Temperature distribution in edge cooled ZnSe lens was numerically analyzed during focusing high power CO₂ laser beam where thermal conductivity K varies with temperature T, K=K(T). Simple analytical solutions at steady state were also derived for different laser modes assuming K is constant. Results obtained are summarized as follows ;
1) Assuming K=const, the accuracy of calculated temperature decreases with increasing steady temperature at the center, T_SC, which becomes 1.5 times as high as the exact value at T_SC=100 C.
(2) Steady temperature gradient calculated with K=const is proportional to r in laser irradiation region for a circular uniform beam of radius a, and is given by a curve having a peak at r= 1.12a for Gaussian beam (a=1/e-radius), of whidh peak is 64% of that of the circular beam.
(3) Simple equations to provide accurate steady temperature distribution and gradient were derived ; T_K (r) =T (r) / (1-mT_sc) and (dT/dr)_K = (dT/dr) / (1-mT_SC), where T (r), T_SC and dT/dr are temperatures at r=r and r=0 and temperature gradient at steady state for K=const, respectively.
(4) The temperature rise of ZnSe lens was measured during focusing CO₂ laser beam by a fluoroptic thermometry, and was found to agree well with calculated values.