Abstract

In this paper we propose a structure to compensate the propagation loss of surface plasmons by using multiple quantum wells as a gain medium. We analyze the required gain for lossless surface plasmon propagation for different thicknesses and widths of the metallic guiding layer. We study the effects of the gain layers and a finite height superstrate on the surface plasmon mode and its propagation loss. It is shown that the gain required for lossless plasmon propagation is achievable with present technology.

©2007 Optical Society of America

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References

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  1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424,824–830 (2003).
    [Crossref] [PubMed]
  2. J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73,035407 (2006).
    [Crossref]
  3. J-Claude Weeber, A. Dereux, and C. Girard, “Plasmon polaritons of metallic nanowires for controlling submicron propagation of light,” Phys. Rev. B 60,9061–9068 (1999).
    [Crossref]
  4. J. J. Burke, G. I. Stegeman, and B. Lamprecht, “Surface polariton like waves guided by thin, lossy metal films,” Phys Rev B 33,5186–5201 (1986).
    [Crossref]
  5. A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, S. Larsen, and S. I. Bozhevolnyi, “Integrated Optical components utilizing long-range surface plasmon polaritons,” J. Lightwave Technol. 23,413–422 (2005).
    [Crossref]
  6. R. Charbonneau and N. Lahoud, “Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons,” Opt. Express 13,977–984 (2005).
    [Crossref] [PubMed]
  7. M. P. Nezhad, K. Tetz, and Y. Fainman, “Gain assisted propagation of surface plasmon polaritons on planar metallic waveguides,” Opt. Express 12,4072–4079 (2004).
    [Crossref] [PubMed]
  8. J. Seidel, S. Garfstrom, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett 94,117401 (2005).
    [Crossref]
  9. M. N. Akram, C. Silfvenius, O. Kjebon, and R. Schatz, “Design optimization of InGaAsP-InGaAlAs 1.55 μm strain-compensated MQW lasers for direct modulation applications,” Semicond. Sci. Technol. 19,615–625 (2004).
    [Crossref]
  10. S. Y. Hu, D. B. Young, S. W. Corzine, A. C. Gossard, and L. A. Coldren, “High-efficiency and low-threshold InGaAs/AlGaAs quantum well lasers,” J. Appl. Phys. 76,3932–3934 (1994).
    [Crossref]
  11. E. D. Palik, “Handbook of optical constants of solids,” (Academic Press, 1985).
  12. I. G. Breukellar, Surface plasmon-polaritons in thin metal strips and slabs: Waveguiding and mode cutoff, M. A. Sc. Thesis, (University of Ottawa, 2004).
  13. Electromagnetics Module User’s Guide (Comsol, 2005).
  14. E. P. Berini, “Plasmon polaritron waves guided by thin lossy metal films of finite width: Bound modes of asymmetric structures,” Phys. Rev. B 63,125417 (2001).
    [Crossref]
  15. A. M. Agarwal, L. Liao, J. S. Foresi, M. R. Black, X. Duan, and L. C. Kimerling, “Low-loss polycrystalline silicon waveguides for silicon photonics,” J. Appl. Phys. 80,6120–6123 (1996).
    [Crossref]
  16. M. I. Manssor and E. A. Davis, “Optical and electrical characteristics of a-GaAs and a-AlGaAs prepared by radio-frequency sputtering,” J. Phys.-Condens. Mat. 2,8063–8074 (1990).
    [Crossref]
  17. A. Degiron and D. R. Smith, “Numerical modeling of long-range plasmons,” Opt. Express 14,1611–16252006.
    [Crossref] [PubMed]

2006 (2)

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

A. Degiron and D. R. Smith, “Numerical modeling of long-range plasmons,” Opt. Express 14,1611–16252006.
[Crossref] [PubMed]

2005 (3)

2004 (2)

M. N. Akram, C. Silfvenius, O. Kjebon, and R. Schatz, “Design optimization of InGaAsP-InGaAlAs 1.55 μm strain-compensated MQW lasers for direct modulation applications,” Semicond. Sci. Technol. 19,615–625 (2004).
[Crossref]

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

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424,824–830 (2003).
[Crossref] [PubMed]

2001 (1)

E. P. Berini, “Plasmon polaritron waves guided by thin lossy metal films of finite width: Bound modes of asymmetric structures,” Phys. Rev. B 63,125417 (2001).
[Crossref]

1999 (1)

J-Claude Weeber, A. Dereux, and C. Girard, “Plasmon polaritons of metallic nanowires for controlling submicron propagation of light,” Phys. Rev. B 60,9061–9068 (1999).
[Crossref]

1996 (1)

A. M. Agarwal, L. Liao, J. S. Foresi, M. R. Black, X. Duan, and L. C. Kimerling, “Low-loss polycrystalline silicon waveguides for silicon photonics,” J. Appl. Phys. 80,6120–6123 (1996).
[Crossref]

1994 (1)

S. Y. Hu, D. B. Young, S. W. Corzine, A. C. Gossard, and L. A. Coldren, “High-efficiency and low-threshold InGaAs/AlGaAs quantum well lasers,” J. Appl. Phys. 76,3932–3934 (1994).
[Crossref]

1990 (1)

M. I. Manssor and E. A. Davis, “Optical and electrical characteristics of a-GaAs and a-AlGaAs prepared by radio-frequency sputtering,” J. Phys.-Condens. Mat. 2,8063–8074 (1990).
[Crossref]

1986 (1)

J. J. Burke, G. I. Stegeman, and B. Lamprecht, “Surface polariton like waves guided by thin, lossy metal films,” Phys Rev B 33,5186–5201 (1986).
[Crossref]

Agarwal, A. M.

A. M. Agarwal, L. Liao, J. S. Foresi, M. R. Black, X. Duan, and L. C. Kimerling, “Low-loss polycrystalline silicon waveguides for silicon photonics,” J. Appl. Phys. 80,6120–6123 (1996).
[Crossref]

Akram, M. N.

M. N. Akram, C. Silfvenius, O. Kjebon, and R. Schatz, “Design optimization of InGaAsP-InGaAlAs 1.55 μm strain-compensated MQW lasers for direct modulation applications,” Semicond. Sci. Technol. 19,615–625 (2004).
[Crossref]

Atwater, H. A.

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

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424,824–830 (2003).
[Crossref] [PubMed]

Berini, E. P.

E. P. Berini, “Plasmon polaritron waves guided by thin lossy metal films of finite width: Bound modes of asymmetric structures,” Phys. Rev. B 63,125417 (2001).
[Crossref]

Black, M. R.

A. M. Agarwal, L. Liao, J. S. Foresi, M. R. Black, X. Duan, and L. C. Kimerling, “Low-loss polycrystalline silicon waveguides for silicon photonics,” J. Appl. Phys. 80,6120–6123 (1996).
[Crossref]

Boltasseva, A.

Bozhevolnyi, S. I.

Breukellar, I. G.

I. G. Breukellar, Surface plasmon-polaritons in thin metal strips and slabs: Waveguiding and mode cutoff, M. A. Sc. Thesis, (University of Ottawa, 2004).

Burke, J. J.

J. J. Burke, G. I. Stegeman, and B. Lamprecht, “Surface polariton like waves guided by thin, lossy metal films,” Phys Rev B 33,5186–5201 (1986).
[Crossref]

Charbonneau, R.

Coldren, L. A.

S. Y. Hu, D. B. Young, S. W. Corzine, A. C. Gossard, and L. A. Coldren, “High-efficiency and low-threshold InGaAs/AlGaAs quantum well lasers,” J. Appl. Phys. 76,3932–3934 (1994).
[Crossref]

Corzine, S. W.

S. Y. Hu, D. B. Young, S. W. Corzine, A. C. Gossard, and L. A. Coldren, “High-efficiency and low-threshold InGaAs/AlGaAs quantum well lasers,” J. Appl. Phys. 76,3932–3934 (1994).
[Crossref]

Davis, E. A.

M. I. Manssor and E. A. Davis, “Optical and electrical characteristics of a-GaAs and a-AlGaAs prepared by radio-frequency sputtering,” J. Phys.-Condens. Mat. 2,8063–8074 (1990).
[Crossref]

Degiron, A.

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424,824–830 (2003).
[Crossref] [PubMed]

J-Claude Weeber, A. Dereux, and C. Girard, “Plasmon polaritons of metallic nanowires for controlling submicron propagation of light,” Phys. Rev. B 60,9061–9068 (1999).
[Crossref]

Dionne, J. A.

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

Duan, X.

A. M. Agarwal, L. Liao, J. S. Foresi, M. R. Black, X. Duan, and L. C. Kimerling, “Low-loss polycrystalline silicon waveguides for silicon photonics,” J. Appl. Phys. 80,6120–6123 (1996).
[Crossref]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424,824–830 (2003).
[Crossref] [PubMed]

Eng, L.

J. Seidel, S. Garfstrom, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett 94,117401 (2005).
[Crossref]

Fainman, Y.

Foresi, J. S.

A. M. Agarwal, L. Liao, J. S. Foresi, M. R. Black, X. Duan, and L. C. Kimerling, “Low-loss polycrystalline silicon waveguides for silicon photonics,” J. Appl. Phys. 80,6120–6123 (1996).
[Crossref]

Garfstrom, S.

J. Seidel, S. Garfstrom, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett 94,117401 (2005).
[Crossref]

Girard, C.

J-Claude Weeber, A. Dereux, and C. Girard, “Plasmon polaritons of metallic nanowires for controlling submicron propagation of light,” Phys. Rev. B 60,9061–9068 (1999).
[Crossref]

Gossard, A. C.

S. Y. Hu, D. B. Young, S. W. Corzine, A. C. Gossard, and L. A. Coldren, “High-efficiency and low-threshold InGaAs/AlGaAs quantum well lasers,” J. Appl. Phys. 76,3932–3934 (1994).
[Crossref]

Hu, S. Y.

S. Y. Hu, D. B. Young, S. W. Corzine, A. C. Gossard, and L. A. Coldren, “High-efficiency and low-threshold InGaAs/AlGaAs quantum well lasers,” J. Appl. Phys. 76,3932–3934 (1994).
[Crossref]

Kimerling, L. C.

A. M. Agarwal, L. Liao, J. S. Foresi, M. R. Black, X. Duan, and L. C. Kimerling, “Low-loss polycrystalline silicon waveguides for silicon photonics,” J. Appl. Phys. 80,6120–6123 (1996).
[Crossref]

Kjaer, K.

Kjebon, O.

M. N. Akram, C. Silfvenius, O. Kjebon, and R. Schatz, “Design optimization of InGaAsP-InGaAlAs 1.55 μm strain-compensated MQW lasers for direct modulation applications,” Semicond. Sci. Technol. 19,615–625 (2004).
[Crossref]

Lahoud, N.

Lamprecht, B.

J. J. Burke, G. I. Stegeman, and B. Lamprecht, “Surface polariton like waves guided by thin, lossy metal films,” Phys Rev B 33,5186–5201 (1986).
[Crossref]

Larsen, S.

Leosson, K.

Liao, L.

A. M. Agarwal, L. Liao, J. S. Foresi, M. R. Black, X. Duan, and L. C. Kimerling, “Low-loss polycrystalline silicon waveguides for silicon photonics,” J. Appl. Phys. 80,6120–6123 (1996).
[Crossref]

Manssor, M. I.

M. I. Manssor and E. A. Davis, “Optical and electrical characteristics of a-GaAs and a-AlGaAs prepared by radio-frequency sputtering,” J. Phys.-Condens. Mat. 2,8063–8074 (1990).
[Crossref]

Nezhad, M. P.

Nikolajsen, T.

Palik, E. D.

E. D. Palik, “Handbook of optical constants of solids,” (Academic Press, 1985).

Polman, A.

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

Schatz, R.

M. N. Akram, C. Silfvenius, O. Kjebon, and R. Schatz, “Design optimization of InGaAsP-InGaAlAs 1.55 μm strain-compensated MQW lasers for direct modulation applications,” Semicond. Sci. Technol. 19,615–625 (2004).
[Crossref]

Seidel, J.

J. Seidel, S. Garfstrom, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett 94,117401 (2005).
[Crossref]

Silfvenius, C.

M. N. Akram, C. Silfvenius, O. Kjebon, and R. Schatz, “Design optimization of InGaAsP-InGaAlAs 1.55 μm strain-compensated MQW lasers for direct modulation applications,” Semicond. Sci. Technol. 19,615–625 (2004).
[Crossref]

Smith, D. R.

Stegeman, G. I.

J. J. Burke, G. I. Stegeman, and B. Lamprecht, “Surface polariton like waves guided by thin, lossy metal films,” Phys Rev B 33,5186–5201 (1986).
[Crossref]

Sweatlock, L. A.

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

Tetz, K.

Weeber, J-Claude

J-Claude Weeber, A. Dereux, and C. Girard, “Plasmon polaritons of metallic nanowires for controlling submicron propagation of light,” Phys. Rev. B 60,9061–9068 (1999).
[Crossref]

Young, D. B.

S. Y. Hu, D. B. Young, S. W. Corzine, A. C. Gossard, and L. A. Coldren, “High-efficiency and low-threshold InGaAs/AlGaAs quantum well lasers,” J. Appl. Phys. 76,3932–3934 (1994).
[Crossref]

J. Appl. Phys. (2)

S. Y. Hu, D. B. Young, S. W. Corzine, A. C. Gossard, and L. A. Coldren, “High-efficiency and low-threshold InGaAs/AlGaAs quantum well lasers,” J. Appl. Phys. 76,3932–3934 (1994).
[Crossref]

A. M. Agarwal, L. Liao, J. S. Foresi, M. R. Black, X. Duan, and L. C. Kimerling, “Low-loss polycrystalline silicon waveguides for silicon photonics,” J. Appl. Phys. 80,6120–6123 (1996).
[Crossref]

J. Lightwave Technol. (1)

J. Phys.-Condens. Mat. (1)

M. I. Manssor and E. A. Davis, “Optical and electrical characteristics of a-GaAs and a-AlGaAs prepared by radio-frequency sputtering,” J. Phys.-Condens. Mat. 2,8063–8074 (1990).
[Crossref]

Nature (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424,824–830 (2003).
[Crossref] [PubMed]

Opt. Express (3)

Phys Rev B (1)

J. J. Burke, G. I. Stegeman, and B. Lamprecht, “Surface polariton like waves guided by thin, lossy metal films,” Phys Rev B 33,5186–5201 (1986).
[Crossref]

Phys. Rev. B (3)

E. P. Berini, “Plasmon polaritron waves guided by thin lossy metal films of finite width: Bound modes of asymmetric structures,” Phys. Rev. B 63,125417 (2001).
[Crossref]

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

J-Claude Weeber, A. Dereux, and C. Girard, “Plasmon polaritons of metallic nanowires for controlling submicron propagation of light,” Phys. Rev. B 60,9061–9068 (1999).
[Crossref]

Phys. Rev. Lett (1)

J. Seidel, S. Garfstrom, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett 94,117401 (2005).
[Crossref]

Semicond. Sci. Technol. (1)

M. N. Akram, C. Silfvenius, O. Kjebon, and R. Schatz, “Design optimization of InGaAsP-InGaAlAs 1.55 μm strain-compensated MQW lasers for direct modulation applications,” Semicond. Sci. Technol. 19,615–625 (2004).
[Crossref]

Other (3)

E. D. Palik, “Handbook of optical constants of solids,” (Academic Press, 1985).

I. G. Breukellar, Surface plasmon-polaritons in thin metal strips and slabs: Waveguiding and mode cutoff, M. A. Sc. Thesis, (University of Ottawa, 2004).

Electromagnetics Module User’s Guide (Comsol, 2005).

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Figures (8)
Fig. 1.
Fig. 1. Proposed multilayer structure for compensating the SP propagation loss

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Fig. 2.
Fig. 2. Dispersion characteristics for a long range SP mode on a silver film as a function of the film width and thickness (10 nm, 20 nm and 30 nm). (a) Real part of the effective mode index (b) Attenuation

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Fig. 3.
Fig. 3. Spatial distributions of Ey for a 100 nm wide silver film for two different film thicknesses. (a) 40 nm thick film (b) 10 nm thick film

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Fig. 4.
Fig. 4. Spatial distributions of Ey for a 1μm wide and 10 nm thick silver film for two different superstrate heights. (a) Semi-infinite superstrate (b) 400 nm thick superstrate

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Fig. 5.
Fig. 5. Spatial distributions of (a) Ez and (b) power profile for a 1μm wide and 10 nm thick silver film covered by a 400 nm thick superstrate.

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Fig. 6.
Fig. 6. Variation of SP characteristics with superstrate height for a 1μm wide and 10 nm thick silver film. (a) Attenuation (b) Confinement

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Fig. 7.
Fig. 7. Variation of attenuation and confinement with superstrate dielectric constant for a 1μm wide and 10 nm thick silver film. Superstrate height is 400 nm. (a) Attenuation (b) Confinement

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Fig. 8.
Fig. 8. Effect of superstrate loss on required gain for lossless SP propagation

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Equations (2)

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∇ t × ( ε r − 1 ∇ t × H → t ) − ∇ t ( μ r − 1 ∇ t . μ r H → t ) − ( k 0 2 μ r − β 2 ) H → t = 0
η = ∬ QW ∣ E y ∣ 2 dxdy ∫ − ∞ ∞ ∫ − ∞ ∞ ∣ E y ∣ 2 dxdy

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