利用Yb³⁺∶KGd(WO₄)₂晶体的热膨胀系数各向异性和折射率温度梯度为负值的特点，就可能找到被光抽运时热透镜效应为零的特定方向，此方向即为“无热透镜方向”。鉴于前人的理论计算中存在着一些缺陷，利用最小二乘法和二阶张量旋转法，精确计算了Yb³⁺∶KGd(WO₄)₂晶体的热膨胀张量以及在不同偏振状态下的无热透镜方向：m偏振时，在p-g 平面内与p 轴成±46.3°的方向；p 偏振时，在m-g 平面内与m 轴顺时针成24.9°以及与m 轴逆时针成81.2°的方向；g 偏振时不存在无热透镜方向。将之与前人的计算结果进行了比较，指出了其理论模型中存在的缺陷。计算了p 偏振时在m-g 平面内与m 轴顺时针成17°的方向上传播以及m 偏振时b 方向传播的单位光程变化值，并与前人已发表的理论与实验结果做了对比分析，证实了所建理论体系的有效性。

Using the anisotropic thermal expansion coefficients and the negative refractive index gradients in temperature of an optical-pumped Yb³⁺∶KGd(WO₄)₂, it is possible to find some special directions without thermallyinduced lens effects which is called“the thermal-lens-free orientation”. Considering there are some defects in the theoretical models created by other researchers, the thermal expansion tensors and thermal-lens-free orientations at different polarized directions have been evaluated by using the least square method and two-order tensor rotation approach. The thermal-lens-free orientations have been determined as follows: The directions located ±46.3° from the p axis in the p-g plane when the light is polarized in the m axis, the directions located 24.9° clockwise from the m axis in the m-g plane and 81.2° counterclockwise from the m axis in the m-g plane when the light is polarized in the p direction. When the light is polarized along the g direction, there is no thermal-lens-free direction for the crystal. The theoretical results in the previous reports are compared and some defects are also pointed out. The optical path changes have been analyzed along the directions of both 17° rotated clockwise from the m axis in the m-g plane (p-polarized) and the b axis (m-polarized) to compare with the previous experimental results. The effectiveness of our theoretical simulation has been therefore demonstrated through the comparison analyses.