Unfolding of an unstable singularity point into a ring

Area of Science:

• Optics
• Wave physics
• Topological defects

Background:

• Phase singularities are topologically stable lines in wave fields.
• Point singularities are exceptions, being unstable and prone to deformation or disappearance under perturbation.
• Nye's recent work provides a theoretical framework for understanding point singularity instability as a higher-order dislocation unfolding.

Purpose of the Study:

• To optically implement Nye's model of higher-order dislocation unfolding.
• To experimentally investigate the behavior of point singularities in a lens's focal region.
• To demonstrate the transformation of point singularities into ring singularities under controlled perturbation.

Main Methods:

• Optical implementation of a theoretical model for dislocation unfolding.
• Experimental setup involving a lens system to create focal regions.
• Introduction of controlled spherical aberration as a perturbation.

Main Results:

• Observed points of zero intensity (singularities) on the optical axis in the focal region of a lens.
• Demonstrated that these point singularities deform into ring singularities upon the application of small spherical aberration.
• Validated the theoretical model of higher-order dislocation unfolding in an optical system.

Conclusions:

• The focal region of a lens provides an experimental platform for studying unstable point singularities.
• Spherical aberration acts as a perturbation that unfolds point singularities into ring singularities, consistent with theoretical predictions.
• This study experimentally confirms the topological instability and transformation dynamics of point singularities in wave fields.