Spiral Transformation for High-Resolution and Efficient Sorting of Optical Vortex Modes

Mode sorting is an essential function for optical multiplexing systems that exploit the orthogonality of the orbital angular momentum mode space. The familiar log-polar optical transformation provides a simple yet efficient approach whose resolution is, however, restricted by a considerable overlap between adjacent modes resulting from the limited excursion of the phase along a complete circle around the optical vortex axis. We propose and experimentally verify a new optical transformation that maps spirals (instead of concentric circles) to parallel lines. As the phase excursion along a spiral in the wave front of an optical vortex is theoretically unlimited, this new optical transformation can separate orbital angular momentum modes with superior resolution while maintaining unity efficiency.

Figure 1

Principle of (a) the log-polar transformation scheme, and (b) the introduced spiral transformation scheme for OAM mode sorting.

Figure 2

Phase masks used for implementing (a) the log-polar and (b) the spiral transformation. (c) Schematic of the experimental setup. BS denotes beam splitter.

Figure 3

(a),(c) Numerical and (b),(d) experimental intensity distributions of vortex beams with topological charges $-2\le l\le 2$ transformed by (a),(b) the log-polar and (c),(d) the spiral transformation scheme. All images refer to the plane just after (or just before) the phase corrector [SLM3 in Fig. 2] and have the same spatial scale.

Figure 4

(a),(c) Numerical and (b),(d) experimental intensity distributions of sorted vortex beams with topological charges $-2\le l\le 2$ in the focal (Fourier) plane of the lens, based on (a),(b) the log-polar and (c),(d) the spiral transformation scheme. All images have the same spatial scale.

Figure 5

Intensity profiles along the dashed middle lines in the images of Fig. 4 for different OAM modes. (a),(c) Numerical and (b),(d) experimental results for (a),(b) the log-polar and (c),(d) the spiral transformation scheme.