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Advanced Design and Fabrication Techniquesof Fiber Grating Devices
Yinchieh Lai (賴暎杰 )Institute of Electro-Optical Engineering
National Chiao Tung UniversityHsinchu, Taiwan, R.O.C.
[Outline]1. Introduction2. Overlap-Step-Scan Exposure Fabrication of Fiber Bragg Gratings3. True Apodization Achieved by the Polarization Control of UV Beam4. Evolutionary Programming Design of Optimal Fiber Gratings5. Conclusions
What are Fiber Gratings ?
Fiber grating: index grating (induced by UV) on the fiber core.
Slanted FBG
ReflectionFilter Transmission Filter
Fiber Bragg Grating(FBG)
Long Period Grating(LPG)
Standard Fiber Gratings and Applications
λ1, λ2 … λn λ1, λ2 … λnFBG at λi
Drop λi Add λi
Circulator Circulator
diode laser
Non-AR coatingPump laser
3% reflectivityEDFA
LPGSlanted FBGChirped FBG
(1) DWDM OADM
(2) Dispersion Compensation
(3) EDFA gain flattening
(4) Fiber sensor
ASEsource
wavelengthmeasurement
FBG FBG FBG
(5) Pump laser stabilization
Advantages of FBG OADM
Data source: Southampton Photonics
-35
-30
-25
-20
-15
-10
-5
0
5
(a)
Ref
lect
ion
(dB)
-100
-50
0
50
100
150
200
250
300
Time delay (ps)
1547.2 1547.6 1548.0 1548.4 1548.8 1549.2-35
-30
-25
-20
-15
-10
-5
0
5
(b)
W avelength (nm)
Ref
lect
ion
(dB)
-100
-50
0
50
100
150
200
250
300
Time delay (ps)
15 20 25 30 35
DLP method LS fitting
ng Position (mm)
Dispersionless FBG
Gaussian Apodization
0.2 0.4 0.6 0.8 1Position
0.2
0.4
0.6
0.8
1
Index Difference
DispersionlessFBG by LP
Require: 1. Constant dc-index (True Apodization). 2. Special ac-index apodization. 3. Multiple phase-shifts
0.0
0.5
1.0
Phas
e (x
ra
d)π
0 5 10
0.0
0.2
0.4
0.6
0.8
1.0
Grati
Nor
mal
ized
Ref
ract
ive
Inde
x Pr
ofile
Index envelope
Fiber Bragg Grating (FBG) as 1-D photonic crystalExposureMethods (a)
(d)
(e)
(b)
(c)
(f)
(g)
1549.6 1550.0 1550.4 1550.8 1551.2Wavelength (nm)
0.0
0.2
0.4
0.6
0.8
1.0
Ref
lect
ivity
0.0
0.2
0.4
0.6
0.8
1.0
λΒ = 2neffΛ
ΛReflectionFilter
Photonicbandgap
FBG
Tran
smis
sion
LPG
Double exposure method for achieving true apodization
phase mask
Optical SpectrumAnalyzer
ASE lightsource
UV laserbeam
Cylindrical lens
2x2 couplerExcimer laser(248 or 193nmwavelength) Optical
SpectrumAnalyzer
Multiple exposureby moving the
phase mask
0.2 0.4 0.6 0.8 1Position
0.2
0.4
0.6
0.8
1
index difference
0.2 0.4 0.6 0.8 1Position
0.2
0.4
0.6
0.8
1
Index Difference
Ordinary Apodization True Apodization
1552.0 1552.4 1552.8 1553.2 1553.6 1554.0 1554.4
-70
-60
-50
-40
-30
Raised GaussianApodization
Gaussian Apodization
20dB
Ref
lect
ion(
dBm
)
Wavelength(nm)
1551 1552 1553 1554 1555 1556
-60
-55
-50
-45
-40
-35
-30
Tran
smis
sion
(dB
m)
Wavelength(nm)
1. C. Yang and Y. Lai, Journal of Optics A 2, 422(2000).2. C. Yang and Y. Lai, Electronics Letters, 665(2000)3. C. Yang and Y. Lai, Optics & Laser Technology, 32, 307(2000).
Step-Scan Exposure System
Movable Linear StagePZT
Fiber
ReflectorArgon Ion Laser ( λ=244nm)
RotatableReflector
Reflector
Reflector
Beamsplitter
Cylindrical Lens
Cylindrical Lens
OSA
ASESource
Translation Stage
Laser Interferometer
Linear Stage and PZT Stage Controllers
Mask Mask orInterfer-ometer
Require nm accuracy!!
Lab Picture with Visitors from Duke University
Overlap-Step-Scan Exposure
∑
+
Λ⋅−=∆
mmmm
zzzSAzn )(cos)()( 2 φπη
0.2 0.4 0.6 0.8 1Position
0.2
0.4
0.6
0.8
1
indexdifference
Typical parameters:Grating period = 535 nm,UV Gaussion beam diameter = 1 - 5 mm Scan step size = beam diameter/10,grating length = 2 - 10 cm Not True
Apodization!
New method for true apodization and phase-shift
He-Ne LaserInterferometer
Translation Stage
Fiber
244nm UV Laser
Rotatable Mirror
Beam Splitter
Mirror
half-wave plate
θ s
fMirror
Shutter
1 5 5 1 .0 1 5 5 1 .5 1 5 5 2 .0 1 5 5 2 .5 1 5 5 3 .0-4 0
-3 5
-3 0
-2 5
-2 0
-1 5
-1 0
-5
0
5
W a v e le n g th (n m )
Ref
lect
ivity
(dB)
-4 0
-3 5
-3 0
-2 5
-2 0
-1 5
-1 0
-5
0
5
(b )
Transmission (dB)
1 5 4 4 .0 1 5 4 4 .5 1 5 4 5 .0 1 5 4 5 .5 1 5 4 6 .0-3 0
-2 5
-2 0
-1 5
-1 0
-5
0
5 P u re a p o d iz e d F B G C o s 2 a p o d iz e d F B G
W a v e le n g th (n m )
Ref
lect
ivity
(dB)
(a )
To be publishedOn Optics Letters∑
+
Λ⋅+⋅−=∆
mmmm
zzzSzn )2cos()2(cos1)()( 2 φπθη
Another new method for true apodization
244nm UV Laserp
s
Rotatable λ/2 waveplatePolarization Beam Splitter
Reflection Mirror
Reflection Mirror
Reflection Mirror
Translation StageFiber
Phase Mask
Z
I
Z
I
s
p
Z
I
Can be used with phase mask or two beam inter-Ferometer.
To be published on PTL.
Fabricated Dispersionless FBG
-35
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-5
0
5
(a)
Ref
lect
ion
(dB)
-100
-50
0
50
100
150
200
250
300
Time delay (ps)
1547.2 1547.6 1548.0 1548.4 1548.8 1549.2-35
-30
-25
-20
-15
-10
-5
0
5
(b)
W avelength (nm)
Ref
lect
ion
(dB)
-100
-50
0
50
100
150
200
250
300
Time delay (ps)
0.0
0.5
1.0
Phas
e (x
ra
d)π
0 5 10 15 20 25 30 35
0.0
0.2
0.4
0.6
0.8
1.0 DLP method LS fitting
Grating Position (mm)
Nor
mal
ized
Ref
ract
ive
Inde
x Pr
ofile
An interferometric side-diffraction monitoring technique for UV writing of advanced Bragg gratings
He-Ne Laser
θ1
2θ
3θCCD
Fiber Translation
SLSL
SL
SL
M
M
M
BS
BC
Grating
UV beams
A
1548.0 1548.5 1549.0 1549.5-40
-35
-30
-25
-20
-15
-10
-5
0
5
W avelength (nm )
Ref
lect
ion
(dB)
-40
-35
-30
-25
-20
-15
-10
-5
0
5
Transmission (dB)
Iinter Fourier Transform
Filter Inverse Fourier Transform
Take The Phase δ
(a)
0 50 100 150 200
-1
0
1
2 Exp. interference fitted interference Phase of interference
CCD position (pixel)
Nor
mal
ized
am
plitu
de (%
)
-4
-2
0
2
4
Phase (rad)
(b)
5cm FBG
To be presented in CLEO 2004
Final Fabrication Goal
Fabrication of FBGs with Arbitrary Profile, Phase-Shifts, and Long Length
Movable Linear StagePZT
Fiber
ReflectorArgon Ion Laser (λ=244nm)
RotatableReflector
Reflector
Reflector
Beamsplitter
Cylindrical Lens
Cylindrical Lens
OSA
ASESource
Translation Stage
Laser Interferometer
Linear Stage and PZT Stage Controllers
Mask Mask orInterfer-ometer
Final Design Goal: Optimal Inverse DesignSynthesis of fiber gratings based on the optimization approach
for arbitrary reflection or transmission properties
Reflection orTransmission
Spectrum(Amplitude and Phase)
Garting Index profile∆n(z)
[or equivalently κ(z)]
Analysis based on CME
( ) ( ) ( ) ( ) 4exp 0
′′∆−
∆= ∫
z
dcac zdznzjznjz
λπηθ
ληπκ
Coupled Mode Equation Analysis
azikzbidzdb
bzikzaidzda
g
g
]exp[)(
]exp[)(*
−+−=
+=
κβ
κβ
−=
=
−=
+−=
+= ∗
zk
iBb
zk
iAa
k
AzBidzdB
BzAidzdA
g
g
g
2exp
2exp
2
)(
)(
βδ
κδ
κδ
ββ
gk
0)(
)()(2 2
=
−+−=
=
∗
Lr
rzzridzdr
ABr
κκδ
Coupled modeequations
∫=
−=L
z
zi dzezr0
2)()( δκδ
∫∞
−∞=
−−=δ
δ δδπ
κ derz zi 2)(1)(
r(δ) κ(z)FT
( ) ( ) ( ) ( ) 4exp 0
′′∆−
∆= ∫
z
dcac zdznzjznjz
λπηθ
ληπκ
ac index (amplitude and phase)+ dc index
Ricatti equationAnti-directional coupling(FBG)
For |r|
Design Methodology of Advanced Fiber Gratings1. Inverse Methods
(1) GLM inverse scattering method(E. Peral, et al., IEEE JQE, 32, 2078, 1996.)
(2) Layer-Peeling method(R. Feced, ei al., IEEE JQE 35, 1105, 1999.)
2. Optimization Methods(1) Genetic algorithm
(J. Skaar and K. M. Risvik, J. Lightwave Tech. 16, 1928, 1998.) (2) Evolutionary Programming
(C.-L. Lee and Y. Lai, IEEE Photon. Tech. Lett, November, 2002.)(C.-L. Lee and Y. Lai, CLEO 2003, USA; also to be published on OC
Layer Peeling Method
τ=0
∆τ
∆z=∆τ/2)(2)(1)
2( τδδ
πτκ
δ
τδ ∆−=−=∆
∫∞
−∞=
∆− hder i
(1) FBG
τ > 0
(2) LPG
τ=0
τ=0∆ττ=0 τ > 0
∆z=∆τ
-35
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-10
-5
0
5
(a)
Ref
lect
ion
(dB)
-100
-50
0
50
100
150
200
250
300
Time delay (ps)
1547.2 1547.6 1548.0 1548.4 1548.8 1549.2-35
-30
-25
-20
-15
-10
-5
0
5
(b)
W avelength (nm)
Ref
lect
ion
(dB)
-100
-50
0
50
100
150
200
250
300
Time delay (ps)
5 10 15 20 25 30 35
DLP method LS fitting
Grating Position (mm)
Dispersionless FBG by the LP Method
Gaussian Apodization
0.2 0.4 0.6 0.8 1Position
0.2
0.4
0.6
0.8
1
Index Difference
DispersionlessFBG by LP
Index envelope
Require: 1. Constant dc-index (True Apodization). 2. Special ac-index apodization. 3. Multiple phase-shifts
0.0
0.5
1.0
Phas
e (x
ra
d)π
0
0.0
0.2
0.4
0.6
0.8
1.0
Nor
mal
ized
Ref
ract
ive
Inde
x Pr
ofile
The Least Square Fitting Method
{ }( ) ( )∫ ∑
−= dzzAzAC
mmidm
2
)(σ
( ) ( )exp smmm wzzCzA −−⋅= ( )22( )
0)exp()()(A-2C
2
idm
∫ ∑ =−
−⋅
−=
∂∂ dz
wzz
zAzs
m
mm
σ
To determine the experimental exposure parameters.
Dispersion Compensation Fiber Bragg Grating by Single Period Overlap-Step-Scan Exposure
Phase profile Reflection SpectrumProfile of κ(z)
Phase error tolerancePhase-shifted approximation
PTL 2003.
Advantages and Disadvantages of Layer Peeling Method
1. Advantages:(1) Very fast.(2) Single solution.
2. Disadvantages:(1) Complete spectra information (amplitude
and phase) must be provided.(2) Reconstruction sometimes fails.(3) Can not impose additional constrains.(4) Not necessary optimal solution for
applications.
Synthesis of advanced FGs using EP(Flow chart of the algorithm)
STARTThe parent set with N individuals of
Calculate the spectrum reponse for each using the coupled-mode equation .
YESStop
Find the error and the fitness values for each
Check
NO Selection: by probability algorithm
Mutation: add a perturbation to one section of κ κ
κ
κ
•the only operator in EP• with higher fitness value lower Perturbation factor (vice versa)
A new set of N-offspring
• will be discretized into m sections
• with higher fitness has higher probability to be chosen
κ
κ
κ
Design of Dispersionless Fiber Bragg Grating
1549.9 1549.95 1550 1550.05 1550.1-6000
-4000
-2000
0
2000
4000
6000EP(4cm) LP(4cm) LP(20cm) Gaussian-apodized(4cm)
Wave le ngth (nm)
Dispersion (ps/nm)
Dispersion Spectrum
0 1 2 3 4-4
0
4
8
Grating Le ngth (cm)
Coupling Coefficient (1/c
m)
EP
LP
Gauss ian-apodized
λ1, λ2 … λn λ1, λ2 … λnFBG at λi
Drop λi Add λi
Circulator Circulator
Reflection Spectrum
To be published on Optics Communications
Convergence of the Stochastic Search
0 1000 2000 3000 4000 5000 60000
0.5
1
1.5
2
2.5x 10
5
Dispersion(in-band) Error (ps/nm)
0 1000 2000 3000 4000 5000 60000
2
4
6
8
10
12
Ge ne ration
Reflectivity Error
DE
RE
Comparison of the Computation Time Matlab Programming
3min 20secLP (20cm) with N=4000, M=8000
12 sec
1~4 hrs
CPU timeDesigned Methods for the designed example
EP (4cm) with 20 sections,
LP (4cm) with N=800, M=1600
Obviously the EP Optimization approach should compete with the LP methodon the designed flexibility and achieved performance, not on computation time.
Design of Gain Flattening Long Period Grating
1510 1520 1530 1540 1550 1560 1570 1580-12
-8
-4
0
Wavelength (nm)
Transmission (dB)
Max. 50nm Exact
1510 1520 1530 1540 1550 1560 1570 1580-0.2
0
0.2
Error (dB)
Error
1510 1520 1530 1540 1550 1560 1570 1580-15
-10
-5
0
Wavelength(nm)
Tran
smis
sion
Los
s(dB
)
Desired Synthesized
(a)
1515 1525 1535 1545 1555 1565 1575 15855
10
15
20
25
30
35
40
45
Wavelength(nm)
Gai
n(dB
)
UnflattenFlatten
(b)
0 10 20 30 40 500
0.1
0.2
0.3
0.4
Grating Length(mm)
Am
plitu
de o
f Cou
plin
g C
oeffi
cien
t(1/m
m)
Amplitude
0 10 20 30 40 50-1
-0.5
0
0.5
1
Phas
e of
Cou
plin
g C
oeffi
cien
t(rad
)
Phase
(c)
Filter Response Gain Flattening
Index Profile Phase Error Tolerance
Long Period Grating
EDFALPG
(C.-L. Lee and Y. Lai, IEEE Photon. Tech. Lett, November, 2002.)
Coupling of Modes
Co-directional coupling:(LPG)
−
+=
+
+=
−−=
−−=
+= ∗
zk
iziAa
zk
iziAa
k
AzAidz
dA
AzAidzdA
g
g
g
22exp
22exp
2
)(
)(
2122
2111
21
122
211
ββ
ββ
ββδ
κδ
κδ
122
211
]exp[)(
]exp[)(
azikzaidzda
azikzaidzda
g
g
−−=
+= ∗
κβ
κβ
1β
2β gk
Long Period GratingCoupling between the core and cladding modes
Comparison of the single- and multi-objective EP algorithms
Adaptive with multiple actual error valuesAdaptive with single fitness valueMutation process
Roulette wheel with elitism selection algorithm:1. Keep the best for the next generation2. The with higher F has higher probabilityto be chosen
Roulette wheel selection algorithmSelection process
Fitness functions
Error functions
1. In-band zero-dispersion2. Desired reflectivity spectrum
1. Desired transmission spectrumTargets
21Number of targets
FBG Dispersionless Filters for DWDM OADM(Multi-objective optimization)
LPG EDFA Gain Flattening Filters(Single-objective optimization)
Examples
∑=
−=n
iiT TTE1
,,target)(κ [ ])()()( iDDiRRitot EWEWE κκκ ×+×=
)(1)(
itoti E κ
κ =F)(
1)(FiT
i E κκ =
Quantum Effects of Fiber Bragg Grating Solitons
Kerr nonlinearity
Fiber GratingAmplitudeSqueezed
R.-K. Lee and Y. Lai, To be published on Phys. Rev. A Rapid Communication.
Conclusions• Standard Fiber Gratings and Applications are
mature technologies.• Advanced Fiber Gratings and Applications are
under intense development and will find more and more important applications.
• Precision Fiber Grating Design and Fabrication techniques are the keys for the development of advanced fiber gratings and applications.
• At IEO/NCTU we have established a firm basis forthe design and fabrication of advanced fiber gratings.
AcknowledgementOur Lab Members
Cheng-Ling Lee (李澄鈴)Kai-Ping Chuang(莊凱評)
Dr. Lih-Gen Sheu (許立根﹐Van Nung Institute of Technology)………….