Thermal effects limit the gain, quality, and stability of high power fiber lasers and amplifiers. In this paper, different values of heat conductive coefficients at the core, the first and second clad with the complete form of the heat transfer equation are considered. A quartic equation was proposed to determine the temperature at the fiber laser surface. Using the surface temperature value, the temperature can be determined at the longitudinal and radial position of the double clad fiber laser. The different definitions of heat sources which were previously presented in articles is used to describe the heat generation at a double clad high pump power fiber laser condition. The results were compared to each other, and the percentage of each factor in heat generation was calculated.
2. Kelson, I. and A. Hardy, "Optimization of strongly pumped fiber lasers," J. Ligthwave Technol., Vol. 17, 891-897, 1999.
3. Zervas, M. N. and C. A. Codemard, "High power fiber lasers: A review," IEEE J. Select. Topic. Quant. Electron., Vol. 20, 0904123, 2014.
4. Susnjar, P., V. Agrez, and R. Petkovsek, "Photodarkening as a heat source in ytterbium doped fiber amplifiers," Opt. Express, Vol. 26, 6420-642615265-15277, 2018.
5. Engholm, M., L. Norin, C. Hirt, S. T. Fredrich-Thorntonc, K. Petermannc, and G. Huberc, "Quenching processes in Yb lasers correlation to the valence stability of the Yb ion," Proc. of SPIE, Vol. 7193, 71931U-1, 2009.
6. Ward, B., "Theory and modeling of photodarkening induced quasi static degradation in fiber amplifiers," Opt. Express, Vol. 24, 3488-3501, 2016.
7. Ding, M. and P. K. Cheo, "Dependence of ion-pair induced self-pulsing in Er-doped fiber lasers on emission to absorption ratio," IEEE. Photon. Technol. Lett., Vol. 8, 1627-1629, 1996.
8. Huang, L., H. Zhang, X. Wang, and P. Zhou, "Diode-pumped 1178-nm high-power Yb-doped fiber laser operating at 125 C," IEEE Photonics Journal, Vol. 8, 1501407, 2016.
9. Brown, D. C. and H. J. Hoffman, "Thermal, stress, and thermo-optic effects in high average power double-clad silica fiber lasers," IEEE J. Quant. Electron., Vol. 37, 207-217, 2001.
10. Oron, R. and A. A. Hardy, "Rayleigh backscattering and amplified spontaneous emission in high-power Ytterbium-doped fiber amplifiers," J. Opt. Soc. Am. B, Vol. 16, 695-801, 1999.
11. Kaushal, H. and G. Kaddoum, "Applications of lasers for tactical military operations," Digital Object Identifier 10.1109/ACCESS, Vol. 5, 20736-20753, 2017.
12. Dong, L. and B. Samson, Fiber Lasers: Basics, Technology, and Applications, CRC Press, printed on acid-free paper, 2017.
13. Shao, H., K. Duan, Y. Zhu, H. Yan, H. Yang, and W. Zhao, "Numerical analysis of Ytterbium-doped double-clad fiber lasers based on the temperature-dependent rate equation," Optik, Vol. 124, 4336-4340, 2013.
14. Yang, J., Y. Wang, Y. Tang, and J. Xu, "Influences of pump transitions on thermal effects of multi-kilowatt thulium-doped fiber lasers,", arXiv:1503.07256v1 [physics.optics], 2015.
15. Baravets, Y., F. Todorov, and P. Honzatko, "High-power thulium-doped fiber laser in an all-fiber configuration," Proceedings of the SPIE, Vol. 10142, id. 101420G 4, 2016.
16. Wagener, J. L., P. F. Wysocki, M. J. F. Digonnet, H. J. Shaw, and D. J. Digiovanni, "Effects of concentration and clusters in erbium-doped fiber lasers," Opt. Lett., Vol. 18, 2014-2016, 1993.
17. Dawson, J. W., M. J. Messerly, R. J. Beach, M. Y. Shverdin, E. A. Stappaerts, A. K. Sridharan, P. H. Pax, J. E. Heebner, C. W. Siders, and C. P. J. Barty, "Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power," Opt. Express, Vol. 16, 13240-13266, 2008.
18. Yao, T., J. Ji, and J. Nilsson, "Ultra-low quantum-defect heating in Ytterbium-doped aluminosilicate fibers," J. Lightwav. Technol., Vol. 32, 429-434, 2014.
19. Rimington, N. W., S. L. Schieffer, W. Andreas Schroeder, and B. K. Brickeen, "Thermal lens shaping in Brewster gain media: A high-power, diode-pumped Nd:GdVO4 laser," Opt. Express, Vol. 12, 1426-1436, 2004.
20. Kuznetsov, M. S., O. L. Antipov, A. A. Fotiadi, and P. Megret, "Electronic and thermal refractive index changes in Ytterbium-doped fiber amplifiers," Opt. Express, Vol. 21, 22374-22388, 2013.
21. Sabaeian, M. and H. Nadgaran, "Investigation of thermal dispersion and thermally-induced birefringence on high-power double clad Yb:glass fiber laser," International Journal of Optics and Photonics (IJOP), Vol. 2, 25-31, 2008.
22. Kong, F., J. Xue, R. H. Stolen, and L. Dong, "Direct experimental observation of stimulated thermal Rayleigh scattering with polarization modes in a fiber amplifier," LET Optica, Vol. 3, 975-978, 2016.
23. Kelson, I. and A. A. Hardy, "Strongly pumped fiber lasers," IEEE J. Quant. Electron., Vol. 34, 1570-1577, 1998.
24. Xiao, L., P. Yan, M. Gong, W. Wei, and P. Ou, "An approximate analytic solution of strongly pumped Yb-doped double-clad fiber lasers without neglecting the scattering loss," Opt. Commun., Vol. 230, 401-410, 2004.
25. Hardy, A., "Signal amplification in strongly pumped fiber amplifiers," IEEE. J. Quant. Electron., Vol. 33, 307-313, 1997.
26. Karimi, M. and A. H. Farahbod, "Improved shooting algorithm using answer ranges definition to design doped optical fiber laser," Opt. Commun., Vol. 324, 212-220, 2014.
27. Hu, X., T. Ning, L. Pei, and W. Jian, "Novel shooting method with simple control strategy for fiber lasers," Optik, Vol. 125, 1975-1979, 2014.
28. Luo, Z., C. Ye, G. Sun, Z. Cai, M. Si, and Q. Li, "Simplified analytic solutions and a novel fast algorithm for Yb3+-doped double-clad fiber lasers," Opt. Commun., Vol. 277, 118-124, 2007.
29. Digonnet, M. J. F., "Theory of superfluorescent fiber lasers," J. Lightwave Technol., Vol. 4, 1631-1639, 1986.
30. Desurvire, E., Erbium Doped Fiber Amplifiers: Principles and Applications, Wiley, New York, 1994.
31. Karimi, M., N. Granpayeh, and M. K. Moravvej Farshi, "Analysis and design of the dye doped polymer optical fiber amplifiers," Appl. Physics B, Vol. 78, 387-396, 2004.
32. Brunet, F., Y. Taillon, P. Galarneau, and S. Larochelle, "Practical design of double-clad Ytterbium-doped fiber amplifiers using Giles parameters," IEEE J. Quant. Electron., Vol. 40, 1294-1300, 2004.
33. Yan, P., X. Wang, Y. Huang, C. Fu, J. Sun, Q. Xiao, D. Li, and M. Gong, "Fiber core mode leakage induced by refractive index variation in high-power fiber laser," Chin. Phys. B, Vol. 26, 034205, 2017.
34. Agrawal, G. P., Fiber-optic Communication Systems, 3rd Ed., A John Wiley & Sons, Inc., 2002.
35. Karimi, M., "Optimization of core size in erbium doped holey fiber amplifiers," Optik, Vol. 125, 2780-2783, 2014.
36. Prudenzano, F., "Erbium-doped hole-assisted optical fiber amplifier: Design and optimization," J. Ligthwave Technol., Vol. 23, 330-340, 2005.
37. Marcuse, D., "Loss analysis of single-mode fiber splices," The Bell System Technology Journal, Vol. 56, 703-718, 1977.
38. Leproux, P. and S. Fevrier, "Modeling and optimization of double-clad fiber amplifiers using chaotic propagation of the pump," Optical Fiber Technol., Vol. 6, 324-339, 2001.
39. Kouznetsov, D. and J. V. Moloney, "Highly efficient, high-gain, short-length, and power-scalable incoherent diode slab-pumped fiber amplifier/laser," IEEE J. Quant. Electron., Vol. 39, 1452-1461, 2003.
40. Quintela, M. A., C. Lavin, M. Lomer, A. Quintela, and J. M. Lopez-Higuera, "Superfluorescent erbium doped fiber optic sources comparative study," Proc. of SPIE, Vol. 5952, 1-10, 2005.
41. Casperson, L. W. and A. Yariv, "Spectral narrowing in high-gain lasers," IEEE J. Quantum. Electron., Vol. 8, 80, 1972.
42. Xiao, L., P. Yan, M. Gong, W. Wei, and P. Ou, "An approximate analytic solution of strongly pumped Yb-doped double-clad fiber lasers without neglecting the scattering loss," Opt. Commun., Vol. 230, 401-410, 2004.
43. Pask, H. M., R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, "Ytterbium-doped silica fiber lasers: Versatile sources for the 1-1.2 pm region," IEEE J. Selected Top. in Quant. Electron., Vol. 1, 2-13, 1995.
44. Lim, C. and Y. Izawa, "Modeling of end-pumped CW quasi-three-level lasers," IEEE J. Quant. Electron., Vol. 38, 306-311, 2002.
45. Kong, F., C. Dunn, J. Parsons, M. T. Kalichevsky-Dong, T. W. Hawkins, M. Jones, and L. Dong, "Large-mode-area fibers operating near singlemode regime," Opt. Express, Vol. 24, 10295-10301, 2016.
46. Wielandy, S., "Implications of higher-order mode content in large mode area fibers with good beam quality," Opt. Express, Vol. 15, 15402-15409, 2016.
47. Snitzer, E., H. Po, F. Hakimi, R. Tumminelli, and B. C. McCollum, "Double-clad, offset core Nd fiber laser," The Opt. Fiber Commun. Conf., New Orleans, LA, PD5, 1988.
48. Jauregui, C., H. J. Otto, S. Breitkopf, J. Limpert, and A. T¨unnermann, "Optimizing the mode instability threshold of high-power fiber laser systems," Proc. of SPIE, Fiber Lasers XIII: Technology, Systems, and Applications, Vol. 9728, 97280B, 2015.
49. Otto, H. J., N. Modsching, C. Jauregui, J. Limpert, and A. T¨unnermann, "Impact of photodarkening on the mode instability threshold," Opt. Express, Vol. 23, 15265-15277, 2015.
50. Jauregui, C., H. J. Ottoa, C. Stihler, J. Limpert, and A. Tunnermann, "The impact of core co-dopants on the mode instability threshold of high-power fiber laser systems," Proc. of SPIE, Fiber Lasers XIV: Technology and Systems, Vol. 10083, 100830N, 2017.
51. Li, J., K. Duan, Y. Wang, X. Cao, W. Zhao, Y. Guo, and X. Lin, "Theoretical analysis of the heat dissipation mechanism in Yb3+-doped double-clad fiber lasers," J. Modern Optic, Vol. 55, 459-471, 2008.
52. Yan, P., A. Xu, and M. Gong, "Numerical analysis of temperature distributions in Yb-doped double-clad fiber lasers with consideration of radiative heat transfer," Opt. Engin., Vol. 45, 124201, 2006.
53. Davis, M. K., M. J. F. Digonnet, and R. H. Pantell, "Thermal effects in doped fibers," J. Lightwave Technol., Vol. 16, 1013-1013, 1998.
54. Li, J., Y. Chen, M. Chen, H. Chen, X. Jin, Y. Yang, Z. Dai, and Y. Liu, "Theoretical analysis and heat dissipation of mid-infrared chalcogenide fiber Raman laser," Opt. Commun., Vol. 284, 1278-1283, 2011.
55. Lapointe, M. A., S. Chatigny, M. Pich´e, M. C. Skaff, and J. N. Maran, "Thermal effects in high-power CW fiber lasers," Proc. SPIE Fiber Lasers VI: Technology, Systems, and Applications, Vol. 7195, 1U, 2009.
56. Jauregui, C., H. J. Otto, F. Stutzki, J. Limpert, and A. Tunnermann, "Simplified modelling the mode instability threshold of high power fiber amplifiers in the presence of photodarkening," Opt. Express, Vol. 23, 20203-20218, 2015.
57. Lood, F. and N. P. Kherani, "Influence of luminescent material properties on stimulated emission luminescent solar concentrators (SELSCs) using a 4-level system," Opt. Express, Vol. 25, A1023, 2017.
58. Ward, B., "Theory and modeling of photodarkening induced quasi static degradation in fiber amplifiers," Opt. Express, Vol. 24, 3488-3501, 2016.
59. Kuznetsov, M. S., O. L. Antipov, A. A. Fotiadi, and P. Megret, "Electronic and thermal refractive index changes in Ytterbium-doped fiber amplifiers," Opt. Express, Vol. 21, 22374-22388, 2013.
60. Abouricha, M., A. Boulezhar, and N. Habiballah, "The comparative study of the temperature distribution of fiber laser with different pump schemes," O. J. Metal, Vol. 3, 64-71, 2013.
61. Naderi, S., I. Dajani, T. Madden, and C. Robin, "Investigations of modal instabilities in fiber amplifiers through detailed numerical simulations," Opt. Express, Vol. 21, 16111-16129, 2013.
62. Hansen, K. R., T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, "Theoretical analysis of mode instability in high-power fiber amplifiers," Opt. Express, Vol. 21, 1944-1971, 2013.
63. Smith, A. V. and J. J. Smith, "Increasing mode instability thresholds of fiber amplifiers by gain saturation," Opt. Express, Vol. 21, 15168-15182, 2013.
64. Ward, B., C. Robin, and I. Dajani, "Origin of thermal modal instabilities in large mode area fiber amplifiers," Opt. Express, Vol. 2, 11407-11422, 2012.
65. Ward, B. G., "Accurate modeling of rod-type photonic crystal fiber amplifiers," Proc. of SPIE, Vol. 9728, 97280F-1, 2015.
66. Tao, R., P. Ma, X. Wang, P. Zhou, and Z. Liu, "1.3 kW monolithic linearly polarized single-mode master oscillator power amplifier and strategies for mitigating mode instabilities," Photon. Res., Vol. 3, 86-93, 2015.
67. Tao, R., X. Wang, P. Zhou, and Z. Liu, "Seed power dependence of mode instabilities in high power fiber amplifiers," J. Opt., 103667.R1, 2017.
68. Lægsgaard, J., "Static thermo-optic instability indouble-pass fiber amplifiers," Opt. Express, Vol. 24, 13429-13443, 2016.
69. Gong, M., Y. Yuan, C. Li, P. Yan, H. Zhang, and S. Liao, "Numerical modeling of transverse mode competition in strongly pumped multimode fiber lasers and amplifiers," Opt. Express, Vol. 15, 3236-3246, 2007.
70. Mohammed, Z., H. Saghafifar, and M. Soltanolkotabi, "An approximate analytical model for temperature and power distribution in high power Yb-doped double clad fiber lasers," Laser Phys., Vol. 24, 115107, 2014.
71. Sabaeian, M., H. Nadgaran, M. De Sario, L. Mescia, and F. Prudenzano, "Thermal effects on double clad octagonal Yb:glass fiber laser," Optical Materials, Vol. 31, 1300-1305, 2009.
72. Neumark, S., Solution of Cubic and Quartic Equations, 1st Ed., Pergam on Press, Oxford, London, 1965.
73. Kelson, I. and A. Hardy, "Optimization of strongly pumped fiber lasers," J. of Ligthwave Technol., Vol. 17, 891-897, 1999.
74. Pask, H. M., R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, "Ytterbium-doped silica fiber lasers: Versatile sources for the 1–1.2 pm region," IEEE J. of Quant. Electron., Vol. 1, 2-13, 1995.
75. Fan, Y., B. He, J. Zhou, J. Zheng, H. Liu, Y. Wei, J. Dong, and Q. Lou, "Thermal effects in kilowatt all-fiber MOPA," Opt. Express, Vol. 19, 15162-15172, 2011.