论文标题
近期方程的广义解
Generalized solution of the paraxial equation
论文作者
论文摘要
发现光束的相当一般的表达是作为近轴helmholtz方程的解决方案的。它是通过利用适当选择的复杂变量来实现的，这些变量需要使方程式的分离性。接下来，光束的表达是通过叠加移动的高斯梁独立获得的，从而可以通过真实矢量（在这种情况下，高斯梁的焦点位于圆上）或通过复杂的射线来制作移位。找到的解决方案取决于几个参数，其特定选择允许获得具有完全不同属性的光束。对于几个选定的参数值图，绘制了能量密度和相位的空间分布。在特殊情况下，观察到强度峰从一个分支到另一个分支和相位奇异性的影响。
A fairly general expression for a light beam is found as a solution of the paraxial Helmholtz equation. It is achieved by exploiting appropriately chosen complex variables which entail the separability of the equation. Next, the expression for the beam is obtained independently by superimposing shifted Gaussian beams, whereby the shift can be made either by a real vector (in which case the foci of the Gaussian beams are located on a circle) or by a complex one. The solutions found depend on several parameters, the specific choice of which allows to obtain beams with quite different properties. For several selected parameter values figures are drawn, demonstrating the spatial distribution of the energy density and phase. In special cases, the effect of a shift of the intensity peak from one branch to another and phase singularities are observed.
