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Characterization of passivity in Mueller matrices.

Ignacio San José, José J Gil

Journal of the Optical Society of America. A, Optics, Image Science, and Vision

|March 3, 2020

Summary

Mueller matrices describing passive optical systems must satisfy specific conditions. This study identifies two necessary and sufficient conditions for passivity, crucial for accurate polarimetry measurements.

Area of Science:

Optics and Photonics
Mathematical Physics
Materials Science

Background:

Linear transformations of electromagnetic wave polarization typically reduce intensity, a passive behavior.
This passive behavior imposes mathematical constraints on Mueller matrices.
Previous work established general conditions for Mueller matrix passivity, but lacked complete demonstration.

Purpose of the Study:

Determine and demonstrate the necessary and sufficient conditions for a Mueller matrix to represent a passive medium.
Identify the passive Mueller matrix with maximal intensity transmittance.
Provide a criterion for validating experimentally measured Mueller matrices in polarimetry.

Main Methods:

Decomposition of Mueller matrices into a convex combination of nondepolarizing and passive pure Mueller matrices.

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Mathematical derivation and demonstration of passivity conditions.

Analysis of Mueller matrix properties within the framework of convex combinations.

Main Results:

A complete set of two necessary and sufficient conditions for Mueller matrix passivity is established.
A method is presented to identify the passive Mueller matrix with maximum intensity transmittance.
The derived conditions offer a criterion to discard non-passive experimental Mueller matrices.

Conclusions:

The study rigorously defines passivity conditions for Mueller matrices.
The findings are applicable to absolute Mueller polarimetry, enhancing experimental accuracy.
This work provides a theoretical and practical framework for understanding and verifying optical system passivity.