Recently, the spatial mode multiplexing based on optical vortices (OVs) attracts much attentions as a promissing technology for high-capacity optical communications. For such OV-based telecommunications, optical components for mode decomposition with respect to azimuth mode indices (topological charges) — so-called orbital angular momentum (OAM) sorters — are key devices, and various kinds of OAM sorters have been demonstrated such as computer-generated holograms as far. Among them, the geometric transformation (GT) technique has great advantages that the insertion loss is quite low and it supports inverse transformation (multiplexing) . In earlier studies, GT-based OAM sorters have been realized by using spatial light modulators (SLMs) , and more recently, transparent refractive elements produced by using such as diamond machining  and Pancharatnam Berry phase  have been demonstrated. However, the GT-based method has the serious disadvantage of relatively large crosstalk between the neighboring modes.
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