φ ) e i k z z + Ε m n ( ρ , φ ) e i k z z ,
H m n p ( ρ , φ , z ) = H m n + ( ρ , φ ) e i k z z + H m n ( ρ , φ ) e i k z z ,
E m n + ( ρ , φ ) = E m n t ( ρ , φ ) + E m n z ( ρ , φ ) ,
E m n ( ρ , φ ) = E m n t ( ρ , φ ) E m n z ( ρ , φ ) ,
H m n + ( ρ , φ ) = H m n t ( ρ , φ ) + H m n z ( ρ , φ ) ,
H m n ( ρ , φ ) = H m n t ( ρ , φ ) + H m n z ( ρ , φ ) ,
E -profile : { E z , m n p ~ E m n z ( ρ , φ ) cos ( p π L z ) E ρ , m n p ~ E m n ρ ( ρ , φ ) sin ( p π L z ) E φ , m n p ~ E m n φ ( ρ , φ ) sin ( p π L z ) ,
H -profile: { H z , m n p ~ H m n z ( ρ , φ ) sin ( p π L z ) H ρ , m n p ~ H m n ρ ( ρ , φ ) cos ( p π L z ) H φ , m n p ~ H m n φ ( ρ , φ ) cos ( p π L z ) .
( b λ ) 2 = ( p 2 n core ) 2 ( b L ) 2 + ( χ m n 2 π n core ) 2 ,
λ m n p = 2 π n core ( χ m n b ) 2 + ( p π L ) 2 = 2 π n core ( χ m n a + s ) 2 + ( p π L ) 2 .
Q r a d = 2 π energy   stored   in   cavity radiated   energy   per   optical   period = ω W P r a d           = ω V d r ε 0 4 [ ε g ( r ) + ε R ( r ) ] | E ( r ) | 2 S d s 1 2 Re [ E ( r ) × H * ( r ) ] n ^ ,
ε g ( r ) = [ ω ε R ( r ) ] ω .
Q 1 = Q m a t 1 + Q r a d 1 .
Γ E = V a d r ε 0 4 [ ε g ( r ) + ε R ( r ) ] | E ( r ) | 2 V d r ε 0 4 [ ε g ( r ) + ε R ( r ) ] | E ( r ) | 2 ,
η e x t = Q r a d 1 Q 1 .
g t h = 2 π n g Q Γ E λ ,
I ( θ , φ ) = P ( r , θ , φ ) r ^ Max[ P ( r , θ , φ ) r ^ ] ,
n t = η I q V a R n r ( n ) R s p , c o n t ( n ) R s p ( n ) R s t ( n ) S ,
S t = S τ p + Γ E R s p ( n ) + Γ E R s t ( n ) S ,
R n r ( n ) = A n + C n 3 ,
R s p , c o n t ( n ) = 1 τ r a d V a c , v , k f c , k ( 1 f v , k ) ,
R s t = υ g g ( n ) .
Core   Region:   E z c = A F 1 ( ρ ) sin ( m φ ) e i k z z ,
H z c = B F 2 ( ρ ) cos ( m φ ) e i k z z ,
E ρ c = 1 k ρ c 2 [ A i k z F ' 1 ( ρ ) B i ω μ m ρ F 2 ( ρ ) ] sin ( m φ ) e i k z z ,
E φ c = 1 k ρ c 2 [ A i k z m ρ F 1 ( ρ ) B i ω μ k ρ c F ' 2 ( ρ ) ] cos ( m φ ) e i k z z ,
H ρ c = 1 k ρ c 2 [ A i ω ε core m ρ F 1 ( ρ ) + B i k z k ρ c F ' 2 ( ρ ) ] cos ( m φ ) e i k z z ,
H φ c = 1 k ρ c 2 [ A i ω ε c o r e k ρ c F ' 1 ( ρ ) B i k z m ρ F 2 ( ρ ) ] sin ( m φ ) e i k z z ,
Shell   Region:   E z s = C F 3 ( ρ ) sin ( m φ ) e i k z z ,
H z s = D F 4 ( ρ ) cos ( m φ ) e i k z z ,
E ρ s = 1 k ρ s 2 [ C i k z F ' 3 ( ρ ) D i ω μ m ρ F 4 ( ρ ) ] sin ( m φ ) e i k z z ,
E φ s = 1 k ρ s 2 [ C i k z m ρ F 3 ( ρ ) D i ω μ k ρ s F ' 4 ( ρ ) ] cos ( m φ ) e i k z z ,
H ρ s = 1 k ρ s 2 [ C i ω ε s m ρ F 3 ( ρ ) + D i k z k ρ s F ' 4 ( ρ ) ] cos ( m φ ) e i k z z ,
H φ s = 1 k ρ s 2 [ C i ω ε s k ρ s F ' 3 ( ρ ) D i k z m ρ F 4 ( ρ ) ] sin ( m φ ) e i k z z ,
{ k ρ s 2 + k z 2 = ω 2 μ ε s , k ρ c 2 + k z 2 = ω 2 μ ε c o r e .
F 1 ( ρ ) = J m ( k ρ c ρ ) ,
F 2 ( ρ ) = J m ( k ρ c ρ ) .
F 3 ( ρ ) = K m ( k ρ s ρ ) I m ( k ρ s b ) I m ( k ρ s ρ ) K m ( k ρ s b ) ,
F 4 ( ρ ) = K m ( k ρ s ρ ) I ' m ( k ρ s b ) I m ( k ρ s ρ ) K ' m ( k ρ s b ) ,
A F 1 ( a ) = C F 3 ( a ) ,
B F 2 ( a ) = D F 4 ( a ) ,
1 k ρ c 2 [ B k z m a F 2 ( a ) + A ω ε c o r e k ρ c F ' 1 ( a ) ] = 1 k ρ s 2 [ D k z m a F 4 ( a ) + C ω ε s k ρ s F ' 3 ( a ) ] ,
1 k ρ c 2 [ A k z m a F 1 ( a ) B ω μ k ρ c F ' 2 ( a ) ] = 1 k ρ s 2 [ C k z m a F 3 ( a ) D ω μ k ρ s F ' 4 ( a ) ] .
| F 1 ( a ) 0 F 3 ( a ) 0 0 F 2 ( a ) 0 F 4 ( a ) ω ε c o r e F ' 1 ( a ) k ρ c k z m a k ρ c 2 F 2 ( a ) ω ε s F ' 3 ( a ) k ρ s k z m a k ρ s 2 F 4 ( a ) k z m a k ρ c 2 F 1 ( a ) ω μ F ' 2 ( a ) k ρ c k z m a k ρ s 2 F 3 ( a ) ω μ F ' 4 ( a ) k ρ s | = 0.
( ε s k ρ s F 1 F ' 3 ε c o r e k ρ c F ' 1 F 3 ) = 0   for   TM 0 n ,
( 1 k ρ s F 2 F ' 4 1 k ρ c F ' 2 F 4 ) = 0   for   TE 0 n .

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