Aiming at morphology of laser induced damage mitigation pit on the rear surface of 3ω silica optical component, the mitigated area and its downstream intensity distributions with different morphologies are simulated by finite-difference time-domain method (FDTD) and Rayleigh-Sommerfeld (R-S) diffraction integral method, respectively. The results show that when the angle between the tangent line of endpoints on the section contour of the pit and incident light is over 70°, the maximum intensity inside the mitigated optics is less than 1.66, and mitigation effect is better than that of other angles. The maximum downstream intensities of a pit in shape of parabolic surface, cone and truncated cone are all less than 1.46 with an angle of 70° and a width of 200 μm. But when the width of pit increases to 1 mm, for instance, the maximum downstream intensity is as high as 9.31 and area with high intensity covers a long range. Thus, taking the difficulty of laser machining technology into account, a conical pit with an angle larger than 70° is the first choice for the damage mitigation on the rear surface of silica optical component.

针对三倍频光学元件后表面的损伤修复形貌，分别采用时域有限差分法（FDTD）和瑞利索末菲（R-S）衍射积分法，来模拟不同形貌下元件修复区域内以及其后续的光场分布。结果表明，当修复坑截面轮廓线端点切线与光束传播方向夹角大于70°时，元件内部光强极大值小于1.66，修复效果优于其他角度。夹角为70°、宽200 μm的抛物面型、圆锥型和圆台型凹坑的后续光强极大值小于1.46。但是当修复坑宽度较大如达到1 mm时，圆台型凹坑的后续光强极大值高达9.31，且作用区间长。因此，考虑实际激光修复工艺的难度，夹角大于70°的圆锥型凹坑是石英元件后表面损伤修复的首选形貌。

The physical meaning and essence of Fresnel numbers are discussed, and two definitions of these numbers for offaxis optical systems are proposed. The universal Fresnel number is found to be N=(a2/λz)*C1+C2. The Rayleigh–Sommerfeld nonparaxial diffraction formula states that a simple analytical formula for the nonparaxial intensity distribution after a circular aperture can be obtained. Theoretical derivations and numerical calculations reveal that the first correction factor C1 is equal to cosθ and the second factor C2 is a function of the incident wavefront and the shape of the diffractive aperture. Finally, some diffraction phenomena in off-axis optical systems are explained by the off-axis Fresnel number.

The physical meaning and essence of Fresnel numbers are discussed, and two definitions of these numbers for offaxis optical systems are proposed. The universal Fresnel number is found to be N=(a2/λz)*C1+C2. The Rayleigh–Sommerfeld nonparaxial diffraction formula states that a simple analytical formula for the nonparaxial intensity distribution after a circular aperture can be obtained. Theoretical derivations and numerical calculations reveal that the first correction factor C1 is equal to cosθ and the second factor C2 is a function of the incident wavefront and the shape of the diffractive aperture. Finally, some diffraction phenomena in off-axis optical systems are explained by the off-axis Fresnel number.

基于矢量瑞利索末菲衍射积分，建立了非傍轴条件下四瓣高斯光束经过偏心圆孔光阑在自由空间传输的矢量场模型。选取倾斜光轴作为参考光轴，借助于硬边圆孔的复高斯级数分解，得到了近场模型下衍射场分布的矢量解析式。通过数值计算和模拟，详细讨论了f参数、光束阶次、衍射孔位置和截断参数对像场分布的影响，包括衍射场主瓣强度的位置和光束宽度。这些结论有助于更好地理解四瓣高斯光束在离轴非对称光学系统中的传输特性。

基于瑞利索末菲衍射积分公式，在未作近轴近似的条件下，推导出等束宽超短脉冲高斯光束通过线性色散介质的远场公式，并用于研究其远场特性，所得公式可用于大衍射角情况．结果表明，等束宽脉冲高斯光束的频谱上存在一临界角，小于临界角时，出现蓝移；大于临界角时，出现红移，红移量随着衍射角的增大而增大．而脉冲波形将经历时间移动，移动量随衍射角的增大而增大；远场高斯脉冲波形将不再保持不变．此外，群速度色散将引起啁啾，啁啾量随衍射角的增大而减小．

运用Rayleigh-Sommerfeld衍射积分,详细推导了二元环形孔径全空间在轴光强分布公式.由于未作明显的近似,所得公式对衍射距离大于数倍入射波长的衍射空间都是有效的.计算并分析了这种孔径轴线上的光强分布情况.结果显示,它的最大调制深度是入射光强的16倍,比圆形孔径或环形孔径大4倍,近场的光学层析能力比远场的强.在很近场区,二元环形孔径的在轴光强分布对孔径结构比较敏感,这些特性使这种孔径在光子学和光纤光学的应用方面具有潜在的价值.