Troubleshooting fiber Bragg grating fabrication with modelingFBG with light launched into long...
Transcript of Troubleshooting fiber Bragg grating fabrication with modelingFBG with light launched into long...
AOPC Sept. 10, 1999Fiber Optics and ElectronicsTechnology Center
Troubleshooting fiber Bragggrating fabrication with modeling
Alessandra Chiareli
Fiber Optics & ElectronicsTechnology Center
Collaborators: Jim Brennan (TSD), Dwayne LaBrake (TSD), Charles Haggans
AOPC Sept. 10, 1999Fiber Optics and ElectronicsTechnology Center
AbstractSeveral approaches are available for modelingfiber Bragg gratings, each having their ownstrengths and weaknesses. In this talk, we willdiscuss how different techniques for solvingcoupled mode theory equations can providecomplementary information that is not easilyattainable by using one technique alone. Thiswork is particularly applicable to very longlength fiber Bragg gratings.
AOPC Sept. 10, 1999Fiber Optics and ElectronicsTechnology Center
Outline• Motivation
• What is a fiber Bragg grating
• Reviewing chromatic dispersion
• FGB as dispersion compensator
• We made one and it does not look good
• Using modeling to understand why and toset fabrication tolerances
• Conclusion
AOPC Sept. 10, 1999Fiber Optics and ElectronicsTechnology Center
dispersioncompensation WDM
erbium doped fibersfor fiber amplifiers
bandwidth
Telecommunications has abandwidth problem
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Introduction
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Cor
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Fiber Axis
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Fiber Core Index ModulationOptical Fiber
Signal In
TransmissionReflection
= 2n b e
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Phase Mask: Direct Imprinting
+1 order
-1 order
UV Beam
Phase Mask
Optical Fiber
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Bragg Gratings:Basic Definitions
Apodization : Tailored Spatial Exposure.
Chirp : Non-UniformBragg Grating Period.
Uniform Profile : UniformBragg Grating Period (typical).
∆n
∆n
∆n
∆n
Apodization : Tailored Spatial Exposure.
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Detection Scheme Does NotResolve Pulses
Optical Fiber
> 400 km
Chromatic Dispersion ProblemChromatic Dispersion Problem
Optical Fiber
> 400 km
AOPC Sept. 10, 1999Fiber Optics and ElectronicsTechnology Center
Dispersion Compensation• The Problem
– Standard single-mode fiber has zero dispersion at the 1310nm transmissionband. It is not corrected at the 1550nm band. Dispersion broadens opticalpulses as they travel in single-mode fiber, limiting the ultimate data ratesupported by fiber.
• A Solution– Recompress the optical pulses using chirped gratings.
Input: Long λ lags short λ
Output: Compressed Pulse
Decreasing grating period(Chirp)
Long λ
Short λ
AOPC Sept. 10, 1999Fiber Optics and ElectronicsTechnology Center
Fiber Bragg GratingDispersion Compensator
AOPC Sept. 10, 1999Fiber Optics and ElectronicsTechnology Center
• to compensate the large bandwidth ∆λ of erbiumfiber amplifiers for long distances of fiber links Lf
with dispersion D (D=17ps/nm/km @ 1550 nm)
DLL n
cf
g eff=
2
∆
Dispersion Compensator Goal
D - dispersion per unit lengthLf - fiber link lengthLg - grating lengthneff - effective indexc - speed of light∆λ - grating bandwidth
•For a 80 km link, need to compensate 1360 ps/nm•For a bandwidth of 7 nm, need about 1 m granting
AOPC Sept. 10, 1999Fiber Optics and ElectronicsTechnology Center
Approach to FBG SpectrumSimulation: coupled-mode theory
()()()()()()()()dRizRzizSzdzdSizSzizRzdz=+=−−
•Good quantitative predictor of diffraction efficiencyand spectral dependence of fiber gratings
CoupleModeamplitudeequations
Where R and S are the forward and backward propagatingmodes, respectively, and σ and κ are coupling coefficients
AOPC Sept. 10, 1999Fiber Optics and ElectronicsTechnology Center
Some Solution Approaches
• Direct numericalintegration ofcoupled mode eqs.– advantage - can
resolve effect of smallscale fabricationerrors
– disadvantage - notfast
• Transfer matrix(piecewise-uniformapproach)– advantage -
reasonable simulationtimes for longgratings
– disadvantage -smallest section mustbe about 50 periods inlength
AOPC Sept. 10, 1999Fiber Optics and ElectronicsTechnology Center
Main Modeling ParametersInput
• fiber geometry(dimension, refractiveindices,photosentivity)
• grating length
• central period
• chirp/bandwidth
• grating strength
• apodization
• phase shifts
Output
• reflection
• transmission
• delay (ripple factor)
• dispersion
AOPC Sept. 10, 1999Fiber Optics and ElectronicsTechnology Center
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What is an ideal dispersioncompensating grating spectrum?
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Grating showing instability infabrication process
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Analysis Resultdirect numerical integration
Measurement in blue & Simulation in Red
AOPC Sept. 10, 1999Fiber Optics and ElectronicsTechnology Center
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reflection (d
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wavelength (nm)
Another fabricated DCG: whythe fuzz?
deviation from linear delay is called delay ripple
AOPC Sept. 10, 1999Fiber Optics and ElectronicsTechnology Center
Transfer Matrix piecewise-uniform approach
We imposed stochastic phase shifts and studied their effecton grating spectra as we varied their max. amplitude andtheir frequency along the grating.
AOPC Sept. 10, 1999Fiber Optics and ElectronicsTechnology Center
Figure of merit
Ripple standard deviation
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reflection (d
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delay ripple (
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AOPC Sept. 10, 1999Fiber Optics and ElectronicsTechnology Center
Delay ripple amplitude as a function of...
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ripple amplitud
phase shift amplitude (degrees)
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number of phase shifts, N
...random phase maximumamplitude
... number of random phase shiftsalong the grating length
The simulation results (circles) follow apower law relationship (line).
Analysis Resulttransfer matrix approach
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Delay ripple
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delay ripple (
wavelength (nm)
measurement: delay ripple across chirpedFBG with light launched into long
wavelength side.
simulation: delay ripple acrosschirped FBG with light launched
into long wavelength side
Delay ripple for chirped FBG with periodic phase shifts across its length is shownbelow. The ripple increases with the optical path length through the grating. The
wavelengths on the launch side show the least amount of ripple both in thesimulations and measurements.
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Ripple Amplitu
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Conclusion
A variety of modeling & computational tools isneeded to get the work done.