Abstract

We present a new method of measuring the guided, radiated, and total decay rates in uniform waveguides. It is also shown theoretically that large modifications of the total decay rate can be achieved in realistic erbium-doped fiber amplifiers and erbium-doped waveguide amplifiers with effective mode area radii smaller than 1μm.

© 2005 Optical Society of America

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  1. D. Kleppner, Phys. Rev. Lett. 47, 233 (1981).
    [CrossRef]
  2. S. D. Brorson, H. Yokoyama, and E. P. Ippen, IEEE J. Quantum Electron. 26, 1492 (1990).
    [CrossRef]
  3. H. Yokoyama, Science 256, 5053 (1992).
    [CrossRef]
  4. J. P. Zhang, D. Y. Chu, S. L. Wu, S. T. Ho, W. G. Bi, C. W. Tu, and R. C. Tiberio, Phys. Rev. Lett. 75, 2678 (1995).
    [CrossRef] [PubMed]
  5. T. Sondergaarda and B. Tromborg, Phys. Rev. A 64, 033812 (2001).
    [CrossRef]
  6. A. A. Rieznik and H. L. Fragnito, J. Opt. Soc. Am. B 21, 1732 (2004).
    [CrossRef]
  7. D. Y. Chu and S.-T. Ho, J. Opt. Soc. Am. B 10, 381 (1993).
    [CrossRef]
  8. H. Yokoyama and S. D. Brorson, J. Appl. Phys. 66, 4801 (1989).
    [CrossRef]
  9. E. Desurvire, Device and System Applications (Wiley, New York, 1994), Sect. 4.6.
  10. E. Snoeks, G. N. van den Hoven, and A. Polman, IEEE J. Quantum Electron. 32, 1680 (1996).
    [CrossRef]
  11. T. Georges and E. Delevaque, Opt. Lett. 17, 1113 (1992).
    [CrossRef] [PubMed]
  12. S. Saini, J. Michel, and L. C. Kimerling, J. Lightwave Technol. 21, 2368 (2003).
    [CrossRef]
  13. C. R. Giles and E. Desurvire, J. Lightwave Technol. 9, 271 (1991).
    [CrossRef]
  14. G. P. Agrawal, Fiber-Optics Communication Systems (Wiley, New York, 1992), p. 95.

2004

2003

2001

T. Sondergaarda and B. Tromborg, Phys. Rev. A 64, 033812 (2001).
[CrossRef]

1996

E. Snoeks, G. N. van den Hoven, and A. Polman, IEEE J. Quantum Electron. 32, 1680 (1996).
[CrossRef]

1995

J. P. Zhang, D. Y. Chu, S. L. Wu, S. T. Ho, W. G. Bi, C. W. Tu, and R. C. Tiberio, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

1993

1992

1991

C. R. Giles and E. Desurvire, J. Lightwave Technol. 9, 271 (1991).
[CrossRef]

1990

S. D. Brorson, H. Yokoyama, and E. P. Ippen, IEEE J. Quantum Electron. 26, 1492 (1990).
[CrossRef]

1989

H. Yokoyama and S. D. Brorson, J. Appl. Phys. 66, 4801 (1989).
[CrossRef]

1981

D. Kleppner, Phys. Rev. Lett. 47, 233 (1981).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Fiber-Optics Communication Systems (Wiley, New York, 1992), p. 95.

Bi, W. G.

J. P. Zhang, D. Y. Chu, S. L. Wu, S. T. Ho, W. G. Bi, C. W. Tu, and R. C. Tiberio, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

Brorson, S. D.

S. D. Brorson, H. Yokoyama, and E. P. Ippen, IEEE J. Quantum Electron. 26, 1492 (1990).
[CrossRef]

H. Yokoyama and S. D. Brorson, J. Appl. Phys. 66, 4801 (1989).
[CrossRef]

Chu, D. Y.

J. P. Zhang, D. Y. Chu, S. L. Wu, S. T. Ho, W. G. Bi, C. W. Tu, and R. C. Tiberio, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

D. Y. Chu and S.-T. Ho, J. Opt. Soc. Am. B 10, 381 (1993).
[CrossRef]

Delevaque, E.

Desurvire, E.

C. R. Giles and E. Desurvire, J. Lightwave Technol. 9, 271 (1991).
[CrossRef]

E. Desurvire, Device and System Applications (Wiley, New York, 1994), Sect. 4.6.

Fragnito, H. L.

Georges, T.

Giles, C. R.

C. R. Giles and E. Desurvire, J. Lightwave Technol. 9, 271 (1991).
[CrossRef]

Ho, S. T.

J. P. Zhang, D. Y. Chu, S. L. Wu, S. T. Ho, W. G. Bi, C. W. Tu, and R. C. Tiberio, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

Ho, S.-T.

Ippen, E. P.

S. D. Brorson, H. Yokoyama, and E. P. Ippen, IEEE J. Quantum Electron. 26, 1492 (1990).
[CrossRef]

Kimerling, L. C.

Kleppner, D.

D. Kleppner, Phys. Rev. Lett. 47, 233 (1981).
[CrossRef]

Michel, J.

Polman, A.

E. Snoeks, G. N. van den Hoven, and A. Polman, IEEE J. Quantum Electron. 32, 1680 (1996).
[CrossRef]

Rieznik, A. A.

Saini, S.

Snoeks, E.

E. Snoeks, G. N. van den Hoven, and A. Polman, IEEE J. Quantum Electron. 32, 1680 (1996).
[CrossRef]

Sondergaarda, T.

T. Sondergaarda and B. Tromborg, Phys. Rev. A 64, 033812 (2001).
[CrossRef]

Tiberio, R. C.

J. P. Zhang, D. Y. Chu, S. L. Wu, S. T. Ho, W. G. Bi, C. W. Tu, and R. C. Tiberio, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

Tromborg, B.

T. Sondergaarda and B. Tromborg, Phys. Rev. A 64, 033812 (2001).
[CrossRef]

Tu, C. W.

J. P. Zhang, D. Y. Chu, S. L. Wu, S. T. Ho, W. G. Bi, C. W. Tu, and R. C. Tiberio, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

van den Hoven, G. N.

E. Snoeks, G. N. van den Hoven, and A. Polman, IEEE J. Quantum Electron. 32, 1680 (1996).
[CrossRef]

Wu, S. L.

J. P. Zhang, D. Y. Chu, S. L. Wu, S. T. Ho, W. G. Bi, C. W. Tu, and R. C. Tiberio, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

Yokoyama, H.

H. Yokoyama, Science 256, 5053 (1992).
[CrossRef]

S. D. Brorson, H. Yokoyama, and E. P. Ippen, IEEE J. Quantum Electron. 26, 1492 (1990).
[CrossRef]

H. Yokoyama and S. D. Brorson, J. Appl. Phys. 66, 4801 (1989).
[CrossRef]

Zhang, J. P.

J. P. Zhang, D. Y. Chu, S. L. Wu, S. T. Ho, W. G. Bi, C. W. Tu, and R. C. Tiberio, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

IEEE J. Quantum Electron.

S. D. Brorson, H. Yokoyama, and E. P. Ippen, IEEE J. Quantum Electron. 26, 1492 (1990).
[CrossRef]

E. Snoeks, G. N. van den Hoven, and A. Polman, IEEE J. Quantum Electron. 32, 1680 (1996).
[CrossRef]

J. Appl. Phys.

H. Yokoyama and S. D. Brorson, J. Appl. Phys. 66, 4801 (1989).
[CrossRef]

J. Lightwave Technol.

C. R. Giles and E. Desurvire, J. Lightwave Technol. 9, 271 (1991).
[CrossRef]

S. Saini, J. Michel, and L. C. Kimerling, J. Lightwave Technol. 21, 2368 (2003).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Phys. Rev. A

T. Sondergaarda and B. Tromborg, Phys. Rev. A 64, 033812 (2001).
[CrossRef]

Phys. Rev. Lett.

D. Kleppner, Phys. Rev. Lett. 47, 233 (1981).
[CrossRef]

J. P. Zhang, D. Y. Chu, S. L. Wu, S. T. Ho, W. G. Bi, C. W. Tu, and R. C. Tiberio, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

Science

H. Yokoyama, Science 256, 5053 (1992).
[CrossRef]

Other

G. P. Agrawal, Fiber-Optics Communication Systems (Wiley, New York, 1992), p. 95.

E. Desurvire, Device and System Applications (Wiley, New York, 1994), Sect. 4.6.

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Figures (2)

Fig. 1
Fig. 1

Simulations of the measured lifetimes as a function of the waveguide length for typical (a) EDFAs and (b) EDWAs. Black curves, nonlossy waveguides; gray curves, α loss = 0.3 dB m (EDFAs) (Ref. [11]) and 1 dB cm (EDWAs),[10] values typical of fluorozirconate EDFAs and silica-based EDWAs, respectively.

Fig. 2
Fig. 2

Theoretical lifetimes as a function of the waveguide length for an EDWA with a 0.02 - μ m 2 optical mode area. Other parameters are given in Table 1.

Tables (1)

Tables Icon

Table 1 Parameters Used in the Simulations

Equations (12)

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N 2 ( z , t ) t = N 2 ( z , t ) τ 0 1 ρ S n = 1 M { [ ( α n + γ n ) N 2 ( z , t ) α n ] P n ( z , t ) } ,
P n ( z , t ) z = u n { [ ( α n + γ n ) N 2 ( z , t ) α n α loss ] P n ( z , t ) + 2 γ n Δ ν N 2 ( z , t ) } ,
P n out ( t ) = P n in ( t ) G n ( t ) + 2 N n sp Δ ν [ G n ( t ) 1 ] ,
G n ( t ) = exp [ ( α n + γ n ) N 2 ( t ) L ( α n α loss ) L ] ,
N n sp = γ n N 2 ( t ) ( α n + γ n ) N 2 ( t ) α n α loss .
d N 2 ( t ) d t = N 2 ( t ) τ 0 1 ρ S L n = 1 M [ P n out ( t ) P n in ( t ) 2 γ n Δ ν N 2 ( t ) L + α loss H n ( t ) L ] ,
H n ( t ) = P n in ( t ) ln [ G n ( t ) ] [ G n ( t ) 1 ] + 2 N n sp Δ ν { G n ( t ) 1 ln [ G n ( t ) ] 1 } .
P n out ( t ) = 2 γ n Δ ν N 2 ( t ) α n + α loss { 1 exp [ ( α n + α loss ) L ] } ,
H n ( t ) = P n out ( t ) L ( α n + α loss ) + 2 γ n Δ ν N 2 ( t ) α n + α loss .
d N 2 ( t ) d t = N 2 ( t ) τ 0 n = 1 M { P n out ( t ) ρ S L 2 γ n Δ ν N 2 ( t ) ρ S β n [ P n out ( t ) ρ S L 2 γ n Δ ν N 2 ( t ) ρ S ] } ,
d N 2 ( t ) d t = N 2 ( t ) τ 0 .
d N 2 ( t ) d t = N 2 ( t ) τ r n = 1 M β n N 2 ( t ) τ g n ,

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