Abstract
Modern beam shaping techniques have enabled the generation of optical fields displaying a wealth of structural features, which include three-dimensional topologies such as Möbius, ribbon strips and knots. However, unlike simpler types of structured light, the topological properties of these optical fields have hitherto remained more of a fundamental curiosity as opposed to a feature that can be applied in modern technologies. Due to their robustness against external perturbations, topological invariants in physical systems are increasingly being considered as a means to encode information. Hence, structured light with topological properties could potentially be used for such purposes. Here, we introduce the experimental realization of structures known as framed knots within optical polarization fields. We further develop a protocol in which the topological properties of framed knots are used in conjunction with prime factorization to encode information.
Highlights
Modern beam shaping techniques have enabled the generation of optical fields displaying a wealth of structural features, which include three-dimensional topologies such as Möbius, ribbon strips and knots
In spite of their significant potential, knots created within optical fields[12,13,14,15,21] are mostly investigated in experiments within the framework of information theory in a similar way to simpler optical beams carrying a single singularity[31]. They are more than often treated as two-dimensional transverse optical modes, as opposed to a three-dimensional object defined by prospectively more useful topological invariants. This shortcoming arguably arises from a current lack of overlap between the fields of topological quantum information and singular optics—that is, optical topologies that can currently be realized in the laboratory cannot be readily used as a platform for existing topological information protocols and vice-versa
Knots ubiquitously describe how looped threads are arranged in space. For this reason, when analyzed within a physical framework, knots are typically found within fields defined by regions that unambiguously form curves in threedimensional space. These knotted curves have been demonstrated in systems such as the vortices of fluids[32], the intensity nulls of scalar optical fields[12,13,14], and within the C-lines of optical polarization fields[21]
Summary
Modern beam shaping techniques have enabled the generation of optical fields displaying a wealth of structural features, which include three-dimensional topologies such as Möbius, ribbon strips and knots. In spite of their significant potential, knots created within optical fields[12,13,14,15,21] are mostly investigated in experiments within the framework of information theory in a similar way to simpler optical beams carrying a single singularity[31] They are more than often treated as two-dimensional transverse optical modes, as opposed to a three-dimensional object defined by prospectively more useful topological invariants. We introduce and experimentally demonstrate the generation and observation of structures in optical polarization wavefields forming framed knots We use the latter as information carriers by means of a protocol devised to encode topological information through the conjoined usage of prime factorization and the knots’ own topological invariants
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