An investigation of frequency up-conversion of a laser beam through the phenomenon of second harmonic generation (SHG) in collisional plasma with an upward density ramp is presented. The variational method has been adopted to find a semi-analytical solution of the wave equation for the slowly varying envelope of the laser beam. When a laser beam with frequency ω 0 propagates through plasma it causes the plasma electrons to oscillate at pump frequency ω 0 . These oscillations of the plasma electrons in the presence of thermal velocity generate an electron plasma wave (EPW) at frequency ω 0 . The generated EPW beats with the pump beam to produce its second harmonics. By using a hydrodynamic fluid model of plasma, the source term for the SHG has been obtained. Emphasis is put on investigation of the effect of various laser and plasma parameters on the propagation dynamics of the pump beam and the conversion efficiency of second ha...

中文翻译：

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碰撞等离子体中具有向上密度斜坡的q-高斯激光束的二次谐波的产生

提出了一种通过碰撞等离子体中二次谐波产生（SHG）现象对激光束进行频率上转换的研究，该现象具有较高的密度斜率。已经采用了变分方法来为激光束的缓慢变化的包络找到波动方程的半解析解。当频率为ω0的激光束通过等离子体传播时，会导致等离子体电子以泵浦频率ω0振荡。在存在热速度的情况下，等离子体电子的这些振荡会产生频率为ω0的电子等离子体波（EPW）。产生的EPW用泵浦光束跳动以产生其二次谐波。通过使用等离子体的流体动力流体模型，已经获得了SHG的源项。