高斯光束在三维光滑非均匀介质中的衍射：基于程函的复几何光学方法
Diffraction of Gaussian beam in a 3D smoothly inhomogeneous media: eikonal-based complex geometrical optics approach
摘要：
本文利用傍轴复几何光学（CGO）的从头算方法，研究了标量高斯光束在三维光滑非均匀介质中的传输和衍射。傍轴CGO处理复程函的二次展开，并将波动问题归结为Riccati型常微分方程的解。与全波或抛物线（准光学）方程相比，这大大简化了高斯光束衍射的描述。对于高斯光束在均匀介质中或沿对称轴在类透镜介质中传输，CGO方程具有解析解，否则可以很容易地数值求解。作为一个非平凡的例子，我们考虑高斯光束沿螺旋射线在轴对称波导介质中的传播和衍射。结果表明，长轴的光束的椭圆形横截面无限增长，它主要是在方位角（副法线）方向取向，不服从平行输运定律。
英文摘要：
The paper presents an ab initio account of the paraxial complex geometrical optics (CGO) in application to a scalar Gaussian beam propagation and diffraction in a 3D smoothly inhomogeneous medium. The paraxial CGO deals with quadratic expansion of the complex eikonal and reduces the wave problem to the solution of ordinary differential equations of Riccati type. This substantially simplifies description of Gaussian beams diffraction as compared to full wave or parabolic (quasi-optics) equations. For a Gaussian beam propagating in a homogeneous medium or along the symmetry axis in a lens-like medium, the CGO equations possess analytical solutions, otherwise they can be readily solved numerically. As a non-trivial example we consider Gaussian beam propagation and diffraction along a helical ray in an axially symmetric waveguide medium. It is shown that the major axis of the beam's elliptical cross-section grows unboundedly; it is oriented predominantly in azimuthal (binormal) direction and does not obey the parallel transport law.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
