The curvature type of the thermal lens generated in a zigzag slab laser is numerically analysed. It is found that the curvature type of the thermal lens varies alternatively between the convex and the concave lenses w...The curvature type of the thermal lens generated in a zigzag slab laser is numerically analysed. It is found that the curvature type of the thermal lens varies alternatively between the convex and the concave lenses with the number of bounces of light within the slab, which can be well explained by the trace of the zigzag propagation. In addition, we conclude that the beamlet with a larger number of bounces experiences weaker thermal lensing but more serious wavefront deformation due to the large side lobe portion in the curve of optical path difference.展开更多
Given a positive function F on S^n which satisfies a convexity condition, we introduce the r-th anisotropic mean curvature Mr for hypersurfaces in R^n＋1 which is a generalization of the usual r-th mean curvature Hr. ...Given a positive function F on S^n which satisfies a convexity condition, we introduce the r-th anisotropic mean curvature Mr for hypersurfaces in R^n＋1 which is a generalization of the usual r-th mean curvature Hr. We get integral formulas of Minkowski type for compact hypersurfaces in R^n＋1. We give some new characterizations of the Wulff shape by the use of our integral formulas of Minkowski type, in case F=1 which reduces to some well-known results.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.50721004 and 60978032)
文摘The curvature type of the thermal lens generated in a zigzag slab laser is numerically analysed. It is found that the curvature type of the thermal lens varies alternatively between the convex and the concave lenses with the number of bounces of light within the slab, which can be well explained by the trace of the zigzag propagation. In addition, we conclude that the beamlet with a larger number of bounces experiences weaker thermal lensing but more serious wavefront deformation due to the large side lobe portion in the curve of optical path difference.
基金Tianyuan Fund for Mathematics of NSFC (Grant No.10526030)Grant No.10531090 of the NSFCDoctoral Program Foundation of the Ministry of Education of China (2006)
文摘Given a positive function F on S^n which satisfies a convexity condition, we introduce the r-th anisotropic mean curvature Mr for hypersurfaces in R^n＋1 which is a generalization of the usual r-th mean curvature Hr. We get integral formulas of Minkowski type for compact hypersurfaces in R^n＋1. We give some new characterizations of the Wulff shape by the use of our integral formulas of Minkowski type, in case F=1 which reduces to some well-known results.
