Kotlyar V V, Kovalev A A, Porfirev A P
Opt Express. 2019 Jan 21;27(2):657-666. doi: 10.1364/OE.27.000657.
We find a two-parameter family of astigmatic elliptical Gaussian (AEG) optical vortices, which are free space modes up to scale and rotation. We calculate total normalized orbital angular momentum of AEG vortices, which can be an integer, fractional and zero, and which is equal to the algebraic sum of two terms reflecting the contribution of the vortex and astigmatic components of the light field. In any transverse plane, such a beam has an isolated n-fold degenerate intensity null on the optical axis (an optical vortex) embedded into an elliptical Gaussian beam. In addition to the quadratic elliptical phase, a beam has the phase of a cylindrical lens rotated by an angle of 45 degrees with respect to the principal axes of the ellipse of the Gaussian beam intensity distribution. The degenerated central intensity null in these beams does not split it into n spatially separated intensity nulls, as is usually assumed for elliptical astigmatic beams.
我们发现了一个双参数族的像散椭圆高斯（AEG）光学涡旋，它们是尺度和旋转不变的自由空间模式。我们计算了AEG涡旋的总归一化轨道角动量，其可以是整数、分数或零，并且等于反映光场涡旋分量和像散分量贡献的两项的代数和。在任何横向平面中，这样的光束在光轴上有一个孤立的n重简并强度零点（一个光学涡旋），它嵌入在一个椭圆高斯光束中。除了二次椭圆相位外，光束还有一个相对于高斯光束强度分布椭圆的主轴旋转了45度的柱面透镜的相位。这些光束中简并的中心强度零点并不会像通常对椭圆像散光束所假设的那样将其分裂成n个空间分离的强度零点。
