Differential and product Mueller matrix decompositions: a formal comparison

Area of Science:

• Optics and Photonics
• Polarimetry
• Materials Science

Background:

• Mueller matrix decomposition is crucial for characterizing polarization properties of materials.
• Existing methods like G-polar decomposition treat depolarization as localized.
• Differential representation offers an alternative for continuous depolarization modeling.

Purpose of the Study:

• To demonstrate the formal equivalence of Mueller matrix logarithm and root decompositions.
• To compare the elementary polarization properties derived from these methods with other decomposition techniques.
• To analyze the behavior of these properties in weakly depolarizing media.

Main Methods:

• Utilizing the differential representation of continuously depolarizing media.
• Applying Mueller matrix logarithm and Mueller matrix root decompositions.
• Comparing results with G-polar decomposition and Cloude sum decomposition.

Main Results:

• Mueller matrix logarithm and root decompositions are formally equivalent.
• Both methods yield a set of six elementary polarization properties.
• This set differs from G-polar decomposition but aligns with Cloude sum for weakly depolarizing media.

Conclusions:

• The differential representation provides a unified framework for Mueller matrix logarithm and root decompositions.
• These decompositions offer a more accurate representation of continuously distributed depolarization.
• The findings are particularly relevant for analyzing weakly depolarizing optical components.