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Spectral characterization of differential group delay in uniform fiber Bragg gratings

S. Bette, C. Caucheteur, M. Wuilpart, P. Mégret, R. Garcia-Olcina, S. Sales, and J. Capmany

Open Access Open Access

Abstract

In this paper, we completely study the wavelength dependency of differential group delay (DGD) in uniform fiber Bragg gratings (FBG) exhibiting birefringence. An analytical expression of DGD is established. We analyze the impact of grating parameters (physical length, index modulation and apodization profile) on the wavelength dependency of DGD. Experimental results complete the paper. A very good agreement between theory and experience is reported.

©2005 Optical Society of America

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Figures (4)
Fig. 1.
Fig. 1. Wavelength dependency of DGD and transmission coefficient as a function of Δn

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Fig. 2.
Fig. 2. Wavelength dependency of DGD as a function of L (a) and δn (b)

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Fig. 3.
Fig. 3. Transmission spectrum (a) and wavelength dependency of DGD (b) as a function of the apodization

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Fig. 4.
Fig. 4. Evolution with wavelength of DGD: experimental and simulation results for (a) strong grating and (b) weak grating

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Equations (7)

Equations on this page are rendered with MathJax. Learn more.

n eff , x = n eff + Δn 2 ; n eff , y = n eff − Δn 2
E i , x E i , y = M x e j ξ x M y e j ξ y
E t , x E t , y = J . E i , x E i , y = t x M x e j ξ x t y M y e j ξ y with J = t x 0 0 t y
t x ( y ) = j α x ( y ) σ x ( y ) sinh ( α x ( y ) L ) − j α x ( y ) cosh ( α x ( y ) L )
τ x ( y ) = n eff , x ( y ) c ∙ κ 2 α x ( y ) σ x ( y ) 2 sinh ( α x ( y ) L ) cosh ( α x ( y ) L ) − L κ 2 σ x ( y ) 2 cosh 2 ( α x ( y ) L ) − 1
Δ τ = ∣ Arg ( ρ 1 ρ 2 ) Δω ∣
T ( ω + Δω ) . T − 1 ( ω )
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