# TRANSIENT ANALYTICAL SOLUTION OF TEMPERATURE DISTRIBUTION AND FRACTURE LIMITS IN PULSED SOLID STATE LASER ROD

## Main Article Content

## Abstract

The exact analytical solution of axis-symmetry transient temperature and Tresca failure stress in pulsed mode solid state laser rod is derived using Integral transform method. The result obtained from this work is compared with previously published data and good agreement is found. The effect of increasing period is studied, and it is found that at constant pulse width as the period is increased, the allowable pumping power is increased too. Furthermore, the effect of changing pulse width with a constant period is studied, and it is found that as the pulse width is increased, the allowable pumping power is decreased. The effect of duty cycle is studied also and it is found that as duty cycle is increased the allowable pumping power is decreased. This work permits proper selection of pulse width, period and duty cycle to avoid laser rod fracture while obtaining maximum output laser power in the designing of laser system.

## Article Details

**Thermal Science**, [S.l.], mar. 2017. ISSN 2334-7163. Available at: <http://thermal-science.tech/journal/index.php/thsci/article/view/2090>. Date accessed: 18 oct. 2017. doi: https://doi.org/10.2298/TSCI141011090S.

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Accepted 2017-03-13

Published 2017-03-13

## References

[2] Clarkson, W.A , Thermal Effects and their mitigation in End-Pumped Solid-State lasers, J. Phys. D: Appl. Phys., 34(2001),16, pp.2381-2395

[3] C. Pfistner, R. Weber, H. P. Weber, S Merazzi and R. Gruber, Thermal Beam Distortions in End- Pumped Nd:YAG, Nd:GSGG and Nd:YLF , IEEE J. Quantum Electron.30(1994),7,pp. 1605–1615

[4] A. M. Robinson, Thermal Transient Effects in Optically Pumped Repetitively Pulsed Lasers”, IEEE Journal ofQuantum Electronics,7(1994),5,pp. 1605–1615

[5] Feng Huang, Yuefeng Wang, Wenwu Jia and Wei Dong, Modeling and Resolving Calculation of Thermal Effect in Face-Pumped High Power Heat Capacity Disk Laser , Proc. SPIE 6823, High- Power Lasers and Applications IV, Beijing, China ,2008, Vol 6823,pp.682311-628319

[6] E. H. Bernhardi, A. Forbes, C. Bollig, and M. J. Daniel Esser, Estimation of Thermal Fracture Limits in Quasi–Continuous–Wave End–Pumped Lasers through a Time–Dependent Analytical Model ,Optics Express, 16(2008),15, pp. 11115-11123

[7]T. Liu, Z. M. Yang, and S. H. Xu, Analytical Investigation on Transient Thermal Effects in Pulse End-Pumped Short-Length Fiber Laser, Optics Express , 17(2009), 15,pp.12875-12890

[8] Khalid S. Shibib,Mohammad A. Munshid and Kadhim A. Hubiter,Analytical Model of Transient Thermal Effect on Convectional Cooled End-Pumped Laser Rod, Pramana- Journal of physics, ndian Academy of Sciences, 81(2013), 4, pp. 603–615

[9] Khalid S. Shibib, Mayada M. Tahir and Mohammad A. Mahdi, Analytical Treatment of Transient Temperatureand Thermal Stress Distribution in CW End Pumped Laser Rod: Thermal Response Optimization Study, Thermal Science, 18(2014), 2,pp.399-408

[10] F. P. Incropera, D. P. Dewitt, T. L. Bergman and S. Lavine, Fundamentals of Heat and Mass Transfer, 7th edn ,John Wiley & Sons, UK, 2011.

[11] J. P. Holman, Heat Transfer Tenth Edition, McGraw-Hill ,NY, 2010.

[12] Ananada K. Cousins, Temperature and Thermal Stress Scaling in Finite-Length End-Pumped Laser Rods, IEEE Journal of Quantum Electronics, 28(1992),4,pp. 1057- 1069

[13] M. N. Özisik, Heat Conduction , Wiley, New York, (1980).

[14] J. Frauchiger, P. Albers, and H. P. Weber, Modeling of Thermal Lensing and Higher Order Ring Mode Oscillation in End-Pumped CW Nd:YAG Lasers ,IEEE J. Quantum Electron, 28(1991),4,pp. 1046-1056

[15] Ping Xiuer, Thermal stress and thermal fatigue,National Defense Industry Press, Beijing, 1984.

[16] Khalid S. Shibib, Mayada M. Tahir, Haqi I. Qatta, Analytical Model of Transient Temperature and Thermal Stress in Continuous Wave Double-End-Pumped Laser Rod: Thermal Stress Minimization Study, Paramana Journal of physics, 79(2012), 2,pp. 287–297