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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 15 — Jul. 16, 2012
  • pp: 16348–16357
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Interplay of various loss mechanisms and ultimate size limit of a surface plasmon polariton semiconductor nanolaser

D. B. Li and C. Z. Ning  »View Author Affiliations


Optics Express, Vol. 20, Issue 15, pp. 16348-16357 (2012)
http://dx.doi.org/10.1364/OE.20.016348


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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 × 10-4 λ 0 3 , potentially the smallest semiconductor nanolasers designed or demonstrated so far.

© 2012 OSA

1. Introduction

2. Interplay of loss mechanisms and parametric dependent study

2.1 Dependence on gain layer thickness

2.2 Dependence on in-plane sizes

2.3 Dependence on metal layer thickness

The metal cladding layers are usually designed to be thick enough to prevent mode leakage from the core. However, as we will show later, using thin metal layer is crucial in reducing lasing threshold gain further. Therefore it is necessary to study the influence of the thickness of metal layer. Figure 5(a)
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.
shows the energy profile in the x-z plane for three different values of metal layer thickness. We can see that, as the metal layer thickness increases from 5 to 20 nm, less energy leaks through the metal claddings and most of the light comes out from the side of the cavity in the z direction. The percentage of the energy leaked through the metal cladding as a function of metal layer thickness is plotted in Fig. 5(b). We can see that the leakage decreases exponentially as metal layer thickness increases linearly, and less than 0.1% of the energy leaks through the metal cladding if the thickness of metal layer is 15 nm and thicker. Figure 5(c) shows the relation between the minimum threshold gain and metal layer thickness. The minimum threshold gain increases rapidly from hm = 5 nm to 15 nm and keeps nearly constant as hm>20 nm. The reduction of the minimum threshold gain with decreased metal thickness is partly due to the decreased metal loss, but mainly due to the red shift of the mode with the minimum threshold (TM014 mode). The red-shift of the mode is probably caused by the coupling between the modes inside the core and those outside the metal.

2.4 Effects of insulating layer between metal and gain layers

3. AlGaAs/GaAs quantum well nanolaser: a design example

Using the design and optimization procedures for the MSM cavity discussed above, we now consider a specific example: an Al0.3Ga0.7As/GaAs/Al0.3Ga0.7As single quantum well structure sandwiched between two Ag layers, as shown in Fig. 7(a)
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.
. The thickness of Al0.3Ga0.7As, GaAs and Ag layers is optimized to be 1.5 nm, 5 nm and 15 nm, respectively, and the length and width of the cavity is 100 nm. With the separation of 1.5nm-thick AlGaAs layer, dipole quenching due to pair excitations can be well suppressed. For the electrical injection operation, the whole cavity is usually coated by silicon nitride (SiNx) in the device fabrication for electric isolation and mechanical support [3

3. 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. Photonics 1(10), 589–594 (2007). [CrossRef]

, 4

4. 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]

, 10

10. 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]

]. We use the dielectric constant of silicon nitride in the near infrared range as the ambient dielectric constant (~4). The dielectric constant of AlxGa1-xAs and GaAs can be found in Ref [32

32. 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]

]. Since the material gain is available within a limited frequency range above the bandgap of the active semiconductor, we only study the modes within the gain bandwidth of AlGaAs/GaAs single quantum well (from 1.45 to 1.7 eV according to Ref [25

25. W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals (Springer-Verlag, Berlin, 1999).

].). Our simulation results showed that two modes, TM014 and TM015 exist in this range, as shown in Fig. 7(b). The peak wavelength of TM014 mode is λ0 = 813 nm (1.525 eV) and the lasing threshold gain is 3859 cm−1, achievable at room temperature according to a theoretical calculation [33

33. 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]

]. Since the plasmonic modes have two strong electric field components in the x and z direction, respectively, material gain due to the in-plane (TE) and off-plane (TM) dipole transitions in the quantum well contributes to the mode. The quality factor for this mode without material gain is about 52. TM015 mode is at λ0 = 740 nm (1.677 eV) whose quality factor and lasing threshold gain is 66 and 3641 cm−1. Although the threshold gain is slightly smaller than that of TM014 mode, it can hardly be achieved since the TM gain provided to TM015 mode is from the transition between the first excited state in the conduction band and the first excited state in the light-hole band, which is too small to satisfy the requirement of the threshold gain [25

25. W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals (Springer-Verlag, Berlin, 1999).

]. The cavity hence works as a single-mode device. The physical volume of the Al0.3Ga0.7As/GaAs/Al0.3Ga0.7As cavity is only 8 × 10−5 μm3 (~1.5 × 10-4 λ03), which is the smallest nano-laser cavity reported so far. The total volume of the structure, including metal layers, is 3.8 × 10−4 μm3 (~7.1 × 10-4 λ03). Figure 7(c) shows the near field energy density pattern of TM014 mode at the lasing threshold in the x-z plane. We can see most energy is confined in the cavity, as shown by the deep red color. The far-field pattern, shown in Fig. 7(d), is an important characteristic of any laser. As can be seen, the full-width at the half-maximum of the far-field angle is ~92°.

4. Summary

We point out that many of the quantitative results of this paper depend on the values of metal losses we use for Ag. The values in [24

24. P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

] which were used for our simulation are known to overestimate the metal loss, most likely because they were obtained with metals of low quality available at the time. According to the more recent dielectric function data [34

34. D. W. Lynch and W. R. Hunter, in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, New York, 1998).

] for Ag, the threshold gain could be smaller since the Ag material loss (given by Eq. (1) with a positive sign) is 5% to 10% smaller than that calculated by using Ag dielectric function data from Ref [24

24. P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

]. within the wavelength range studied here. Therefore, the threshold gain required here is likely larger and thus our design and feasibility study represent a more conservative upper limit. We believe that with the improvement of deposition techniques of metals, metal loss can be further reduced, increasing the likelihood of observing the SPP mode lasing studied here. Our results and conclusions can serve as the guideline of the design and optimization of SPP nanolasers.

Acknowledgments

This research was supported by the Defense Advanced Research Project Agency (DARPA) program Nanoscale Architectures of Coherent Hyper-Optical Sources (NACHOS) (Grant No. W911-NF07-1-0314) and by the Air Force Office of Scientific Research (Grant No. FA9550-10-1-0444, Gernot Pomrenke).

References and links

1.

C. Z. Ning, “Semiconductor nanolasers,” Phys. Status Solidi B 247, 774–788 (2010).

2.

M. T. Hill, “Status and prospects for metallic and plasmonic nano-lasers,” J. Opt. Soc. Am. B 27(11), B36–B44 (2010). [CrossRef]

3.

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. Photonics 1(10), 589–594 (2007). [CrossRef]

4.

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]

5.

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,” Nature 461(7264), 629–632 (2009). [CrossRef] [PubMed]

6.

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]

7.

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]

8.

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

9.

C. Y. Lu and S. L. Chuang, “A surface-emitting 3D metal-nanocavity laser: proposal and theory,” Opt. Express 19(14), 13225–13244 (2011). [CrossRef] [PubMed]

10.

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]

11.

K. Ding, Z. C. Liu, L. J. Yin, M. T. Hill, M. J. H. Marell, P. J. van Veldhoven, R. Nöetzel, and C. Z. Ning, “Room-temperature continuous wave lasing in deep-subwavelength metallic cavities under electrical injection,” Phys. Rev. B 85(4), 041301 (2012). [CrossRef]

12.

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. Express 19(16), 15109–15118 (2011). [CrossRef] [PubMed]

13.

A. V. Maslov and C. Z. Ning, “Size reduction of a semiconductor nanowire laser by using metal coating,” Proc. SPIE 6468, 646801 (2007).

14.

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]

15.

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,” Nature 460(7259), 1110–1112 (2009). [CrossRef] [PubMed]

16.

D. B. Li and C. Z. Ning, “All-semiconductor active plasmonic system in mid-infrared wavelengths,” Opt. Express 19(15), 14594–14603 (2011). [CrossRef] [PubMed]

17.

S. Maier, Plasmonics: Fundamentals and Applications (Springer, Berlin, 2007).

18.

M. P. Nezhad, K. Tetz, and Y. Fainman, “Gain assisted propagation of surface plasmon polaritons on planar metallic waveguides,” Opt. Express 12(17), 4072–4079 (2004). [CrossRef] [PubMed]

19.

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

20.

M. A. Noginov, V. A. Podolskiy, G. Zhu, M. Mayy, M. Bahoura, J. A. Adegoke, B. A. Ritzo, and K. Reynolds, “Compensation of loss in propagating surface plasmon polariton by gain in adjacent dielectric medium,” Opt. Express 16(2), 1385–1392 (2008). [CrossRef] [PubMed]

21.

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. B 80(15), 153304 (2009). [CrossRef]

22.

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. Express 18(16), 16327–16334 (2010). [CrossRef] [PubMed]

23.

www.comsol.com.

24.

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

25.

W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals (Springer-Verlag, Berlin, 1999).

26.

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

27.

H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 5th ed. (World Scientific, Hoboken, 2009).

28.

C. Manolatou and F. Rana, “Subwavelength Nanopatch Cavities for Semiconductor Plasmon Lasers,” IEEE J. Quantum Electron. 44(5), 435–447 (2008). [CrossRef]

29.

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]

30.

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]

31.

V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29(11), 1209–1211 (2004). [CrossRef] [PubMed]

32.

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]

33.

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]

34.

D. W. Lynch and W. R. Hunter, in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, New York, 1998).

OCIS Codes
(250.5403) Optoelectronics : Plasmonics
(250.5960) Optoelectronics : Semiconductor lasers

ToC Category:
Optoelectronics

History
Original Manuscript: April 24, 2012
Revised Manuscript: May 28, 2012
Manuscript Accepted: June 22, 2012
Published: July 3, 2012

Citation
D. B. Li and C. Z. Ning, "Interplay of various loss mechanisms and ultimate size limit of a surface plasmon polariton semiconductor nanolaser," Opt. Express 20, 16348-16357 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-15-16348


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References

  1. C. Z. Ning, “Semiconductor nanolasers,” Phys. Status Solidi B247, 774–788 (2010).
  2. M. T. Hill, “Status and prospects for metallic and plasmonic nano-lasers,” J. Opt. Soc. Am. B27(11), B36–B44 (2010). [CrossRef]
  3. 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]
  4. 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]
  5. 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]
  6. 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]
  7. 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]
  8. K. Yu, A. Lakhani, and M. C. Wu, “Subwavelength metal-optic semiconductor nanopatch lasers,” Opt. Express18(9), 8790–8799 (2010). [CrossRef] [PubMed]
  9. C. Y. Lu and S. L. Chuang, “A surface-emitting 3D metal-nanocavity laser: proposal and theory,” Opt. Express19(14), 13225–13244 (2011). [CrossRef] [PubMed]
  10. 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]
  11. 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]
  12. 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]
  13. A. V. Maslov and C. Z. Ning, “Size reduction of a semiconductor nanowire laser by using metal coating,” Proc. SPIE6468, 646801 (2007).
  14. 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]
  15. 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]
  16. D. B. Li and C. Z. Ning, “All-semiconductor active plasmonic system in mid-infrared wavelengths,” Opt. Express19(15), 14594–14603 (2011). [CrossRef] [PubMed]
  17. S. Maier, Plasmonics: Fundamentals and Applications (Springer, Berlin, 2007).
  18. M. P. Nezhad, K. Tetz, and Y. Fainman, “Gain assisted propagation of surface plasmon polaritons on planar metallic waveguides,” Opt. Express12(17), 4072–4079 (2004). [CrossRef] [PubMed]
  19. S. Maier, “Gain-assisted propagation of electromagnetic energy in subwavelength surface plasmon polariton gap waveguides,” Opt. Commun.258(2), 295–299 (2006). [CrossRef]
  20. M. A. Noginov, V. A. Podolskiy, G. Zhu, M. Mayy, M. Bahoura, J. A. Adegoke, B. A. Ritzo, and K. Reynolds, “Compensation of loss in propagating surface plasmon polariton by gain in adjacent dielectric medium,” Opt. Express16(2), 1385–1392 (2008). [CrossRef] [PubMed]
  21. 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]
  22. 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]
  23. www.comsol.com .
  24. P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B6(12), 4370–4379 (1972). [CrossRef]
  25. W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals (Springer-Verlag, Berlin, 1999).
  26. G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep.113(4), 195–287 (1984). [CrossRef]
  27. H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 5th ed. (World Scientific, Hoboken, 2009).
  28. C. Manolatou and F. Rana, “Subwavelength Nanopatch Cavities for Semiconductor Plasmon Lasers,” IEEE J. Quantum Electron.44(5), 435–447 (2008). [CrossRef]
  29. 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]
  30. 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]
  31. V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett.29(11), 1209–1211 (2004). [CrossRef] [PubMed]
  32. 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]
  33. 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]
  34. D. W. Lynch and W. R. Hunter, in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, New York, 1998).

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