In order
to obtain analytical gain expression in Brillouin optical Fiber Amplifiers
(BFAs), coupled intensity equations describing the interaction of pump and
stokes waves must be solved simultaneously. For long optical fibers, although
fiber loss is responsible for the pump depletion and nonnegligible effect, for
short optical fibers less than 2 km, its effect can be discarded. In this
paper, we provide an accurate analytic expression for the BFA gain for fiber
lengths less than 2 km by discarding the optical fiber loss and show results of
experimental validation.
[1] Olsson, N. A., Van der Ziel, J. P. 1986. Cancellation of fiber loss by semiconductor laser pumped Brillouin amplification at 1.5 μm: Applied Physics Letters, vol. 48, p. 1329–1330. DOI: 10.1063/1.96950
[2] Tkach, R. W., Chraplyvy, A. R. and Derosier, R. M. 1989. Performance of a WDM network based on stimulated Brillouin scattering: IEEE Photonics Technology Letters, vol.1, pp. 111–113. DOI: 10.1109/68.34758
[3] Song, K. Y., Herráez, M. G., and Thévenaz, L. 2005 Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering: Optics Express, vol. 13, pp. 82-88. DOI: 10.1364/OPEX.13.000082
[4] Culverhouse, D. Frahi, F. Pannell, C. N. and Jackson, D. A. 1989. Potential of stimulated Brillouin scattering as sensing mechanism for distributed temperature sensor: Electronics Letters. vol. 25, pp. 913–915. DOI: 10.1049/el:19890612
[5] Gokhan, F. S. 2011. Moderate-gain Brillouin amplification: an analytical solution below pump threshold: Optics Communications, vol. 284, pp. 4869–4873. DOI: 10.1016/j.optcom.2011.06.054
[6] Kobyakov, A. Sauer, M. and Chowdhury, D. 2010. Stimulated Brillouin scattering in optical fibers: Advances in Optics and Photonics, vol. 2, pp. 1–59. DOI: 10.1364/AOP.2.000001
[7] Boyd, R.W. 2007. Nonlinear Optics, 3 rd edition. Academic Press, Rochester, New York, chap.9. pp. 442-443
[8] Zel’dovich, B. Ya., Pilipetsky, N. F. and Shkunov, V. V. (Springer-Verlag, 1985). Principles of Phase Conjugation. chap. 2. [9] Daniel Richardson, Bruno Salvy, John Shackell, Joris Van Der Hoeven. 1996. Asymptotic Expansions of exp-log Functions. [Research Report] RR-2859, INRIA.
[10] Agrawal, G. P. 2001. Nonlinear Fiber Optics, 3rd edition, Academic Press, New York, chap.9. p. 360
[11] Boyd, R.W. 2007. Nonlinear Optics, 3rd edition. Academic Press, Rochester, New York, Chap.9. p. 463
[12] Chen, L. and Bao, X. 1998. Analytical and numerical solutions for steady state stimulated Brillouin scattering in a single-mode fiber: Optics Communications, vol. 152, pp. 65-70. DOI: 10.1016/S0030-4018(98)00147-3
[13] Gökhan, F. S., Göktaş, H. and Sorger, V. J. 2018. Analytical approach of Brillouin amplification over threshold: Applied Optics, vol. 57, pp. 607-611. DOI: 10.1364/AO.57.000607
2 km'ye kadar uzunluktaki Brillouin Fiber Kuvvetlendirici kazancının analitik ifadesi
Brillouin
Fiber Kuvvetlendirici (BFK) kazancının analitik ifadesini elde etmek için,
pompa ve Stokes dalgalarının etkileşimini tanımlayan denklemlerin çözümü
gerekmektedir. Uzun optik fiberler için fiber kaybı, pompa lazerini tüketmesi
nedeniyle ihmal edilemez bir parametre olmasına rağmen, 2 km'den kısa BFK’ de
etkisi ihmal edilebilir. Bu makalede, optik fiber kaybı ihmal edilerek, 2
km'den daha kısa optik fiberler için BFK kazancı analitik olarak ifade
edilerek, bu ifadenin doğruluğu deneysel olarak gösterilmiştir.
[1] Olsson, N. A., Van der Ziel, J. P. 1986. Cancellation of fiber loss by semiconductor laser pumped Brillouin amplification at 1.5 μm: Applied Physics Letters, vol. 48, p. 1329–1330. DOI: 10.1063/1.96950
[2] Tkach, R. W., Chraplyvy, A. R. and Derosier, R. M. 1989. Performance of a WDM network based on stimulated Brillouin scattering: IEEE Photonics Technology Letters, vol.1, pp. 111–113. DOI: 10.1109/68.34758
[3] Song, K. Y., Herráez, M. G., and Thévenaz, L. 2005 Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering: Optics Express, vol. 13, pp. 82-88. DOI: 10.1364/OPEX.13.000082
[4] Culverhouse, D. Frahi, F. Pannell, C. N. and Jackson, D. A. 1989. Potential of stimulated Brillouin scattering as sensing mechanism for distributed temperature sensor: Electronics Letters. vol. 25, pp. 913–915. DOI: 10.1049/el:19890612
[5] Gokhan, F. S. 2011. Moderate-gain Brillouin amplification: an analytical solution below pump threshold: Optics Communications, vol. 284, pp. 4869–4873. DOI: 10.1016/j.optcom.2011.06.054
[6] Kobyakov, A. Sauer, M. and Chowdhury, D. 2010. Stimulated Brillouin scattering in optical fibers: Advances in Optics and Photonics, vol. 2, pp. 1–59. DOI: 10.1364/AOP.2.000001
[7] Boyd, R.W. 2007. Nonlinear Optics, 3 rd edition. Academic Press, Rochester, New York, chap.9. pp. 442-443
[8] Zel’dovich, B. Ya., Pilipetsky, N. F. and Shkunov, V. V. (Springer-Verlag, 1985). Principles of Phase Conjugation. chap. 2. [9] Daniel Richardson, Bruno Salvy, John Shackell, Joris Van Der Hoeven. 1996. Asymptotic Expansions of exp-log Functions. [Research Report] RR-2859, INRIA.
[10] Agrawal, G. P. 2001. Nonlinear Fiber Optics, 3rd edition, Academic Press, New York, chap.9. p. 360
[11] Boyd, R.W. 2007. Nonlinear Optics, 3rd edition. Academic Press, Rochester, New York, Chap.9. p. 463
[12] Chen, L. and Bao, X. 1998. Analytical and numerical solutions for steady state stimulated Brillouin scattering in a single-mode fiber: Optics Communications, vol. 152, pp. 65-70. DOI: 10.1016/S0030-4018(98)00147-3
[13] Gökhan, F. S., Göktaş, H. and Sorger, V. J. 2018. Analytical approach of Brillouin amplification over threshold: Applied Optics, vol. 57, pp. 607-611. DOI: 10.1364/AO.57.000607
Gökhan, F. S. (2020). Analytical approach of Brillouin fiber Amplifier Gain up to 2 km long fibers. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen Ve Mühendislik Dergisi, 22(64), 159-166. https://doi.org/10.21205/deufmd.2020226416
AMA
Gökhan FS. Analytical approach of Brillouin fiber Amplifier Gain up to 2 km long fibers. DEUFMD. Ocak 2020;22(64):159-166. doi:10.21205/deufmd.2020226416
Chicago
Gökhan, Fikri Serdar. “Analytical Approach of Brillouin Fiber Amplifier Gain up to 2 Km Long Fibers”. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen Ve Mühendislik Dergisi 22, sy. 64 (Ocak 2020): 159-66. https://doi.org/10.21205/deufmd.2020226416.
EndNote
Gökhan FS (01 Ocak 2020) Analytical approach of Brillouin fiber Amplifier Gain up to 2 km long fibers. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi 22 64 159–166.
IEEE
F. S. Gökhan, “Analytical approach of Brillouin fiber Amplifier Gain up to 2 km long fibers”, DEUFMD, c. 22, sy. 64, ss. 159–166, 2020, doi: 10.21205/deufmd.2020226416.
ISNAD
Gökhan, Fikri Serdar. “Analytical Approach of Brillouin Fiber Amplifier Gain up to 2 Km Long Fibers”. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi 22/64 (Ocak 2020), 159-166. https://doi.org/10.21205/deufmd.2020226416.
JAMA
Gökhan FS. Analytical approach of Brillouin fiber Amplifier Gain up to 2 km long fibers. DEUFMD. 2020;22:159–166.
MLA
Gökhan, Fikri Serdar. “Analytical Approach of Brillouin Fiber Amplifier Gain up to 2 Km Long Fibers”. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen Ve Mühendislik Dergisi, c. 22, sy. 64, 2020, ss. 159-66, doi:10.21205/deufmd.2020226416.
Vancouver
Gökhan FS. Analytical approach of Brillouin fiber Amplifier Gain up to 2 km long fibers. DEUFMD. 2020;22(64):159-66.