Nonregularity of three-dimensional polarization states

Area of Science:

• Optics and Photonics
• Mathematical Physics

Background:

• Regular polarization states are defined by their decomposition into pure and unpolarized states in 2D or 3D.
• Nonregular states involve mixtures of pure states with polarization ellipses in different planes.

Purpose of the Study:

• To identify a perfect nonregular polarization state.
• To introduce a quantitative measure for the degree of nonregularity.
• To analyze polarization-state regularity using polarimetric parameters.

Main Methods:

• Theoretical analysis of polarization states.
• Introduction of the degree of nonregularity.
• Interpretation of regularity via polarimetric parameters.

Main Results:

• Identification of a perfect nonregular state.
• Development of the degree of nonregularity as a proximity measure.
• New insights into the polarimetric structure of 3D light fields.

Conclusions:

• The study advances the understanding of polarization states beyond traditional definitions.
• The degree of nonregularity provides a novel tool for characterizing light fields.
• Results contribute to the field of polarimetry and 3D optics.