Abstract

The use of surface plasmon polariton (SPP)-based waveguides can significantly reduce the size of optical interconnects, but the propagation length of SPPs is limited by Joule heating losses and does not exceed a few micrometers. In this paper, we present an SPP amplification scheme that utilizes compact electrical pumping and gives a possibility for designing really compact on-chip waveguides. Moreover, we demonstrate here numerically that this approach can be easily used to design an electrically pumped cw or pulsed spaser.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. A. B. Miller and H. M. Ozaktas, J. Parallel Distrib. Comput. 41, 42 (1997).
    [CrossRef]
  2. L. Pavesi and G. Guillot, eds., Optical Interconnects: The Silicon Approach (Springer, 2006).
  3. M. A. Noginov, V. A. Podolskiy, G. Zhu, M. Mayy, M. Bahoura, J. A. Adegoke, B. A. Ritzo, and K. Reynolds, Opt. Express 16, 1385 (2008).
    [CrossRef]
  4. I. De Leon and P. Berini, Nat. Photon. 4, 382 (2010).
    [CrossRef]
  5. M. C. Gather, K. Meerholz, N. Danz, and L. Leosson, Nat. Photon. 4, 457 (2010).
    [CrossRef]
  6. D. Yu. Fedyanin and A. V. Arsenin, Opt. Express 19, 12524 (2011).
    [CrossRef]
  7. E. H. Rhoderic, Metal Semiconductor Contacts (Clarendon, 1978).
  8. S. Bhargava, H.-R. Blank, V. Narayanamurti, and H. Kroeme, Appl. Phys. Lett. 70, 759 (1997).
    [CrossRef]
  9. J. R. Lindle, J. R. Meyer, C. A. Hoffman, F. J. Bartoli, G. W. Turner, and H. K. Choi, Appl. Phys. Lett. 67, 3153 (1995).
    [CrossRef]
  10. M. J. Kane, G. Braithwaite, M. T. Emeny, D. Lee, T. Martin, and D. R. Wright, Appl. Phys. Lett. 76, 943 (2000).
    [CrossRef]
  11. M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander, and C. A. Ward, Appl. Opt. 22, 1099 (1983).
    [CrossRef]
  12. F. Matossi and F. Stern, Phys. Rev. 111, 472 (1958).
    [CrossRef]
  13. D. J. Bergman and M. I. Stockman, Phys. Rev. Lett. 90, 027402 (2003).
    [CrossRef]
  14. H. C. Casey and F. Stern, J. Appl. Phys. 47, 631 (1976).
    [CrossRef]
  15. V. J. Sorger, R. F. Oulton, J. Yao, G. Bartal, and X. Zhang, Nano Lett. 9, 3489 (2009).
    [CrossRef]
  16. J. C. Dyment and L. A. D’Asaro, Appl. Phys. Lett. 11, 292 (1967).
    [CrossRef]
  17. R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, Nat. Mater. 10, 110 (2011).
    [CrossRef]

2011

D. Yu. Fedyanin and A. V. Arsenin, Opt. Express 19, 12524 (2011).
[CrossRef]

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, Nat. Mater. 10, 110 (2011).
[CrossRef]

2010

I. De Leon and P. Berini, Nat. Photon. 4, 382 (2010).
[CrossRef]

M. C. Gather, K. Meerholz, N. Danz, and L. Leosson, Nat. Photon. 4, 457 (2010).
[CrossRef]

2009

V. J. Sorger, R. F. Oulton, J. Yao, G. Bartal, and X. Zhang, Nano Lett. 9, 3489 (2009).
[CrossRef]

2008

2003

D. J. Bergman and M. I. Stockman, Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef]

2000

M. J. Kane, G. Braithwaite, M. T. Emeny, D. Lee, T. Martin, and D. R. Wright, Appl. Phys. Lett. 76, 943 (2000).
[CrossRef]

1997

S. Bhargava, H.-R. Blank, V. Narayanamurti, and H. Kroeme, Appl. Phys. Lett. 70, 759 (1997).
[CrossRef]

D. A. B. Miller and H. M. Ozaktas, J. Parallel Distrib. Comput. 41, 42 (1997).
[CrossRef]

1995

J. R. Lindle, J. R. Meyer, C. A. Hoffman, F. J. Bartoli, G. W. Turner, and H. K. Choi, Appl. Phys. Lett. 67, 3153 (1995).
[CrossRef]

1983

1976

H. C. Casey and F. Stern, J. Appl. Phys. 47, 631 (1976).
[CrossRef]

1967

J. C. Dyment and L. A. D’Asaro, Appl. Phys. Lett. 11, 292 (1967).
[CrossRef]

1958

F. Matossi and F. Stern, Phys. Rev. 111, 472 (1958).
[CrossRef]

Adegoke, J. A.

Alexander, R. W.

Arsenin, A. V.

Bahoura, M.

Bartal, G.

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, Nat. Mater. 10, 110 (2011).
[CrossRef]

V. J. Sorger, R. F. Oulton, J. Yao, G. Bartal, and X. Zhang, Nano Lett. 9, 3489 (2009).
[CrossRef]

Bartoli, F. J.

J. R. Lindle, J. R. Meyer, C. A. Hoffman, F. J. Bartoli, G. W. Turner, and H. K. Choi, Appl. Phys. Lett. 67, 3153 (1995).
[CrossRef]

Bell, R. J.

Bell, R. R.

Bell, S. E.

Bergman, D. J.

D. J. Bergman and M. I. Stockman, Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef]

Berini, P.

I. De Leon and P. Berini, Nat. Photon. 4, 382 (2010).
[CrossRef]

Bhargava, S.

S. Bhargava, H.-R. Blank, V. Narayanamurti, and H. Kroeme, Appl. Phys. Lett. 70, 759 (1997).
[CrossRef]

Blank, H.-R.

S. Bhargava, H.-R. Blank, V. Narayanamurti, and H. Kroeme, Appl. Phys. Lett. 70, 759 (1997).
[CrossRef]

Braithwaite, G.

M. J. Kane, G. Braithwaite, M. T. Emeny, D. Lee, T. Martin, and D. R. Wright, Appl. Phys. Lett. 76, 943 (2000).
[CrossRef]

Casey, H. C.

H. C. Casey and F. Stern, J. Appl. Phys. 47, 631 (1976).
[CrossRef]

Choi, H. K.

J. R. Lindle, J. R. Meyer, C. A. Hoffman, F. J. Bartoli, G. W. Turner, and H. K. Choi, Appl. Phys. Lett. 67, 3153 (1995).
[CrossRef]

D’Asaro, L. A.

J. C. Dyment and L. A. D’Asaro, Appl. Phys. Lett. 11, 292 (1967).
[CrossRef]

Danz, N.

M. C. Gather, K. Meerholz, N. Danz, and L. Leosson, Nat. Photon. 4, 457 (2010).
[CrossRef]

De Leon, I.

I. De Leon and P. Berini, Nat. Photon. 4, 382 (2010).
[CrossRef]

Dyment, J. C.

J. C. Dyment and L. A. D’Asaro, Appl. Phys. Lett. 11, 292 (1967).
[CrossRef]

Emeny, M. T.

M. J. Kane, G. Braithwaite, M. T. Emeny, D. Lee, T. Martin, and D. R. Wright, Appl. Phys. Lett. 76, 943 (2000).
[CrossRef]

Fedyanin, D. Yu.

Gather, M. C.

M. C. Gather, K. Meerholz, N. Danz, and L. Leosson, Nat. Photon. 4, 457 (2010).
[CrossRef]

Guillot, G.

L. Pavesi and G. Guillot, eds., Optical Interconnects: The Silicon Approach (Springer, 2006).

Hoffman, C. A.

J. R. Lindle, J. R. Meyer, C. A. Hoffman, F. J. Bartoli, G. W. Turner, and H. K. Choi, Appl. Phys. Lett. 67, 3153 (1995).
[CrossRef]

Kane, M. J.

M. J. Kane, G. Braithwaite, M. T. Emeny, D. Lee, T. Martin, and D. R. Wright, Appl. Phys. Lett. 76, 943 (2000).
[CrossRef]

Kroeme, H.

S. Bhargava, H.-R. Blank, V. Narayanamurti, and H. Kroeme, Appl. Phys. Lett. 70, 759 (1997).
[CrossRef]

Lee, D.

M. J. Kane, G. Braithwaite, M. T. Emeny, D. Lee, T. Martin, and D. R. Wright, Appl. Phys. Lett. 76, 943 (2000).
[CrossRef]

Leosson, L.

M. C. Gather, K. Meerholz, N. Danz, and L. Leosson, Nat. Photon. 4, 457 (2010).
[CrossRef]

Lindle, J. R.

J. R. Lindle, J. R. Meyer, C. A. Hoffman, F. J. Bartoli, G. W. Turner, and H. K. Choi, Appl. Phys. Lett. 67, 3153 (1995).
[CrossRef]

Long, L. L.

Ma, R.-M.

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, Nat. Mater. 10, 110 (2011).
[CrossRef]

Martin, T.

M. J. Kane, G. Braithwaite, M. T. Emeny, D. Lee, T. Martin, and D. R. Wright, Appl. Phys. Lett. 76, 943 (2000).
[CrossRef]

Matossi, F.

F. Matossi and F. Stern, Phys. Rev. 111, 472 (1958).
[CrossRef]

Mayy, M.

Meerholz, K.

M. C. Gather, K. Meerholz, N. Danz, and L. Leosson, Nat. Photon. 4, 457 (2010).
[CrossRef]

Meyer, J. R.

J. R. Lindle, J. R. Meyer, C. A. Hoffman, F. J. Bartoli, G. W. Turner, and H. K. Choi, Appl. Phys. Lett. 67, 3153 (1995).
[CrossRef]

Miller, D. A. B.

D. A. B. Miller and H. M. Ozaktas, J. Parallel Distrib. Comput. 41, 42 (1997).
[CrossRef]

Narayanamurti, V.

S. Bhargava, H.-R. Blank, V. Narayanamurti, and H. Kroeme, Appl. Phys. Lett. 70, 759 (1997).
[CrossRef]

Noginov, M. A.

Ordal, M. A.

Oulton, R. F.

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, Nat. Mater. 10, 110 (2011).
[CrossRef]

V. J. Sorger, R. F. Oulton, J. Yao, G. Bartal, and X. Zhang, Nano Lett. 9, 3489 (2009).
[CrossRef]

Ozaktas, H. M.

D. A. B. Miller and H. M. Ozaktas, J. Parallel Distrib. Comput. 41, 42 (1997).
[CrossRef]

Pavesi, L.

L. Pavesi and G. Guillot, eds., Optical Interconnects: The Silicon Approach (Springer, 2006).

Podolskiy, V. A.

Reynolds, K.

Rhoderic, E. H.

E. H. Rhoderic, Metal Semiconductor Contacts (Clarendon, 1978).

Ritzo, B. A.

Sorger, V. J.

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, Nat. Mater. 10, 110 (2011).
[CrossRef]

V. J. Sorger, R. F. Oulton, J. Yao, G. Bartal, and X. Zhang, Nano Lett. 9, 3489 (2009).
[CrossRef]

Stern, F.

H. C. Casey and F. Stern, J. Appl. Phys. 47, 631 (1976).
[CrossRef]

F. Matossi and F. Stern, Phys. Rev. 111, 472 (1958).
[CrossRef]

Stockman, M. I.

D. J. Bergman and M. I. Stockman, Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef]

Turner, G. W.

J. R. Lindle, J. R. Meyer, C. A. Hoffman, F. J. Bartoli, G. W. Turner, and H. K. Choi, Appl. Phys. Lett. 67, 3153 (1995).
[CrossRef]

Ward, C. A.

Wright, D. R.

M. J. Kane, G. Braithwaite, M. T. Emeny, D. Lee, T. Martin, and D. R. Wright, Appl. Phys. Lett. 76, 943 (2000).
[CrossRef]

Yao, J.

V. J. Sorger, R. F. Oulton, J. Yao, G. Bartal, and X. Zhang, Nano Lett. 9, 3489 (2009).
[CrossRef]

Zhang, X.

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, Nat. Mater. 10, 110 (2011).
[CrossRef]

V. J. Sorger, R. F. Oulton, J. Yao, G. Bartal, and X. Zhang, Nano Lett. 9, 3489 (2009).
[CrossRef]

Zhu, G.

Appl. Opt.

Appl. Phys. Lett.

J. C. Dyment and L. A. D’Asaro, Appl. Phys. Lett. 11, 292 (1967).
[CrossRef]

S. Bhargava, H.-R. Blank, V. Narayanamurti, and H. Kroeme, Appl. Phys. Lett. 70, 759 (1997).
[CrossRef]

J. R. Lindle, J. R. Meyer, C. A. Hoffman, F. J. Bartoli, G. W. Turner, and H. K. Choi, Appl. Phys. Lett. 67, 3153 (1995).
[CrossRef]

M. J. Kane, G. Braithwaite, M. T. Emeny, D. Lee, T. Martin, and D. R. Wright, Appl. Phys. Lett. 76, 943 (2000).
[CrossRef]

J. Appl. Phys.

H. C. Casey and F. Stern, J. Appl. Phys. 47, 631 (1976).
[CrossRef]

J. Parallel Distrib. Comput.

D. A. B. Miller and H. M. Ozaktas, J. Parallel Distrib. Comput. 41, 42 (1997).
[CrossRef]

Nano Lett.

V. J. Sorger, R. F. Oulton, J. Yao, G. Bartal, and X. Zhang, Nano Lett. 9, 3489 (2009).
[CrossRef]

Nat. Mater.

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, Nat. Mater. 10, 110 (2011).
[CrossRef]

Nat. Photon.

I. De Leon and P. Berini, Nat. Photon. 4, 382 (2010).
[CrossRef]

M. C. Gather, K. Meerholz, N. Danz, and L. Leosson, Nat. Photon. 4, 457 (2010).
[CrossRef]

Opt. Express

Phys. Rev.

F. Matossi and F. Stern, Phys. Rev. 111, 472 (1958).
[CrossRef]

Phys. Rev. Lett.

D. J. Bergman and M. I. Stockman, Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef]

Other

E. H. Rhoderic, Metal Semiconductor Contacts (Clarendon, 1978).

L. Pavesi and G. Guillot, eds., Optical Interconnects: The Silicon Approach (Springer, 2006).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

Schematic view of an Au/p-InAs Schottky diode under zero bias, its band diagram, and an SPP propagating along the metal–semiconductor interface. L is the thickness of the semiconductor layer, Fm is the Fermi level in the metal, and β is the SPP wave vector.

Fig. 2.
Fig. 2.

Dependence of the net SPP gain on the bias voltage and current density (in the inset) for the Au/p-InAs Schottky diode under consideration for different values of the SPP power flow per unit guide width (from top to bottom, 1μW/μm, yellow line; 0.1mW/μm, green line; 1mW/μm, red line; 10mW/μm, purple line).

Fig. 3.
Fig. 3.

(a) Sketch of a Fabry–Perot plasmonic cavity. l is the cavity length, and r and R are the amplitude reflection coefficients from the front and back mirrors, respectively. (b) Gain spectrum of p-type InAs calculated using the Gaussian Halperin–Lax band-tail model for the densities of states and Stern’s approach [14] for the envelope matrix element, pNd=2.33×1018cm1 and n=1.8×1016cm3. (c) Spectral response of a 100-μm-long Fabry–Perot plasmonic cavity with smooth uncovered facets. (d) Spectral response of a 10.2-μm-long cavity with 15-nm-thick Au mirrors at the facets. In panels (c) and (d), only radiation losses are considered and I is the intensity of the SPP field inside the cavity.

Fig. 4.
Fig. 4.

Sketch of a spaser coupled to a plasmonic waveguide. l=10.2μm is the length of the cavity, d and D are the thicknesses of the front and back mirrors, respectively, and h2μm is the height of the mirrors. The refractive index of the semiconductor in the plasmonic waveguide region is assumed to be equal to 3.5.

Equations (6)

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

FnFpωEg,
UAuger=Cnn2p+Cpnp2,
Uspont=Bnp,
Ustim=gS/ω,
G=0Lg(z)Sx(z)dz+Sx(z)dzω8π0ImεAu|E|2dz+Sx(z)dz.
G=12lln(1|r|2|R|2),

Metrics