Numerical analysis of the harmonic components of the Bragg wavelength content in spectral responses of apodized fiber Bragg gratings written by means of a phase mask with a variable phase step height

Tomasz Osuch

doi:10.1364/JOSAA.33.000172

Journal of the Optical Society of America A
Vol. 33,
Issue 2,
pp. 172-178
(2016)
•https://doi.org/10.1364/JOSAA.33.000172

Numerical analysis of the harmonic components of the Bragg wavelength content in spectral responses of apodized fiber Bragg gratings written by means of a phase mask with a variable phase step height

Tomasz Osuch

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Tomasz Osuch, "Numerical analysis of the harmonic components of the Bragg wavelength content in spectral responses of apodized fiber Bragg gratings written by means of a phase mask with a variable phase step height," J. Opt. Soc. Am. A 33, 172-178 (2016)

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Table of Contents Category
- Diffraction and Gratings
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About this Article
History
- Original Manuscript: October 16, 2015
- Revised Manuscript: December 1, 2015
- Manuscript Accepted: December 7, 2015
- Published: January 6, 2016

Abstract

The influence of the complex interference patterns created by a phase mask with variable diffraction efficiency in apodized fiber Bragg grating (FBGs) formation on their reflectance spectra is studied. The effect of the significant contributions of the zeroth and higher ( $m > \pm 1$ ) diffraction orders on the Bragg wavelength peak and its harmonic components is analyzed numerically. The results obtained for Gaussian and tanh apodization profiles are compared with similar data calculated for a uniform grating. It is demonstrated that when an apodized FBG is written using a phase mask with variable diffraction efficiency, significant enhancement of the harmonic components and a reduction of the Bragg wavelength peak in the grating spectral response are observed. This is particularly noticeable for the Gaussian apodization profile due to the substantial contributions of phase mask sections with relatively small phase steps in the FBG formation.

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	$η_{m, n} (%)$			$Δ l_{n}$ and $Δ l_{N}$
$ϕ_{n}$	0	$\pm 1$	$\pm 3$	Gaussian	tanh
$π$	0.0	40.5	4.5	0.151	0.363
$7 π / 8$	3.8	39.0	4.3	0.063	0.039
$6 π / 8$	14.6	34.6	3.8	0.045	0.019
$5 π / 8$	30.9	28.0	3.1	0.045	0.015
$4 π / 8$	50.0	20.3	2.3	0.045	0.012
$3 π / 8$	69.1	12.5	1.4	0.051	0.012
$2 π / 8$	85.4	5.9	0.7	0.063	0.015
$π / 8$	96.2	1.5	0.2	0.111	0.026

$S (Λ_{PM} / Λ$ )
	$Λ_{PM}$	$Λ_{PM} / 2$	$Λ_{PM} / 3$	$Λ_{PM} / 4$	$Λ_{PM} / 5$	$Λ_{PM} / 6$
$ϕ_{n}$	$2 λ_{B}$	$λ_{B}$	$2 λ_{B} / 3$	$λ_{B} / 2$	$2 λ_{B} / 5$	$λ_{B} / 3$
$π$	0.002	0.398	0.001	0.006	0.000	0.044
$7 π / 8$	0.057	0.383	0.001	0.006	0.000	0.042
$6 π / 8$	0.105	0.340	0.001	0.005	0.000	0.037
$5 π / 8$	0.137	0.275	0.001	0.004	0.000	0.030
$4 π / 8$	0.148	0.199	0.001	0.003	0.000	0.022
$3 π / 8$	0.137	0.123	0.000	0.002	0.000	0.014
$2 π / 8$	0.105	0.058	0.000	0.001	0.000	0.006
$π / 8$	0.057	0.015	0.000	0.000	0.000	0.002

$S (Λ_{PM} / Λ$ )
	$Λ_{PM}$	$Λ_{PM} / 2$	$Λ_{PM} / 3$	$Λ_{PM} / 4$	$Λ_{PM} / 5$	$Λ_{PM} / 6$
	$2 λ_{B}$	$λ_{B}$	$2 λ_{B} / 3$	$λ_{B} / 2$	$2 λ_{B} / 5$	$λ_{B} / 3$
Gaussian	0.083	0.205	0.001	0.003	0.000	0.023
tanh	0.027	0.350	0.001	0.006	0.000	0.039
Uniform	0.002	0.398	0.001	0.006	0.000	0.044

	$η_{m, n} (%)$			$Δ l_{n}$ and $Δ l_{N}$
$ϕ_{n}$	0	$\pm 1$	$\pm 3$	Gaussian	tanh
$π$	0.0	40.5	4.5	0.151	0.363
$7 π / 8$	3.8	39.0	4.3	0.063	0.039
$6 π / 8$	14.6	34.6	3.8	0.045	0.019
$5 π / 8$	30.9	28.0	3.1	0.045	0.015
$4 π / 8$	50.0	20.3	2.3	0.045	0.012
$3 π / 8$	69.1	12.5	1.4	0.051	0.012
$2 π / 8$	85.4	5.9	0.7	0.063	0.015
$π / 8$	96.2	1.5	0.2	0.111	0.026

$S (Λ_{PM} / Λ$ )
	$Λ_{PM}$	$Λ_{PM} / 2$	$Λ_{PM} / 3$	$Λ_{PM} / 4$	$Λ_{PM} / 5$	$Λ_{PM} / 6$
$ϕ_{n}$	$2 λ_{B}$	$λ_{B}$	$2 λ_{B} / 3$	$λ_{B} / 2$	$2 λ_{B} / 5$	$λ_{B} / 3$
$π$	0.002	0.398	0.001	0.006	0.000	0.044
$7 π / 8$	0.057	0.383	0.001	0.006	0.000	0.042
$6 π / 8$	0.105	0.340	0.001	0.005	0.000	0.037
$5 π / 8$	0.137	0.275	0.001	0.004	0.000	0.030
$4 π / 8$	0.148	0.199	0.001	0.003	0.000	0.022
$3 π / 8$	0.137	0.123	0.000	0.002	0.000	0.014
$2 π / 8$	0.105	0.058	0.000	0.001	0.000	0.006
$π / 8$	0.057	0.015	0.000	0.000	0.000	0.002

Abstract

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Journal of the Optical Society of America A