Abstract

We have developed a coupled mode analysis for an erbium-doped coaxial fiber (EDCF) with doping only in the inner rod. With this analysis, the gain characteristics of the EDCF can be obtained in terms of the gain characteristics of a conventional single-core erbium-doped fiber. We have illustrated the use of this method in studying an EDCF and shown its application for inherent gain flattening.

© 2013 Optical Society of America

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References

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  1. A. C. Boucouvalas, “Coaxial optical fiber coupling,” J. Lightwave Technol. 3, 1151–1158 (1985).
    [CrossRef]
  2. J. W. Attridge, J. R. Cozens, K. D. Leaver, and N. L. Webster, “Coaxial fiber sensors,” J. Lightwave Technol. 3, 1084–1091 (1985).
    [CrossRef]
  3. S. Fevrier, P. Roy, D. Pagnoux, J. L. Auguste, J. M. Blondy, and J. Marcou, “12 nm FWHM 20 dB stop-band filter based on cascaded dual concentric core fiber filters,” Electron. Lett. 37, 1113–1115 (2001).
    [CrossRef]
  4. K. Thyagarajan, R. K. Varshney, P. Palai, A. K. Ghatak, and I. C. Goyal, “A novel design of dispersion compensating fiber,” IEEE Photon. Technol. Lett. 8, 1510–1512 (1996).
    [CrossRef]
  5. V. Rastogi, R. Kumar, and A. Kumar, “Large effective area all-solid dispersion compensating fiber,” J. Opt. 13, 125707 (2011).
    [CrossRef]
  6. K. Thyagarajan, and J. Kaur, “A novel design of an intrinsically gain flattened erbium doped fiber,” Opt. Commun. 183, 407–413 (2000).
    [CrossRef]
  7. B. Nagaraju, M. C. Paul, M. Pal, A. Pal, R. K. Varshney, B. P. Pal, S. K. Bhadra, G. Monnom, and B. Dussardier, “Design and fabrication of an intrinsically gain flattened Erbium doped fiber amplifier,” Opt. Commun. 282, 2335–2338 (2009).
    [CrossRef]
  8. R. Singh, Sunanda, and E. K. Sharma, “Gain flattening by long period gratings in erbium doped fibers,” Opt. Commun. 240, 123–132 (2004).
    [CrossRef]
  9. J. Anand, J. Kaur Anand, and E. K. Sharma, “Study of the amplification characteristics of a coaxial EDF with varying coupling conditions,” Opt. Laser Technol. 44, 688–695 (2012).
    [CrossRef]
  10. A. K. Ghatak and K. Thyagarajan, Introduction to Fiber Optics (Cambridge University, 1999).
  11. A. K. Ghatak and K. Thyagarajan, Contemporary Optics(Plenum, 1978).
  12. A. C. Boucouvalas, “Mode-cutoff frequencies of coaxial optical couplers,” Opt. Lett. 10, 95–97 (1985).
    [CrossRef]
  13. A. C. Boucouvalas and X. Qian, “Mode dispersion and delay characteristics of optical waveguides using equivalent T-L circuits,” IEEE J. Quantum Electron. 41, 951–957 (2005).
    [CrossRef]
  14. K. Morishita, “Numercal analysis of pulse broadening in graded index optical fibers,” IEEE Trans. Microw. Theory Tech. MTT-29, 348–352 (1981).
    [CrossRef]
  15. K. Thyagarajan, S. Diggavi, A. Taneja, and A. K. Ghatak, “Simple numerical technique for the analysis of cylindrically symmetric refractive index profile optical fibers,” Appl. Opt. 30, 3877–3879 (1991).
    [CrossRef]
  16. B. Pedersen, “Small-signal erbium-doped fiber amplifiers pumped at 980 nm: a design study,” Opt. Quantum. Electron. 26, S273–S284 (1994).
    [CrossRef]
  17. E. Desurvire, Erbium Doped Fiber Amplifiers: Principle and Applications (Wiley-Interscience, 1994).
  18. X. Qian and A. C. Boucouvalas, “Propagation characteristics of single-mode optical fibers with arbitrary complex index profiles,” IEEE J. Quantum Electron. 40, 771–777 (2004).
    [CrossRef]
  19. G. Jain, E. K. Sharma, and S. Vashisth, “Gain calculation in erbium-doped LiNbO3 channel waveguides by defining a complex index profile,” Opt. Eng. 43, 1454–1460 (2004).
    [CrossRef]
  20. Sunanda, G. Jain, and E. K. Sharma, “Gain calculations in erbium-doped fibers using field approximations,” Microw. Opt. Technol. Lett. 29, 256–259 (2001).
    [CrossRef]

2012 (1)

J. Anand, J. Kaur Anand, and E. K. Sharma, “Study of the amplification characteristics of a coaxial EDF with varying coupling conditions,” Opt. Laser Technol. 44, 688–695 (2012).
[CrossRef]

2011 (1)

V. Rastogi, R. Kumar, and A. Kumar, “Large effective area all-solid dispersion compensating fiber,” J. Opt. 13, 125707 (2011).
[CrossRef]

2009 (1)

B. Nagaraju, M. C. Paul, M. Pal, A. Pal, R. K. Varshney, B. P. Pal, S. K. Bhadra, G. Monnom, and B. Dussardier, “Design and fabrication of an intrinsically gain flattened Erbium doped fiber amplifier,” Opt. Commun. 282, 2335–2338 (2009).
[CrossRef]

2005 (1)

A. C. Boucouvalas and X. Qian, “Mode dispersion and delay characteristics of optical waveguides using equivalent T-L circuits,” IEEE J. Quantum Electron. 41, 951–957 (2005).
[CrossRef]

2004 (3)

X. Qian and A. C. Boucouvalas, “Propagation characteristics of single-mode optical fibers with arbitrary complex index profiles,” IEEE J. Quantum Electron. 40, 771–777 (2004).
[CrossRef]

G. Jain, E. K. Sharma, and S. Vashisth, “Gain calculation in erbium-doped LiNbO3 channel waveguides by defining a complex index profile,” Opt. Eng. 43, 1454–1460 (2004).
[CrossRef]

R. Singh, Sunanda, and E. K. Sharma, “Gain flattening by long period gratings in erbium doped fibers,” Opt. Commun. 240, 123–132 (2004).
[CrossRef]

2001 (2)

S. Fevrier, P. Roy, D. Pagnoux, J. L. Auguste, J. M. Blondy, and J. Marcou, “12 nm FWHM 20 dB stop-band filter based on cascaded dual concentric core fiber filters,” Electron. Lett. 37, 1113–1115 (2001).
[CrossRef]

Sunanda, G. Jain, and E. K. Sharma, “Gain calculations in erbium-doped fibers using field approximations,” Microw. Opt. Technol. Lett. 29, 256–259 (2001).
[CrossRef]

2000 (1)

K. Thyagarajan, and J. Kaur, “A novel design of an intrinsically gain flattened erbium doped fiber,” Opt. Commun. 183, 407–413 (2000).
[CrossRef]

1996 (1)

K. Thyagarajan, R. K. Varshney, P. Palai, A. K. Ghatak, and I. C. Goyal, “A novel design of dispersion compensating fiber,” IEEE Photon. Technol. Lett. 8, 1510–1512 (1996).
[CrossRef]

1994 (1)

B. Pedersen, “Small-signal erbium-doped fiber amplifiers pumped at 980 nm: a design study,” Opt. Quantum. Electron. 26, S273–S284 (1994).
[CrossRef]

1991 (1)

1985 (3)

A. C. Boucouvalas, “Mode-cutoff frequencies of coaxial optical couplers,” Opt. Lett. 10, 95–97 (1985).
[CrossRef]

A. C. Boucouvalas, “Coaxial optical fiber coupling,” J. Lightwave Technol. 3, 1151–1158 (1985).
[CrossRef]

J. W. Attridge, J. R. Cozens, K. D. Leaver, and N. L. Webster, “Coaxial fiber sensors,” J. Lightwave Technol. 3, 1084–1091 (1985).
[CrossRef]

1981 (1)

K. Morishita, “Numercal analysis of pulse broadening in graded index optical fibers,” IEEE Trans. Microw. Theory Tech. MTT-29, 348–352 (1981).
[CrossRef]

Anand, J.

J. Anand, J. Kaur Anand, and E. K. Sharma, “Study of the amplification characteristics of a coaxial EDF with varying coupling conditions,” Opt. Laser Technol. 44, 688–695 (2012).
[CrossRef]

Attridge, J. W.

J. W. Attridge, J. R. Cozens, K. D. Leaver, and N. L. Webster, “Coaxial fiber sensors,” J. Lightwave Technol. 3, 1084–1091 (1985).
[CrossRef]

Auguste, J. L.

S. Fevrier, P. Roy, D. Pagnoux, J. L. Auguste, J. M. Blondy, and J. Marcou, “12 nm FWHM 20 dB stop-band filter based on cascaded dual concentric core fiber filters,” Electron. Lett. 37, 1113–1115 (2001).
[CrossRef]

Bhadra, S. K.

B. Nagaraju, M. C. Paul, M. Pal, A. Pal, R. K. Varshney, B. P. Pal, S. K. Bhadra, G. Monnom, and B. Dussardier, “Design and fabrication of an intrinsically gain flattened Erbium doped fiber amplifier,” Opt. Commun. 282, 2335–2338 (2009).
[CrossRef]

Blondy, J. M.

S. Fevrier, P. Roy, D. Pagnoux, J. L. Auguste, J. M. Blondy, and J. Marcou, “12 nm FWHM 20 dB stop-band filter based on cascaded dual concentric core fiber filters,” Electron. Lett. 37, 1113–1115 (2001).
[CrossRef]

Boucouvalas, A. C.

A. C. Boucouvalas and X. Qian, “Mode dispersion and delay characteristics of optical waveguides using equivalent T-L circuits,” IEEE J. Quantum Electron. 41, 951–957 (2005).
[CrossRef]

X. Qian and A. C. Boucouvalas, “Propagation characteristics of single-mode optical fibers with arbitrary complex index profiles,” IEEE J. Quantum Electron. 40, 771–777 (2004).
[CrossRef]

A. C. Boucouvalas, “Mode-cutoff frequencies of coaxial optical couplers,” Opt. Lett. 10, 95–97 (1985).
[CrossRef]

A. C. Boucouvalas, “Coaxial optical fiber coupling,” J. Lightwave Technol. 3, 1151–1158 (1985).
[CrossRef]

Cozens, J. R.

J. W. Attridge, J. R. Cozens, K. D. Leaver, and N. L. Webster, “Coaxial fiber sensors,” J. Lightwave Technol. 3, 1084–1091 (1985).
[CrossRef]

Desurvire, E.

E. Desurvire, Erbium Doped Fiber Amplifiers: Principle and Applications (Wiley-Interscience, 1994).

Diggavi, S.

Dussardier, B.

B. Nagaraju, M. C. Paul, M. Pal, A. Pal, R. K. Varshney, B. P. Pal, S. K. Bhadra, G. Monnom, and B. Dussardier, “Design and fabrication of an intrinsically gain flattened Erbium doped fiber amplifier,” Opt. Commun. 282, 2335–2338 (2009).
[CrossRef]

Fevrier, S.

S. Fevrier, P. Roy, D. Pagnoux, J. L. Auguste, J. M. Blondy, and J. Marcou, “12 nm FWHM 20 dB stop-band filter based on cascaded dual concentric core fiber filters,” Electron. Lett. 37, 1113–1115 (2001).
[CrossRef]

Ghatak, A. K.

K. Thyagarajan, R. K. Varshney, P. Palai, A. K. Ghatak, and I. C. Goyal, “A novel design of dispersion compensating fiber,” IEEE Photon. Technol. Lett. 8, 1510–1512 (1996).
[CrossRef]

K. Thyagarajan, S. Diggavi, A. Taneja, and A. K. Ghatak, “Simple numerical technique for the analysis of cylindrically symmetric refractive index profile optical fibers,” Appl. Opt. 30, 3877–3879 (1991).
[CrossRef]

A. K. Ghatak and K. Thyagarajan, Contemporary Optics(Plenum, 1978).

A. K. Ghatak and K. Thyagarajan, Introduction to Fiber Optics (Cambridge University, 1999).

Goyal, I. C.

K. Thyagarajan, R. K. Varshney, P. Palai, A. K. Ghatak, and I. C. Goyal, “A novel design of dispersion compensating fiber,” IEEE Photon. Technol. Lett. 8, 1510–1512 (1996).
[CrossRef]

Jain, G.

G. Jain, E. K. Sharma, and S. Vashisth, “Gain calculation in erbium-doped LiNbO3 channel waveguides by defining a complex index profile,” Opt. Eng. 43, 1454–1460 (2004).
[CrossRef]

Sunanda, G. Jain, and E. K. Sharma, “Gain calculations in erbium-doped fibers using field approximations,” Microw. Opt. Technol. Lett. 29, 256–259 (2001).
[CrossRef]

Kaur, J.

K. Thyagarajan, and J. Kaur, “A novel design of an intrinsically gain flattened erbium doped fiber,” Opt. Commun. 183, 407–413 (2000).
[CrossRef]

Kaur Anand, J.

J. Anand, J. Kaur Anand, and E. K. Sharma, “Study of the amplification characteristics of a coaxial EDF with varying coupling conditions,” Opt. Laser Technol. 44, 688–695 (2012).
[CrossRef]

Kumar, A.

V. Rastogi, R. Kumar, and A. Kumar, “Large effective area all-solid dispersion compensating fiber,” J. Opt. 13, 125707 (2011).
[CrossRef]

Kumar, R.

V. Rastogi, R. Kumar, and A. Kumar, “Large effective area all-solid dispersion compensating fiber,” J. Opt. 13, 125707 (2011).
[CrossRef]

Leaver, K. D.

J. W. Attridge, J. R. Cozens, K. D. Leaver, and N. L. Webster, “Coaxial fiber sensors,” J. Lightwave Technol. 3, 1084–1091 (1985).
[CrossRef]

Marcou, J.

S. Fevrier, P. Roy, D. Pagnoux, J. L. Auguste, J. M. Blondy, and J. Marcou, “12 nm FWHM 20 dB stop-band filter based on cascaded dual concentric core fiber filters,” Electron. Lett. 37, 1113–1115 (2001).
[CrossRef]

Monnom, G.

B. Nagaraju, M. C. Paul, M. Pal, A. Pal, R. K. Varshney, B. P. Pal, S. K. Bhadra, G. Monnom, and B. Dussardier, “Design and fabrication of an intrinsically gain flattened Erbium doped fiber amplifier,” Opt. Commun. 282, 2335–2338 (2009).
[CrossRef]

Morishita, K.

K. Morishita, “Numercal analysis of pulse broadening in graded index optical fibers,” IEEE Trans. Microw. Theory Tech. MTT-29, 348–352 (1981).
[CrossRef]

Nagaraju, B.

B. Nagaraju, M. C. Paul, M. Pal, A. Pal, R. K. Varshney, B. P. Pal, S. K. Bhadra, G. Monnom, and B. Dussardier, “Design and fabrication of an intrinsically gain flattened Erbium doped fiber amplifier,” Opt. Commun. 282, 2335–2338 (2009).
[CrossRef]

Pagnoux, D.

S. Fevrier, P. Roy, D. Pagnoux, J. L. Auguste, J. M. Blondy, and J. Marcou, “12 nm FWHM 20 dB stop-band filter based on cascaded dual concentric core fiber filters,” Electron. Lett. 37, 1113–1115 (2001).
[CrossRef]

Pal, A.

B. Nagaraju, M. C. Paul, M. Pal, A. Pal, R. K. Varshney, B. P. Pal, S. K. Bhadra, G. Monnom, and B. Dussardier, “Design and fabrication of an intrinsically gain flattened Erbium doped fiber amplifier,” Opt. Commun. 282, 2335–2338 (2009).
[CrossRef]

Pal, B. P.

B. Nagaraju, M. C. Paul, M. Pal, A. Pal, R. K. Varshney, B. P. Pal, S. K. Bhadra, G. Monnom, and B. Dussardier, “Design and fabrication of an intrinsically gain flattened Erbium doped fiber amplifier,” Opt. Commun. 282, 2335–2338 (2009).
[CrossRef]

Pal, M.

B. Nagaraju, M. C. Paul, M. Pal, A. Pal, R. K. Varshney, B. P. Pal, S. K. Bhadra, G. Monnom, and B. Dussardier, “Design and fabrication of an intrinsically gain flattened Erbium doped fiber amplifier,” Opt. Commun. 282, 2335–2338 (2009).
[CrossRef]

Palai, P.

K. Thyagarajan, R. K. Varshney, P. Palai, A. K. Ghatak, and I. C. Goyal, “A novel design of dispersion compensating fiber,” IEEE Photon. Technol. Lett. 8, 1510–1512 (1996).
[CrossRef]

Paul, M. C.

B. Nagaraju, M. C. Paul, M. Pal, A. Pal, R. K. Varshney, B. P. Pal, S. K. Bhadra, G. Monnom, and B. Dussardier, “Design and fabrication of an intrinsically gain flattened Erbium doped fiber amplifier,” Opt. Commun. 282, 2335–2338 (2009).
[CrossRef]

Pedersen, B.

B. Pedersen, “Small-signal erbium-doped fiber amplifiers pumped at 980 nm: a design study,” Opt. Quantum. Electron. 26, S273–S284 (1994).
[CrossRef]

Qian, X.

A. C. Boucouvalas and X. Qian, “Mode dispersion and delay characteristics of optical waveguides using equivalent T-L circuits,” IEEE J. Quantum Electron. 41, 951–957 (2005).
[CrossRef]

X. Qian and A. C. Boucouvalas, “Propagation characteristics of single-mode optical fibers with arbitrary complex index profiles,” IEEE J. Quantum Electron. 40, 771–777 (2004).
[CrossRef]

Rastogi, V.

V. Rastogi, R. Kumar, and A. Kumar, “Large effective area all-solid dispersion compensating fiber,” J. Opt. 13, 125707 (2011).
[CrossRef]

Roy, P.

S. Fevrier, P. Roy, D. Pagnoux, J. L. Auguste, J. M. Blondy, and J. Marcou, “12 nm FWHM 20 dB stop-band filter based on cascaded dual concentric core fiber filters,” Electron. Lett. 37, 1113–1115 (2001).
[CrossRef]

Sharma, E. K.

J. Anand, J. Kaur Anand, and E. K. Sharma, “Study of the amplification characteristics of a coaxial EDF with varying coupling conditions,” Opt. Laser Technol. 44, 688–695 (2012).
[CrossRef]

R. Singh, Sunanda, and E. K. Sharma, “Gain flattening by long period gratings in erbium doped fibers,” Opt. Commun. 240, 123–132 (2004).
[CrossRef]

G. Jain, E. K. Sharma, and S. Vashisth, “Gain calculation in erbium-doped LiNbO3 channel waveguides by defining a complex index profile,” Opt. Eng. 43, 1454–1460 (2004).
[CrossRef]

Sunanda, G. Jain, and E. K. Sharma, “Gain calculations in erbium-doped fibers using field approximations,” Microw. Opt. Technol. Lett. 29, 256–259 (2001).
[CrossRef]

Singh, R.

R. Singh, Sunanda, and E. K. Sharma, “Gain flattening by long period gratings in erbium doped fibers,” Opt. Commun. 240, 123–132 (2004).
[CrossRef]

Sunanda,

R. Singh, Sunanda, and E. K. Sharma, “Gain flattening by long period gratings in erbium doped fibers,” Opt. Commun. 240, 123–132 (2004).
[CrossRef]

Sunanda, G. Jain, and E. K. Sharma, “Gain calculations in erbium-doped fibers using field approximations,” Microw. Opt. Technol. Lett. 29, 256–259 (2001).
[CrossRef]

Taneja, A.

Thyagarajan, K.

K. Thyagarajan, and J. Kaur, “A novel design of an intrinsically gain flattened erbium doped fiber,” Opt. Commun. 183, 407–413 (2000).
[CrossRef]

K. Thyagarajan, R. K. Varshney, P. Palai, A. K. Ghatak, and I. C. Goyal, “A novel design of dispersion compensating fiber,” IEEE Photon. Technol. Lett. 8, 1510–1512 (1996).
[CrossRef]

K. Thyagarajan, S. Diggavi, A. Taneja, and A. K. Ghatak, “Simple numerical technique for the analysis of cylindrically symmetric refractive index profile optical fibers,” Appl. Opt. 30, 3877–3879 (1991).
[CrossRef]

A. K. Ghatak and K. Thyagarajan, Contemporary Optics(Plenum, 1978).

A. K. Ghatak and K. Thyagarajan, Introduction to Fiber Optics (Cambridge University, 1999).

Varshney, R. K.

B. Nagaraju, M. C. Paul, M. Pal, A. Pal, R. K. Varshney, B. P. Pal, S. K. Bhadra, G. Monnom, and B. Dussardier, “Design and fabrication of an intrinsically gain flattened Erbium doped fiber amplifier,” Opt. Commun. 282, 2335–2338 (2009).
[CrossRef]

K. Thyagarajan, R. K. Varshney, P. Palai, A. K. Ghatak, and I. C. Goyal, “A novel design of dispersion compensating fiber,” IEEE Photon. Technol. Lett. 8, 1510–1512 (1996).
[CrossRef]

Vashisth, S.

G. Jain, E. K. Sharma, and S. Vashisth, “Gain calculation in erbium-doped LiNbO3 channel waveguides by defining a complex index profile,” Opt. Eng. 43, 1454–1460 (2004).
[CrossRef]

Webster, N. L.

J. W. Attridge, J. R. Cozens, K. D. Leaver, and N. L. Webster, “Coaxial fiber sensors,” J. Lightwave Technol. 3, 1084–1091 (1985).
[CrossRef]

Appl. Opt. (1)

Electron. Lett. (1)

S. Fevrier, P. Roy, D. Pagnoux, J. L. Auguste, J. M. Blondy, and J. Marcou, “12 nm FWHM 20 dB stop-band filter based on cascaded dual concentric core fiber filters,” Electron. Lett. 37, 1113–1115 (2001).
[CrossRef]

IEEE J. Quantum Electron. (2)

X. Qian and A. C. Boucouvalas, “Propagation characteristics of single-mode optical fibers with arbitrary complex index profiles,” IEEE J. Quantum Electron. 40, 771–777 (2004).
[CrossRef]

A. C. Boucouvalas and X. Qian, “Mode dispersion and delay characteristics of optical waveguides using equivalent T-L circuits,” IEEE J. Quantum Electron. 41, 951–957 (2005).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

K. Thyagarajan, R. K. Varshney, P. Palai, A. K. Ghatak, and I. C. Goyal, “A novel design of dispersion compensating fiber,” IEEE Photon. Technol. Lett. 8, 1510–1512 (1996).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (1)

K. Morishita, “Numercal analysis of pulse broadening in graded index optical fibers,” IEEE Trans. Microw. Theory Tech. MTT-29, 348–352 (1981).
[CrossRef]

J. Lightwave Technol. (2)

A. C. Boucouvalas, “Coaxial optical fiber coupling,” J. Lightwave Technol. 3, 1151–1158 (1985).
[CrossRef]

J. W. Attridge, J. R. Cozens, K. D. Leaver, and N. L. Webster, “Coaxial fiber sensors,” J. Lightwave Technol. 3, 1084–1091 (1985).
[CrossRef]

J. Opt. (1)

V. Rastogi, R. Kumar, and A. Kumar, “Large effective area all-solid dispersion compensating fiber,” J. Opt. 13, 125707 (2011).
[CrossRef]

Microw. Opt. Technol. Lett. (1)

Sunanda, G. Jain, and E. K. Sharma, “Gain calculations in erbium-doped fibers using field approximations,” Microw. Opt. Technol. Lett. 29, 256–259 (2001).
[CrossRef]

Opt. Commun. (3)

K. Thyagarajan, and J. Kaur, “A novel design of an intrinsically gain flattened erbium doped fiber,” Opt. Commun. 183, 407–413 (2000).
[CrossRef]

B. Nagaraju, M. C. Paul, M. Pal, A. Pal, R. K. Varshney, B. P. Pal, S. K. Bhadra, G. Monnom, and B. Dussardier, “Design and fabrication of an intrinsically gain flattened Erbium doped fiber amplifier,” Opt. Commun. 282, 2335–2338 (2009).
[CrossRef]

R. Singh, Sunanda, and E. K. Sharma, “Gain flattening by long period gratings in erbium doped fibers,” Opt. Commun. 240, 123–132 (2004).
[CrossRef]

Opt. Eng. (1)

G. Jain, E. K. Sharma, and S. Vashisth, “Gain calculation in erbium-doped LiNbO3 channel waveguides by defining a complex index profile,” Opt. Eng. 43, 1454–1460 (2004).
[CrossRef]

Opt. Laser Technol. (1)

J. Anand, J. Kaur Anand, and E. K. Sharma, “Study of the amplification characteristics of a coaxial EDF with varying coupling conditions,” Opt. Laser Technol. 44, 688–695 (2012).
[CrossRef]

Opt. Lett. (1)

Opt. Quantum. Electron. (1)

B. Pedersen, “Small-signal erbium-doped fiber amplifiers pumped at 980 nm: a design study,” Opt. Quantum. Electron. 26, S273–S284 (1994).
[CrossRef]

Other (3)

E. Desurvire, Erbium Doped Fiber Amplifiers: Principle and Applications (Wiley-Interscience, 1994).

A. K. Ghatak and K. Thyagarajan, Introduction to Fiber Optics (Cambridge University, 1999).

A. K. Ghatak and K. Thyagarajan, Contemporary Optics(Plenum, 1978).

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Figures (6)

Fig. 1.
Fig. 1.

(a) Index profile of coaxial fiber along with the normalized modal profiles of the rod and tube waveguide modes (a=5.22μm, b=16μm, c=17.8μm, n1=1.453274, n2=n4=1.4440236, n3=1.4617, and λph1531nm). (b) Variation of effective mode indices of the mode of the rod and tube waveguides with wavelength.

Fig. 2.
Fig. 2.

(a) Periodic variation of normalized power in waveguide 1 (rod) for different wavelengths (as marked in nanometers on curves) with length of the coaxial fiber. (b) Variation of the maximum out-coupled power (normalized) with wavelength. Note that the power coupled out of the rod waveguide is maximum at the phase matching wavelength and reduces on either side of it.

Fig. 3.
Fig. 3.

(a) Comparison of the effective mode indices of the LP01 and LP02 modes obtained using TMM and CMA (a=5.22μm, b=16μm, c=17.8μm, n1=1.453274, n2=n4=1.4440236, n3=1.4617, and λph1531nm). (b) Comparison of the modal fields of the LP01 and LP02 modes obtained using TMM and CMA (a=5.22μm, b=16μm, c=17.8μm, n1=1.453274, n2=n4=1.4440236, n3=1.4617, and λph1531nm).

Fig. 4.
Fig. 4.

Variation of the gain coefficients of the two supermodes (γs and γa) and gain coefficient of the amplifying rod waveguide (γ1/2) with the length of the EDCF for four different wavelengths: (a) λ=1520nm, (b) λ=1531nm, (c) λ=1540nm, and (d) λ=1550nm.

Fig. 5.
Fig. 5.

Variation of power in the rod waveguide at wavelengths marked in nanometers on the curves for a single-core EDF (dashed) and EDCF (solid).

Fig. 6.
Fig. 6.

Comparison of the gain spectra of the configuration using the coaxial EDF (solid curve) with that obtained by a single-core EDF (dotted curve).

Equations (40)

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

Δi=2(ni2n22)2n22,i=1,3
Ψ(r,z)=a(z)ψ1(r)+b(z)ψ2(r),
ΨS(r,z)=1as2+bs2[asψ1(r)+bsψ2(r)]ejβsz,
Ψa(r,z)=1aa2+ba2[aaψ1(r)+baψ2(r)]ejβaz
βs,a=12(β1+β2)±(β1β22)2+κ2,
κ12=k02(n12n22)0aψ1ψ2rdr,
κ21=k02(n32n22)bcψ1ψ2rdr.
bsas=βsβ1κ12,baaa=βaβ1κ12.
β¯s,a=(β1+β22)±p2+j(γ12±q2)=βs,a+jγs,a
βs,a=(β1+β22)±p2andγs,a=(γ12±q2)
p2=12Δ1/2[1+(β1β2)2γ124Δ2+1]12,q2=±12Δ1/2[1+(β1β2)2γ124Δ21]12
Δ=(β1β22)2+(κ2γ124)andpq=(β1β2)γ1.
βs,a=β0±(κ2γ124)1/2andγs,a=γ12
ΨT(λ,r)=A0(λ)ψ1(λ,r)=A0(λ)[a1(λ)ψs(λ,r)+a2(λ)ψa(λ,r)],
a1=1as[12+Δβ4Δβ24+κ2]anda2=1aa[12Δβ4Δβ24+κ2].
ΨT(r,z)=As(λ,z)a1(λ)ψs(λ,r)ejβs(λ)z+Aa(λ,z)a2(λ)ψa(λ,r)ejβa(λ)z,
As,a(λ,z)=A0eΣm=0Mγs,a(λ,mΔz)Δz.
γs,a(λ,z)=γ12±q2.
ΨT(r,z)=(asa1Asejβsz+aaa2Aaejβaz)ψ1+(bsa1Asejβsz+baa2Aaejβaz)ψ2.
I(r,z)=P1(z)ψ12(λ,r),
P1(z)=Pin(λ)f(λ)
f(λ)=[As2(asa1)2+Aa2(aaa2)2+2AsAa(asa1)(aaa2)cos(pz)].
Pout(z)=Pin(λ)f(λ).
N2(r,z)=Wa(r,z)Wa(r,z)+We(r,z)NEr,
N1(r,z)=We(r,z)Wa(r,z)+We(r,z)NEr,
Wa(r,z)=K=1N[σa(λk)λkhc]P1k(z)ψ1k2(λk,r)+[σa(λp)λphc]Pp(z)ψ12(λp,r),
We(r,z)=k=1N[σe(λk)λkhc]P1k(z)ψ1k2(λk,r)+1tsp,
P1k(z)=Pin(λk)f(λk)
f(λk)=[As2as2a12+Aa2aa2a22+2AsAaasaaa1a2cos(pz)].
γ1j(λj,z)=12[0a{σe(λj)N2(r,z)σa(λj)N1(r,z)}ψ12(λj,r)rdr].
Pp(z)=Pin(λp)eΣm=0M2αp(mΔz)Δz,
αp(z)=120aσa(λp)N1(r,z)ψ12(λp,r)rdr.
ψ12(r<a)=A12J02(Ur/a),
A1=UK0(W)2aVJ0(U)K1(W)
ψ12(λk)=Γka2,
Γk=Uk2K02(Wk)4Vk2J02(Uk)K12(Wk)[J02(Uk)+J12(Uk)].
Wa(z)=k=1N[σa(λk)λkhca2]ΓkPk(z)+[σa(λp)λphca2]ΓkPp(z),
We(z)=k=1N[σe(λk)λkhca2]ΓkPk(z)+1tsp.
γ1j(λj,z)=12{σe(λj)N2σa(λj)N1}Γja2,
αp(z)=12σa(λp)N1Γpa2.

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