## THERMAL SCIENCE

International Scientific Journal

### ANALYTICAL TREATMENT OF TRANSIENT TEMPERATURE AND THERMAL STRESS DISTRIBUTION IN CW END PUMPED LASER ROD: THERMAL RESPONSE OPTIMIZATION STUDY

**ABSTRACT**

The analytical solution of transient temperature distribution and Tresca failure stress in CW end- pumped laser rod has been derived using integral transform method. The analytical result is compared with numerical solutions presented by other works and good agreement has been found. Analytical solution with its clear physical meaning and its explicit form permits to predict the influence of various factors on the solution. The optical path difference which gives a valuable means to quantify the optical properties of laser material such as designed beam quality, will converge to a constant value as steady state temperature distribution is reached. One can obtain the dominate factors which affect the laser response to bring the laser rod to the thermal equilibrium; it has been found that fast response can be achieved by reducing pumping power, increasing extracted heat from the rod , choosing a crystal having high thermal diffusivity and decreasing laser rod radius while its volume remains constant. One final advantage of the analytical solution is that a fast result can be obtained where the numerical solution usually is a time consuming technique.

**KEYWORDS**

PAPER SUBMITTED: 2011-07-01

PAPER REVISED: 2011-12-01

PAPER ACCEPTED: 2011-12-19

**THERMAL SCIENCE** YEAR

**2014**, VOLUME

**18**, ISSUE

**2**, PAGES [399 - 408]

- Edward H. Bernhardi , Modeling diode-pumped solid-state lasers, Msc thesis ,University of Kwazulu-Natal ,School of Physics,SA,2008
- Ivan Mukhin (et.al), Reduction of thermally induced depolarization of laser radiation in oriented cubic crystals, Optics Express, 17(2009),7,pp. 5496-5501
- Feng Huang(et.al) , Modeling and resolving calculation of thermal effect in face-pumped high power heat capacity disk laser, Proc. of SPIE ,Vol. 6823, 682311 pp.1-8, (2007)
- Bories A.Usievich (et.al) ,Analytical treatment of thermal problem in axially pumped solid state lasers,IEEE J. of Quantum Electronics ,37(2001),9,pp.1210-1214
- E. H. Bernhardi1 (et..al), 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.
- Zhigang Li a, Xiulan Huai a,, Li Wang b , A study of the axisymmetric thermal strain in a laser rod with longitudinal temperature rise, Applied Thermal Engineering, 29 (2009), pp. 2927-2934.
- ABAQUS Finite Element Software Package (ABAQUS, 2008), www.simulia.com/products/abaqus_fea.html
- M. N. Özisik, Heat Conduction ,Wiley, New York, 1980.pp.543-544
- 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.
- . LASCAD Manual, (LASCAD, 2008) , www.las-cad.com/files/PP_FEA.pdf.
- Y.Tian,G.Li,B.Q.Yao,Y.Z.Wang,Time-dependent analytical model of thermal effects in continuous-wave end-pumped Tm:Yap lasers ,Applied Phys B, 103(2011) ,pp.107-112.
- Khalid S, Shibib (et.al), Thermal and stress analysis in Nd:YAG laser rod with different double end pumping method ,International Journal thermal Science (2011), accepted for publishing : http://thermalscience.vinca.rs/pdfs/papers/TSCI101201004S.pdf
- W. Koechner, Solid-State Laser Engineering, 6th edition, Springer Series .in Opt. Sci., USA,2006.
- J.P.Holman, Heat Transfer in SI units , 5th edition ,McGRAW-HILL inyernational book company ,JAPAN,1981, p5.