Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group

Theory of group delay ripple generated by chirped fiber gratings

Open Access Open Access

Abstract

The theory of the group delay ripple generated by apodized chirped fiber gratings is developed using the analogy between noisy gratings and superstructure Bragg gratings. It predicts the fundamental cutoff of the high frequency spatial noise of grating parameters in excellent agreement with the experimental data. We find simple general relationship between the high-frequency ripple in the grating period and the group delay ripple. In particular, we show that the amplitude of a single-frequency group delay ripple component changes with grating period chirp, C, as C -3/2 and is proportional to the grating index modulation, while its phase shift and period changes as C -1 .

©2002 Optical Society of America

Full Article  |  PDF Article
More Like This
Group-delay ripple correction in chirped fiber Bragg gratings

M. Sumetsky, P. I. Reyes, P. S. Westbrook, N. M. Litchinitser, B. J. Eggleton, Y. Li, R. Deshmukh, and C. Soccolich
Opt. Lett. 28(10) 777-779 (2003)

Impact of group delay ripples of chirped fiber grating on optical beamforming networks

Bo Zhou, Xiaoping Zheng, Xianbin Yu, Hanyi Zhang, Yili Guo, and Bingkun Zhou
Opt. Express 16(4) 2398-2404 (2008)

Reduction of group delay ripple of multi-channel chirped fiber gratings using adiabatic UV correction

P. I. Reyes, M. Sumetsky, N. M. Litchinitser, and P. S. Westbrook
Opt. Express 12(12) 2676-2687 (2004)

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig 1.
Fig 1. Reflection of light from chirped Bragg fiber grating
Fig. 2.
Fig. 2. Physical picture of the GDR cutoff effect
Fig 3.
Fig 3. a – comparison of the single-harmonic GDR amplitude calculated from Eq. (4) with numerical calculations and with classical ray approximation Eq. (2) for the amplitude of spatial ripple 0.0025 nm; b – fitting the numerically calculated GDR amplitude vs. chirp dependence (squares) by C -3/2 power law (solid lines) for the spatial period ripple 5 mm and 20 mm.
Fig. 4.
Fig. 4. Ripple in grating parameters and corresponding GDR
Fig.5.
Fig.5. a - Experimentally measured group delay and GDR of a typical CFBG; b - Fourier spectrum of this GDR calculated for different bandwidths ∆λ measured from the high-wavelength edge of the reflection band and demonstrating the cutoff frequencies coincident with the ones predicted by Eq. (4).

Equations (21)

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

Λ ( z ) = Λ 0 + C ( z z 0 ) + Δ Λ ( z ) ,
Δ Λ ( z ) = q > 0 Δ Λ q exp [ i q ( z z 0 ) ] + c . c . ,
Δ τ ( λ ) = 2 n 0 c 0 C Δ Λ ( z t ) , z t = z 0 + ( λ 2 n 0 Λ 0 ) 2 n 0 C ,
2 k eff ( z st ) = q , k eff ( z ) = π 2 n 0 Λ 0 2 [ Δ λ 2 n 0 C ( z z 0 ) ] 2 Λ 0 2 Δ n 2 ( z ) .
q c = π Δ λ n 0 Λ 0 2 , ν c = π Δ λ 2 C n 0 2 Λ 0 2 .
Δ τ ( Δ λ ) = 0 < q < q c Δ τ q exp [ i q Δ λ 2 n 0 C ] + c . c . ,
Δ τ q = 2 i π Δ n c 0 ( 2 C ) 3 / 2 exp ( i q 2 Λ 0 2 4 π C ) Δ Λ q .
n ( z ) = n 0 + Δ n cos ( 2 π Λ 0 z + 2 π Λ 0 2 Z d z ( Λ ( z ) ) Λ 0 )
u ( z ) = + i [ δ ( z ) u ( z ) + κ ( z ) v ( z ) ]
v ( z ) = i [ δ ( z ) v ( z ) + κ ( z ) u ( z ) ]
δ ( z ) = β π Λ 0 2 ( Λ ( z ) Λ 0 ) , κ ( z ) = π Δ n ( z ) 2 n 0 Λ 0 ,
β = 2 π n 0 λ π Λ 0 π Δ λ 2 n 0 Λ 0 2
Δ τ = Δ τ 1 + Δ τ 2 , Δ τ i = 2 π n 0 c 0 Λ 0 2 d d β Re [ z 0 d x Δ Λ ( z ) G i ( z ) ]
G 1 = u 0 + ( u 0 + ) * + u 0 ( u 0 ) * , G 2 = r 0 1 u 0 + ( u 0 ) * + r 0 u 0 ( u 0 + ) *
( u 0 ± ( z ) v 0 ± ( z ) ) = e ± i z 0 z k eff ( z ) d z , 2 Q ( z ) ( Q ( z ) ± 1 Q ( z ) ± 1 ) ,
Q ( z ) = δ 0 ( z ) κ ( z ) δ 0 ( z ) + κ ( z ) , k eff ( z ) = δ 0 2 ( z ) κ 2 ( z )
Δ τ = Δ τ 1 + Δ τ 2
Δ τ 1 = π n 0 c 0 Λ 0 2 q > 0 Δ Λ q d d β z 0 z t d z δ 0 ( z ) k eff ( z ) e i q ( z z 0 ) + c . c .
Δ τ 2 = π n 0 2 c 0 Λ 0 2 q > 0 Δ Λ q d d β z 0 z t d z κ ( z ) k eff ( z ) ( r 0 1 e i q ( z z 0 ) + 2 i z 0 z k eff ( z ) d z + r 0 e i q ( z z 0 ) 2 i z 0 z k eff ( z ) d z ) + c . c .
2 k eff ( z st ) = q .
z t = Λ 0 2 β π C , z st = Λ 0 2 π C ( β q 2 ) .
Select as filters


Select Topics Cancel
© Copyright 2024 | Optica Publishing Group. All Rights Reserved