Author Affiliations
1Fujian Provincial Key Laboratory of Light Propagation and Transformation, College of Information Science & Engineering, Huaqiao University, Xiamen 361021, China2National Laboratory on High Power Laser and Physics Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Qinghe Road, Jiading District 390, Shanghai 201800, Chinashow less
Fig. 1. (Colour online) Schematic illustration of a super-Gaussian beam passing through a nonlinear medium.
Fig. 2. (Colour online) The normalized peak intensity of a super-Gaussian beam against the propagation distance for different bandwidths. $n_{0}(\lambda _{0})=1.812$, $n_{2}(\lambda _{0})=2.28\times 10^{ - 6}\ {\rm cm}^{2}/{\rm GW}$, $L=6\ {\rm cm}$, the super-Gaussian beam $I_{0}=12\ {\rm GW}/{\rm cm}^{2}$, $N=4$, $w_{0}=3\ {\rm mm}$.
Fig. 3. (Colour online) Evolution of the normalized peak intensity of a broadband super-Gaussian beam passing through different thicknesses of nonlinear medium along the propagation direction. (a) The incident intensity is fixed, $I_{0} =12\ {\rm GW}/{\rm cm}^{2}$, (b) The $B$ integral is fixed. $I_{0} =36\ {\rm GW}/{\rm cm}^{2}$ when $L=2\ {\rm cm}$; $I_{0} =24\ {\rm GW}/{\rm cm}^{2}$ when $L=3\ {\rm cm}$; $ I_{0} =12\ {\rm GW}/{\rm cm}^{2}$ when $L=6\ {\rm cm}$. $N=4$, $w_{0}=3\ {\rm mm}$, and $\Delta \lambda =40\ {\rm nm}$.
Fig. 4. Intensity distribution of a narrowband beam, $\Delta \lambda =0\ {\rm nm}$ (a) and a broadband beam, $\Delta \lambda =40\ {\rm nm}$ (b) at different distances. $n_{0}(\lambda _{0})=1.812$, $n_{2}(\lambda _{0})=2.28\times 10^{ - 6}\ {\rm cm}^{2}/{\rm GW}$, $ L=6\ {\rm cm}$, $I_{0} =12\ {\rm GW}/{\rm cm}^{2}$, $N=20$, and $w_{0}=3\ {\rm mm}$.
Fig. 5. (Colour online) Evolution of the normalized peak intensity of a super-Gaussian beam for different bandwidths, considering the medium’s front surface to have a defect. The defect size $a=100\ \mathrm {\mu} {\rm m}$, $A=1$, $x_{0}=0$; $n_{0}(\lambda _{0})=1.812$, $n_{2}(\lambda _{0})=2.28\times 10^{- 6}\ {\rm cm}^{2}/{\rm GW}$, $ L=6\ {\rm cm}$, $I_{0}=12\ {\rm GW}/{\rm cm}^{2}$, $N=4$, and $w_{0}=3\ {\rm mm}$.
Fig. 6. The propagation of a narrowband beam, $\Delta \lambda =0\ {\rm nm}$ (a) and a broadband beam, $\Delta \lambda =40\ {\rm nm}$ (b) through a nonlinear medium whose front surface contains a defect. Here, the parameters are the same as in Figure 5.
Fig. 7. The propagation of a narrowband beam (a) and a broadband beam (b) when the defect is not in the centre, $x_{0}=0.001\ {\rm m}$, the other parameters are the same as in Figure 6.