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.

Thermal analysis of end pumped fiber lasers subjected to jacket fluid cooling

“…The prediction of steady state temperature distribution in Nd:YAG laser rod has been obtained using finite element analysis [28] where the laser rod was cooled by water. Transient temperature distribution in CW-End-pumped laser rod has been obtained analytically [29] where thermal stress distribution has been also obtained. Another analytical work derived the transient temperature distribution in pulsed solid-state laser rod [30].…”

Transient analytical solution of temperature distribution and fracture limits in pulsed solid-state laser rod

“…Assuming z = 0 then Tresca failure could be written [9,16]: Incorporating the equation of θ and carrying the integration result in:…”

“…For the arbitrary temporal shape of pump pulse, a 3-D temperature expression was derived via an integral transform method, and the thermal stress field was deduced through solving the Navier displacement equations. Shibib et al [8,9] derived the transient analytical solutions of temperature distribution, stress, strain, and optical path difference in convectional cooled (CW) end-pumped laser rod. The results were compared with other works and good agreements were found.…”

Analytical solution of transient temperature in continuous wave end-pumped laser slab: Reduction of temperature distribution and time of thermal response

“…Here -3 ] -the heat source density, and T [K] -the temperature. This equation can be solved by the successive application of integral transform to the x, y, and z variables, The part of absorbed power that converts to heat act as a heat source and it can has different profile [5,6,11].…”

“…3, pp. 1223-1230 ing [5][6][7]. Few literature dealt with analytical solution of transient temperature in laser slab.…”