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

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(a)

Ref

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(dB)

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Time delay (ps)

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(dB)

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Time delay (ps)

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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

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e (x

ra

d)π

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Nor

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ized

Ref

ract

ive

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ofile

Index envelope

Fiber Bragg Grating (FBG) as 1-D photonic crystalExposureMethods (a)

(d)

(e)

(b)

(c)

(f)

(g)

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1.0

Ref

lect

ivity

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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

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0.8

1

Index Difference

Ordinary Apodization True Apodization

1552.0 1552.4 1552.8 1553.2 1553.6 1554.0 1554.4

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Raised GaussianApodization

Gaussian Apodization

20dB

Ref

lect

ion(

dBm

)

Wavelength(nm)

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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

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5

W a v e le n g th (n m )

Ref

lect

ivity

(dB)

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-1 0

-5

0

5

(b )

Transmission (dB)

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-2 0

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-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

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Time delay (ps)

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0

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(b)

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lect

ion

(dB)

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0

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150

200

250

300

Time delay (ps)

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1.0

Phas

e (x

ra

d)π

0 5 10 15 20 25 30 35

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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

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W avelength (nm )

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lect

ion

(dB)

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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 (%

)

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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

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Time delay (ps)

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0

5

(b)

W avelength (nm)

Ref

lect

ion

(dB)

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0

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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

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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

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-8

-4

0

Wavelength (nm)

Transmission (dB)

Max. 50nm Exact

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0

0.2

Error (dB)

Error

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-5

0

Wavelength(nm)

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smis

sion

Los

s(dB

)

Desired Synthesized

(a)

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10

15

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25

30

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40

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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)………….