Characterization method of the effective phase retardation in linear
birefringent thin sheets

Jhon Pabón; Karol Salazar; Rafael Torres

doi:10.1364/AO.422820

Applied Optics
Vol. 60,
Issue 14,
pp. 4251-4258
(2021)
•https://doi.org/10.1364/AO.422820

Characterization method of the effective phase retardation in linear birefringent thin sheets

Jhon Pabón, Karol Salazar, and Rafael Torres

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Jhon Pabón, Karol Salazar, and Rafael Torres, "Characterization method of the effective phase retardation in linear birefringent thin sheets," Appl. Opt. 60, 4251-4258 (2021)

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Abstract

Characterization of the birefringence of materials offers the opportunity to develop applications and elements to manipulate the polarization of light. We propose a new method for characterizing the effective phase retardation based on the linear birefringent law. The proposed method is flexible and easy to implement; it also determines the retardation introduced by a linear birefringent as from an input polarization state and a specific output state generated by the rotated material. The method is evaluated experimentally by characterizing the birefringence of cellophane samples.

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Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Input State	${\bar{S}}_{1} \pm {\bar{σ}}_{S_{1}}$	${\bar{S}}_{2} \pm {\bar{σ}}_{S_{2}}$	${\bar{S}}_{3} \pm {\bar{σ}}_{S_{3}}$	$P \pm Δ P$
$S_{1}$ ( $2 α$ , 0)	$0.9998 \pm 1 \times 10^{- 4}$	$0.0196 \pm 1 \times 10^{- 4}$	$0.0012 \pm 1 \times 10^{- 4}$	$0.999 \pm 5 \times 10^{- 3}$
$S_{2}$ ( $2 α$ , $2 χ$ )	$0.9706 \pm 1 \times 10^{- 4}$	$1 \times 10^{- 4} \pm 3.7 \times 10^{- 3}$	$- 0.2403 \pm 4 \times 10^{- 4}$	$0.999 \pm 5 \times 10^{- 3}$
$S_{3}$ ( $2 α$ , $2 χ$ )	$0.9346 \pm 1 \times 10^{- 4}$	$1.1 \times 10^{- 3} \pm 1 \times 10^{- 4}$	$- 0.3555 \pm 1 \times 10^{- 4}$	$0.999 \pm 5 \times 10^{- 3}$
$S_{4}$ ( $2 α$ , $2 χ$ )	$0.8656 \pm 2 \times 10^{- 4}$	$4.5 \times 10^{- 3} \pm 9 \times 10^{- 4}$	$- 0.5005 \pm 3 \times 10^{- 4}$	$0.999 \pm 5 \times 10^{- 3}$

Cellophane	${\bar{S}}_{1} \pm {\bar{σ}}_{S_{1}}$	${\bar{S}}_{2} \pm {\bar{σ}}_{S_{2}}$	${\bar{S}}_{3} \pm {\bar{σ}}_{S_{3}}$	$P \pm Δ P$
$S_{u p p e r}$ -Sample 1- $S_{1}$	$- 0.2737 \pm 4 \times 10^{- 4}$	$- 0.0069 \pm 4 \times 10^{- 4}$	$0.9617 \pm 1 \times 10^{- 4}$	$0.999 \pm 5 \times 10^{- 3}$
$S_{u p p e r}$ -Sample 2- $S_{1}$	$- 0.4708 \pm 1.8 \times 10^{- 3}$	$- 0.0151 \pm 2 \times 10^{- 3}$	$0.882 \pm 9 \times 10^{- 4}$	$0.999 \pm 5 \times 10^{- 3}$
$S_{u p p e r}$ -Sample 3- $S_{1}$	$- 0.4062 \pm 3 \times 10^{- 4}$	$0.01 \pm 4 \times 10^{- 4}$	$0.9137 \pm 1 \times 10^{- 4}$	$0.999 \pm 5 \times 10^{- 3}$
$S_{l o w e r}$ -Sample 1- $S_{1}$	$- 0.293 \pm 2 \times 10^{- 4}$	$4.5 \times 10^{- 2} \pm 3 \times 10^{- 4}$	$- 0.955 \pm 1 \times 10^{- 4}$	$0.999 \pm 5 \times 10^{- 3}$
$S_{l o w e r}$ -Sample 2- $S_{1}$	$- 0.4403 \pm 1.3 \times 10^{- 3}$	$3.54 \times 10^{- 2} \pm 1.6 \times 10^{- 3}$	$- 0.8971 \pm 6 \times 10^{- 4}$	$0.999 \pm 5 \times 10^{- 3}$
$S_{l o w e r}$ -Sample 3- $S_{1}$	$- 0.4056 \pm 3 \times 10^{- 4}$	$0.1004 \pm 3 \times 10^{- 4}$	$- 0.9084 \pm 1 \times 10^{- 4}$	$0.999 \pm 5 \times 10^{- 3}$
$S_{l o w e r}$ -Sample 3- $S_{2}$	$- 0.6437 \pm 1.1 \times 10^{- 3}$	$1.29 \times 10^{- 2} \pm 1.8 \times 10^{- 3}$	$- 0.7651 \pm 9 \times 10^{- 4}$	$0.999 \pm 5 \times 10^{- 3}$
$S_{l o w e r}$ -Sample 3- $S_{3}$	$- 0.7354 \pm 1.3 \times 10^{- 3}$	$- 6.66 \times 10^{- 2} \pm 2 \times 10^{- 3}$	$- 0.6743 \pm 1 \times 10^{- 4}$	$0.999 \pm 5 \times 10^{- 3}$
$S_{l o w e r}$ -Sample 3- $S_{4}$	$- 0.8236 \pm 1 \times 10^{- 3}$	$1.59 \times 10^{- 2} \pm 1.8 \times 10^{- 3}$	$- 0.5668 \pm 1.5 \times 10^{- 3}$	$0.999 \pm 5 \times 10^{- 3}$

Cellophane	$δ_{\exp_{1}} + Δ δ_{\exp_{1}}$
Sample 1	$0.5886 π \pm 1 \times 10^{- 3}$
Sample 2	$0.6335 π \pm 9 \times 10^{- 4}$
Sample 3	$0.6565 π \pm 4 \times 10^{- 3}$
$\bar{δ_{\exp}} \pm \bar{Δ δ}$	$0.6262 π \pm 2 \times 10^{- 3}$

Cellophane	$δ_{\exp}^{'} \pm Δ δ^{'}$
Sample 1	$1.4053 π \pm 6 \times 10^{- 4}$
Sample 2	$1.355 π \pm 3.1 \times 10^{- 3}$
Sample 3	$1.3652 π \pm 8 \times 10^{- 4}$
$\bar{{δ^{'}}_{\exp}} \pm \bar{Δ δ^{'}}$	$1.3752 π \pm 1.5 \times 10^{- 3}$
Cellophane	$δ_{\exp_{2}} \pm Δ δ_{\exp_{2}}$
Sample 1	$0.5946 π \pm 6 \times 10^{- 4}$
Sample 2	$0.6449 π \pm 3.1 \times 10^{- 3}$
Sample 3	$0.6347 π \pm 8 \times 10^{- 4}$
$\bar{δ_{\exp}} \pm \bar{Δ δ}$	$0.6247 π \pm 1.5 \times 10^{- 3}$

Cellophane	$δ_{\exp}^{'} \pm Δ δ^{'}$
Sample 3- $S_{l o w e r} - S_{2}$	$1.3546 π \pm 2.8 \times 10^{- 3}$
Sample 3- $S_{l o w e r} - S_{3}$	$1.3515 π \pm 2.5 \times 10^{- 3}$
Sample 3- $S_{l o w e r} - S_{4}$	$1.3587 π \pm 2.3 \times 10^{- 3}$
${\bar{δ}}_{\exp} \pm \bar{Δ} δ$	$1.3549 π \pm 2.5 \times 10^{- 3}$
Cellophane	$δ_{\exp} \pm Δ δ$
Sample 3- $S_{l o w e r} - S_{2}$	$0.6453 π \pm 2.8 \times 10^{- 3}$
Sample 3- $S_{l o w e r} - S_{3}$	$0.6484 π \pm 2.5 \times 10^{- 3}$
Sample 3- $S_{l o w e r} - S_{4}$	$0.6412 π \pm 2.3 \times 10^{- 3}$
$\bar{δ_{\exp}} \pm \bar{Δ δ}$	$0.645 π \pm 2.5 \times 10^{- 3}$

Abstract

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Figures (8)

Tables (5)

Equations (20)

Applied Optics