Abstract

Absorption and stimulated emission coefficients for a pump power at 1480 nm are determined experimentally for three types of erbium-doped silica fiber. Starting from these coefficients and using previous gain measurements, we calculate absorption and stimulated emission cross sections of the erbium laser transition. The results obtained are in good agreement with the ones that appear in the literature.

© 1998 Optical Society of America

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References

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  1. E. Desurvire, J. R. Simpson, “Amplification of spontaneous emission in erbium-doped single-mode fibres,” J. Lightwave Technol. 7, 835–845 (1989).
    [CrossRef]
  2. M. Ohashi, “Design considerations for an Er3+ doped fiber amplifier,” J. Lightwave Technol. 9, 1099–1104 (1991).
    [CrossRef]
  3. B. Pedersen, A. Bjarklev, J. H. Povlsen, K. Dybdal, C. C. Larsen, “The design of erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 1105–1112 (1991).
    [CrossRef]
  4. M. A. Rebolledo, S. Jarabo, “Erbium-doped silica fiber modeling with overlapping factors,” Appl. Opt. 33, 5585–5593 (1994).
    [CrossRef] [PubMed]
  5. S. Jarabo, M. A. Rebolledo, “Analytic modeling of erbium-doped fiber amplifiers based on intensity-dependent overlapping factors,” Appl. Opt. 34, 6158–6163 (1995).
    [CrossRef] [PubMed]
  6. S. Jarabo, J. M. Alvarez, “Experimental verification of analytic modeling of erbium-doped silica fiber amplifiers pumped at 1480 nm,” Appl. Opt. 35, 4759–4766 (1996).
    [CrossRef] [PubMed]
  7. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), pp. 208–279, 420–441.
  8. W. J. Miniscalco, “Optical and electronic properties of rare earth ions in glasses,” in Rare Earth Doped Fiber Lasers and Amplifiers, M. J. F. Digonnet, ed. (Marcel Dekker, New York, 1993), pp. 19–134.
  9. R. Wyatt, “Spectroscopy of rare earth doped fibres,” in Optical Fiber Lasers and Amplifiers, P. W. France, ed. (Blackie, Glasgow, 1991), pp. 79–105.

1996 (1)

1995 (1)

1994 (1)

1991 (2)

M. Ohashi, “Design considerations for an Er3+ doped fiber amplifier,” J. Lightwave Technol. 9, 1099–1104 (1991).
[CrossRef]

B. Pedersen, A. Bjarklev, J. H. Povlsen, K. Dybdal, C. C. Larsen, “The design of erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 1105–1112 (1991).
[CrossRef]

1989 (1)

E. Desurvire, J. R. Simpson, “Amplification of spontaneous emission in erbium-doped single-mode fibres,” J. Lightwave Technol. 7, 835–845 (1989).
[CrossRef]

Alvarez, J. M.

Bjarklev, A.

B. Pedersen, A. Bjarklev, J. H. Povlsen, K. Dybdal, C. C. Larsen, “The design of erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 1105–1112 (1991).
[CrossRef]

Desurvire, E.

E. Desurvire, J. R. Simpson, “Amplification of spontaneous emission in erbium-doped single-mode fibres,” J. Lightwave Technol. 7, 835–845 (1989).
[CrossRef]

Dybdal, K.

B. Pedersen, A. Bjarklev, J. H. Povlsen, K. Dybdal, C. C. Larsen, “The design of erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 1105–1112 (1991).
[CrossRef]

Jarabo, S.

Larsen, C. C.

B. Pedersen, A. Bjarklev, J. H. Povlsen, K. Dybdal, C. C. Larsen, “The design of erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 1105–1112 (1991).
[CrossRef]

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), pp. 208–279, 420–441.

Miniscalco, W. J.

W. J. Miniscalco, “Optical and electronic properties of rare earth ions in glasses,” in Rare Earth Doped Fiber Lasers and Amplifiers, M. J. F. Digonnet, ed. (Marcel Dekker, New York, 1993), pp. 19–134.

Ohashi, M.

M. Ohashi, “Design considerations for an Er3+ doped fiber amplifier,” J. Lightwave Technol. 9, 1099–1104 (1991).
[CrossRef]

Pedersen, B.

B. Pedersen, A. Bjarklev, J. H. Povlsen, K. Dybdal, C. C. Larsen, “The design of erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 1105–1112 (1991).
[CrossRef]

Povlsen, J. H.

B. Pedersen, A. Bjarklev, J. H. Povlsen, K. Dybdal, C. C. Larsen, “The design of erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 1105–1112 (1991).
[CrossRef]

Rebolledo, M. A.

Simpson, J. R.

E. Desurvire, J. R. Simpson, “Amplification of spontaneous emission in erbium-doped single-mode fibres,” J. Lightwave Technol. 7, 835–845 (1989).
[CrossRef]

Snyder, A. W.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), pp. 208–279, 420–441.

Wyatt, R.

R. Wyatt, “Spectroscopy of rare earth doped fibres,” in Optical Fiber Lasers and Amplifiers, P. W. France, ed. (Blackie, Glasgow, 1991), pp. 79–105.

Appl. Opt. (3)

J. Lightwave Technol. (3)

E. Desurvire, J. R. Simpson, “Amplification of spontaneous emission in erbium-doped single-mode fibres,” J. Lightwave Technol. 7, 835–845 (1989).
[CrossRef]

M. Ohashi, “Design considerations for an Er3+ doped fiber amplifier,” J. Lightwave Technol. 9, 1099–1104 (1991).
[CrossRef]

B. Pedersen, A. Bjarklev, J. H. Povlsen, K. Dybdal, C. C. Larsen, “The design of erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 1105–1112 (1991).
[CrossRef]

Other (3)

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), pp. 208–279, 420–441.

W. J. Miniscalco, “Optical and electronic properties of rare earth ions in glasses,” in Rare Earth Doped Fiber Lasers and Amplifiers, M. J. F. Digonnet, ed. (Marcel Dekker, New York, 1993), pp. 19–134.

R. Wyatt, “Spectroscopy of rare earth doped fibres,” in Optical Fiber Lasers and Amplifiers, P. W. France, ed. (Blackie, Glasgow, 1991), pp. 79–105.

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Figures (8)

Fig. 1
Fig. 1

Experimental values of the absorption coefficient for pump power and interpolated curves as a function of pump power before the attenuator. Circles, triangles, and squares represent values for fibers A, B, and C, respectively. Crosses represent the mean value of the absorption coefficient.

Fig. 2
Fig. 2

Values of the absorption (solid curve) and stimulated emission (dotted–dashed curve) coefficients for fiber A as a function of the signal wavelength.

Fig. 3
Fig. 3

Same as Fig. 2, but for fiber B.

Fig. 4
Fig. 4

Same as Fig. 2, but for fiber C.

Fig. 5
Fig. 5

Values of the absorption (solid curve) and stimulated emission (dotted–dashed curve) cross sections for fiber A as a function of the signal wavelength.

Fig. 6
Fig. 6

Same as Fig. 5, but for fiber B.

Fig. 7
Fig. 7

Same as Fig. 5, but for fiber C.

Fig. 8
Fig. 8

Relative error in the approximation based on Eqs. (1), (3), and (A11)–(A15) as a function of the pump power when the signal power is 0.1 μW (dashed curve) and 1 mW (solid curve).

Equations (25)

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fiber   A : τ = 10.5   ms ,   ρ = 3.3   μ m ,   and   N ¯ T = 2 × 10 24   m - 3 ; fiber   B : τ = 12.1   ms ,   ρ = 1.95   μ m ,   and   N ¯ T = 5 × 10 24   m - 3 ; fiber   C : τ = 10.5   ms ,   ρ = 1.9   μ m ,   and   N ¯ T = 3.4 × 10 24   m - 3 .
η 0 ν = 1 N ¯ T A d d s   ψ r ,   ϕ ,   ν N T r ,   ϕ ,
η 2 ν = 1 N ¯ 2 A d d s   ψ r ,   ϕ ,   ν N 2 0 ,   r ,   ϕ ,
η 2 ν / η 0 ν = 1 + 1 / C + C p P p + C s P s ,
γ i ν = η 0 ν σ i ν N ¯ T ,     i = a ,   e ,
γ a ν = β ν γ a ν p - γ ν ,
γ e ν = β ν γ e ν p + γ ν ,
γ a ν p L + ln P p L P p 0 + q ν p P p L P p 0 - 1 = 0 ,
q ν p = γ a ν p + γ e ν p A d N ¯ T τ P p 0 h ν p η 2 ν p η 0 ν p ,
C = η 0 ν η 0 ν p η ν ,   ν p - η 0 ν η 0 ν p ,
C p = τ γ a ν p + γ e ν p h ν p A d N ¯ T × η 0 ν η 0 ν p η 0 ν p η ν ,   ν p ,   ν p - η ν p ,   ν p η ν ,   ν p η ν ,   ν p - η 0 ν η 0 ν p 2 ,
C s = τ γ a ν s + γ e ν s h ν s A d N ¯ T × η 0 ν η 0 ν s η 0 ν p η 0 ν s 2 η 0 ν s η ν ,   ν s ,   ν s - η ν s ,   ν s η ν ,   ν s η ν ,   ν p - η 0 ν η 0 ν p 2 ,
η ν ,   ν = A d N ¯ T A d d s   ψ r ,   ϕ ,   ν ψ r ,   ϕ ,   ν N T r ,   ϕ ,
η ν ,   ν ,   ν = A d 2 N ¯ T A d d s   ψ r ,   ϕ ,   ν ψ r ,   ϕ ,   ν 2 N T r ,   ϕ .
η 1 ν n 1 z + η 2 ν n 2 z = η 0 ν N ¯ T ,
η 1 ν n 1 z - n 1 z = η 2 ν n 2 z - n 2 z ,
N ¯ T n 2 z = 1 - 1 - η 2 ν / η 0 ν 1 - n 1 ν / η 0 ν ,
χ 1 ν = η ν ,   ν η 0 ν = A d A d d s ψ r ,   ϕ ,   ν 2 N T r ,   ϕ A d d s   ψ r ,   ϕ ,   ν N T r ,   ϕ ,
χ 2 ν = η ν ,   ν ,   ν η 0 ν = A d 2 A d d s ψ r ,   ϕ ,   ν 3 N T r ,   ϕ A d d s   ψ r ,   ϕ ,   ν N T r ,   ϕ ,
C = 1 χ 1 ν p / η 0 ν p - 1 ,
C p = τ γ a ν p + γ e ν p h ν p A d N ¯ T χ 2 ν p - χ 1 2 ν p χ 1 ν p - η 0 ν p 2 ,
C s = τ γ a ν s + γ e ν s h ν s A d N ¯ T η 0 ν p η 0 ν s 2 χ 2 ν s - χ 1 2 ν s χ 1 ν p - η 0 ν p 2 .
q ν p = χ ν p q 0 ν p + χ 1 ν p χ ν p q 0 ν p + η 0 ν p   q 0 ν p ,
q 0 ν p = γ a ν p + γ e ν p A d N ¯ T τ P p 0 h ν p ,
χ ν p = χ 2 ν p - χ 1 2 ν p χ 1 ν p - η 0 ν p .

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