Optical vortex beams (VB) have been extensively applied in many fields for their unique features. In this paper, we explore the defocusing intensity of VB modulated by axial symmetry polarization. Combining appropriate polarization order of the modulator, we show that defocusing can result in a spiral structure of intensity distribution, of which the number of spiral arms is determined by the polarization order of the modulator, and the rotation direction of spiral arms depends on the topological charge (TC) of incident beams. The helical structure of defocusing intensity holds a small solid spot when the TC value of VB matches the polarization order number. Therefore, the magnitude of the tested TC can be inferred from the small solid spot distribution, and the sign of the TC can be determined by the rotation direction of the helical intensity. The peculiar phenomena exploited in this paper stimulate the new applications of VB in many fields.

中文翻译：

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用散焦强度测量涡旋光束的轨道角动量状态

光学涡旋光束（VB）具有独特的功能，已在许多领域得到广泛应用。在本文中，我们探索了由轴向对称极化调制的VB的散焦强度。结合调制器的适当偏振阶，我们表明散焦可以导致强度分布的螺旋结构，其中螺旋臂的数量由调制器的偏振阶确定，并且螺旋臂的旋转方向取决于拓扑入射光束的电荷（TC）。当VB的TC值与偏振阶数匹配时，散焦强度的螺旋结构将保持较小的实心点。因此，可以从小的固体斑点分布推断出被测TC的大小，并且可以通过螺旋强度的旋转方向来确定TC的符号。