Mueller matrix polarimetry of bianisotropic materials [Invited]

Oriol Arteaga; Bart Kahr

doi:10.1364/JOSAB.36.000F72

Journal of the Optical Society of America B
Vol. 36,
Issue 8,
pp. F72-F83
(2019)
•https://doi.org/10.1364/JOSAB.36.000F72

Mueller matrix polarimetry of bianisotropic materials [Invited]

Oriol Arteaga and Bart Kahr

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Oriol Arteaga and Bart Kahr, "Mueller matrix polarimetry of bianisotropic materials [Invited]," J. Opt. Soc. Am. B 36, F72-F83 (2019)

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History
- Original Manuscript: March 4, 2019
- Revised Manuscript: April 18, 2019
- Manuscript Accepted: April 18, 2019
- Published: May 17, 2019

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Abstract

Mueller matrix polarimetry is a powerful optical technique for characterization of both anisotropic and bianisotropic materials. This review emphasizes methods for the interpretation of measured Mueller matrices, from the meanings of matrix symmetries, to ab initio calculations of Mueller matrices that begin with Maxwell’s equations operating on materials with permittivity, permeability, and magnetoelectric constitutive tensors. We present an overview of polarimetry measurements in crystals as well as metamaterials that have optically responsive features on the order of the wavelength of visible light. Examples of the full measurement of the constitutive tensors of bianisotropic media from the analysis of their Mueller matrices, collected in either transmission or reflection, are illustrated for natural crystals, polycrystals, and nanofabricated metamaterials. Experimental and theoretical research into the complex optical responses of bianisotropic materials with polarized light is best expressed in terms of the Mueller matrix, as it offers an unambiguous and mathematically robust platform for analysis of light–matter interactions.

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Material	Symmetry Description	Mueller Matrix Symmetry
Isotropic	Rotational symmetry and mirror symmetry	$(\begin{matrix} M_{00} & 0 & 0 & 0 \\ 0 & M_{11} & 0 & 0 \\ 0 & 0 & M_{11} & 0 \\ 0 & 0 & 0 & M_{33} \end{matrix})$
Biisotropic	Rotational symmetry	$(\begin{matrix} M_{00} & 0 & 0 & M_{03} \\ 0 & M_{11} & M_{12} & 0 \\ 0 & - M_{12} & M_{11} & 0 \\ M_{30} & 0 & 0 & M_{33} \end{matrix})$
Anisotropic	Mirror symmetry	$(\begin{matrix} M_{00} & M_{01} & M_{02} & M_{03} \\ M_{01} & M_{11} & M_{12} & M_{13} \\ M_{02} & M_{12} & M_{22} & M_{23} \\ - M_{30} & - M_{13} & - M_{23} & M_{33} \end{matrix})$
Bianisotropic	No symmetry	$(\begin{matrix} M_{00} & M_{01} & M_{02} & M_{03} \\ M_{10} & M_{11} & M_{12} & M_{13} \\ M_{20} & M_{21} & M_{22} & M_{23} \\ M_{30} & M_{31} & M_{32} & M_{33} \end{matrix})$

Material	Symmetry Transmission	Symmetry Backreflection
Isotropic	$(\begin{matrix} M_{00} & 0 & 0 & 0 \\ 0 & M_{11} & 0 & 0 \\ 0 & 0 & M_{11} & 0 \\ 0 & 0 & 0 & M_{33} \end{matrix})$	$(\begin{matrix} M_{00} & 0 & 0 & 0 \\ 0 & M_{11} & 0 & 0 \\ 0 & 0 & - M_{11} & 0 \\ 0 & 0 & 0 & M_{33} \end{matrix})$
Biisotropic	$(\begin{matrix} M_{00} & 0 & 0 & M_{03} \\ 0 & M_{11} & M_{12} & 0 \\ 0 & - M_{12} & M_{11} & 0 \\ M_{03} & 0 & 0 & M_{33} \end{matrix})$	$(\begin{matrix} M_{00} & 0 & 0 & M_{03} \\ 0 & M_{11} & 0 & 0 \\ 0 & 0 & - M_{11} & 0 \\ M_{03} & 0 & 0 & M_{33} \end{matrix})$
Anisotropic	$(\begin{matrix} M_{00} & M_{01} & 0 & 0 \\ M_{01} & M_{11} & 0 & 0 \\ 0 & 0 & M_{22} & M_{23} \\ 0 & 0 & - M_{23} & M_{33} \end{matrix})$	$(\begin{matrix} M_{00} & M_{01} & M_{02} & M_{03} \\ M_{01} & M_{11} & M_{12} & M_{13} \\ - M_{02} & - M_{12} & M_{22} & M_{23} \\ M_{03} & M_{13} & - M_{23} & M_{33} \end{matrix})$
Bianisotropic	$(\begin{matrix} M_{00} & M_{01} & M_{02} & M_{03} \\ M_{01} & M_{11} & M_{12} & M_{13} \\ - M_{02} & - M_{12} & M_{22} & M_{23} \\ M_{03} & M_{13} & - M_{23} & M_{33} \end{matrix})$	$(\begin{matrix} M_{00} & M_{01} & M_{02} & M_{03} \\ M_{01} & M_{11} & M_{12} & M_{13} \\ - M_{02} & - M_{12} & M_{22} & M_{23} \\ M_{03} & M_{13} & - M_{23} & M_{33} \end{matrix})$

Effect	Symbol	Definition^a
Isotropic phase retardation	$η$	$2 π n l / λ_{0}$
Isotropic amplitude absorption	$k$	$2 π κ l / λ_{0}$
( $x - y$ ) linear dichroism	LD	$\frac{2 π}{λ_{0}} (κ_{x} - κ_{y}) l$
( $x - y$ ) linear birefringence	LB	$\frac{2 π}{λ_{0}} (n_{x} - n_{y}) l$
45° linear dichroism	${LD}^{'}$	$\frac{2 π}{λ_{0}} (κ_{45} - κ_{135}) l$
45° linear birefringence	${LB}^{'}$	$\frac{2 π}{λ_{0}} (n_{45} - n_{135}) l$
Circular dichroism	CD	$\frac{2 π}{λ_{0}} (κ_{-} - κ_{+}) l$
Circular birefringence	CB	$\frac{2 π}{λ_{0}} (n_{-} - n_{+}) l$

Material	Symmetry Description	Mueller Matrix Symmetry
Isotropic	Rotational symmetry and mirror symmetry	$(\begin{matrix} M_{00} & 0 & 0 & 0 \\ 0 & M_{11} & 0 & 0 \\ 0 & 0 & M_{11} & 0 \\ 0 & 0 & 0 & M_{33} \end{matrix})$
Biisotropic	Rotational symmetry	$(\begin{matrix} M_{00} & 0 & 0 & M_{03} \\ 0 & M_{11} & M_{12} & 0 \\ 0 & - M_{12} & M_{11} & 0 \\ M_{30} & 0 & 0 & M_{33} \end{matrix})$
Anisotropic	Mirror symmetry	$(\begin{matrix} M_{00} & M_{01} & M_{02} & M_{03} \\ M_{01} & M_{11} & M_{12} & M_{13} \\ M_{02} & M_{12} & M_{22} & M_{23} \\ - M_{30} & - M_{13} & - M_{23} & M_{33} \end{matrix})$
Bianisotropic	No symmetry	$(\begin{matrix} M_{00} & M_{01} & M_{02} & M_{03} \\ M_{10} & M_{11} & M_{12} & M_{13} \\ M_{20} & M_{21} & M_{22} & M_{23} \\ M_{30} & M_{31} & M_{32} & M_{33} \end{matrix})$

Material	Symmetry Transmission	Symmetry Backreflection
Isotropic	$(\begin{matrix} M_{00} & 0 & 0 & 0 \\ 0 & M_{11} & 0 & 0 \\ 0 & 0 & M_{11} & 0 \\ 0 & 0 & 0 & M_{33} \end{matrix})$	$(\begin{matrix} M_{00} & 0 & 0 & 0 \\ 0 & M_{11} & 0 & 0 \\ 0 & 0 & - M_{11} & 0 \\ 0 & 0 & 0 & M_{33} \end{matrix})$
Biisotropic	$(\begin{matrix} M_{00} & 0 & 0 & M_{03} \\ 0 & M_{11} & M_{12} & 0 \\ 0 & - M_{12} & M_{11} & 0 \\ M_{03} & 0 & 0 & M_{33} \end{matrix})$	$(\begin{matrix} M_{00} & 0 & 0 & M_{03} \\ 0 & M_{11} & 0 & 0 \\ 0 & 0 & - M_{11} & 0 \\ M_{03} & 0 & 0 & M_{33} \end{matrix})$
Anisotropic	$(\begin{matrix} M_{00} & M_{01} & 0 & 0 \\ M_{01} & M_{11} & 0 & 0 \\ 0 & 0 & M_{22} & M_{23} \\ 0 & 0 & - M_{23} & M_{33} \end{matrix})$	$(\begin{matrix} M_{00} & M_{01} & M_{02} & M_{03} \\ M_{01} & M_{11} & M_{12} & M_{13} \\ - M_{02} & - M_{12} & M_{22} & M_{23} \\ M_{03} & M_{13} & - M_{23} & M_{33} \end{matrix})$
Bianisotropic	$(\begin{matrix} M_{00} & M_{01} & M_{02} & M_{03} \\ M_{01} & M_{11} & M_{12} & M_{13} \\ - M_{02} & - M_{12} & M_{22} & M_{23} \\ M_{03} & M_{13} & - M_{23} & M_{33} \end{matrix})$	$(\begin{matrix} M_{00} & M_{01} & M_{02} & M_{03} \\ M_{01} & M_{11} & M_{12} & M_{13} \\ - M_{02} & - M_{12} & M_{22} & M_{23} \\ M_{03} & M_{13} & - M_{23} & M_{33} \end{matrix})$

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Journal of the Optical Society of America B