Abstract

We report a new model of a high-concentration erbium-doped fiber amplifier (EDFA) accounting for the statistical nature of the migration and up-conversion processes. By fitting experimental results, we conclude that the statistical model shows better applicability for the characterization of high-concentration EDFAs than the model accounting for the homogeneous upconversion and pair-induced quenching.

© 2006 Optical Society of America

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  1. B.-C. Hwang, S. Jiang, T. Luo, K. Seneschal, G. Sorbello, M. Morell, F. Smektala, S. Honkanen, J. Lucas, and N. Peyghambarian, "Performance of high-concentration Er3+-doped phosphate fiber amplifiers," IEEE Photon. Technol. Lett. 13, 197-199 (2001).
    [CrossRef]
  2. T. Nishi, K. Nakagawa, Y. Ohishi, and S. Takahashi, "The amplification properties of high Er3+-doped phosphate fiber," Jpn. J. Appl. Phys. Part 2 31, L177-L179 (1992).
    [CrossRef]
  3. S. Tammela, M. Hotoleanu, P. Kiiveri, H. Valkonen, S. Sarkilahti, and K. Janka, "Very short Er-doped silica glass fiber for L-band amplifiers," in Conference on Optical Fiber Communications, Vol. 1 of 2003 OSA Technical Digest Series (Optical Society of America, 2003), pp. 376-377.
  4. P. Myslinski, C. Szubert, A. J. Bruce, D. J. DiGiovanni, and B. Palsdottir, "Performance of high-concentration erbium-doped fiber amplifiers," IEEE Photon. Technol. Lett. 11, 973-975 (1999).
    [CrossRef]
  5. P. Myslinski, D. Nguyen, and J. Chrostowski, "Effects of concentration on the performance of erbium-doped fiber amplifiers," J. Lightwave Technol. 15, 112-119 (1997).
    [CrossRef]
  6. C. Jiang, W. Hu, and Q. Zeng, "Numerical analysis of concentration quenching model of Er3+-doped phosphate fiber amplifier," IEEE J. Quantum Electron. 39, 1266-1271 (2003).
    [CrossRef]
  7. S. V. Sergeyev, "Model of high-concentration erbium-doped fibre amplifier: effects of migration and upconversion processes," Electron. Lett. 39, 511-512 (2003).
    [CrossRef]
  8. S. Sergeyev, S. Popov, and A. T. Friberg, "Effect of erbium ions local distribution on excitation migration and upconversion in multicomponent glasses," Opt. Lett. 30, 1258-1260 (2005).
    [CrossRef] [PubMed]
  9. P. M. Peters and S. N. Houde-Walter, "Local structure of Er3+ in multicomponent glasses," J. Non-Cryst. Solids 328, 162-169 (1998).
    [CrossRef]
  10. S. V. Sergeyev and B. Jaskorzynska, "Statistical model for energy-transfer-induced up-conversion in Er3+-doped glasses," Phys. Rev. B 62, 15628-15633 (2000).
    [CrossRef]
  11. A. I. Burstein, "Concentration quenching of noncoherent excitation in solutions," Sov. Phys. Usp. 143, 553-600 (1984).
    [CrossRef]
  12. E. Desurvire, Erbium-Doped Fiber Amplifiers (Wiley, 1994).

2005 (1)

2003 (2)

C. Jiang, W. Hu, and Q. Zeng, "Numerical analysis of concentration quenching model of Er3+-doped phosphate fiber amplifier," IEEE J. Quantum Electron. 39, 1266-1271 (2003).
[CrossRef]

S. V. Sergeyev, "Model of high-concentration erbium-doped fibre amplifier: effects of migration and upconversion processes," Electron. Lett. 39, 511-512 (2003).
[CrossRef]

2001 (1)

B.-C. Hwang, S. Jiang, T. Luo, K. Seneschal, G. Sorbello, M. Morell, F. Smektala, S. Honkanen, J. Lucas, and N. Peyghambarian, "Performance of high-concentration Er3+-doped phosphate fiber amplifiers," IEEE Photon. Technol. Lett. 13, 197-199 (2001).
[CrossRef]

2000 (1)

S. V. Sergeyev and B. Jaskorzynska, "Statistical model for energy-transfer-induced up-conversion in Er3+-doped glasses," Phys. Rev. B 62, 15628-15633 (2000).
[CrossRef]

1999 (1)

P. Myslinski, C. Szubert, A. J. Bruce, D. J. DiGiovanni, and B. Palsdottir, "Performance of high-concentration erbium-doped fiber amplifiers," IEEE Photon. Technol. Lett. 11, 973-975 (1999).
[CrossRef]

1998 (1)

P. M. Peters and S. N. Houde-Walter, "Local structure of Er3+ in multicomponent glasses," J. Non-Cryst. Solids 328, 162-169 (1998).
[CrossRef]

1997 (1)

P. Myslinski, D. Nguyen, and J. Chrostowski, "Effects of concentration on the performance of erbium-doped fiber amplifiers," J. Lightwave Technol. 15, 112-119 (1997).
[CrossRef]

1992 (1)

T. Nishi, K. Nakagawa, Y. Ohishi, and S. Takahashi, "The amplification properties of high Er3+-doped phosphate fiber," Jpn. J. Appl. Phys. Part 2 31, L177-L179 (1992).
[CrossRef]

1984 (1)

A. I. Burstein, "Concentration quenching of noncoherent excitation in solutions," Sov. Phys. Usp. 143, 553-600 (1984).
[CrossRef]

Bruce, A. J.

P. Myslinski, C. Szubert, A. J. Bruce, D. J. DiGiovanni, and B. Palsdottir, "Performance of high-concentration erbium-doped fiber amplifiers," IEEE Photon. Technol. Lett. 11, 973-975 (1999).
[CrossRef]

Burstein, A. I.

A. I. Burstein, "Concentration quenching of noncoherent excitation in solutions," Sov. Phys. Usp. 143, 553-600 (1984).
[CrossRef]

Chrostowski, J.

P. Myslinski, D. Nguyen, and J. Chrostowski, "Effects of concentration on the performance of erbium-doped fiber amplifiers," J. Lightwave Technol. 15, 112-119 (1997).
[CrossRef]

Desurvire, E.

E. Desurvire, Erbium-Doped Fiber Amplifiers (Wiley, 1994).

DiGiovanni, D. J.

P. Myslinski, C. Szubert, A. J. Bruce, D. J. DiGiovanni, and B. Palsdottir, "Performance of high-concentration erbium-doped fiber amplifiers," IEEE Photon. Technol. Lett. 11, 973-975 (1999).
[CrossRef]

Friberg, A. T.

Honkanen, S.

B.-C. Hwang, S. Jiang, T. Luo, K. Seneschal, G. Sorbello, M. Morell, F. Smektala, S. Honkanen, J. Lucas, and N. Peyghambarian, "Performance of high-concentration Er3+-doped phosphate fiber amplifiers," IEEE Photon. Technol. Lett. 13, 197-199 (2001).
[CrossRef]

Hotoleanu, M.

S. Tammela, M. Hotoleanu, P. Kiiveri, H. Valkonen, S. Sarkilahti, and K. Janka, "Very short Er-doped silica glass fiber for L-band amplifiers," in Conference on Optical Fiber Communications, Vol. 1 of 2003 OSA Technical Digest Series (Optical Society of America, 2003), pp. 376-377.

Houde-Walter, S. N.

P. M. Peters and S. N. Houde-Walter, "Local structure of Er3+ in multicomponent glasses," J. Non-Cryst. Solids 328, 162-169 (1998).
[CrossRef]

Hu, W.

C. Jiang, W. Hu, and Q. Zeng, "Numerical analysis of concentration quenching model of Er3+-doped phosphate fiber amplifier," IEEE J. Quantum Electron. 39, 1266-1271 (2003).
[CrossRef]

Hwang, B.-C.

B.-C. Hwang, S. Jiang, T. Luo, K. Seneschal, G. Sorbello, M. Morell, F. Smektala, S. Honkanen, J. Lucas, and N. Peyghambarian, "Performance of high-concentration Er3+-doped phosphate fiber amplifiers," IEEE Photon. Technol. Lett. 13, 197-199 (2001).
[CrossRef]

Janka, K.

S. Tammela, M. Hotoleanu, P. Kiiveri, H. Valkonen, S. Sarkilahti, and K. Janka, "Very short Er-doped silica glass fiber for L-band amplifiers," in Conference on Optical Fiber Communications, Vol. 1 of 2003 OSA Technical Digest Series (Optical Society of America, 2003), pp. 376-377.

Jaskorzynska, B.

S. V. Sergeyev and B. Jaskorzynska, "Statistical model for energy-transfer-induced up-conversion in Er3+-doped glasses," Phys. Rev. B 62, 15628-15633 (2000).
[CrossRef]

Jiang, C.

C. Jiang, W. Hu, and Q. Zeng, "Numerical analysis of concentration quenching model of Er3+-doped phosphate fiber amplifier," IEEE J. Quantum Electron. 39, 1266-1271 (2003).
[CrossRef]

Jiang, S.

B.-C. Hwang, S. Jiang, T. Luo, K. Seneschal, G. Sorbello, M. Morell, F. Smektala, S. Honkanen, J. Lucas, and N. Peyghambarian, "Performance of high-concentration Er3+-doped phosphate fiber amplifiers," IEEE Photon. Technol. Lett. 13, 197-199 (2001).
[CrossRef]

Kiiveri, P.

S. Tammela, M. Hotoleanu, P. Kiiveri, H. Valkonen, S. Sarkilahti, and K. Janka, "Very short Er-doped silica glass fiber for L-band amplifiers," in Conference on Optical Fiber Communications, Vol. 1 of 2003 OSA Technical Digest Series (Optical Society of America, 2003), pp. 376-377.

Lucas, J.

B.-C. Hwang, S. Jiang, T. Luo, K. Seneschal, G. Sorbello, M. Morell, F. Smektala, S. Honkanen, J. Lucas, and N. Peyghambarian, "Performance of high-concentration Er3+-doped phosphate fiber amplifiers," IEEE Photon. Technol. Lett. 13, 197-199 (2001).
[CrossRef]

Luo, T.

B.-C. Hwang, S. Jiang, T. Luo, K. Seneschal, G. Sorbello, M. Morell, F. Smektala, S. Honkanen, J. Lucas, and N. Peyghambarian, "Performance of high-concentration Er3+-doped phosphate fiber amplifiers," IEEE Photon. Technol. Lett. 13, 197-199 (2001).
[CrossRef]

Morell, M.

B.-C. Hwang, S. Jiang, T. Luo, K. Seneschal, G. Sorbello, M. Morell, F. Smektala, S. Honkanen, J. Lucas, and N. Peyghambarian, "Performance of high-concentration Er3+-doped phosphate fiber amplifiers," IEEE Photon. Technol. Lett. 13, 197-199 (2001).
[CrossRef]

Myslinski, P.

P. Myslinski, C. Szubert, A. J. Bruce, D. J. DiGiovanni, and B. Palsdottir, "Performance of high-concentration erbium-doped fiber amplifiers," IEEE Photon. Technol. Lett. 11, 973-975 (1999).
[CrossRef]

P. Myslinski, D. Nguyen, and J. Chrostowski, "Effects of concentration on the performance of erbium-doped fiber amplifiers," J. Lightwave Technol. 15, 112-119 (1997).
[CrossRef]

Nakagawa, K.

T. Nishi, K. Nakagawa, Y. Ohishi, and S. Takahashi, "The amplification properties of high Er3+-doped phosphate fiber," Jpn. J. Appl. Phys. Part 2 31, L177-L179 (1992).
[CrossRef]

Nguyen, D.

P. Myslinski, D. Nguyen, and J. Chrostowski, "Effects of concentration on the performance of erbium-doped fiber amplifiers," J. Lightwave Technol. 15, 112-119 (1997).
[CrossRef]

Nishi, T.

T. Nishi, K. Nakagawa, Y. Ohishi, and S. Takahashi, "The amplification properties of high Er3+-doped phosphate fiber," Jpn. J. Appl. Phys. Part 2 31, L177-L179 (1992).
[CrossRef]

Ohishi, Y.

T. Nishi, K. Nakagawa, Y. Ohishi, and S. Takahashi, "The amplification properties of high Er3+-doped phosphate fiber," Jpn. J. Appl. Phys. Part 2 31, L177-L179 (1992).
[CrossRef]

Palsdottir, B.

P. Myslinski, C. Szubert, A. J. Bruce, D. J. DiGiovanni, and B. Palsdottir, "Performance of high-concentration erbium-doped fiber amplifiers," IEEE Photon. Technol. Lett. 11, 973-975 (1999).
[CrossRef]

Peters, P. M.

P. M. Peters and S. N. Houde-Walter, "Local structure of Er3+ in multicomponent glasses," J. Non-Cryst. Solids 328, 162-169 (1998).
[CrossRef]

Peyghambarian, N.

B.-C. Hwang, S. Jiang, T. Luo, K. Seneschal, G. Sorbello, M. Morell, F. Smektala, S. Honkanen, J. Lucas, and N. Peyghambarian, "Performance of high-concentration Er3+-doped phosphate fiber amplifiers," IEEE Photon. Technol. Lett. 13, 197-199 (2001).
[CrossRef]

Popov, S.

Sarkilahti, S.

S. Tammela, M. Hotoleanu, P. Kiiveri, H. Valkonen, S. Sarkilahti, and K. Janka, "Very short Er-doped silica glass fiber for L-band amplifiers," in Conference on Optical Fiber Communications, Vol. 1 of 2003 OSA Technical Digest Series (Optical Society of America, 2003), pp. 376-377.

Seneschal, K.

B.-C. Hwang, S. Jiang, T. Luo, K. Seneschal, G. Sorbello, M. Morell, F. Smektala, S. Honkanen, J. Lucas, and N. Peyghambarian, "Performance of high-concentration Er3+-doped phosphate fiber amplifiers," IEEE Photon. Technol. Lett. 13, 197-199 (2001).
[CrossRef]

Sergeyev, S.

Sergeyev, S. V.

S. V. Sergeyev, "Model of high-concentration erbium-doped fibre amplifier: effects of migration and upconversion processes," Electron. Lett. 39, 511-512 (2003).
[CrossRef]

S. V. Sergeyev and B. Jaskorzynska, "Statistical model for energy-transfer-induced up-conversion in Er3+-doped glasses," Phys. Rev. B 62, 15628-15633 (2000).
[CrossRef]

Smektala, F.

B.-C. Hwang, S. Jiang, T. Luo, K. Seneschal, G. Sorbello, M. Morell, F. Smektala, S. Honkanen, J. Lucas, and N. Peyghambarian, "Performance of high-concentration Er3+-doped phosphate fiber amplifiers," IEEE Photon. Technol. Lett. 13, 197-199 (2001).
[CrossRef]

Sorbello, G.

B.-C. Hwang, S. Jiang, T. Luo, K. Seneschal, G. Sorbello, M. Morell, F. Smektala, S. Honkanen, J. Lucas, and N. Peyghambarian, "Performance of high-concentration Er3+-doped phosphate fiber amplifiers," IEEE Photon. Technol. Lett. 13, 197-199 (2001).
[CrossRef]

Szubert, C.

P. Myslinski, C. Szubert, A. J. Bruce, D. J. DiGiovanni, and B. Palsdottir, "Performance of high-concentration erbium-doped fiber amplifiers," IEEE Photon. Technol. Lett. 11, 973-975 (1999).
[CrossRef]

Takahashi, S.

T. Nishi, K. Nakagawa, Y. Ohishi, and S. Takahashi, "The amplification properties of high Er3+-doped phosphate fiber," Jpn. J. Appl. Phys. Part 2 31, L177-L179 (1992).
[CrossRef]

Tammela, S.

S. Tammela, M. Hotoleanu, P. Kiiveri, H. Valkonen, S. Sarkilahti, and K. Janka, "Very short Er-doped silica glass fiber for L-band amplifiers," in Conference on Optical Fiber Communications, Vol. 1 of 2003 OSA Technical Digest Series (Optical Society of America, 2003), pp. 376-377.

Valkonen, H.

S. Tammela, M. Hotoleanu, P. Kiiveri, H. Valkonen, S. Sarkilahti, and K. Janka, "Very short Er-doped silica glass fiber for L-band amplifiers," in Conference on Optical Fiber Communications, Vol. 1 of 2003 OSA Technical Digest Series (Optical Society of America, 2003), pp. 376-377.

Zeng, Q.

C. Jiang, W. Hu, and Q. Zeng, "Numerical analysis of concentration quenching model of Er3+-doped phosphate fiber amplifier," IEEE J. Quantum Electron. 39, 1266-1271 (2003).
[CrossRef]

Electron. Lett. (1)

S. V. Sergeyev, "Model of high-concentration erbium-doped fibre amplifier: effects of migration and upconversion processes," Electron. Lett. 39, 511-512 (2003).
[CrossRef]

IEEE J. Quantum Electron. (1)

C. Jiang, W. Hu, and Q. Zeng, "Numerical analysis of concentration quenching model of Er3+-doped phosphate fiber amplifier," IEEE J. Quantum Electron. 39, 1266-1271 (2003).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

B.-C. Hwang, S. Jiang, T. Luo, K. Seneschal, G. Sorbello, M. Morell, F. Smektala, S. Honkanen, J. Lucas, and N. Peyghambarian, "Performance of high-concentration Er3+-doped phosphate fiber amplifiers," IEEE Photon. Technol. Lett. 13, 197-199 (2001).
[CrossRef]

P. Myslinski, C. Szubert, A. J. Bruce, D. J. DiGiovanni, and B. Palsdottir, "Performance of high-concentration erbium-doped fiber amplifiers," IEEE Photon. Technol. Lett. 11, 973-975 (1999).
[CrossRef]

J. Lightwave Technol. (1)

P. Myslinski, D. Nguyen, and J. Chrostowski, "Effects of concentration on the performance of erbium-doped fiber amplifiers," J. Lightwave Technol. 15, 112-119 (1997).
[CrossRef]

J. Non-Cryst. Solids (1)

P. M. Peters and S. N. Houde-Walter, "Local structure of Er3+ in multicomponent glasses," J. Non-Cryst. Solids 328, 162-169 (1998).
[CrossRef]

Jpn. J. Appl. Phys. Part 2 (1)

T. Nishi, K. Nakagawa, Y. Ohishi, and S. Takahashi, "The amplification properties of high Er3+-doped phosphate fiber," Jpn. J. Appl. Phys. Part 2 31, L177-L179 (1992).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (1)

S. V. Sergeyev and B. Jaskorzynska, "Statistical model for energy-transfer-induced up-conversion in Er3+-doped glasses," Phys. Rev. B 62, 15628-15633 (2000).
[CrossRef]

Sov. Phys. Usp. (1)

A. I. Burstein, "Concentration quenching of noncoherent excitation in solutions," Sov. Phys. Usp. 143, 553-600 (1984).
[CrossRef]

Other (2)

E. Desurvire, Erbium-Doped Fiber Amplifiers (Wiley, 1994).

S. Tammela, M. Hotoleanu, P. Kiiveri, H. Valkonen, S. Sarkilahti, and K. Janka, "Very short Er-doped silica glass fiber for L-band amplifiers," in Conference on Optical Fiber Communications, Vol. 1 of 2003 OSA Technical Digest Series (Optical Society of America, 2003), pp. 376-377.

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Figures (2)

Fig. 1
Fig. 1

Small-signal gain error (difference between theoretical and experimental lines obtained for I s I s s ) as a function of the fitting parameter R up .

Fig. 2
Fig. 2

Gain of erbium-doped phosphate fiber as a function of the input signal power. Experimental, circles[1]; presented statistical model, solid curves [Eqs. (7, 9, 10)]; model accounting for HUC and PIQ, dashed curves [Eqs. (8, 9, 10)]. Parameters for erbium-doped phosphate fiber are from Table 1. Fitting parameters; Statistical model, r = 60 , R up = 0.995 nm ( λ s = 1535 nm ) , and R up = 1.00 nm ( λ s = 1550 nm ) ; model accounting for HUC and PIQ, C = 26.5 , k = 7.4 % ( λ s = 1535 nm ) , k = 9.7 % ( λ s = 1550 nm ) .

Tables (2)

Tables Icon

Table 1 Parameters of Erbium-Doped Phosphate Fiber a

Tables Icon

Table 2 Noise Figure for the Experiment, the Statistical Model, and the Model Accounting for HUC and PIQ

Equations (11)

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d n k d k = ( 1 n k β p ) I p I p s ( 1 n k β s ) I s I s s n k n k i = 1 , i k n N P k i n k j = 1 , j k N W k j + j = 1 , j k N W k j n j .
P k i = ( R up R k i ) 6 , W k j = ( R m R k j ) 6 ,
n k = I p I p s + I s I s s 1 + β p I p I p s + β s I s I s s 0 e t exp ( t i = 1 , k n N P k i 1 + β p I p I p s + β s I s I s s ) exp ( t j = 1 , j k n N W k j 1 + β p I p I p s + β s I s I s s ) d t n 0 e t exp ( t i = 1 , k n N P k i 1 + β p I p I p s + β s I s I s s ) t exp ( t j = 1 , j k N W k j 1 + β p I p I p s + β s I s I s s ) d t .
n = n k R k , 1 , , R k , n N , R k , 1 , R k , N = ( 4 π V ) n N + N i = 1 , i k n N 0 h ( R k , i ) R k , i 2 d R k , i j = 1 , j k N 0 h ( R k , j ) R k , j 2 d R k , j n ( R k , 1 , , R k , n N , R k , 1 , , R k , N ) .
n = I p I p s + I s I s s 1 + β p I p I p s + β s I s I s s 0 e t P ( t ) Q ( t ) d t 1 + 0 e t P ( t ) Q ( t ) t d t ,
Q ( t ) = exp ( t 1 + β p I p I p s + β s I s I s s i k N W k i ) = lim N ( 1 4 π c Er N 0 h ( r ) { 1 exp [ t 1 + β p I p I p s + β s I s I s s ( R m r ) 6 ] } r 2 d r ) N exp ( 4 π c Er 0 h ( r ) { 1 exp [ t 1 + β p I p I p s + β s I s I s s ( R m r ) 6 ] } r 2 d r ) ,
P ( t ) = exp ( t 1 + β p I p I p s + β s I s I s s i k N ( n ) P k i ) = lim N ( 1 4 π c Er n N 0 h ( r ) { 1 exp [ t 1 + β p I p I p s + β s I s I s s ( R up r ) 6 ] } r 2 d r ) N exp ( 4 π c Er n 0 h ( r ) { 1 exp [ t 1 + β p I p I p s + β s I s I s s ( R up r ) 6 ] } r 2 d r ) .
n = ( I s I s s + I p I p s ) ( n + r 2 ) 1 + β s I s I s s + β p I p I p s F [ π c Er c up ( n + r 2 ) 2 1 + β s I s I s s + β p I p I p s ] { n + r 2 F [ π c Er c up ( n + r 2 ) 2 1 + β s I s I s s + β p I p I p s ] } ,
n = ( 1 + β s I s I s s + β p I p I p s ) + ( 1 + β s I s I s s + β p I p I p s ) 2 + 4 C ( I s I s s + I p I p s ) 2 C ( 1 2 k ) + 2 k ( I s I s s + I p I p s ) 1 + ( 1 + β s ) I s I s s + ( 1 + β s ) I s I p s .
d I i d z = I i [ α i ( β i n 1 ) ] ( i = s , p ) ,
F = 2 Γ s σ e s c Er 0 L n ( z ) I s ( z ) I s ( 0 ) d z .

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