Analytic inversion of the Mueller-Jones polarization matrices for homogeneous media

Oriol Arteaga; Adolf Canillas

doi:10.1364/OL.35.000559

Optics Letters
Vol. 35,
Issue 4,
pp. 559-561
(2010)
•https://doi.org/10.1364/OL.35.000559

Analytic inversion of the Mueller–Jones polarization matrices for homogeneous media

Oriol Arteaga and Adolf Canillas

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Oriol Arteaga and Adolf Canillas, "Analytic inversion of the Mueller-Jones polarization matrices for homogeneous media," Opt. Lett. 35, 559-561 (2010)

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Abstract

In this Letter we present the equations to calculate the six independent polarization effects of an arbitrary normalized Mueller–Jones matrix corresponding to homogenous media. A comparison between this method and other inversion procedures is discussed, and the application of the analytic inversion to experimental Mueller matrices is illustrated.

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Corrections

Oriol Arteaga and Adolf Canillas, "Analytic inversion of the Mueller–Jones polarization matrices for homogeneous media: erratum," Opt. Lett. 35, 3525-3525 (2010)
https://opg.optica.org/ol/abstract.cfm?uri=ol-35-20-3525

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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	$2 π (κ_{x} - κ_{y}) l / λ_{0}$
(x–y) linear birefringence	LB	$2 π (n_{x} - n_{y}) l / λ_{0}$
45° linear dichroism	${LD}^{'}$	$2 π (κ_{45} - κ_{135}) l / λ_{0}$
45° linear birefringence	${LB}^{'}$	$2 π (n_{45} - n_{135}) l / λ_{0}$
Circular dichroism	CD	$2 π (κ_{-} - κ_{+}) l / λ_{0}$
Circular birefringence	CB	$2 π (n_{-} - n_{+}) l / λ_{0}$

Case	Mueller Matrix	Generation/Analytic Inver.^a	Polar Decomp.	Pseudopolar Decomp.^b
1	$(\begin{matrix} 1 & - 0.0291 & - 0.0111 & 0.0295 \\ - 0.0029 & 0.9993 & - 0.0190 & 0.0049 \\ - 0.0093 & 0.0188 & 0.9957 & 0.0802 \\ 0.0305 & - 0.0073 & - 0.0804 & 0.9963 \end{matrix})$	$CD = 0.0300$	$CD = 0.0295$	$CD = 0.0300$
		$CB = - 0.0189$	$CB = - 0.0189$	$CB = - 0.0189$
		$LD = 0.0289$	$LD = 0.0291$	$LD = 0.0289$
		$LB = - 0.0805$	$LB = - 0.0805$	$LB = - 0.0805$
		${LD}^{'} = 0.0102$	${LD}^{'} = 0.0111$	${LD}^{'} = 0.0102$
		${LB}^{'} = 0.0061$	${LB}^{'} = 0.0061$	${LB}^{'} = 0.0061$
2	$(\begin{matrix} 1 & - 0.5074 & 0.2220 & - 0.5061 \\ - 0.6388 & 0.7389 & 0.0525 & 0.5444 \\ - 0.3932 & - 0.0750 & 0.6392 & - 0.4212 \\ 0.0156 & - 0.3780 & 0.2740 & 0.4684 \end{matrix})$	$CD = 0.0202$	$CD = - 0.3127$	$CD = 0.0337$
		$CB = 0.0778$	$CB = 0.0725$	$CB = 0.0746$
		$LD = 0.8289$	$LD = 0.7871$	$LD = 0.8428$
		$LB = 0.4805$	$LB = 0.4525$	$LB = 0.4481$
		${LD}^{'} = - 0.5102$	${LD}^{'} = - 0.4335$	${LD}^{'} = - 0.5172$
		${LB}^{'} = 0.6061$	${LB}^{'} = 0.5599$	${LB}^{'} = 0.5639$

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	$2 π (κ_{x} - κ_{y}) l / λ_{0}$
(x–y) linear birefringence	LB	$2 π (n_{x} - n_{y}) l / λ_{0}$
45° linear dichroism	${LD}^{'}$	$2 π (κ_{45} - κ_{135}) l / λ_{0}$
45° linear birefringence	${LB}^{'}$	$2 π (n_{45} - n_{135}) l / λ_{0}$
Circular dichroism	CD	$2 π (κ_{-} - κ_{+}) l / λ_{0}$
Circular birefringence	CB	$2 π (n_{-} - n_{+}) l / λ_{0}$

Case	Mueller Matrix	Generation/Analytic Inver.^a	Polar Decomp.	Pseudopolar Decomp.^b
1	$(\begin{matrix} 1 & - 0.0291 & - 0.0111 & 0.0295 \\ - 0.0029 & 0.9993 & - 0.0190 & 0.0049 \\ - 0.0093 & 0.0188 & 0.9957 & 0.0802 \\ 0.0305 & - 0.0073 & - 0.0804 & 0.9963 \end{matrix})$	$CD = 0.0300$	$CD = 0.0295$	$CD = 0.0300$
		$CB = - 0.0189$	$CB = - 0.0189$	$CB = - 0.0189$
		$LD = 0.0289$	$LD = 0.0291$	$LD = 0.0289$
		$LB = - 0.0805$	$LB = - 0.0805$	$LB = - 0.0805$
		${LD}^{'} = 0.0102$	${LD}^{'} = 0.0111$	${LD}^{'} = 0.0102$
		${LB}^{'} = 0.0061$	${LB}^{'} = 0.0061$	${LB}^{'} = 0.0061$
2	$(\begin{matrix} 1 & - 0.5074 & 0.2220 & - 0.5061 \\ - 0.6388 & 0.7389 & 0.0525 & 0.5444 \\ - 0.3932 & - 0.0750 & 0.6392 & - 0.4212 \\ 0.0156 & - 0.3780 & 0.2740 & 0.4684 \end{matrix})$	$CD = 0.0202$	$CD = - 0.3127$	$CD = 0.0337$
		$CB = 0.0778$	$CB = 0.0725$	$CB = 0.0746$
		$LD = 0.8289$	$LD = 0.7871$	$LD = 0.8428$
		$LB = 0.4805$	$LB = 0.4525$	$LB = 0.4481$
		${LD}^{'} = - 0.5102$	${LD}^{'} = - 0.4335$	${LD}^{'} = - 0.5172$
		${LB}^{'} = 0.6061$	${LB}^{'} = 0.5599$	${LB}^{'} = 0.5639$

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Equations (19)

Optics Letters