Abstract

In this paper a Raman Fiber Lasers (RFLs) with several embedded cavities are studied. A novel algorithm is proposed to solve the coupled equations describing the optical power evolution in a RFL. By using some invariant constants as the boundary condition at the output end, the problem of solving ordinary differential equations (ODEs) with guessing boundary value is translated into a two-boundary-condition ODE problem. The algorithm is based on Newton-Raphson method and proved rather fast and stable. Quantitative analysis is performed based on the algorithm.

© 2006 Optical Society of America

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  1. S. Namiki and Y. Emori “Ultrabroad-band Raman amplifiers pumped and gain-equalized by wavelength-division-multiplexed high-power laser diodes,” IEEE J. Sel. Top. Quantum Electron. 7, 3–16 (2001).
    [Crossref]
  2. J. AuYeung and A. Yariv, “Theory of CW Raman oscillation in optical fibers,” J. Opt. Soc. Amer. 69, 803–807)(1979).
    [Crossref]
  3. P. N. Kean, B. D. Sinclair, K. Smith, W. Sibbett, C. J. Rowe, and D. C. J. Reid, “Experimental evaluation of a fibre Raman oscillator having fibre grating reflectors,” J. Mod. Opt. 35, 397–406 (1988).
    [Crossref]
  4. M. Rini, I. Christiani, and V. Degiorgio, “Numerical modeling and optimization of cascaded Raman fiber lasers,” IEEE J. Quantum Electron. 36, 1117–1122 (2000).
    [Crossref]
  5. N. Kurukitkoson, H. Sugahara, S. K. Tusitsyn, O. N. Egorova, A. S. Kurkov, V. M. Paramonov, and E. M. Dianov, “Optimization of two stage Raman converter based on phosphosilicate core fiber: Modeling and experiment,” Electron. Lett. 37, 1281–1283 (2001).
    [Crossref]
  6. Michael Krause and Hagen Renner, “Theory and design of double-cavity Raman Fiber Lasers,” IEEE J. Lightwave Technol. 23, 2474–2483 (2005).
    [Crossref]
  7. Bumki Min, Won Jae Lee, and Namkyoo Park. “Efficient formulation of Raman amplifier propagation equations with average power analysis,” IEEE Photon. Technol. Lett. 12, 392–394 (2002).
  8. Xueming Liu, H. Y zhang, and Y. L Guo. “A novel method for Raman amplifer propagation equations,” IEEE Photon. Technol. Lett. 15, 392–394 (2003).
    [Crossref]
  9. Xueming Liu and B. Lee, “A fast and stable method for Raman amplifier propagation equations,” Opt. Express. 11, 2163–2176 (2003).
    [Crossref] [PubMed]
  10. F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, D. Bayart, F. Castella, P. Chartier, and E. Faou, “Modeling of multiwavelength Raman fiber lasers using a new and fast algorithm,” IEEE Photon. Technol. Lett. 16, 2601–2603 (2004).
    [Crossref]
  11. G. P. Agrawal, Nonlinear Fiber Optics, (Academic Press, New York,2001).
  12. Yoko Inoue and Shuichi Fujikawa, “Diode-pumped Nd:YAG laser producing 122W CW power at 1.319μm,” IEEE J.Quantum Electron. 36, 751–756 (2000).
    [Crossref]

2005 (1)

Michael Krause and Hagen Renner, “Theory and design of double-cavity Raman Fiber Lasers,” IEEE J. Lightwave Technol. 23, 2474–2483 (2005).
[Crossref]

2004 (1)

F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, D. Bayart, F. Castella, P. Chartier, and E. Faou, “Modeling of multiwavelength Raman fiber lasers using a new and fast algorithm,” IEEE Photon. Technol. Lett. 16, 2601–2603 (2004).
[Crossref]

2003 (2)

Xueming Liu, H. Y zhang, and Y. L Guo. “A novel method for Raman amplifer propagation equations,” IEEE Photon. Technol. Lett. 15, 392–394 (2003).
[Crossref]

Xueming Liu and B. Lee, “A fast and stable method for Raman amplifier propagation equations,” Opt. Express. 11, 2163–2176 (2003).
[Crossref] [PubMed]

2002 (1)

Bumki Min, Won Jae Lee, and Namkyoo Park. “Efficient formulation of Raman amplifier propagation equations with average power analysis,” IEEE Photon. Technol. Lett. 12, 392–394 (2002).

2001 (2)

S. Namiki and Y. Emori “Ultrabroad-band Raman amplifiers pumped and gain-equalized by wavelength-division-multiplexed high-power laser diodes,” IEEE J. Sel. Top. Quantum Electron. 7, 3–16 (2001).
[Crossref]

N. Kurukitkoson, H. Sugahara, S. K. Tusitsyn, O. N. Egorova, A. S. Kurkov, V. M. Paramonov, and E. M. Dianov, “Optimization of two stage Raman converter based on phosphosilicate core fiber: Modeling and experiment,” Electron. Lett. 37, 1281–1283 (2001).
[Crossref]

2000 (2)

Yoko Inoue and Shuichi Fujikawa, “Diode-pumped Nd:YAG laser producing 122W CW power at 1.319μm,” IEEE J.Quantum Electron. 36, 751–756 (2000).
[Crossref]

M. Rini, I. Christiani, and V. Degiorgio, “Numerical modeling and optimization of cascaded Raman fiber lasers,” IEEE J. Quantum Electron. 36, 1117–1122 (2000).
[Crossref]

1988 (1)

P. N. Kean, B. D. Sinclair, K. Smith, W. Sibbett, C. J. Rowe, and D. C. J. Reid, “Experimental evaluation of a fibre Raman oscillator having fibre grating reflectors,” J. Mod. Opt. 35, 397–406 (1988).
[Crossref]

1979 (1)

J. AuYeung and A. Yariv, “Theory of CW Raman oscillation in optical fibers,” J. Opt. Soc. Amer. 69, 803–807)(1979).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, (Academic Press, New York,2001).

AuYeung, J.

J. AuYeung and A. Yariv, “Theory of CW Raman oscillation in optical fibers,” J. Opt. Soc. Amer. 69, 803–807)(1979).
[Crossref]

Bayart, D.

F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, D. Bayart, F. Castella, P. Chartier, and E. Faou, “Modeling of multiwavelength Raman fiber lasers using a new and fast algorithm,” IEEE Photon. Technol. Lett. 16, 2601–2603 (2004).
[Crossref]

Borne, S.

F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, D. Bayart, F. Castella, P. Chartier, and E. Faou, “Modeling of multiwavelength Raman fiber lasers using a new and fast algorithm,” IEEE Photon. Technol. Lett. 16, 2601–2603 (2004).
[Crossref]

Castella, F.

F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, D. Bayart, F. Castella, P. Chartier, and E. Faou, “Modeling of multiwavelength Raman fiber lasers using a new and fast algorithm,” IEEE Photon. Technol. Lett. 16, 2601–2603 (2004).
[Crossref]

Chartier, P.

F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, D. Bayart, F. Castella, P. Chartier, and E. Faou, “Modeling of multiwavelength Raman fiber lasers using a new and fast algorithm,” IEEE Photon. Technol. Lett. 16, 2601–2603 (2004).
[Crossref]

Christiani, I.

M. Rini, I. Christiani, and V. Degiorgio, “Numerical modeling and optimization of cascaded Raman fiber lasers,” IEEE J. Quantum Electron. 36, 1117–1122 (2000).
[Crossref]

Degiorgio, V.

M. Rini, I. Christiani, and V. Degiorgio, “Numerical modeling and optimization of cascaded Raman fiber lasers,” IEEE J. Quantum Electron. 36, 1117–1122 (2000).
[Crossref]

Dianov, E. M.

N. Kurukitkoson, H. Sugahara, S. K. Tusitsyn, O. N. Egorova, A. S. Kurkov, V. M. Paramonov, and E. M. Dianov, “Optimization of two stage Raman converter based on phosphosilicate core fiber: Modeling and experiment,” Electron. Lett. 37, 1281–1283 (2001).
[Crossref]

Egorova, O. N.

N. Kurukitkoson, H. Sugahara, S. K. Tusitsyn, O. N. Egorova, A. S. Kurkov, V. M. Paramonov, and E. M. Dianov, “Optimization of two stage Raman converter based on phosphosilicate core fiber: Modeling and experiment,” Electron. Lett. 37, 1281–1283 (2001).
[Crossref]

Emori, Y.

S. Namiki and Y. Emori “Ultrabroad-band Raman amplifiers pumped and gain-equalized by wavelength-division-multiplexed high-power laser diodes,” IEEE J. Sel. Top. Quantum Electron. 7, 3–16 (2001).
[Crossref]

Faou, E.

F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, D. Bayart, F. Castella, P. Chartier, and E. Faou, “Modeling of multiwavelength Raman fiber lasers using a new and fast algorithm,” IEEE Photon. Technol. Lett. 16, 2601–2603 (2004).
[Crossref]

Fujikawa, Shuichi

Yoko Inoue and Shuichi Fujikawa, “Diode-pumped Nd:YAG laser producing 122W CW power at 1.319μm,” IEEE J.Quantum Electron. 36, 751–756 (2000).
[Crossref]

Guo, Y. L

Xueming Liu, H. Y zhang, and Y. L Guo. “A novel method for Raman amplifer propagation equations,” IEEE Photon. Technol. Lett. 15, 392–394 (2003).
[Crossref]

Inoue, Yoko

Yoko Inoue and Shuichi Fujikawa, “Diode-pumped Nd:YAG laser producing 122W CW power at 1.319μm,” IEEE J.Quantum Electron. 36, 751–756 (2000).
[Crossref]

Kean, P. N.

P. N. Kean, B. D. Sinclair, K. Smith, W. Sibbett, C. J. Rowe, and D. C. J. Reid, “Experimental evaluation of a fibre Raman oscillator having fibre grating reflectors,” J. Mod. Opt. 35, 397–406 (1988).
[Crossref]

Krause, Michael

Michael Krause and Hagen Renner, “Theory and design of double-cavity Raman Fiber Lasers,” IEEE J. Lightwave Technol. 23, 2474–2483 (2005).
[Crossref]

Kurkov, A. S.

N. Kurukitkoson, H. Sugahara, S. K. Tusitsyn, O. N. Egorova, A. S. Kurkov, V. M. Paramonov, and E. M. Dianov, “Optimization of two stage Raman converter based on phosphosilicate core fiber: Modeling and experiment,” Electron. Lett. 37, 1281–1283 (2001).
[Crossref]

Kurukitkoson, N.

N. Kurukitkoson, H. Sugahara, S. K. Tusitsyn, O. N. Egorova, A. S. Kurkov, V. M. Paramonov, and E. M. Dianov, “Optimization of two stage Raman converter based on phosphosilicate core fiber: Modeling and experiment,” Electron. Lett. 37, 1281–1283 (2001).
[Crossref]

Lee, B.

Xueming Liu and B. Lee, “A fast and stable method for Raman amplifier propagation equations,” Opt. Express. 11, 2163–2176 (2003).
[Crossref] [PubMed]

Lee, Won Jae

Bumki Min, Won Jae Lee, and Namkyoo Park. “Efficient formulation of Raman amplifier propagation equations with average power analysis,” IEEE Photon. Technol. Lett. 12, 392–394 (2002).

Leplingard, F.

F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, D. Bayart, F. Castella, P. Chartier, and E. Faou, “Modeling of multiwavelength Raman fiber lasers using a new and fast algorithm,” IEEE Photon. Technol. Lett. 16, 2601–2603 (2004).
[Crossref]

Liu, Xueming

Xueming Liu and B. Lee, “A fast and stable method for Raman amplifier propagation equations,” Opt. Express. 11, 2163–2176 (2003).
[Crossref] [PubMed]

Xueming Liu, H. Y zhang, and Y. L Guo. “A novel method for Raman amplifer propagation equations,” IEEE Photon. Technol. Lett. 15, 392–394 (2003).
[Crossref]

Lorcy, L.

F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, D. Bayart, F. Castella, P. Chartier, and E. Faou, “Modeling of multiwavelength Raman fiber lasers using a new and fast algorithm,” IEEE Photon. Technol. Lett. 16, 2601–2603 (2004).
[Crossref]

Martinelli, C.

F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, D. Bayart, F. Castella, P. Chartier, and E. Faou, “Modeling of multiwavelength Raman fiber lasers using a new and fast algorithm,” IEEE Photon. Technol. Lett. 16, 2601–2603 (2004).
[Crossref]

Min, Bumki

Bumki Min, Won Jae Lee, and Namkyoo Park. “Efficient formulation of Raman amplifier propagation equations with average power analysis,” IEEE Photon. Technol. Lett. 12, 392–394 (2002).

Namiki, S.

S. Namiki and Y. Emori “Ultrabroad-band Raman amplifiers pumped and gain-equalized by wavelength-division-multiplexed high-power laser diodes,” IEEE J. Sel. Top. Quantum Electron. 7, 3–16 (2001).
[Crossref]

Paramonov, V. M.

N. Kurukitkoson, H. Sugahara, S. K. Tusitsyn, O. N. Egorova, A. S. Kurkov, V. M. Paramonov, and E. M. Dianov, “Optimization of two stage Raman converter based on phosphosilicate core fiber: Modeling and experiment,” Electron. Lett. 37, 1281–1283 (2001).
[Crossref]

Park, Namkyoo

Bumki Min, Won Jae Lee, and Namkyoo Park. “Efficient formulation of Raman amplifier propagation equations with average power analysis,” IEEE Photon. Technol. Lett. 12, 392–394 (2002).

Reid, D. C. J.

P. N. Kean, B. D. Sinclair, K. Smith, W. Sibbett, C. J. Rowe, and D. C. J. Reid, “Experimental evaluation of a fibre Raman oscillator having fibre grating reflectors,” J. Mod. Opt. 35, 397–406 (1988).
[Crossref]

Renner, Hagen

Michael Krause and Hagen Renner, “Theory and design of double-cavity Raman Fiber Lasers,” IEEE J. Lightwave Technol. 23, 2474–2483 (2005).
[Crossref]

Rini, M.

M. Rini, I. Christiani, and V. Degiorgio, “Numerical modeling and optimization of cascaded Raman fiber lasers,” IEEE J. Quantum Electron. 36, 1117–1122 (2000).
[Crossref]

Rowe, C. J.

P. N. Kean, B. D. Sinclair, K. Smith, W. Sibbett, C. J. Rowe, and D. C. J. Reid, “Experimental evaluation of a fibre Raman oscillator having fibre grating reflectors,” J. Mod. Opt. 35, 397–406 (1988).
[Crossref]

Sibbett, W.

P. N. Kean, B. D. Sinclair, K. Smith, W. Sibbett, C. J. Rowe, and D. C. J. Reid, “Experimental evaluation of a fibre Raman oscillator having fibre grating reflectors,” J. Mod. Opt. 35, 397–406 (1988).
[Crossref]

Sinclair, B. D.

P. N. Kean, B. D. Sinclair, K. Smith, W. Sibbett, C. J. Rowe, and D. C. J. Reid, “Experimental evaluation of a fibre Raman oscillator having fibre grating reflectors,” J. Mod. Opt. 35, 397–406 (1988).
[Crossref]

Smith, K.

P. N. Kean, B. D. Sinclair, K. Smith, W. Sibbett, C. J. Rowe, and D. C. J. Reid, “Experimental evaluation of a fibre Raman oscillator having fibre grating reflectors,” J. Mod. Opt. 35, 397–406 (1988).
[Crossref]

Sugahara, H.

N. Kurukitkoson, H. Sugahara, S. K. Tusitsyn, O. N. Egorova, A. S. Kurkov, V. M. Paramonov, and E. M. Dianov, “Optimization of two stage Raman converter based on phosphosilicate core fiber: Modeling and experiment,” Electron. Lett. 37, 1281–1283 (2001).
[Crossref]

Tusitsyn, S. K.

N. Kurukitkoson, H. Sugahara, S. K. Tusitsyn, O. N. Egorova, A. S. Kurkov, V. M. Paramonov, and E. M. Dianov, “Optimization of two stage Raman converter based on phosphosilicate core fiber: Modeling and experiment,” Electron. Lett. 37, 1281–1283 (2001).
[Crossref]

Yariv, A.

J. AuYeung and A. Yariv, “Theory of CW Raman oscillation in optical fibers,” J. Opt. Soc. Amer. 69, 803–807)(1979).
[Crossref]

zhang, H. Y

Xueming Liu, H. Y zhang, and Y. L Guo. “A novel method for Raman amplifer propagation equations,” IEEE Photon. Technol. Lett. 15, 392–394 (2003).
[Crossref]

Electron. Lett. (1)

N. Kurukitkoson, H. Sugahara, S. K. Tusitsyn, O. N. Egorova, A. S. Kurkov, V. M. Paramonov, and E. M. Dianov, “Optimization of two stage Raman converter based on phosphosilicate core fiber: Modeling and experiment,” Electron. Lett. 37, 1281–1283 (2001).
[Crossref]

IEEE J. Lightwave Technol. (1)

Michael Krause and Hagen Renner, “Theory and design of double-cavity Raman Fiber Lasers,” IEEE J. Lightwave Technol. 23, 2474–2483 (2005).
[Crossref]

IEEE J. Quantum Electron. (1)

M. Rini, I. Christiani, and V. Degiorgio, “Numerical modeling and optimization of cascaded Raman fiber lasers,” IEEE J. Quantum Electron. 36, 1117–1122 (2000).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

S. Namiki and Y. Emori “Ultrabroad-band Raman amplifiers pumped and gain-equalized by wavelength-division-multiplexed high-power laser diodes,” IEEE J. Sel. Top. Quantum Electron. 7, 3–16 (2001).
[Crossref]

IEEE J.Quantum Electron. (1)

Yoko Inoue and Shuichi Fujikawa, “Diode-pumped Nd:YAG laser producing 122W CW power at 1.319μm,” IEEE J.Quantum Electron. 36, 751–756 (2000).
[Crossref]

IEEE Photon. Technol. Lett. (3)

F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, D. Bayart, F. Castella, P. Chartier, and E. Faou, “Modeling of multiwavelength Raman fiber lasers using a new and fast algorithm,” IEEE Photon. Technol. Lett. 16, 2601–2603 (2004).
[Crossref]

Bumki Min, Won Jae Lee, and Namkyoo Park. “Efficient formulation of Raman amplifier propagation equations with average power analysis,” IEEE Photon. Technol. Lett. 12, 392–394 (2002).

Xueming Liu, H. Y zhang, and Y. L Guo. “A novel method for Raman amplifer propagation equations,” IEEE Photon. Technol. Lett. 15, 392–394 (2003).
[Crossref]

J. Mod. Opt. (1)

P. N. Kean, B. D. Sinclair, K. Smith, W. Sibbett, C. J. Rowe, and D. C. J. Reid, “Experimental evaluation of a fibre Raman oscillator having fibre grating reflectors,” J. Mod. Opt. 35, 397–406 (1988).
[Crossref]

J. Opt. Soc. Amer. (1)

J. AuYeung and A. Yariv, “Theory of CW Raman oscillation in optical fibers,” J. Opt. Soc. Amer. 69, 803–807)(1979).
[Crossref]

Opt. Express. (1)

Xueming Liu and B. Lee, “A fast and stable method for Raman amplifier propagation equations,” Opt. Express. 11, 2163–2176 (2003).
[Crossref] [PubMed]

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics, (Academic Press, New York,2001).

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Figures (4)

Fig. 1.
Fig. 1.

The structure for RFL with several embedded cavities.

Fig. 2.
Fig. 2.

Pump power and lasing power evolution along the fiber.

Fig. 3.
Fig. 3.

The output lasing power at 1580nm versus input pump power at 1318.8nm.

Fig. 4.
Fig. 4.

The output lasing power versus reflectivity at 1580nm.

Equations (11)

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

± P i ± z = j = 1 , j i n g ( ν j , ν i ) P i ± ( P j + + P j ) α i P i ±
P 1 + ( 0 ) = P p
P 1 ( L ) = R L 1 P 1 + ( L )
P i + ( 0 ) = R 0 i P i ( 0 ) P i ( L ) = R Li P i + ( L ) ( i = 2 n )
g ( ν i , ν j ) = { gr ( ν i ν j ) 2 A eff ( ν i > ν j ) ( ν j ν i ) gr ( ν j ν i ) 2 A eff ( ν i < ν j )
( P 1 ( L ) ) 2 R L 1 P 1 ( 0 ) = P p
P i + ( L ) P i + ( 0 ) = 1 R 0 i R Li i = 2 n
output ( L ) = F ( P ( 0 ) )
output ( L ) = ( ( P 1 ( L ) ) 2 R L 1 P 1 ( 0 ) P 2 + ( L ) P 2 + ( 0 ) P n + ( L ) P n + ( 0 ) )
P ( 0 ) = ( P i ( 0 ) P 2 + ( 0 ) P n + ( 0 ) )
tragetoutput ( L ) = ( P p 1 R 02 R L 2 1 R 0 n R L n )

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