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transcript
Fiber Bragg Gratings: fundamentals and applications
Patrice Mégret Sébatien Bette Cathy Crunelle Christophe Caucheteur
3rd May 2007
Outline. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Introduction 3Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Key elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Periodic modulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Hill’s discovery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Self-induced FBG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Limitation of Hill’s FBG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10External writing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Holographic technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Photosensitivity in fibers 13Photosensitivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Silica structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Silica defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Ge-doping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17GODC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Hand and Russel’s model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Hydrogen loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22FBG types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Spectra evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24OH absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Type IA gratings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Temperature sensitivities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27UV bands. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28240 nm band . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29193 nm band . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Properties of FBG 32Grating theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33FBG theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34Tailoring of FBG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Typical index profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Fourier profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Coupled mode theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38Analytical solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
1
Effect of L and δn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40Bandwidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41Group delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42FBG, LPG and TFBG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43FBG spectral response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44LPG spectral response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45TFBG spectral response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Fabrication of FBG 47Holographic technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48Phase mask technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Point to point technique. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
Telecom applications of FBG 53. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Non-telecom applications of FBG 55Strain and temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56Strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58OTDR principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59OTDR advantages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60OTDR resolution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61OTDR parameter extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62OTDR trace analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63More links towards PhD student’s work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
Conclusions 65Acknowlegdement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
2
Outline
Introduction
Photosensitivity in fibers
Properties of FBG
Fabrication of FBG
Telecom applications of FBG
Non-telecom applications of FBG
Conclusions
FBG course, April 2007 2 / 67
Introduction 3 / 67
Components for fiber optics are vital
■ Fiber optic telecommunication is now a well established technology
■ A major drawback is on the component side for controlling the light like coupling in and out,filtering, . . . which mainly relies on bulk optics:
◆ hight losses
◆ stringent tolerance for alignment
◆ huge size
⇒ it is interesting to have fiber components because:
◆ low losses
◆ high stability
◆ small size (compatible with fiber sizes)
◆ "low cost"
FBG course, April 2007 4 / 67
Fiber Bragg Gratings are key elements in fiber components
■ EDFA and fused couplers are examples of successful fiber components
■ Fiber Bragg Gratings (FBG) have revolutionnized optical fiber components:
◆ mainly filters as building blocks for telecom and sensors
◆ low losses
◆ done into the fiber
◆ easy shaping of the spectral response
◆ stability
◆ reduced maintenance
FBG course, April 2007 5 / 67
3
A fiber Bragg is a z-periodic modulation of the refractive index
Λ
λ
P
∆λ
λ
P
∆λ
λ
P
z
n
neff
neff + δn
■ Periodic modulation of n ⇒ coupling between forward and backward waves⇒ λB = 2neffΛ λmax = 2(neff + δn)Λ
■ 0.5 ≤ Λ ≤ 100 µm, 10-5 ≤ δn ≤ 10-3, 1 mm ≤ L ≤ 1 m
■ R can be as high as 100% and 0.1 nm < ∆λ < 100 nm
FBG course, April 2007 6 / 67
Applications are multiple
■ filters
■ selective mirrors ⇒ feedback in fiber lasers
■ compensator for dispersion and polarization
■ coupling from one mode to another
■ possibility to write non-uniform gratings and exotic gratings ⇒ exponential grow of applications
■ temperature and strain change λB ⇒ sensors
◆ 10 pm/◦C around 1550 nm
◆ 1 pm/µǫ
◆ information on the wavelength and not on the power (+ OTDR)
■ easy fabrication by phase mask technique
FBG course, April 2007 7 / 67
4
The first fiber grating has been discovered accidentally by Hill et al at the CanadianResearch Center, Ottawa
■ in 1978, Hill et al studied nonlinear effects
■ 1 m germanium-doped silica fibers
■ Argon visible light (488 nm)
■ under prolongated exposure, fiber attenua-tion increased
■ 4% Fresnel reflection ⇒ standing wave pat-tern inside the fiber
■ creation of a permanent modulation of n withthe same periodicity as the interference pat-tern
[7]
FBG course, April 2007 8 / 67
This first fiber grating is called self-induced grating
[7]
■ the light back-reflected increased with timeuntil almost 100%
■ reflection increase of δn
■ photosensitivity is since then a Science
[7]
■ spetral measurement showed R = 90%, δλ <200 MHz and δn ≈ 10-6 − 10-5
■ only work at the writing wavelength !
FBG course, April 2007 9 / 67
5
Hill grating allows to realize fiber filters but it works only at the written laser wave-length
■ first demonstration of the fiber photosensitivity: increase of the fiber refractive index at highintensity points of the interference pattern
■ called ’Hill Grating’ (Self-induced Grating)
■ this discovery allows news applications: wavelength selective fiber filters but some limitations:
◆ Filter only works at the writing laser wavelength
◆ The writing process has been showed only at the Argon laser wavelength (488 nm)
■ the work of Lam and Garside (1981) shows that the refractive index modification was related tothe square of the Argon laser intensity ⇒ in the Hill experiment, the refractive index variation is atwo photons mechanism
FBG course, April 2007 10 / 67
External writing has been developed to overcome internal writing limitation
■ internal writing allows only self-induced gratings which only work at the writing wavelength(generally 488 nm)
■ external writing uses phase mask technique or holograhic technique and consists to irradiate thefiber from the side with a periodic UV light pattern ⇒ absorption by colour centers and defects ⇒periodic modulation of n with δn as high as 10-3 is possible ⇒ the working wavelength is notnecessarily equal to the writing wavelength
◆ writing at 244 nm by Ar doubled laser
◆ writing at 248 nm by KrF excimer laser
◆ writing at 193 nm by ArF excimer laser
but induced birefringence
■ hydrogen loading increases δn up to 10-2
FBG course, April 2007 11 / 67
6
In 1989, Meltz realized Fiber Bragg Grating at any wavelength with the holographictechnique
[15]
■ efficiency of writing is higher at 244 nm(cladding is transparent, core not)
■ periodic pattern from two beam interference
[15]
Λ =λUV
2 sin ϕ
Here ϕ = 39◦ and neff = 1.486 ⇒ λB =576.15 nm
FBG course, April 2007 12 / 67
Photosensitivity in fibers 13 / 67
Photosensitivity is a difficult subject
■ The photosensitivity of a fiber is its capability to change locally its refractive index when it isirradiated by a UV light
■ Photosensitivity allows to realize Fiber Bragg Grating because spatial periodic irradiation of thefiber leads to periodic refractive index variation
■ Photosensitivity mechanisms are not yet completely understood
■ Photosensitivity depends on several factors such as:
◆ Irradiation source (wavelength, intensity, exposition time, pulsed or continuous laser, . . . )
◆ Fiber core composition
◆ The past history of the fiber before the irradiation (technique and conditions of manufacturing)
■ In germanium doped fibers, it is linked to defects
FBG course, April 2007 14 / 67
7
The molecular structure of silica is a pseudo-crystal made from random tetrahedralunits of SiO
4
Si
O
O O
O
SiO4
tetrahedralunit
Si
O
O
O
O
Si
O O
O
144◦
Si
O
O
Si
O
bridging oxygen O
O O
O
FBG course, April 2007 15 / 67
Defects are multiple and are responsible of attenuation bands
Si
O
O O
O
Si
O
O
O
O
Si
O O
Si
O
O
Si
O
Si
Cl chlorine termination
O
O
O
Si
O O
O
H hydroxil termination
Si
O
OO
peroxy linkage
Si
O
neutraloxygenvacancy
FBG course, April 2007 16 / 67
8
Doping with Ge consists of replacing some Si by Ge
Si
O
O O
O
Si
O
O
O
O
Si
O O
Si
O
O
Si
O
Ge
Ge
Ge
FBG course, April 2007 17 / 67
In Ge-doped fiber, germanium oxygen deficient center is Ge with only 3 oxygenatoms and absorbs at 240 nm
Si
O
O O
O
Ge
O
O
O
O
Ge
O O
SiO
O
Ge
O
FBG course, April 2007 18 / 67
9
Another kind of germanium oxygen deficient center is a Ge with olny 2 oxygen atomsand absorbs at 240 nm
Ge
O
O O
O
Si
O
O
O
O
Ge
O O
SiO
O
bb
FBG course, April 2007 19 / 67
UV insolation creates new defects by breaking Ge − Si and Ge − Ge which lead tophotosensitivity
Mechanism of Hand and Russel in Ge-dopedfiber is a several step process
1. bond breakage of GODC byUV
2. new defects GeE’ centers +free electrons
3. capture of e− and newdefects Ge(1) and Ge(2)
4. UV interaction with Ge(1)and Ge(2)
FBG course, April 2007 20 / 67
10
The Kramer-Kronig relation has been used by Hand and Russel to explain the pho-tosensitivity of Ge-doped fibers
[2]
■ concentration of GODC decreases and so ab-sorption at 240 nm decreases
■ concentration of GeE’ centers increases andso absorption at 195 nm increases
By the Kramer-Kronig relation, one can show that the attenuation modification leads to a refractiveindex modification given by:
∆n(ω′) =c
π
�∞
0
∆α(ω)
ω2 − ω′2dω (1)
Remark: photosensitivity is strongest in multi-doped fibers (ex: co-doped boron in Ge-doped fibers)
FBG course, April 2007 21 / 67
Photosensitivity can be enhanced by H2
loading
Fiber hydrogenation loading before UV irradiation allows to obtain higher index variation (δn ≈ 10-2)by creating more GODC
[3]
■ hydrogenation with H2
at low temperature(< 100 ◦C) and high pressure (> 100 atm)
■ deuterium can also be used to avoid the OHabsorption peak around 1380 nm
■ flame brushing at 1700 ◦C in an hydrogen at-mosphere allows hydrogen to diffuse into thefiber core
FBG course, April 2007 22 / 67
11
There are several types of Bragg gratings produced by varying the UV irradiationconditions
Type I Monotonic increase of δn (and thus of λmax, red-shifted) under moderate UV irradiation and due toelectronic defects. These FBG can be erased at around 200 ◦C. These FBGs are the most used intelecommunication and sensing in a temperature range of -40 — +80 ◦C.
Type IIA By a prolongated UV irradiation in a photosensitive fiber, the first order grating is erased and asecond grating is created with a decrease of λmax (blue-shifted). The writing process is slow (30 min)and δn variation is due to densification. These FBGs are erased at around 500 ◦C and thus veryinteresting for sensing at high temperature.
Type II High fluence UV irradiation which creates damage at the interface core-cladding. These FBGs resistup to 700 ◦C.
Type IA FBG written into an hydrogenated fiber after a prolongated exposure to UV irradiation. neff greatlyincreases and λB can be shifted towards the red up to 20 nm.
FBG course, April 2007 23 / 67
Spectra evolution shows the grating writing dynamics with a red shift of λmax
Typical result for a 1 cm long FBG at 110 mW UV powerType I grating ⇒ destruction of the grating ⇒ type IA grating
FBG course, April 2007 24 / 67
12
OH− absorption band increases with time during the blank beam exposure
■ absorption due to vibration of Si− OH bondat 1390 nm
■ absorption due to vibration of Ge − OH bondat 1410 nm
■ high correlation between the increase of OH−
and the neff variation
■ by deconvolution, one can show thatSi − OH absorption is predominant whichcauses a better thermal stability to the typeIA gratings compared to the type I gratings
FBG course, April 2007 25 / 67
Type IA gratings can be explained by a modification of the mean refractive index
z
n
neff (I)
neff + δn (I)
neff (IA)
neff + δn (IA)
This type of grating has a smaller temperature coefficient making them better for strain sensors.
FBG course, April 2007 26 / 67
13
The different grating types have different temperature sensitivities
Type Description ∆T (pm/◦C)
I Standard grating written into a fiberwith or without H
2loading
≈ 9.5
IA Grating regenerated after an erasureof a type I grating in an hydrogenatedfiber
≈ 7.0
II Grating characterized by a damagedcore-cladding interface
IIA Grating regenerated after an erasureof a type I grating in a non hydro-genated Ge-doped fiber (with B co-doped)
≈ 10.5
FBG course, April 2007 27 / 67
A lot of UV bands can be used (acrylate is transparent to the 330 nm band)
Refractive index change
Internal writing
488 nmband
Ge : SiO2
Self-induced grating
External writing
157 nmband
H2
loaded
δn ∼ 10-4
193 nmband
240 nmband
330 nmband
H2
loaded
δn ∼ 10-2
Ge co-dopants
B, Er, Ce
δn ∼ 10-4
FBG course, April 2007 28 / 67
14
240 nm band is the most used (part 1)
240 nm band
Pure silica
Densification
Germanosilicates
1. B − Ge : SiO2
Photosensitivitybetter than 2-3thermal stability
worst
2. Ge : SiO2
Low powerdensity
H2
loaded
Type I enhancedphotosensitivity
H2
unloaded
Low fluence
Type Idensification
High fluence
Type IIA
High powerdensity
Type II
3. Sn − Ge : SiO2
Photosensitivity andthermal stabilitybetter than 1-2
FBG course, April 2007 29 / 67
240 nm band is the most used (part 2)
240 nm band
Phosphosilicates
Photosensitivity
without H2
loading but byincreasing
temperature
Photosensitivity
with H2
loading inP-doped fiber
Ce3+ : P2O
5
Tb3+ : P2O
5
Aluminosilicates
Eu2+ : Al2O
3
Ce3+ : Al2O
3
Tb3+ : Al2O
3
Fluorides
Ce3+ : ZBLAN
Ce3+ : HBLAN
pulse laser only
Rare earths
Er3+
Pr3+
Tb3+
FBG course, April 2007 30 / 67
15
193 nm is another useful band
193 nm band
Germanosilicates
Low powerdensity
δn up to 10-3
Type IFor high Ge-doped,δn÷ power densityFor low Ge-doped,δn÷ square ofpower density
High powerdensity
Type II
Phosphosilicates
H2
loaded
Enhancedphotosensitivity
H2
unloaded
One order betterthan at 244 nm
Fused silica
δn ≈ 5 · 10-5
stressbirefringence
Rare earths
Er3+/Yb3+
transientgratings
FBG course, April 2007 31 / 67
Properties of FBG 32 / 67
Gratings consist of periodic structures which give them wavelength dependent prop-erties
A grating is a repetitive array of diffracting elements (apertures or obstacles) which has the effect ofproducing periodic alterations in the phase, amplitude, or both of an emergent wave.
θi
θmb
D
b
A
b B
b
Cd
AB −CD = d(sin θm − sin θi)
The path difference should be a multiple of the wavelength λ, so:
sin θm − sin θi = mλ
d
The smaller d, the fewer will be the number of diffracted orders.For θi = 0, if d < λ, only m = 0 is possible, and if λ < d < 2λ,we have m = 0,±1.Rmk: also true for reflection gratings.
FBG course, April 2007 33 / 67
16
Elementary theory of FBG is simply based on classical diffraction gratings
FBG caseLPG caseFor a fiber grating of period Λ, the medium issilica with refractive index n:
n(sin θ2 − sin θ1) = mλ
Λ
The propagation constant of a guided mode isβ = neff2π/λ with neff = nco sin θ, so:
±β2 = β1 + m2π
Λ
with + if the coupled mode 2 is forward and − ifit is backward.
[5]If the first-order m = −1 is dominant, there is acoupling between the fundamental forward modeand a backward mode:
λ = (neff,1 + neff,2)Λ
If the two modes are the same:
λ = 2neffΛ
At λB = 1550 nm, Λ ≈ 550 nm
[5]If the first-order m = −1 is dominant, there is acoupling between the fundamental forward modeand a cladding forward mode:
λ = (neff,1 − neff,2)Λ
At λB = 1550 nm, Λ ≈ 100 µm
FBG course, April 2007 34 / 67
17
Many kinds of Fiber Bragg Gratings can be built by varying the beam profile
The UV beam profile can be tailored to provide a refractive index variation of the form:
δn(z) = δn(z)
{
1 + ν(z) cos
[
2π
Λ(z)z + φ(z)
]}
where:
■ δn(z) is the mean (over one periode grating) component of the index variation
■ ν(z) is the visibility (0 < ν < 1)
■ Λ(z) is the spatial period which can vary with z
■ φ(z) is the phase variation along z
It is thus possible to build a lot of gratings with dedicated properties: uniform, apodized, chirped,phase-shifted, sampled, . . .
FBG course, April 2007 35 / 67
Typical Fiber Bragg Gratings are numerous because one can combine all the char-acteristics
■ uniform
z
δn
■ apodized with zero mean value
z
δn
■ apodized with non-zero mean value
z
δn
■ chirped (here linearly)
z
δn
■ phase-shifted
z
δn
■ sampled
z
δn
FBG course, April 2007 36 / 67
18
Fourier transform of δn(z) gives a pretty good idea of the reflection spectrum
δn(z) = δn(z) {1+
ν(z) cos
[
2π
Λ(z)z + φ(z)
]}
Apodization is realized by adjusting δn(z) andν(z) and can be used to suppress side lobes.
FBG course, April 2007 37 / 67
Coupled mode theory leads to a differential set of equations
The grating creates a coupling between a forward R(z) and a backward S(z) waves:
dR(z)
dz= iσ̂R(z) + iκS(z) σ =
2π
λδn(z)
dS(z)
dz= −iκ∗R(z) − iσ̂R(z) κ = κ∗ =
π
λν(z)δn(z)
where:
■ R(z) = A(z) exp(iδz − φ/2)
■ S(z) = B(z) exp(−iδz + φ/2)
■ κ coupling coefficient
■ σ̂ = δ + σ − 12
dφdt
is the general self-coupling coefficient
■ δ = β − π/Λ is the detuning
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Analytical solution exists for a uniform grating
δn(z) = δn
{
1 + ν cos
[
2π
Λz + φ
]}
For a uniform grating, σ̂ and κ are z-independent and the system is linear with constant coefficientsand has an analytical solution with the initial conditions R(0) = 1 and S(L) = 0:
R(z) = R(0)
[
cosh(αz) + iσ̂
αsinh(αz)
]
+ S(0)iκ∗
αsinh(αz)
S(z) = −R(0)iκ
αsinh(αz) + S(0)
[
cosh(αz) − iσ̂
αsinh(αz)
]
with α =√
κ2 − σ̂2
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By adjusting L and δn, spectral properties can be tailored: rmax increases with L andδn
ρ =S(0)
R(0)=
−κ sinh(αL)
σ̂ sinh(αL) + iα cosh(αL)⇒ r =
κ2 sinh2(αL)
κ2 cosh2(αL) − σ̂2
τ =R(L)
S(0)=
iα)
σ̂ sinh(αL) + iα cosh(αL)⇒ t =
α2
κ2 cosh2(αL) − σ̂2
L = 1.07 cm, Λ = 0.534 µm, δn =0.5, 1 and 2 10-4
δn = 10-4, Λ = 0.534 µm, L = 0.5, 1 and 2 cm
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Bandwidth decreases with L and increases with δn
λB = 2neffΛ λmax = 2(neff + δn)Λ
rmax = tanh2(κL)∆λ0
λB
=νδn
neff
√
1 +
(
λB
νδnL
)2
■ Bandwidth ∆λ0 is defined from the first zerosaround the maximum.
■ Strong gratings (rmax ≈ 1):∆λ0
λB
=λB
neffL=
2
N
■ Weak gratings (rmax ≪ 1):∆λ0
λB
=νδnL
neff
L = 1.07 cm, Λ = 0.534 µm
δn = 10-4, Λ = 0.534 µm
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Group delay is an important characteristic of FBG and can be tailored for dispersioncompensation
θp = phase(ρ) τp =dθp
dω= − λ2
2πc
dθp
dλdp =
dτp
dλ
L = 1.07 cm, Λ = 0.534 µm, δn = 10-4, κL = 2 (weak FBG)
L = 1.07 cm, Λ = 0.534 µm, δn = 4 · 10-4, κL = 8 (strong FBG)
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Fiber Bragg Gratings, long period gratings and tilted gratings form the basic unitsfor applications
■ Bragg gratings or reflection gratings (FBG) when the period Λ is so that a coupling between theforward and backward propagating fiber modes is realized:
λB = 2neffΛ
with Λ < 1 µm
■ Long period gratings or transmission gratings (LPG) when the period Λ is so that a couplingbetween two different forward propagating fiber modes is realized:
λB = (neff,1 − neff,2)Λ
with Λ ≫ 10 µm
■ Tilted gratings when the inscription mask is not in the z-axis of the fiber. These gratings cancouple light to radiation modes
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22
FBG has a central lobe and is mainly used in reflection
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LPG has several resonances to the cladding modes and is used in transmission
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TFBG has many lobes and can radiate
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23
Fabrication of FBG 47 / 67
Holographic technique is very versatile but sensitive to vibrations and the coherenceof the beam
2ϕ
Λ
Λ =λUV
2 sin ϕ⇒ λB =
neffλUV
sin ϕ
Any λB by varying ϕ
[16]Not the same number of reflections ⇒
[16]
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Phase mask technique is very simple but requires one different mask for each λB
−1 order +1 order
e
d
θi
θm
sin θm − sin θi =mλUV
d⇒ for θi = 0 m = 0,±1 if λUV ≤ d < 2λUV
The zeroth-order diffraction beam power can be minimized by adjusting themask depth e to:
m = 0 ⇒ θ0 = 0 ⇒ e =λUV
2(nUV − 1)
The first order beams interfere with an angle:
m = ±1 ⇒ sin θ1 = ±λUV
d
and:
Λ =d
2⇒ λB = neffd
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24
Phase mask technique is mainly used for mass production at low cost
■ The phase mask is designed to maximize equal powers in ±1 diffraction orders (around 40%) andminimize power in zeroth diffraction order (around 3%)
■ The grating period Λ is independent of the UV wavelength, so many UV sources can be used
■ The grating period Λ is independent of the exposure angle of incidence which requires lessstringent accuracy in alignment
■ The grating period only depends on the mask period which can also be non-uniform for chirpedand/or apodized FBG
■ The coherence of the UV source is less critical
■ This technique allows mass production
■ The defects in the mask are reproduced in the fiber grating
■ One phase mask per different gratings
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Phase mask can also be used in the interferometric technique to separate the beam
■ zeroth order si blocked
■ ±1 orders interference to give the Bragg pattern
■ by adjusting simultaneously the angles of the two mirrors, one can tune the Bragg wavelength
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25
Point to point technique is also used
■ Principle is simple
◆ UV light is focused on one point on the fiber core
◆ After irradiation, the fiber is moved for one grating period Λ
■ Advantages
◆ No need for optical stability
◆ No need for coherence
■ Drawbacks
◆ Need to realize very short displacement (< µm)
◆ Long time needed
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Telecom applications of FBG 53 / 67
see: FBG telecom applications
FBG course, April 2007 54 / 67
Non-telecom applications of FBG 55 / 67
Strain and temperature simultaneously change the Bragg wavelength
∆λB = 2
(
Λ∂neff
∂ℓ+ neff
∂Λ
∂ℓ
)
∆ℓ + 2
(
Λ∂neff
∂T+ neff
∂Λ
∂T
)
∆T
where:
■ ∆ℓ is the length variation
■ ∆T is the temperature variation
We clearly see that srain and temperature have the same effect to shift the Bragg wavelength. Thereare thus not separable in a single grating.By using, at the same location, two gratings with different sensistivities, it is possible to simlutaneouslyextract strain and temperature.
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26
Strain changes linearly the Bragg wavelength without hysteresis
∆λB
λB
=
{
1 − n2eff
2[p12 − ν(p11 + p12)]
}
ǫz = (1 − pe)ǫz = bǫz
where:
■ ǫz = ∆ℓ/ℓ
■ pe is an effective strain-optic constant of sil-ica (0.22 · 10-6 µǫ-1)
■ p11 (≈ 0.113), p12 (≈ 0.252) and ν (≈ 0.16)are the strain-optic tensor components andthe Poisson’s ratio
∆λB/∆ǫ = 1.1 pm/µǫ
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Temperature changes linearly the Bragg wavelength without hysteresis
∆λB
λB
=
{
1
neff
∂neff
∂T+
1
Λ
∂Λ
∂T
)
∆T = (ξ + α)∆T = a∆T (2)
where:
■ ξ is the thermo-optic coefficient of silica (≈8.6 · 10-6 ◦C-1)
■ α is the thermal expansion coefficient of silica(≈ 0.55 · 10-6 ◦C-1)
■ Christophe’s work:
◆ FBG sensing
◆ Hydrogen sensor∆λB/∆T = 10.1 pm/◦C
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27
OTDR is a very simple and interesting tool that can be used with FBG
receiver
laser
3 dBcoupler
connector
absorbingend
fiber undertest
z z + dzz = 0
�
-
P0
Pd(z)�
-
Pi(z)
Pr(z)
■ pulse width D (in time)
■ pulse peak power P0
■ Rayleigh attenuation coeffient αs =Cλ4
Pr(z) = Pi(z)αsFdz
⇓
Pd(z) ≈ vgαsF
2P0De−2αz
⇓5 log Pd(z) = K − az
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OTDR is one of the most useful field metrology equipment
■ access to one end only
■ simple set-up
■ laboratory and field measurements
■ information on spatial behavior
■ precision less than other techniques
■ 1,300, 1,550 and 1,625 nm
■ P0 around 10 mW with repetition rate 1 kHz(long fibers) and 20 kHz (short fibers)
■ D ns- µs
0 1 2 3 4 5 6 7
10
15
20
25
30
35
Longueur (km)
Atté
nuat
ion
(dB
)
Trace OTDR
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Spatial resolution between consecutive defects is linked to pulse width
z1 z2
2W
z1 − d
t1 = z1/vg
t2 = t1 + d/vg
-
�
-
��
■ Two localized defects separated by a distance d = z2 − z1 are located in z1 and z2.
■ rectangular pulse idealization of spatial width W with 2W =vgD
■ defect descrimination if:
d ≥ W
This means that D should be as small as possible but this reduces the dynamic range
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Insertion loss, return loss, defect position, attenuation coefficient, . . . can be ana-lyzed from OTDR trace
IL(zd) = 10 logPi(zd)
Pi(z+
d )= P ′
i (zd) − P ′
i (z+d )
RL(zd) = 10 logPi(zd)
Pr(zd)= P ′
i (zd) − P ′
r(zd)
If H [dB] is the peak height (no clipping!):
RL = −Bs − 10 log[(
10H5 − 1
)
D]
where Bs = 10 logvgαsF
2and is dependent on the fiber param-
eters
Pi(zd)
Pr(zd) Pi(z+d )
0 1 2 3 4 5 6 7
10
15
20
25
30
35
Longueur (km)
Atté
nuat
ion
(dB
)
Trace OTDR
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29
An OTDR trace gives a lot of information about the link and components
■ λ = 1,300 nm
■ D = 200 ns
■ Bs = 9.7 dB
G.653 G.652 G.652
Length (m) 2,500 500 2,500Position (m) 2,527 3,028 5,541a (dB/km) 0.367 0.380 0.313
Cathy’s work: FBG with OTDR
From P. Mégret et al, « Métrologie des fibres optiques »,
chapter 3 of « Physique et technologie des fibres optiques »,
pp.149-189, edited by J.-P. Meunier, Editions Hermes Sci-
ence - Lavoisier, 2003
0 1 2 3 4 5 6 7
10
15
20
25
30
35
Longueur (km)
Atté
nuat
ion
(dB
)
Trace OTDR
IL=2.59 dB
H=6.73 dBRL=44.0 dBIL=0.41 dB
H=11.37 dBRL=34.6 dB
b
bb
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More links towards PhD student’s work
■ Polarization effects in FBG
■ FBG in PCF
■ Simplex method
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Conclusions 65 / 67
Acknowlegdement
■ Ir Sébastien Bette for his course on FBG and the polarization experiments
■ Ir Cathy Crunelle for OTDR and FBG experiments
■ Ir Kivilcim Yüksel for experimental data
■ Ir Christophe Caucheteur for a lot of sensing devices based on FBG
■ and finally, Ms Mariline Mura for her help and careful proofreading (in rush as usual) of thispresentation
■ Thank you for your kind attention
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30
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