Abstract

Applying a pair-correlation function of erbium ions that is known from x-ray absorption fine structure spectroscopy, we develop a new statistical model of migration-assisted upconversion in erbium-doped glasses. The results of modeling show that short-range coordination order of erbium ions contributes to the upconversion rate for both low and high population inversion. In addition, we report the methods of suppression of the short-range order of erbium ions in multicomponent glasses.

© 2005 Optical Society of America

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  1. P. Myslinski, D. Nguyen, and J. Chrostowski, J. Lightwave Technol. 15, 112 (1997).
    [CrossRef]
  2. C. Jiang, W. Hu, and Q. Zeng, IEEE Photonics Technol. Lett. 16, 774 (2004).
    [CrossRef]
  3. P. M. Peters and S. N. Houde-Walter, J. Non-Cryst. Solids 328, 162 (1998).
    [CrossRef]
  4. S. V. Sergeyev and B. Jaskorzynska, Phys. Rev. B 62, 15628 (2000).
    [CrossRef]
  5. S. V. Sergeyev, Electron. Lett. 39, 511 (2003).
    [CrossRef]
  6. D. L. Huber, D. S. Hamilton, and B. Barnet, Phys. Rev. B 16, 4642 (1977).
    [CrossRef]
  7. J. Lægsgaard, Phys. Rev. B 65, 174114 (2002).
    [CrossRef]
  8. B.-C. Hwang, S. Jiang, T. Luo, K. Seneschal, G. Sorbello, M. Morell, F. Smektala, S. Honkanen, J. Lucas, and N. Peyghambarian, IEEE Photonics Technol. Lett. 13, 197 (2001).
    [CrossRef]
  9. S. Tammela, M. Hotoleanu, P. Kiiveri, H. Valkonen, S. Sarkilahti, and K. Janka, in Conference on Optical Fiber Communications, Vol. 88 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), pp. 376–377.

2004 (1)

C. Jiang, W. Hu, and Q. Zeng, IEEE Photonics Technol. Lett. 16, 774 (2004).
[CrossRef]

2003 (1)

S. V. Sergeyev, Electron. Lett. 39, 511 (2003).
[CrossRef]

2002 (1)

J. Lægsgaard, Phys. Rev. B 65, 174114 (2002).
[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, IEEE Photonics Technol. Lett. 13, 197 (2001).
[CrossRef]

2000 (1)

S. V. Sergeyev and B. Jaskorzynska, Phys. Rev. B 62, 15628 (2000).
[CrossRef]

1998 (1)

P. M. Peters and S. N. Houde-Walter, J. Non-Cryst. Solids 328, 162 (1998).
[CrossRef]

1997 (1)

P. Myslinski, D. Nguyen, and J. Chrostowski, J. Lightwave Technol. 15, 112 (1997).
[CrossRef]

1977 (1)

D. L. Huber, D. S. Hamilton, and B. Barnet, Phys. Rev. B 16, 4642 (1977).
[CrossRef]

Barnet, B.

D. L. Huber, D. S. Hamilton, and B. Barnet, Phys. Rev. B 16, 4642 (1977).
[CrossRef]

Chrostowski, J.

P. Myslinski, D. Nguyen, and J. Chrostowski, J. Lightwave Technol. 15, 112 (1997).
[CrossRef]

Hamilton, D. S.

D. L. Huber, D. S. Hamilton, and B. Barnet, Phys. Rev. B 16, 4642 (1977).
[CrossRef]

Honkanen, S.

B.-C. Hwang, S. Jiang, T. Luo, K. Seneschal, G. Sorbello, M. Morell, F. Smektala, S. Honkanen, J. Lucas, and N. Peyghambarian, IEEE Photonics Technol. Lett. 13, 197 (2001).
[CrossRef]

Hotoleanu, M.

S. Tammela, M. Hotoleanu, P. Kiiveri, H. Valkonen, S. Sarkilahti, and K. Janka, in Conference on Optical Fiber Communications, Vol. 88 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), pp. 376–377.

Houde-Walter, S. N.

P. M. Peters and S. N. Houde-Walter, J. Non-Cryst. Solids 328, 162 (1998).
[CrossRef]

Hu, W.

C. Jiang, W. Hu, and Q. Zeng, IEEE Photonics Technol. Lett. 16, 774 (2004).
[CrossRef]

Huber, D. L.

D. L. Huber, D. S. Hamilton, and B. Barnet, Phys. Rev. B 16, 4642 (1977).
[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, IEEE Photonics Technol. Lett. 13, 197 (2001).
[CrossRef]

Janka, K.

S. Tammela, M. Hotoleanu, P. Kiiveri, H. Valkonen, S. Sarkilahti, and K. Janka, in Conference on Optical Fiber Communications, Vol. 88 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), pp. 376–377.

Jaskorzynska, B.

S. V. Sergeyev and B. Jaskorzynska, Phys. Rev. B 62, 15628 (2000).
[CrossRef]

Jiang, C.

C. Jiang, W. Hu, and Q. Zeng, IEEE Photonics Technol. Lett. 16, 774 (2004).
[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, IEEE Photonics Technol. Lett. 13, 197 (2001).
[CrossRef]

Kiiveri, P.

S. Tammela, M. Hotoleanu, P. Kiiveri, H. Valkonen, S. Sarkilahti, and K. Janka, in Conference on Optical Fiber Communications, Vol. 88 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), pp. 376–377.

Lægsgaard, J.

J. Lægsgaard, Phys. Rev. B 65, 174114 (2002).
[CrossRef]

Lucas, J.

B.-C. Hwang, S. Jiang, T. Luo, K. Seneschal, G. Sorbello, M. Morell, F. Smektala, S. Honkanen, J. Lucas, and N. Peyghambarian, IEEE Photonics Technol. Lett. 13, 197 (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, IEEE Photonics Technol. Lett. 13, 197 (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, IEEE Photonics Technol. Lett. 13, 197 (2001).
[CrossRef]

Myslinski, P.

P. Myslinski, D. Nguyen, and J. Chrostowski, J. Lightwave Technol. 15, 112 (1997).
[CrossRef]

Nguyen, D.

P. Myslinski, D. Nguyen, and J. Chrostowski, J. Lightwave Technol. 15, 112 (1997).
[CrossRef]

Peters, P. M.

P. M. Peters and S. N. Houde-Walter, J. Non-Cryst. Solids 328, 162 (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, IEEE Photonics Technol. Lett. 13, 197 (2001).
[CrossRef]

Sarkilahti, S.

S. Tammela, M. Hotoleanu, P. Kiiveri, H. Valkonen, S. Sarkilahti, and K. Janka, in Conference on Optical Fiber Communications, Vol. 88 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 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, IEEE Photonics Technol. Lett. 13, 197 (2001).
[CrossRef]

Sergeyev, S. V.

S. V. Sergeyev, Electron. Lett. 39, 511 (2003).
[CrossRef]

S. V. Sergeyev and B. Jaskorzynska, Phys. Rev. B 62, 15628 (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, IEEE Photonics Technol. Lett. 13, 197 (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, IEEE Photonics Technol. Lett. 13, 197 (2001).
[CrossRef]

Tammela, S.

S. Tammela, M. Hotoleanu, P. Kiiveri, H. Valkonen, S. Sarkilahti, and K. Janka, in Conference on Optical Fiber Communications, Vol. 88 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), pp. 376–377.

Valkonen, H.

S. Tammela, M. Hotoleanu, P. Kiiveri, H. Valkonen, S. Sarkilahti, and K. Janka, in Conference on Optical Fiber Communications, Vol. 88 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), pp. 376–377.

Zeng, Q.

C. Jiang, W. Hu, and Q. Zeng, IEEE Photonics Technol. Lett. 16, 774 (2004).
[CrossRef]

Electron. Lett. (1)

S. V. Sergeyev, Electron. Lett. 39, 511 (2003).
[CrossRef]

IEEE Photonics Technol. Lett. (2)

C. Jiang, W. Hu, and Q. Zeng, IEEE Photonics Technol. Lett. 16, 774 (2004).
[CrossRef]

B.-C. Hwang, S. Jiang, T. Luo, K. Seneschal, G. Sorbello, M. Morell, F. Smektala, S. Honkanen, J. Lucas, and N. Peyghambarian, IEEE Photonics Technol. Lett. 13, 197 (2001).
[CrossRef]

J. Lightwave Technol. (1)

P. Myslinski, D. Nguyen, and J. Chrostowski, J. Lightwave Technol. 15, 112 (1997).
[CrossRef]

J. Non-Cryst. Solids (1)

P. M. Peters and S. N. Houde-Walter, J. Non-Cryst. Solids 328, 162 (1998).
[CrossRef]

Phys. Rev. B (3)

S. V. Sergeyev and B. Jaskorzynska, Phys. Rev. B 62, 15628 (2000).
[CrossRef]

D. L. Huber, D. S. Hamilton, and B. Barnet, Phys. Rev. B 16, 4642 (1977).
[CrossRef]

J. Lægsgaard, Phys. Rev. B 65, 174114 (2002).
[CrossRef]

Other (1)

S. Tammela, M. Hotoleanu, P. Kiiveri, H. Valkonen, S. Sarkilahti, and K. Janka, in Conference on Optical Fiber Communications, Vol. 88 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), pp. 376–377.

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Figures (2)

Fig. 1
Fig. 1

Pair-correlation functions h ( R ) to find two erbium ions at separation R as a function of distance R. Thin solid curve, function obtained from XAFS experiments[4]; dashed line, simplified form h ( R ) 1 ; thick solid curve, model pair-correlation functions [Eqs. (12)] ( 1 Å = 0.1 nm ) .

Fig. 2
Fig. 2

Upconversion coefficient C up as a function of population inversion n for the pump at 980 nm. Advanced model [solid curve, Eqs. (5, 9, 12)]: R 0 = 1.07 nm , r = 60 , β = 1 , R 1 = 0.325 nm , R 2 = 0.45 nm , c Er c up = 0.452 , and a = 1 (diamonds), a = 1.8 (circles), a = 3 (squares). Simplified model [dashed curve, Eqs. (5, 11)]: R 0 = 1.07 nm, r = 60 , β = 1 , c Er c up = 0.452 .

Equations (17)

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d n k d t = ( 1 n k β ) P p P p 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 j i ) 6 ,
d n d t = ( 1 n β ) P p P p s n C up n 2 .
C up = d n d t + ( 1 n β ) P p P p s n n 2 .
n k = P p P p s 1 + β P p P p s 0 exp ( t ) Y k X k d t n 0 exp ( t ) Y k X k t d t ,
X k = exp ( t j = 1 , j k N W kj 1 + β P p P p s ) , Y k = exp ( t i = 1 , i k n N P ki 1 + β P p P p s ) .
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 = P p P p s 1 + β P p P p s 0 exp ( t ) P ( t ) Q ( t ) d t 1 + 0 exp ( t ) P ( t ) Q ( t ) t d t ,
P ( t ) = X k = exp ( 4 π c Er 0 h ( r ) { 1 exp [ t 1 + β P p P p s ( R m r ) 6 ] } r 2 d r ) ,
Q ( t ) = Y k = exp ( 4 π c Er n 0 h ( r ) { 1 exp [ t 1 + β P p P p s ( R up r ) 6 ] } r 2 d r ) .
P ( t ) = exp ( k r t 2 ) , Q ( t ) = exp ( k n t ) ,
n = P p P p s 1 + β P p P p s ( n + r 2 ) F [ k ( n + r 2 ) 2 ( 1 + β P p P p s ) 1 2 ] n + r 2 F [ k ( n + r 2 ) 2 ( 1 + β P p P p s ) 1 2 ] ,
h ( R ) { 0 , R < R 1 a , R 1 < R < R 2 1 , R > R 2 } ,
Q ( t ) = exp ( γ n { ( a 1 ) [ F ( R 2 ) + G ( R 2 ) ] + ( π t 1 + β P p P p s ) 1 2 + a [ F ( R 1 ) + G ( R 1 ) ] } ) ,
P ( t ) = exp ( γ r 2 { ( a 1 ) [ F ( R 2 r 1 6 ) + G ( R 2 r 1 6 ) ] + ( π t 1 + β P p P p s ) 1 2 + a [ F ( R 1 r 1 6 ) + G ( R 1 r 1 6 ) ] } ) ,
F ( x ) = ( x R up ) 3 { 1 exp [ t ( 1 + β P p P p s ) ( R up x ) 6 ] } ,
G ( x ) = ( π t 1 + β P p P p s ) 1 2 erfc [ ( t 1 + β P p P p s ) 1 2 ( R up x ) 3 ] .

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