Fiber Bragg Gratings: fundamentals and · PDF fileFiber Bragg Gratings (FBG) ... Photosensitivity allows to realize Fiber Bragg Grating because spatial periodic irradiation of the

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"


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


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


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


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]


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 !


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


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


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


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


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


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


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


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


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


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)


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)


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


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.


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


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


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.


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


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


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


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+


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


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.


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


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, . . .


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


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.


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


19

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


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


20

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


21

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)


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


22

FBG has a central lobe and is mainly used in reflection


LPG has several resonances to the cladding modes and is used in transmission


TFBG has many lobes and can radiate


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]


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


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


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


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


Telecom applications of FBG 53 / 67

see: FBG telecom applications


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.


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


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


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


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


28

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


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


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


More links towards PhD student’s work

■ Polarization effects in FBG

■ FBG in PCF

■ Simplex method


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


30

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[2] R. Atkins and V. Mizrahi, “Observations of changes in UV absorption bands of singlemode germanosilicate core optical fibers on writing and thermallyerasing refractive index gratings,” Electronics Letters, vol. 28, pp. 1743–1744, 1992.

[3] K. H. Awazu, K. H. Kawazoe, and M. Yamane, “Simultaneous generation of optical absorption bands at 5.14 and 0.452 eV in 9SiO2 : GeO2 glassesheated under an H2 atmosphere,” Journal of Applied Physics, vol. 68, pp. 2731–2738, 1990.

[4] F. Bilodeau, B. Malo, J. Albert, J. D. C. Johnson, and K. O. Hill, “Photosensitization of optical fiber and silica-on-silicon/silica waveguides,” Optics

Letters, vol. 18, p. 953, 1993.

[5] T. Erdogan, “Fiber grating spectra,” Journal of Lightwave Technology, vol. 15, no. 8, pp. 1277–1294, 1997.

[6] P. Ferdinand, “Capteurs à fibres optiques à réeseaux de Bragg,” in Techniques de l’Ingénieur, Traité Mesures et Contrôlle, R 6 735.

[7] K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: Application to reflection filter fabrication,” AppliedPhysics Letter, vol. 32, pp. 647–649, 1978.

[8] K. O. Hill, B. Malo, F. Bilodeau, D. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposurethrough a phase mask,” Applied Physics Letters, vol. 62, pp. 1035–1037, 1993.

[9] K. O. Hill and G. Meltz, “Fiber Bragg grating technology - fundamentals and overview,” Journal of Lightwave Technology, vol. 15, no. 8, pp. 1263–1276,1997.

[10] R. Kashyap, Fiber Bragg Gratings. Academic Press, 1999.

[11] A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” Journal ofLightwave Technology, vol. 15, pp. 1442–1463, 1997.

[12] D. K. W. Lam and B. K. Garside, “Characterization of single-mode optical fiber filters,” Applied Optics, vol. 20, pp. 440–445, 1981.

[13] S. Lee, R. Khosravani, J. Peng, V. Grubsky, D. S. Starodubov, A. E. Willner, and J. J. Feinberg, “Adjustable compensation of polarization modedispersion using a high- birefringence nonlinearly chirped fiber bragg grating,” Photonics Technology Letters, vol. 11, no. 10, pp. 1277–1279, 1999.

[14] P. J. Lemaire, R. M. Atkins, V. Mizrahi, and W. A. Reed, “High pressure H2 loading as a technique for achieving ultrahigh UV photosensitivity andthermal sensitivity in GeO2 doped optical fibres,” Electronics Letters, vol. 29, pp. 1191–1193, 1993.

[15] G. Meltz, W. W. Morey, and W. H. Glenn, “Formation of bragg gratings in optical fibers by a transverse holographic method,” Optics Letters, vol. 14,pp. 823–825, 1989.

[16] A. Othonos and K. Kyriac, Fiber Bragg Gratings. Artech House, 1999.


31

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