Approximate analytical expression for intensity of hot image of intensity laser beam in media with gain saturation region
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摘要: 高功率激光系统中的热像效应可能导致光束的峰值功率剧烈增加，增益非线性介质会使这种光强增幅更为强烈。基于菲涅尔-基尔霍夫衍射理论和非线性近轴波动方程，对强激光在增益克尔介质工作在饱和区时的热像产生过程进行理论分析，将光束传输方程中增益饱和部分进行麦克劳林展开，取其近似，经过推导得出了介质薄近似时热像强度解析式和热像位置。通过数值模拟对解析结论预测的热像强度和位置进行验证。仿真结果表明，热像的位置在衍射物相对于介质对称处，热像强度解析结果与模拟结果相符，在薄介质时，解析解与模拟结果拟合较好。热像强度随非线性介质内非线性效应增强而停止增加，此外，讨论了热像强度随调制类型的变化。Abstract: The hot image effect of the high power laser system may cause the peak power of the beam to increase drastically, and the amplifying Keer medium will make this increase in light intensity more intense. When the input beam power is strong enough, the gain saturation effect of the amplifying Keer medium on the beam is more obvious. Based on the Fresnel-Kirchhoff diffraction theory and the nonlinear paraxial wave equation, the hot image generation process of the intense laser in the gain saturation region of the amplifying Keer medium is theoretically analyzed, and the gain saturation part of the beam transmission equation is subjected to the Maclaurin expansion for approximation. After deriving the analytical formula of hot image intensity and hot image position when the medium is thin, the hot image intensity and position predicted by the analytical conclusion are verified by numerical simulation. The simulation results show that the position of the hot image is symmetrical to the diffracted object with respect to the medium, and the analysis results of hot image intensity are consistent with the simulation results. The intensity of the hot image stops increasing as the nonlinear effect of the nonlinear medium increases. In addition, the change of the intensity of the hot image with the obscuration type is discussed.
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图 2 光路的峰值光强演化图和热像的光强分布图（输入光输强度：
$ 28{\text{ GW/c}}{{\text{m}}^2} $ ，$ \tau = 0 $ ，$ \theta = {\text{π}} $ ，增益饱和光强$ 100{\text{ GW/c}}{{\text{m}}^2} $ ）Figure 2. Peak light intensity evolution diagram of the light path and the light intensity distribution diagram of the hot image (incident light intensity：
$ 28{\text{ GW/c}}{{\text{m}}^2} $ ，$ \tau = 0 $ ，$ \theta = {\text{π}} $ ，saturation light intensity is$ 10\;{\text{GW/c}}{{\text{m}}^2} $ )
图 5 热像的峰值强度随克尔介质厚度的变化（相位调制
$ \theta {\text{ = }}{\text{π}} $ ，$ \tau {\text{ = }}1 $ ；入射光强$ {\text{20 GW/c}}{{\text{m}}^2} $ ，增益饱和光强$ 100{\text{ GW/c}}{{\text{m}}^2} $ ）Figure 5. Variation of hot image intensity with the thickness of the amplifying Kerr medium slab (phase obscurations
$ \theta {\text{ = }}{\text{π}}$ ,$ \tau {\text{ = }}1 $ ; Amplitude obscurations$ \tau {\text{ = 0}} $ ; incident light intensity$ {\text{20 GW/c}}{{\text{m}}^2} $ , saturation light intensity$ 100{\text{ GW/c}}{{\text{m}}^2} $ )
图 6 热像的峰值强度随输入光强的变化
Figure 6. Variation of hot image intensity with the intensity of saturation light
图 7 入射光强
$ {\text{20 GW/c}}{{\text{m}}^2} $ 时，介质后方光束峰值强度（相位调制$ \theta {\text{ = }}{\text{π}} $ ，$ \tau {\text{ = }}1 $ ，增益饱和光强$ 100{\text{ GW/c}}{{\text{m}}^2} $ ）Figure 7. Incident light intensity
$ {\text{20 GW/c}}{{\text{m}}^2} $ , peak-to-mean intensity of the light after the Kerr medium slab (phase obscurations$ \theta {\text{ = }}{\text{π}} $ ,$ \tau {\text{ = }}1 $ , saturation light intensity$ 100\;{\text{ GW/c}}{{\text{m}}^2} $ ) -
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