The absorption front model for laser induced damage of optical materials is modified. Different from the original model, the impurity defect absorption term is introduced, and the one-dimensional model is extended to a three-dimensional model. Using the modified absorption front model, temperature distribution near impurity(taking metal iron as an example), damage radius and damage threshold of infrared optical material of monocrystalline silicon are numerically studied, which is irradiated by 1064nm picosecond laser. The influence of initial temperature of the optical material on damage threshold is also studied. Our results show that: (1) Different from the traditional heat thermal transport models, near the damage threshold, a small change of laser field energy density from below to equal to or beyond damage threshold leads to a great change of temperature field in the presently modified absorption front model; (2) The maximum temperature near impurity and damage radius characterized by the absorption front increase approximately linearly with the increase of the irradiation energy density as the laser energy density goes far beyond damage threshold; (3) The laser damage threshold decreases with the increase of the initial temperature of the material. Our results prove that the presently modified absorption front model can better describe the laser damage induced by impurity defects in optical materials. Compared with the traditional thermal transport models, the present absorption front model can represent the sudden change of temperature field near the damage threshold more reasonably, and can quantitatively analyze laser damage size of optical materials induced by impurities. In addition, our results also show that increasing the initial temperature of the material can effectively reduce its laser damage threshold, which provides a way to improve the laser damage efficiency of photodetectors in photoelectric countermeasures.