Expressions for parallel decomposition of the Mueller matrix.

Area of Science:

• Optics and Photonics
• Quantum Mechanics
• Matrix Algebra

Background:

• Optical materials and systems are often characterized using Mueller matrices.
• Hermitian matrices offer an alternative representation for optical properties.
• Transformations between these matrix representations are crucial for analysis.

Purpose of the Study:

• To introduce matrix forms for transforming between Mueller and Hermitian matrices.
• To review relevant matrix algebra for these transformations.
• To compare the utility of different ordering conventions for Stokes parameters.

Main Methods:

• Development of specific matrix forms for interconversion.
• Application of matrix algebra principles.
• Comparative analysis of ordering conventions.

Main Results:

• Established forms for transforming between Mueller and Hermitian matrices.
• Demonstrated matrix algebra techniques for optical characterization.
• Found no significant advantage of quantum mechanics ordering over optical ordering for Stokes parameters in matrix manipulation.

Conclusions:

• The introduced matrix forms facilitate the conversion between Mueller and Hermitian matrices.
• Matrix algebra provides a robust framework for optical system analysis.
• The choice of ordering for Stokes parameters does not offer a significant advantage for matrix manipulation.