Abstract

The issue of an ultimate size limit of a surface plasmon polariton (SSP) nanolaser is investigated by a systematic simulation study. We consider a prototypic design of a metal-insulator-semiconductor multi-layer structure with finite, varying lateral sizes. Our focus is on the design of such lasers operating at room temperature under the electrical injection. We find that there is an interesting interplay between the facet loss and the SPP propagation loss and that such interplay leads to the existence of a minimum-threshold mode in each mode group. The red-shift of the minimum-threshold mode with the decrease of device thickness leads to a further reduction of threshold gain, making the threshold for the SPP nanolaser achievable for many semiconductors, even at room temperature. In addition, we find that the threshold can be further reduced by using thinner metal cladding without much exacerbated mode leakage. Finally, a specific design example is optimized using Al0.3Ga0.7As/GaAs/Al0.3Ga0.7As single quantum well sandwiched between silver layers, which has a physical volume of 1.5 × 10-4λ03, potentially the smallest semiconductor nanolasers designed or demonstrated so far.

© 2012 OSA

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2012 (1)

K. Ding, Z. C. Liu, L. J. Yin, M. T. Hill, M. J. H. Marell, P. J. van Veldhoven, R. Nöetzel, and C. Z. Ning, “Room-temperature continuous wave lasing in deep-subwavelength metallic cavities under electrical injection,” Phys. Rev. B85(4), 041301 (2012).
[CrossRef]

2011 (4)

2010 (7)

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. Photonics4(6), 395–399 (2010).
[CrossRef]

K. Yu, A. Lakhani, and M. C. Wu, “Subwavelength metal-optic semiconductor nanopatch lasers,” Opt. Express18(9), 8790–8799 (2010).
[CrossRef] [PubMed]

C. Z. Ning, “Semiconductor nanolasers,” Phys. Status Solidi B247, 774–788 (2010).

M. T. Hill, “Status and prospects for metallic and plasmonic nano-lasers,” J. Opt. Soc. Am. B27(11), B36–B44 (2010).
[CrossRef]

G. Colas des Francs, P. Bramant, J. Grandidier, A. Bouhelier, J.-C. Weeber, and A. Dereux, “Optical gain, spontaneous and stimulated emission of surface plasmon polaritons in confined plasmonic waveguide,” Opt. Express18(16), 16327–16334 (2010).
[CrossRef] [PubMed]

D. B. Li and C. Z. Ning, “Peculiar features of confinement factors in a metal-semiconductor waveguide,” Appl. Phys. Lett.96(18), 181109 (2010).
[CrossRef]

2009 (4)

D. B. Li and C. Z. Ning, “Giant modal gain, amplified surface plasmon-polariton propagation, and slowing down of energy velocity in a metal-semiconductor-metal structure,” Phys. Rev. B80(15), 153304 (2009).
[CrossRef]

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. Express17(13), 11107–11112 (2009).
[CrossRef] [PubMed]

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature461(7264), 629–632 (2009).
[CrossRef] [PubMed]

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

2008 (3)

2007 (2)

A. V. Maslov and C. Z. Ning, “Size reduction of a semiconductor nanowire laser by using metal coating,” Proc. SPIE6468, 646801 (2007).

M. 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. Photonics1(10), 589–594 (2007).
[CrossRef]

2006 (1)

S. Maier, “Gain-assisted propagation of electromagnetic energy in subwavelength surface plasmon polariton gap waveguides,” Opt. Commun.258(2), 295–299 (2006).
[CrossRef]

2004 (2)

2003 (1)

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett.90(2), 027402 (2003).
[CrossRef] [PubMed]

1989 (1)

W. Batty, U. Ekenberg, A. Ghit, and E. P. O'Reilly, “Valence subband structure and optical gain of GaAs-AlGaAs (111) quantum wells,” Semicond. Sci. Technol.4(11), 904–909 (1989).
[CrossRef]

1985 (1)

S. Adachi, “GaAs, AlAs, and AlxGa1−xAs B: Material parameters for use in research and device applications,” J. Appl. Phys.58(3), R1–R29 (1985).
[CrossRef]

1984 (1)

G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep.113(4), 195–287 (1984).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Adachi, S.

S. Adachi, “GaAs, AlAs, and AlxGa1−xAs B: Material parameters for use in research and device applications,” J. Appl. Phys.58(3), R1–R29 (1985).
[CrossRef]

Adegoke, J. A.

Almeida, V. R.

Bahoura, M.

Bakker, R.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

Barcones, B.

Barrios, C. A.

Bartal, G.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature461(7264), 629–632 (2009).
[CrossRef] [PubMed]

Batty, W.

W. Batty, U. Ekenberg, A. Ghit, and E. P. O'Reilly, “Valence subband structure and optical gain of GaAs-AlGaAs (111) quantum wells,” Semicond. Sci. Technol.4(11), 904–909 (1989).
[CrossRef]

Belgrave, A. M.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

Bergman, D. J.

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett.90(2), 027402 (2003).
[CrossRef] [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. Photonics4(6), 395–399 (2010).
[CrossRef]

Bouhelier, A.

Bramant, P.

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Chuang, S. L.

Colas des Francs, G.

Dai, L.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature461(7264), 629–632 (2009).
[CrossRef] [PubMed]

de Vries, T.

M. 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. Photonics1(10), 589–594 (2007).
[CrossRef]

de Waardt, H.

M. 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. Photonics1(10), 589–594 (2007).
[CrossRef]

Dereux, A.

Ding, K.

K. Ding, Z. C. Liu, L. J. Yin, M. T. Hill, M. J. H. Marell, P. J. van Veldhoven, R. Nöetzel, and C. Z. Ning, “Room-temperature continuous wave lasing in deep-subwavelength metallic cavities under electrical injection,” Phys. Rev. B85(4), 041301 (2012).
[CrossRef]

K. Ding, Z. C. Liu, L. J. Yin, H. Wang, R. B. Liu, M. T. Hill, M. J. H. Marell, P. J. van Veldhoven, R. Nötzel, and C. Z. Ning, “Electrical injection, continuous wave operation of subwavelength-metallic-cavity lasers at 260 K,” Appl. Phys. Lett.98(23), 231108 (2011).
[CrossRef]

Eijkemans, T. J.

M. 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. Photonics1(10), 589–594 (2007).
[CrossRef]

Ekenberg, U.

W. Batty, U. Ekenberg, A. Ghit, and E. P. O'Reilly, “Valence subband structure and optical gain of GaAs-AlGaAs (111) quantum wells,” Semicond. Sci. Technol.4(11), 904–909 (1989).
[CrossRef]

Fainman, Y.

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. Photonics4(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]

Ford, G. W.

G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep.113(4), 195–287 (1984).
[CrossRef]

Geluk, E. J.

Ghit, A.

W. Batty, U. Ekenberg, A. Ghit, and E. P. O'Reilly, “Valence subband structure and optical gain of GaAs-AlGaAs (111) quantum wells,” Semicond. Sci. Technol.4(11), 904–909 (1989).
[CrossRef]

Gladden, C.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature461(7264), 629–632 (2009).
[CrossRef] [PubMed]

Grandidier, J.

Herz, E.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

Hill, M.

M. 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. Photonics1(10), 589–594 (2007).
[CrossRef]

Hill, M. T.

K. Ding, Z. C. Liu, L. J. Yin, M. T. Hill, M. J. H. Marell, P. J. van Veldhoven, R. Nöetzel, and C. Z. Ning, “Room-temperature continuous wave lasing in deep-subwavelength metallic cavities under electrical injection,” Phys. Rev. B85(4), 041301 (2012).
[CrossRef]

M. J. Marell, B. Smalbrugge, E. J. Geluk, P. J. van Veldhoven, B. Barcones, B. Koopmans, R. Nötzel, M. K. Smit, and M. T. Hill, “Plasmonic distributed feedback lasers at telecommunications wavelengths,” Opt. Express19(16), 15109–15118 (2011).
[CrossRef] [PubMed]

K. Ding, Z. C. Liu, L. J. Yin, H. Wang, R. B. Liu, M. T. Hill, M. J. H. Marell, P. J. van Veldhoven, R. Nötzel, and C. Z. Ning, “Electrical injection, continuous wave operation of subwavelength-metallic-cavity lasers at 260 K,” Appl. Phys. Lett.98(23), 231108 (2011).
[CrossRef]

M. T. Hill, “Status and prospects for metallic and plasmonic nano-lasers,” J. Opt. Soc. Am. B27(11), B36–B44 (2010).
[CrossRef]

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. Express17(13), 11107–11112 (2009).
[CrossRef] [PubMed]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Kang, J. H.

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

Karouta, F.

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]

Koopmans, B.

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]

Kwon, S.-H.

M. 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. Photonics1(10), 589–594 (2007).
[CrossRef]

Lakhani, A.

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]

Lee, Y.-H.

M. 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. Photonics1(10), 589–594 (2007).
[CrossRef]

Leong, E. S. P.

Li, D. B.

D. B. Li and C. Z. Ning, “All-semiconductor active plasmonic system in mid-infrared wavelengths,” Opt. Express19(15), 14594–14603 (2011).
[CrossRef] [PubMed]

D. B. Li and C. Z. Ning, “Peculiar features of confinement factors in a metal-semiconductor waveguide,” Appl. Phys. Lett.96(18), 181109 (2010).
[CrossRef]

D. B. Li and C. Z. Ning, “Giant modal gain, amplified surface plasmon-polariton propagation, and slowing down of energy velocity in a metal-semiconductor-metal structure,” Phys. Rev. B80(15), 153304 (2009).
[CrossRef]

Lieber, C. M.

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M. J. Marell, B. Smalbrugge, E. J. Geluk, P. J. van Veldhoven, B. Barcones, B. Koopmans, R. Nötzel, M. K. Smit, and M. T. Hill, “Plasmonic distributed feedback lasers at telecommunications wavelengths,” Opt. Express19(16), 15109–15118 (2011).
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Figures (7)

Fig. 1
Fig. 1

(a) Schematic of a MSM cavity studied in this paper. (b) The intensity spectrum of a MSM cavity with W = L = 50 nm and hs = hm = 10 nm without gain. The color inset is the field pattern of TM012 mode in the x-z plane.

Fig. 2
Fig. 2

Threshold gain of consecutive TM01m (m = 1, 2, 3, …) modes (symbols connected by lines) in the cavity with different core layer thickness, hs. The threshold gain of all TM02m and TM03m modes in the cavity with hs = 10 nm is shown by the un-connected squares.

Fig. 3
Fig. 3

Threshold gain of consecutive TM01m (m = 1, 2, 3, …) modes for different in-plane sizes, W and L.

Fig. 4
Fig. 4

The minimum threshold gain vs. core layer thickness (a) with (dashed line) and without (solid line) pair-excitation loss, and vs. in-plane size (b). We also include the facet loss in Fig. 4(a) and the cavity volume (in λ 0 3 ) in Fig. 4(b).

Fig. 5
Fig. 5

(a) Energy profiles in the x-z plane with metal layer thicknesses: 5 nm, 10 nm, and 20 nm, for W = L = 100 nm and hs = 10 nm. (b) The percentage of the energy leaked through the metal cladding layers out of the cavity, (c) the minimum threshold gain, and (d) the position of the mode with minimum threshold gain as a function of the metal layer thickness.

Fig. 6
Fig. 6

(a) Minimum threshold gain as a function of the insulating layer thickness with a fixed total thickness of insulating and core layers of 20 nm. The |E|2 profile of a slot mode mixed with a SPP mode along the x axis in a MISIM cavity is shown in the inset. (b) Minimum threshold gain as a function of the core layer thickness with two values of the insulating layer thickness: 3 and 5 nm.

Fig. 7
Fig. 7

(a) Schematic structure of an optimized MISIM nanolaser. (b) Intensity spectrum of the nanolaser within the gain bandwidth of AlGaAs/GaAs/AlGaAs quantum well showing two possible modes. (c) Near field energy density pattern of the TM014 mode at lasing threshold in the x-z plane. (d) Angular dependence of the far field |E|2 radiation pattern of the TM014 mode at the lasing threshold in the z-x plane.

Equations (1)

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G 0 = ε s ω n s c

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