Correlation between topological structure and its properties in dynamic singular vector fields

Area of Science:

• Physics
• Optics
• Complex Systems

Background:

• Singular vector fields are crucial in optics and fluid dynamics.
• Understanding their topology, including C points and L lines, is essential for various applications.
• Existing measurement techniques have limitations in precision and scope.

Purpose of the Study:

• To develop a new, precise technique for establishing topology measurements of static and dynamic singular vector fields.
• To investigate the relationship between optical vortices and the morphological parameters of C points.
• To explore the role of percolation phenomena in the behavior of singular vector fields.

Main Methods:

• Precise measurement of the 3D ellipticity distribution landscape in singular optical fields.
• Identification and analysis of C points located at the peaks of ellipticity.
• Experimental confirmation of rules governing the connection between optical vortices and C point morphology.

Main Results:

• A three-component topology of vector fields was identified, including right-hand (RH) and left-hand (LH) elliptical areas and L lines as singularities.
• The azimuth map of polarization ellipses was found to be common for both RH and LH ellipses and does not sense L lines.
• Strict experimental rules were confirmed, establishing a link between optical vortex sign and C point morphology.
• Percolation phenomena were shown to explain the realization and long duration (up to 10^3 s) of chains in singular vector fields.

Conclusions:

• The new technique provides precise topology measurements for singular vector fields.
• The confirmed rules offer a deeper understanding of the relationship between optical vortices and C points.
• Percolation phenomena play a significant role in the observed long-duration chains within these fields.