Abstract:When a laser beam irradiates an optical material, a light standing wave field should be observed inside the optical material due to the interference between the beam reflected from the rear surface and the incident beam. If there are scratches on the surface, the incident light can be modulated and the distribution of the standing wave field inside the material is not uniform any more. Therefore, the appearance of the local enhancement of light will change the damage characteristics of optical material. To analyze the field damage characteristics of optical material with scratches, a theoretical analysis model is established. It can be used to study the damage characteristics and build a priori model of actual optical material. Fused quartz is employed as the study object, and the modulation effect of defect on light field is simulated by finite difference time domain (FDTD). Based on the electron multiplication theory, the effect of the number and the positions of scratches on the damage characteristics of fused quartz are calculated in detail. The results show that the phase modulation of the scratch will destroy the uniformity of the standing wave field when the scratch defect material is irradiated by laser. Due to the influence of the standing wave field, the maximum field intensity appears near the rear surface of the material, which explains the phenomenon that the rear surface of the material is more prone to damage points. When there are multiple scratches on the material surface, the distribution of light field is related to the number of the scratches. Specifically, the maximum field intensity increases with the number of scratches increasing. Taking fused quartz material for example, when a 10-ps pulse is incident on it, if three scratches are located on its surface, then the modulation effect on the light field is strongest, and the damage threshold is 66.1% lower than that of the ideal material. In addition, the scratch spacing also has an effect on the standing wave field and field damage characteristics of the material, and the specific effect of the interval can be analyzed directly by using the calculation model proposed in this paper. Keywords:surface scratches/ standing wave field/ ionization rate/ damage threshold
由(8)式可知, 不同数量的划痕会引入不同的相位, 使驻波场分布发生变化. 利用有限差分算法分别对单划痕、双划痕和三条划痕以及理想表面熔融石英材料的驻波场进行了计算, 结果如图2所示. 图中的矩形方框表示划痕所在位置. 图 2 表面存在不同数量划痕时熔融石英内部的驻波场分布 (a) N = 0; (b) N =1; (c) N = 2; (d) N = 3 Figure2. Standing wave field distribution inside fused quartz with different number of scratches on the surface: (a) N = 0; (b) N =1; (c) N = 2; (d) N = 3
$\frac{{{\rm{d}}N\left( t \right)}}{{{\rm{d}}t}} = {R_{{\rm{ai}}}} \times N\left( t \right) + {R_{{\rm{pi}}}} - g \times N\left( t \right) - \mu \times N{\left( t \right)^2},$
其中$N\left( t \right)$为自由电子密度, g和μ分别为自由电子扩散与复合速率, ${R_{{\rm{ai}}}}$是雪崩电离速率, 根据Thornber雪崩电离模型, 其表达式为[16,19,20]
由(10)式和(11)式可知, 材料的电离速率与光场有关. 下面对缺陷熔融石英内电子的电离速率进行计算. 图4为理想熔融石英和表面存在单划痕、双划痕、三条划痕时, 材料后表面沿划痕宽度方向的雪崩电离速率和光生电子速率分布. 图 4 熔融石英后表面的电离速率随划痕数量的变化 (a)雪崩电离速率分布; (b)光生电子速率分布 Figure4. Changes of the ionization rate of fused quartz with the number of scratches: (a) Avalanche ionization rate distribution; (b) photoelectron ionization rate distribution.
由图4可知, 缺陷熔融石英的雪崩电离速率和光生电子速率有相同的变化规律, 是由于两种电离速率都与场强成正相关的关系. 划痕调制使材料内的场强增大, 从而使缺陷材料的两种电离速率都大于理想情况, 且最大速率出现在光场最大值位置. 随着表面划痕的数量增加, 调制光场之间的相互干涉作用也随之增强, 从而使得两种电离速率的最大值均随划痕数量的增多而增大. 当表面存在三条划痕时, 两种电离速率都出现了数值接近的三个峰, 恰好与驻波场中的最大场强位置一致. 结合(9)式, 计算了划痕数量不同时, 缺陷熔融石英内自由电子随时间的增值规律, 如图5所示. 图 5 划痕数量不同的熔融石英内自由电子积累过程 Figure5. Free electron accumulation in fused quartz with different number of scratches.
从图5可以看出, 随着划痕数量的增加, 缺陷熔融石英材料内自由电子积累越快. 因为划痕增加时, 调制后的光场越强, 雪崩电离速率和多光子电离速率都增大, 因而材料更快积累自由电子, 也更易发生损伤. 利用(12)式计算不同划痕数量缺陷熔融石英的损伤阈值, 如图6所示. 存在表面划痕缺陷时的损伤阈值明显低于理想表面的熔融石英. 划痕数量从0增加到3时, 由于调制后的场强随划痕数量的增多而增大, 因而损伤阈值随划痕数量的增加而降低. 当脉宽为10 ps时, 理想熔融石英的损伤阈值为0.53 J/cm2, 有三条划痕材料的阈值为0.35 J/cm2, 降低到理想阈值的66.1%. 图 6 不同划痕数量熔融石英的损伤阈值 Figure6. Damage thresholds of fused quartz with different number of scratches.