Up to now, Gaussian optical vortices (OVs) were investigated with the finite topological charge (TC). Here, we study an OV with the infinite TC. Such OVs have a countable number of phase singularities (isolated intensity nulls), which typically have the unitary TC and are located either equidistantly or not equidistantly on a straight line in the beam transverse cross section. Such OVs are structurally stable (form-invariant) and their transverse intensity is conserved on propagation, changing only in scale and rotation. Orbital angular momentum (OAM) of such OVs is finite, since only a finite number of screw dislocations are within the Gaussian beam in the area of notable intensity, whereas the other phase singularities are in the periphery (and in the infinity), where the intensity is very small. Increasing the Gaussian beam waist radius leads to the parabolic growth of the OAM of such beams. A unique feature of these beams is that their normalized OAM can be adjusted (both increased and decreased) by simple change of the waist radius of the Gaussian beam. In addition to the two form-invariant beams, we studied a Gaussian beam with a countable number of edge dislocations (zero-intensity lines), which is not form-invariant, but, after an astigmatic transform by a cylindrical lens, also becomes an infinite-topological-charge beam.

到目前为止，高斯光学涡旋（OVs）是用有限拓扑电荷（TC）来研究的。在这里，我们研究具有无限 TC 的 OV。这样的 OV 具有可数数量的相位奇点（孤立的强度零点），它们通常具有单一的 TC 并且等距或不等距地位于光束横截面的一条直线上。这种 OV 在结构上是稳定的（形式不变），并且它们的横向强度在传播时是守恒的，仅在尺度和旋转上发生变化。这种 OV 的轨道角动量 (OAM) 是有限的，因为只有有限数量的螺旋位错位于高斯光束内的显着强度区域，而其他相位奇点位于外围（和无穷远），其中强度非常小。增加高斯束腰半径会导致此类束的 OAM 的抛物线增长。这些光束的独特之处在于它们的归一化 OAM 可以通过简单改变高斯光束的腰部半径来调整（增加和减少）。除了两束形状不变的光束外，我们还研究了具有可数个边缘位错（零强度线）的高斯光束，它不是形状不变的，但经过柱面透镜的像散变换后，也变成了无限拓扑电荷束。