Measurement of phase and group refractive indices and dispersion of thermo-optic and strain-optic coefficients of optical fibers using weak fiber Bragg gratings

J. L. Cruz; Y. O. Barmenkov; A. Díez; M. V. Andres

doi:10.1364/AO.418049

Applied Optics
Vol. 60,
Issue 10,
pp. 2824-2832
(2021)
•https://doi.org/10.1364/AO.418049

Measurement of phase and group refractive indices and dispersion of thermo-optic and strain-optic coefficients of optical fibers using weak fiber Bragg gratings

J. L. Cruz, Y. O. Barmenkov, A. Díez, and M. V. Andres

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J. L. Cruz, Y. O. Barmenkov, A. Díez, and M. V. Andres, "Measurement of phase and group refractive indices and dispersion of thermo-optic and strain-optic coefficients of optical fibers using weak fiber Bragg gratings," Appl. Opt. 60, 2824-2832 (2021)

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- Fiber Optics, Fiber Sensors, and Optical Communications
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About this Article
History
- Original Manuscript: December 22, 2020
- Revised Manuscript: February 8, 2021
- Manuscript Accepted: March 5, 2021
- Published: March 23, 2021

Abstract

In this work we report on the measurement, with record accuracy, of the absolute modal effective refraction index (phase index) of single-mode optical fibers by using Bragg gratings. We also demonstrate a new method to measure the group index of the fibers from the grating’s Bragg wavelength. We present as well the characterization of the thermo-optic and strain-optic coefficients as a function of the wavelength; the values we have obtained are the closest to those of pristine fiber measured with gratings technology so far. The phase index is measured with a set of gratings in the wavelength ranges from 1509 to 1563 nm, and the group index is obtained from the wavelength dependence of the phase index. Very weak gratings with reflectivity down to ${{1}}{{{0}}^{- 3}}$ have been used in order to minimize the perturbation of the pristine fiber. Results are presented at a temperature of 22°C and zero strain after preliminary calibration of the thermo-optic and strain-optic coefficients as a function of the wavelength. Accuracies better than ${{3}} \times {{1}}{{{0}}^{- 5}}$ and ${{7}} \times {{1}}{{{0}}^{- 4}}$ have been achieved for the phase and group indices, respectively. It is also shown that the main source of error relates to the uncertainty in pitch of the phase masks used for grating inscription. The technique is useful for testing different kinds of fibers including telecommunication, amplifying, and polarization maintaining.

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			Fiber			Wavelength
UV Induced	Phase Mask	Angles	Uniformity	Temperature	Zero Strain	Measurement	Overall
$0.2 \times 1 0^{- 5}$	$1.35 \times 1 0^{- 5}$	$0.09 \times 1 0^{- 5}$	$(0.2 t o 1) \times 1 0^{- 5}$	$0.43 \times 1 0^{- 5}$	$0.06 \times 1 0^{- 5}$	$0.33 \times 1 0^{- 5}$	$\pm (1.6 t o 1.9) \times 10^{- 5}$

	$ζ = A + B (λ - 1535)$			$p_{e} = A + B (λ - 1535)$
	A ( $K^{- 1})$	B ( $K^{- 1} n m^{- 1}$ )	Standard Error	A	B ( $n m^{- 1}$ )	Standard Error
SMF28	$5.99 \times 1 0^{- 6}$	$2.6 \times 1 0^{- 9}$	$\pm 0.05 \times 1 0^{- 6}$	$0.215$	$2 \times 1 0^{- 5}$	$\pm 0.004$
M5	$6.27 \times 1 0^{- 6}$	$2.7 \times 1 0^{- 9}$	$\pm 0.04 \times 1 0^{- 6}$	$0.218$	$- 9 \times 1 0^{- 5}$	$\pm 0.003$
HB1250 fast	$6.34 \times 1 0^{- 6}$	$5.0 \times 1 0^{- 9}$	$\pm 0.04 \times 1 0^{- 6}$	$0.203$	$0.3 \times 1 0^{- 5}$	$\pm 0.003$
HB1250 slow	$6.07 \times 1 0^{- 6}$	$4.2 \times 1 0^{- 9}$	$\pm 0.04 \times 1 0^{- 6}$	$0.199$	$- 13 \times 1 0^{- 5}$	$\pm 0.003$

	$n_{e f f} = A + B (λ - 1535)$			Group Index
	A	B ( $n m^{- 1}$ )	Standard Error	Group Index	Standard Error
SMF28	1.44749	$- 1.334 \times 1 0^{- 5}$	$\pm 2 \times 1 0^{- 5}$	$1.4680$	$\pm 0 . 0006$
M5	1.44903	$- 1.868 \times 1 0^{- 5}$	$\pm 3 \times 1 0^{- 5}$	$1.4777$	$\pm 0 . 0007$
HB1250 fast	1.44770	$- 1.665 \times 1 0^{- 5}$	$\pm 3 \times 1 0^{- 5}$	$1.4733$	$\pm 0 . 0007$
HB1250 slow	1.44805	$- 1.672 \times 1 0^{- 5}$	$\pm 3 \times 1 0^{- 5}$	$1.4737$	$\pm 0 . 0007$

Parameter	Value	Standard Error	Fiber or Material	Wavelength (nm)	Method	Reference
Phase index	1.44750	$2 \times 1 0^{- 5}$	SMF 28e+	1534.06	Gratings	[t.w.] ^a
Phase index	1.44728	$14 \times 1 0^{- 5}$	SMF 28	1534.06	Gratings	[18]
Refractive index	1.504426	$1.1 \times 1 0^{- 5}$	Soda glass	1592	Interferometer	[8]
Group index	1.4680	0.0006	SMF 28e+	C band	Gratings	[t.w.] ^a
Group index	1.4679	n. s. ^a	SMF 28 e+	C band	n.s. ^a	[37]
Group index	1.4393	0.0007	PCF ^a	632.82	Interferometer	[9,10]
$ζ$ ( $K^{- 1}$ )	$6.03 \times 1 0^{- 6}$	$0.05 \times 1 0^{- 6}$	SMF 28e+	1548.7	Gratings	[t.w.] ^a
$ζ$ ( $K^{- 1}$ )	$6.16 \times 1 0^{- 6}$	n.s. ^a	n.s. ^a	1548.7	Estimation	[33]
$ζ$ ( $K^{- 1}$ )	$5.32 \times 1 0^{- 6}$	n.s. ^a	SMF 28	1548.7	Gratings	[32]
$ζ$ ( $K^{- 1}$ )	$7.5 \times 1 0^{- 6}$	$0.3 \times 1 0^{- 6}$	SMF 28	1544.2	Gratings	[34]
$p_{e}$	0.215	0.004	SMF 28e+	1533.7	Gratings	[t.w.] ^a
$p_{e}$	0.22	n.s. ^a	n.s. ^a	1533.7	Estimation	[33]
$p_{e}$	0.28	0.02	SMF 28	1536.1	Gratings	[34]
$p_{e}$	0.205	0.004	SMF 28	1533.7	Gratings	[36]

			Fiber			Wavelength
UV Induced	Phase Mask	Angles	Uniformity	Temperature	Zero Strain	Measurement	Overall
$0.2 \times 1 0^{- 5}$	$1.35 \times 1 0^{- 5}$	$0.09 \times 1 0^{- 5}$	$(0.2 t o 1) \times 1 0^{- 5}$	$0.43 \times 1 0^{- 5}$	$0.06 \times 1 0^{- 5}$	$0.33 \times 1 0^{- 5}$	$\pm (1.6 t o 1.9) \times 10^{- 5}$

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Applied Optics