This work presents the scheme of optical channeling of the intense Hermite Gaussian laser beam and second-harmonic generation in plasma having the preformed plasma channel, where relativistic nonlinearity is operative. Excitation of the electron plasma wave at the incident beam frequency leads its coupling with the latter produces the second harmonics of the beam. For the formulation of differential equations for the beam waists of the Hermite Gaussian laser beam propagating through the channel, the method of moments has been used. The solutions of the coupled differential equations are found using Runge Kutta fourth-order numerical method. Perturbation theory has been applied to find the equation governing the excitation of electron plasma wave and hence the source term for the second-harmonic yield. It has been observed that the preformed plasma channel helps to optically guide the laser beam and enhances the efficiency of second-harmonic generation of various modes of the Hermite Gaussian laser beam in plasma.

这项工作提出了强厄米高斯激光束的光通道方案和具有预制等离子体通道的等离子体中的二次谐波产生，其中相对论非线性是有效的。以入射束频率激发电子等离子体波导致其与后者耦合产生束的二次谐波。对于通过通道传播的 Hermite 高斯激光束的束腰的微分方程的公式化，使用了矩量法。耦合微分方程的解是使用 Runge Kutta 四阶数值方法找到的。微扰理论已被应用于找到控制电子等离子体波激发的方程，从而找到二次谐波产额的源项。