Thermal stresses and end-bulging in the laser disc from a tetragonal crystal: the case of LiYF₄

Abstract

Analytical solution of the thermal stress-strain problem is presented for discs from a-cut and c-cut tetragonal crystals with a point group 4, 4 or 4/m. Thermal stresses, strains and displacements, as well as the contribution of the end-bulging to the optical power of the thermal lens are calculated for the discs from Tm:LiYF 4 . The stress fracture issues are also analyzed for this crystal.

Thermal lensing in diode-pumped [001]-cut tetragonal crystals

“…The rule for the representation of tensor values as a column or matrix can be found in Appendix A. The strain components ε′ m for an c-cut disc from a tetragonal crystal were derived analytically in [15]. Derivation of parameters P′ mn in the "rotated" frame from ones defined the crystal-physical one, P mn , is described in Appendix B.…”

“…Parameter ν* indicates the contribution of end-bulging effect that occurs due to the thermal stresses (in contrast to the part that originates solely from the thermal expansion) [15]. For isotropic materials, this parameter is equal to the Poisson ratio, ν*≡ν [4].…”

“…Analytical expression for the end-bulging term χ′ for any c-cut tetragonal crystal was derived in [14,15] using the method of Airy stress function [20]. However, analytical expressions for the photo-elastic term χ″ and, more specifically, for the photo-elastic constants Q A(B) have been never derived for laser discs from tetragonal crystals.…”

“…The 6 Â 6 matrix of the elasto-optical constants P mn for tetragonal crystals with point groups 4, 4 , or 4/m in the crystal-physical frame is written as [15]: , 422, or 4/mmm, the matrix P mn can be obtained from Eq. (A2.1) considering P 45 ¼ P 16 ¼P 61 ¼ 0.…”

“…In an analytical form, this has been performed for laser discs from isotropic and high-symmetry (cubic) materials [4,13]. Recently, the first part (derivation of thermal stresses and strains) was also done for the discs from tetragonal crystals [14,15].…”