optical fibres - cuso...l.thévenaz ‐epfl ‐introduction to optical fibres, nonlinear effects...

L.Thévenaz ‐ EPFL ‐ Introduction to optical fibres, nonlinear effects & basics on fibre sensing

CUSO 09.03.2016

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Optical fibres and metrology applicationsLecture I – March 9, 2016Introduction to optical fibres, nonlinear effects, basics on fibre sensingProf. Luc THEVENAZ

Group for Fibre OpticsInstitute of Electrical EngineeringEcole Polytechnique Fédérale de Lausanne

CUSO Seminar I: Optical fibres and metrology applications Luc Thévenaz

OverviewGeneral introduction

I. Theory of light guiding in optical fibres

II. Transmission through an optical fibreLimitation due to loss and dispersion

III.Nonlinear effects in optical fibresA. GeneralitiesB. Self- and cross-phase modulationC. Modulation instabilityD. 4-wave mixing and parametric amplificationE. Stimulated Brillouin and Raman scatterings

IV.Distributed fibre sensing

A warm credit to my friend and colleague Prof. Moshe Tur from Tel-Aviv University for handingover some of his teaching material to me.

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Optical Fibres:The waveguides of the present AND the future

• Optical fibres carry the bulk of telecommunications

• Soon all homes will be connected to optical fibres, providing, telephone, internet and television

• Optical fibre sensors are revolutionizing distributed and point sensors

• Fibre lasers can emit Kilowatts of optical power

• Fibres are small in size, light in weight, and being dielectric (SiO2), they do not emit electromagnetic radiation, nor are they affected by such radiation

• They are low cost

3 CUSO Seminar I: Optical fibres and metrology applications Luc Thévenaz

THE OPTICAL FIBRE:

CLADDINGDIAMETER: 125 MICRONPURE GLASS

JACKETDIAMETER: 250 MICRON

COREPURE GLASS (MOSTLY) CONTAINING CONTROLLED DOPINGS (e.g GERMANIUM)DIAMETER: 5-50 MICRON.

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Optical Fibres

ncore > nclad (Refractive Indices)

CladdingCore

nclad

ncore


Snell’s Law

• Guidance is achieved through total internal reflection

ncore

nclad

'

)'cos()cos( cladcore nnSnell’s Law:

6


Total Internal Reflection

• 100% reflection if 1)cos()'cos( clad

core

nn

core

cladc n

n1cos

ncore

nclad

'

• All rays with are totallyreflected


Numerical Aperture(measures the light gathering power of the fibre)

22sin)( cladcoreAIRc nnNAApertureNumerical

ccoreAIRc n sinsin

AIRc

c

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Fibre Types

1. Multimode (name explained later)

a

n

r

n

r

a

STEP INDEX GRADED INDEX

ma 15025

core

cladcore

core

cladcore

nnn

nnn

2

22

2

03.001.0


Fibre Types (cont.)

2. Single-Mode:

(Depending on λ)

3. Polarization Preserving Fibres

4. Polarizing Fibres

5. Doped, amplifying fibres

6. Holey Fibres

ma 10401.0003.0

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I. Theory of light guiding in fibres


Theory of Light Propagation in Optical Fibres

• Ray (geometric) Theory

• It works well for fibres whose core radius is much larger than - the wavelength of the propagating light

• However, as the core radius approaches , diffraction cannot be ignored

• Ray theory fails as a

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Diffraction

2a d

nad

Geometrical Guidance FAILS when cd

d

cV

2 1V Multimode (Geometricaltheory works well)


Goos-Hänchen Effect

• When light is totally internally reflected, there are photons ALSO in the cladding!!!

• The field in the cladding quickly decays (away from the core) and is called the Evanescent Field (very useful in components and sensors)

Evanescent Field

ncore

nclad

14


Wave Theory(Step-Index Fibre)

ncorenclad

r a

2

2

2

22

tE

cnE

2

2

2

22

tH

cnH

= Electric Field= Magnetic Field

n = Refractive index fieldc = Light Velocity in

Vacuum

E

H


Cylindrical Coordinates

z

y

z

x

Ez

Er

Eφ

φr

)(exp),(),(

),,,(),,,(

0

0 ztjrHrE

tzrHtzrE

Looking for solutionsof the type:

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Wave Equation for Ez

2 22

2 2 2

222 2 2 2 2 2 2

2

1 1 0

2

z z zt z

t

E E E Er r r r

nn k nc

FrequencyOpticalHz 14102

Problem:

Given (a single optical frequency), find the

solutions subject to boundary conditions.


Separation of Variables

22

2

2 22

2 2

0

1 0t

q

d R dR q Rdr r dr r

( ) exp ;exp

must be Integer so that exp ( 2 ) exp

jq jq

q jq jq

( )Solutions for have the form:

( ) ( )expzE R r j z

18


Separation of Variables (cont.)

Bessel Equation for r :

22

2

2222

2

2

22

01

cladcore nn

Rrqnk

drdR

rdrRd

Integer2t

CONSTANT IN CORE:

CONSTANT IN CLAD:ar ar


Ordinary Bessel Functions

Positive Number

012

2

2

2

R

rq

drdR

rdrRd

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Ordinary Bessel Functions (cont.)

Positive Number

012

2

2

2

R

rq

drdR

rdrRd


Modified Bessel Functions

Negative Number

012

2

2

2

R

rq

drdR

rdrRd

22


Modified Bessel Functions (cont.)

Negative Number

012

2

2

2

R

rq

drdR

rdrRd


Possible Solutions

012

22

2

2

R

rq

drdR

rdrRd

t

2222 nkt Can be either Positive or Negative

)(rR

)(')( rNArAJ tqtq realt

t

02

)(')( rIcrcK tqtq imaginaryt

t

02

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Guided SolutionsCLADDING: To ensure guidance, we need a solution which decays forand is finite at the centre of the core

r

00,

)()(:2222

cladt

tq

nkTherefore

rKrRarFor

00,

)()(:2222

coret

tq

nkTherefore

rJrRarFor

coreclad knkn


The V Number2222 nkt

02222 coret nkarFor

02222222 ankau coret

02222 cladt nkarFor

02222222 ankaw cladt

2222222cladcore nnakwuV

*

*

*

* Dimensionless

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The V Number (cont.)

core

cladcore

core

cladcore

nnn

nnn

2

22

2

d

ccorecladcore

annnkaV

22222

V is a very important number. It only depends on the fibre geometry, refractive index profile and wavelength


The Fields

qq

sincos

arjqaruAJ zq

expsin

arjqarwCK zq

expsin

zE

arjqaruBJ zq

expcos

arjqarwDK zq

expcos

zH

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Boundary Conditions

cladcore

cladz

corez

cladcore

cladz

corez

HH

HH

EE

EE

To satisfy these boundary conditions, must obey an equation, called:

The Characteristic Equation


Boundary Conditions (cont.)

)/)()((;1111

)()(

)()(

)()(

)()(

222

2

222

2

2

duudJuJwun

nwu

q

wwKwK

uuJuJ

nn

wwKwK

uJuuJ

qqclad

core

q

q

q

q

clad

core

q

q

q

q

22222 coreanwuV

For a given optical frequency, i.e., for a given V, this is an equation in β, having at most a discrete set of solutions, called .MODES

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Mode Classification

• Cases when q = 0

Many components vanish, and we get two families of modes:

Transverse Magnetic (TM)

Transverse Electric (TE)


Mode Classification (cont.)

• TM (Transverse Magnetic)

Mode Designation: TM0m

0)()('

)()('

0

0

0

02

2

wwKwK

uuJuJ

nn

clad

core

Counts the solutions of the Characteristic Equation for β

( , )

0

z r

z r

Only E E andH exist

H H E

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Mode Classification (cont.)

• TE (Transverse Electric)

Mode Designation: TE0m

0 0

0 0

'( ) '( ) 0( ) ( )

J u K wuJ u wK w

Counts the solutions of the Characteristic Equation for β

( , )

0

r z

z r

Only E H andH exist

E E H


Hybrid Modes

For , all modes have

z components for both and .

0qE

H

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Hybrid Modes (cont.)

Mode Designation:

HEqm (Generally, Hz makes the major contribution to the transverse fields).

EHqm (Generally, Ez makes the major contribution to the transverse fields).

q Determines the φ dependence through cos(qφ); sin(qφ).

m Counts the solutions of the characteristic Equation for β.


Mode Cutoff

• For any given V , there are many solutions to the Characteristic Equation for

• Therefore, many modes co-exist in the fibre

• For almost every mode, as V decreases, it reaches a critical value where the mode disappear. This value of V, Vc , is the cutoff of that mode.

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vs V for a Step-Index Fibre:

V=2.405

n

k

)1( n0 1 2 3 4 5 6

HE11 TE01 TM01

HE21

EH11

HE31

HE12 HE41

EH21

TM02

HE22TE02

-n0n0(1-Δ)

2a


405.222

an

cutoff

core

cladcore

nnn

eff

eff

nkn

2

V=2.405

n

k

)1( n0 1 2 3 4 5 6

HE11 TE01 TM01

HE21

EH11

HE31HE12

HE41

EH21

TM02

HE22

TE02

Only one mode survives for V<2.405. Under these conditions, we have a single-mode fibre (SMF), supporting only the HE11 mode

vs V for a Step-Index Fibre:

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Mode Shapes

TE01

HE11

TM01

HE21

The directions of the electric and magnetic field vectors, denoted by the continuous and broken curves, for low order modes, showing the pattern cross-section of a step-index fibre. When nclad~ ncore , the fundamental mode-pattern becomes a rectangular grid, i.e., LINEARLY POLARIZED

EH


The Weakly Guiding Approximation (WGA)

In all practical fibres

(to within less than 0.5%)

and substantial simplifications can be achieved!

coreclad nn

12 2

22

core

cladcore

nnn

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The Weakly Guiding Approximation (cont.)

222

2

222

2

2

1111

)()(

)()(

)()(

)()(

wunn

wuq

wwKwK

uuJuJ

nn

wwKwK

uuJuJ

clad

core

q

q

qclad

core

q

q

q

q

22

11)(

)()(

)(wu

qwwK

wKuuJ

uJ

q

q

q


WGA Characteristic Equation

22

11)(

)()()(

wuq

wwKwK

uuJuJ

q

q

q

q

q = 0 (using various Bessel functions inter-relationships).

)()(

)()(

1

0

1

0

wKwK

wuJuJ

u TE0m

TM0m

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WGA Characteristic Equation (q=0)

For a given V, this equation may have several solutions for u.

TE01 is the mode with the smallest solution u1, etc.

Note:TE0m and TM0m have the same characteristic equation. They are now DEGENERATE.


)()(

)()(

:)1(11 wKwK

wuJ

uJuqEH

q

q

q

qqm

WGA Characteristic Equation (q0)

)()(

)()(

:)1(11 wKwK

wuJ

uJuqHE

q

q

q

qqm

q – Controls the φ dependence through {cos(qφ) ; sin(qφ) }.

m – For a given q, m counts the solutions of the

characteristic equation in an ascending order of u.

22

11)(

)()()('

vuq

wwKwK

uuJuJ

q

q

q

q

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The LP Mode DesignationTwo important observations (Δ<<1):1. All previous forms of the characteristic equation can be

cast into:

lwKwKw

uJuJu

l

l

l

l ;)()(

)()( 11

omom TMTE ,1

11 qqmEHq

11 qHEq qm

There is now certain degeneracy:

a. l=0 HE1m

b. l=1 TE0m, TM0m, HE2m

c. l≥2 EH(l-1)m, HE(l+1)m


2. Modes belonging to the same l can be combined to produce modes having LINEAR POLARIZATION.

The LP Mode Designation (cont.)

LPlm – Linearly Polarized Modes

46


Electric Field Distributions of the LP01=HE11 modes

)ˆ(11 xHE )ˆ(11 yHE


Second Order Mode Electric Field Distributions in Circular Core Step-Index Fibre

evenHE21oddHE21

01TM 01TE

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Summation of the true second order modes to yield the LP11 modes

+ =

evenHE21 01TM evenxLP11

oddHE21 01TE

+ =

oddxLP11


oddHE21 01TE

- =

evenyLP11

evenHE21 01TM oddyLP11

- =

Summation of the true second order modes to yield the LP11 modes (cont.)

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Forms of the LP11 mode

HxEy

Ey

Fibre core

Intensity Distribution

ExHy

HyEx

HyEx

ExHy

EyHx

HxEy

E vertically polarized

E horizontally polarized

The four possible transverse electric field and magnetic field directions, and the corresponding intensity distributions for the LP11 mode.


)()( 220

22cceff nnnnb The LP Modes

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Cutoff values of V for some low-order LP modes

V m = 1 m = 2 m = 3 m = 4

l = 0 0 3.832 7.016 10.173

l = 1 2.405 5.520 8.654 11.792

l = 2 3.832 7.016 10.173 13.323

l = 3 5.136 8.417 11.620 14.796

l = 4 6.379 9.760 13.017 16.224


Intensity Plots for modes

LP01 (u = 2)

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LP11 (u = 3)

Intensity Plots for modes (cont.)


LP21 (u = 4.5)


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LP02 (u = 4.5)



LP31 (u = 5.6)


58


LP12 (u = 6.3)



Relation between Traditional- and LP-Mode Designations for the 10 Lowest LP Modes

Number of degenerating modes

Traditional-mode designations and number of modes

LP-mode Designation

2HE11 2LP01

4TE01, TM01, HE21 2LP11

4EH11 2, HE31 2LP21

2HE12 2LP02

4EH21 2, HE41 2LP31

4TE02, TM02, HE22 2LP12

4EH31 2, HE51 2LP41

4EH12 2, HE32 2LP22

2HE13 2LP03

4EH41 2, HE61 2LP51

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405.222

an

cutoff

core

cladcore

nnn

eff

eff

nkn

2

V=2.405

n

k

)1( n0 1 2 3 4 5 6

HE11 TE01 TM01

HE21

EH11

HE31HE12

HE41

EH21

TM02

HE22

TE02

For any given mode, the lower V the lower its effective index neff=/k becomes. This means that mode extends deeper into the lower index cladding

vs V for a Step-Index Fibre


The Effect of on Mode Shape

r r

ncore

λ1 λ2<λ1

nclad < ncore /1V

62


Effective Phase Velocity increases with decreasing V


Power in Cladding

0 2 4 6

.25

0.5

.75

1.0HE11

TE01+TM01+HE21

HE12+EH11+H31

POW

ER R

ATIO

PCL

AD/P

TOTA

L

222cladcore nnaV

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Summary of Light Propagationin Ideal Straight Fibres

• Light propagates in MODES, the number of which increase like V 2

• For small enough V (<2.405 in a step index fibre), only one SPATIAL mode, the HE11 also called LP01 can propagate

• Practically, ncore~nclad and this mode is LINEARLY polarized, having a two-fold degeneracy, i.e., it can exists in either of two polarizations(so a single-mode fibre is NOT purely single-moded!)


• A fibre is spatially single-moded only for wavelengths exceeding the cutoff (the wavelength for which V=2.405)

• A fibre with cutoff=1270nm is single-moded at 1310nm but NOT at 850nm

• So, if we want to work at both 850nm AND 1310nm should we buy a fibre with cutoff=800nm? NO WAY!!!

• As V decreases for a given mode, more and more of its power resides in the cladding, giving rise to BENDING losses!

Summary of Light Propagationin Ideal Straight Fibres (cont.)

66


II. Transmission through an optical fibreLimitations due to loss and dispersion


The “Decibel (dB)” Scale

milliwattPower

dBminRatio1

log10 1

In particular

Since detector voltage is proportional to the incidentoptical power, one should be very careful to specify if the dB-measure is optical or electrical.

2

1

2

1 log20log10VoltageVoltage

PowerPower

dBinRatio

The decibel measures ratios

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Fibre Loss

2.5 2.0 1.5 1.0 0.5 00.1

1

10

1001.5 30.5 0.6 0.7 0.81 1.2 2 5 10

Infrared Absorption Loss

UV Absorption

Scattering Loss

Total Loss

OH Absorption

Photon Energy

Loss

(dB

/km

)

Wavelength (μm)


Optical Attenuation of Different Materials

1000

100

10

1

0.1

0.01

kmdB

enuationAtt

Window Glass At Visible (500nm)(1 cm Glass 0.004 dB)

Window Glass At 1310nm-1970 Silica Fibre-Today’s Halide Fibre

Today’s Silica Fibre

Projected Halide Fibre

70


Fibre Loss

• In classical single-mode fibre the OH absorption peak defines two minima:▫ one at 1310nm (0.35dB/km) &

one at 1550nm (0.25dB/km)

• Modern fibres have their OH peak removed

• This low loss is achieved by special synthesizing techniques, starting from vapors of SiCl4 for both core and cladding, GeCl4 for the doping of the core and O2, thereby avoiding contamination with metal ions


Maximum Tolerable Limits for Various Elements

Concentration parts per billion (ppb)*

Element

20Iron50Copper20Chromium2Cobalt100Manganese20Nickel100Vanadium

*Calculated from literature values of extinction coefficients at absorption peaks assuming element to be present in its “worst” valence state.

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Modified Chemical Vapor Deposition (MCVD)


Optical fibres:The ‘transparent’ Highway of the Information Era

• Miracle #1: Light attenuation in optical fibres is extremely low

• At 1550 nm, light transmission through 10 km of single-mode optical fibre is as high as 60% !!!!!

• Nevertheless, before optical amplifiers were put in use, electronic regenerators had had to be installed every 100 km of the link

Laser

Light pulses

00 11 0 00 110 Receiver

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1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Wavelength (m)0.1

1.0

10

Atte

nuat

ion

(dB/

km)

Low water peak fibre

Standard waterpeak fibre

1625-1675 U-band1565-1625 L-band

1530-1565 C-band1460-1530 S-band1360-1460 E-band

1260-1360 O-band

Note 1. This definition of spectral bands is to facilitate discussion and is not for specification. Note 2. The specifications of operating wavelength bands are given in the appropriate system recommendations. It should be noted

that the G.65x Fibre Recommendations have not confirmed the applicability of all of these wavelength bands for system operation or maintenance purposes.

Note 3. The boundary between the E- and S-bands continues under study. Note 4. The U-band is for possible maintenance purposes only, and transmission of traffic-bearing signals is not currently foreseen.

Operation of the fibre in this band is not assured.

O = OriginalE = ExtendedS = ShortC = ConventionalL = LongU = Ultra-long

Optical Fibre Spectral Bands


Loss Mechanisms other than Absorption

• Glass is made of un-ordered molecules (Rayleigh scattering)

• Index in-homogeneities and defects (Scattering)

• Micro-bending

• Macro-bending

• Dopants (e.g., Germanium in the core)

• Phonons (molecular vibrations): Raman scattering

• Acoustic waves: Brillouin scattering

• Nonlinear phenomena

• You will learn more about scattering and nonlinear effects in fibres later during this lecture

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Bending Loss

Cladding

Core Radiation

An illustration of the radiation loss at a fibre bend. The part of the mode in the cladding outside the dashed arrow line may be required to travel faster than the velocity of

light in order to maintain a planar wavefront. Since it cannot do this, the energy contained in this part of the mode is radiated away.

RCCrad 21 exp Radius of Bend


Waves

ztjAztAtzA 2expRe2cos),( 00

Wav

e a

mpl

itude

Distance [cm]

-0.8

-0.4

0

0.4

0.8

1.2

-2 0 2

λ

78


Waves (cont.)• While the amplitude oscillates in time with period - T, and temporal

frequency (=1/T= /2), the crest travels one full wavelength – λ

• The spatial frequency is =2/λ

Wav

e a

mpl

itude

Distance [cm]

-0.8

-0.4

0

0.4

0.8

1.2

-2 0 2

λ

pvT

:VelocityPhase

ztjAztAtzA expRecos),( 00


Phase velocity in matter• In matter, the phase velocity of light is smaller by a

factor of n (the refractive index)

Vacuum VacuumMatter

TTnnTncv matter

p1)matterin(

without subscript – in vacuum; without subscript – in matter

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Group velocity ztAztAtzE 220110 coscos),(

2

22

1

11 )()(

pp vv

ztztAtzE avgavg coscos2),( 0

2/)(2/)(

2/)(

2/)(

21

21

21

21

avg

avg

But:

ddvg

pv


Group velocity

ztztAtzE avgavg coscos2),( 0

2/)(2/)(

2/)(

2/)(

21

21

21

21

avg

avg

ddvg

pv

When the light comprises two close by frequencies, each traveling with its own phase velocity, the combination is characterized by an envelope that propagates with vg rather than with vp:

82


Group velocity

Wav

e am

plitu

de

Distance [cm]

-0.8

-0.4

0

0.4

0.8

1.2

-16 -12 -8 -4 0 4 8 12 16

ztztA

ztAztAtzE

avgavg

coscos2coscos),(

0

220110

While the optical phase travels at vp,the envelope moves at vg


Group Propagation

'' '00 deAetA tjtj

An optical pulse, or any other waveform, carried by

an optical carrier at frequency 0, can be described

by A(t)exp[j0t], which can then be spectrally

decomposed using the Fourier integral.

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)])((exp[]exp[ 0 LtjAtjA Lzz

0z Lz

Group Propagation

Each optical frequency propagates with its own phase velocity

)()(

pv


Group Propagation

'' '00 deAetA tjtj

'''exp', 00 dLtjAtLzA

86


Group Propagation (1st order approx.)

0

)(1)(;

)()(exp

)('exp')(exp

')('exp')(exp

'')()(exp'exp'

0'0

000

0'

00

0'

00

0'

00

ddv

vLtALtj

LtjALtj

LtjALtj

dLLjtjA

gg

')()'(0

00 dd


Group Propagation

)()(exp),(

000

gvLtALtjtLzA

DelayGroupVelocity;Group)(1

00

'

gg

g vL

ddv

Emerging waveform retains its shape(but not its optical phase)

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Types of dispersion

•Modal dispersion

•Material dispersion

•Waveguide dispersion


Modal dispersion: Delay Spread(Step Index Fibre)

1

2

Φc Φc

L n1core

n2 cladding

n2 cladding

1ncvcore

cLn

VLtcore

11

2

211

2 sin cnLn

cLnt

cMax

cLn

nn

cLntt Max

1

2

1112 1

Each ray goes through a different path (a different length) from the fibre input to its output, giving rise to pulse spreading:

90


A Multimode Graded Index FibreThe core refractive index is not constant but decreases with radius

r

n2

n1a

CoreCladding

Axial ray(a) (b)

Each ray still follows a different path, but thanks to the parabolic profile of the refractive index, it traverses the same distance!! (the velocity increases with radius)


A Ray Model Demonstrating MODAL Dispersion in Multimode Fibres

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Limit on the [bit rate x distance] product due to modal dispersion in a step-index and a graded-index fibre. In both cases, ∆=0.01 and ncore=1.5


Material Dispersion

ncv

ddnnNg

gg N

cv

Phase Velocity

Group Index

Group Velocity

λ

Refractive Index n

Pulse Delay

(nsec/km) Lg /

Material Dispersion

DMAT(psec/nm-km)

94


Material Dispersion (cont.)

ddnn

ccN

vLg

g

g 11

2

2

dnd

cDMAT

ddn

dnd

ddn

cdd

Lg

2

211


Waveguide Dispersion

• Assume the core and the cladding to have NO material dispersion

• For a single-mode fibre, there is NO modal dispersion

• Yet, for the HE11 mode, its effective index of, /k (which determines its phase velocity) changes with wavelength, i.e., WAVEGUIDE dispersion:

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Waveguide DispersionStep-Index Propagation

n

k

)1( n0 1 2 3 4 5 6

HE11TE01 TM01

HE21

EH11

HE31

HE12HE41

EH21

TM02

HE22

TE02

ncore

nclad

)/1( V


Waveguide Dispersion

• As increases, diffraction pushes the mode deeper into the cladding, so that its effective index decreases, approaching that of the cladding

• Conversely, as decreases, the mode is very well guided, with most of its power within the core. Consequently, its effective index increases, approaching that of the core

98


Variation of Material Dispersion With Wavelength for Silica-based Fibres


Material dispersion vs. wavelength for Silicon and Germanium-doped SiO2

13% Ge

-320-280-240-200-160-120-80-40

600 800 1000 1200

WAVELENGTH (nm)

MAT

ERIA

L D

ISPE

RSIO

N

(ps/

km-n

m)

100


CUSO 09.03.2016

26


Waveguide dispersion versus V value for single-mode fibre

2

0

-2

-4

-6

1 2 3

NORMALIZED FREQUENCY V

WAV

EGU

IDE

DIS

PERS

ION

(p

s/km

-nm

)

0.5

0

-0.5

-1

-1.5

DIS

PERS

ION

CO

EFFI

CIEN

T D1 2 3 4 5 6 7 8

CORE RADIUS a (μm)


Dispersion in Single-mode Fibres• Fibre-optic telecommunication systems are DIGITAL:

information is encoded into PULSES

• Silica (SiO2) is dispersive:

• A pulse propagating through a dispersive fibre, moves with a wavelength-dependent group delay:

(N - group index, L - propagation distance)

)( nn

cLN

NcLL

g

/)(

)()(v

)(g

102


Dispersion

kmnmps)(

kmnmps)(1

2

2

2

ddDS

dnd

cdd

LD g

SlopeDispersionSDispersionD

Due to Dispersion, the propagation delay depends on the wavelength:


Every optical pulse comprises a rangeof wavelengths (or frequencies)

time

Optical spectrum)/( c

)(

An optical pulse with average wavelengthor average frequency

104


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27


Every optical pulse comprisesa range of wavelengths

• The optical source emits many wavelengths (LED):

• The optical source has a very narrow linewidth but the modulation process increases it (DFB+Chirp):

• Ultimate reason : the source is very narrow with no chirp (external modulation), but still from basic theory: A time varying signal has a finite spectrum which increases with the speed of the variation

is not zero either because:

Source

Chirp


Every optical pulse comprisesa range of wavelengths

• Ultimate reason: A time varying signal has a finite spectrum which increases with the speed of the variation

WidthPulse1;

WidthPulse1 2

c

RateBit

At 10Gbit/sec at =1550nm:

nm08.0;GHz10

106


Dispersion gives rise to pulse spreading

1 1

1 10

11 1

Errors!!!

Normal dispersion (SMF28 below 1310nm):Longer wavelengths travel faster

0


Gaussian Pulse Spreading as a Function of Distance

For large z, the width increases at the rate , which is inversely proportional to the initial width .

0vD0

108


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28


Dispersion

•Miracle #2:Single-mode fibres(of the conventional type, e.g. SMF28) have ZERO dispersion at 1310nm!

•Therefore, NO pulse broadening, resulting in virtually infinite bandwidth (capacity)

•(True to 1st order only)


Dispersion – some relations

LtjAE )(exp

303

202

010

61

21

)()(

0

)(

n

n

ngvd

d 101

110


Dispersion

Dispersion Slope

Dispersion (cont.)

2221

cdd

dd

vddDD

g

323222 cc

ddDS


Dispersion Limit

BTLD BD

1

Dispersion

Line-Width

Link Length (max)

Bit Width Bit Rate

nmkmnmpsDsGbB 5.0;/17;/5.2 Direct Modulation

kmLD 47

External Modulation (NRZ): ;2.1 B 22 /6100 sGbkmB

LD

112


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29


Trends in Fibre-Optic Telecommunication systems

)kmps/(nm17)1550( D

0)1310( D

• Transmission at 1550nm:Lowest fibre loss, EDFA amplification, but

for the fibre infrastructure (SMF28).

O.K. up to [email protected]/sec

• Transmission at 1310nm:

but higher fibre loss and no amplification


Dispersion Shifted (or Flattened) Fibres

The dispersion characteristics of DSF and DFF were engineered by using sophisticated refractive index profiles to control waveguide dispersion

0)1550( D

(DSF) (DFF)

114


Typical Index Profiles

1300 nm-Optimized

Dispersion-Shifted

Dispersion Flattened


Topographic index profiles of different types of optical fibres

Depressed-Cladding Single-Mode Fibre

Triangular Index Dispersion-Shifted Single-Mode Fibre

Quadruply-clad, Dispersion-Flattened

Single-Mode FibreGraded- Index

Multimode Fibre

116


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III. Nonlinear effects in fibresA. Generalities


Preamble

Presently, nonlinear effects are mainly considered detrimental intransmission systems, HOWEVER• Nonlinear effects are the only route to control light by light• Not so far from reality, applications already in use include:

▫ Robust long-haul transmission in optical networks

▫ Wavelength conversion and data demultiplexing

▫ Optical regeneration

▫ All-optical switching

▫ Distributed sensing

▫ Supercontinuum sources (e.g. for medical applications)

• Essential in future high-capacity (all-optical) networking!!

118


Basics

Nonlinear medium The polarization field P is no longer proportional to the incident field E

Nonlinear effects are weak Taylor's limited expansion of P over E

- Scalar approximation of the expansion.

- Using real fields is required (no complex amplitude!)

2 31 2 3

32 3

1 12 62 4o

a a a

d

P E E E

E E E


BasicsWave equation obtained from Maxwell equations in a homogeneous dielectric medium:

Decomposition of the polarization into a main linear contribution and a nonlinear correction term:

Wave equation:

Nonlinear term: source term in the wave equation radiating into a linear medium of index n.

Since this term is weak, it is usually handled as a perturbation.

2 222 2 21

ooc t t

E E P

o NLP E P

2 222 2 21

o NLc t tE E P

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Nonlinearities in optical fibres

• Silica symmetry 2nd-ordernon-linearities are negligible

• Third-order non-linear response

• Power densities 0.1 GW/m2

▫ Already reached with P~10mWin standard fibres

• Quasi-linear response


Nonlinearities in optical fibres

• Two types of nonlinear effectscan be distinguished:▫ Inelastic scattering effects

(Raman, Brillouin): the incidentphotons are annihilated to createa (normally) lower energyphoton and a phonon (netenergy loss)

▫ Elastic effects (Kerr effects):the incident photons sufferphase and/or frequency shiftsbut overall there is no energyloss.

122


Optical effects in fibres

Medium reaction Scatterings

Line

aref

fect

s

Medium polarization

Index of refraction

Dispersion n() ‐ Absorption ()

ElasticRayleigh scattering

Spontaneous inelastic scatterings (phonon-photon)Brillouin scattering - Raman scattering

Non

linea

ref

fect

s Medium polarization

Index of refraction n = no + n2 I

Altered spectrumHarmonic generation - Pulse compression - Solitons

Stimulated inelastic scatterings

Scattered wave sustains the scattering wave

Amplification of the scattered wave

GainBrillouin scattering - Raman scattering

n =

P = (E) E


The Clausius-Mossotti relation

1 using 13 2 3

rr

r o

N

Clausius-Mossotti relation

This gives an essential relation between a microscopic quantity intrinsic to a molecule− the polarisability − and a macroscopic quantity giving the global dielectric response of a material − the susceptibility .For a tenuous material with << 1 (low pressure gas), the dielectric response is proportional to the molecule density (≈ pressure): /

In presence of an electric field the total dipole of a polar molecule is:

Intrinsicdipole

Induceddipole

N: Molecule density [number/m3]

: Molecule polarisability (≠!)

124


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32


The Elasto-optic effect

In the optical regime, the Clausius-Mossotti relation can be expressed for the index of refraction :

2

2

12 3 3

A

o

n N Nn M

with

NA : Avogadro’s constant : Material densityM : Molar mass

The refractive index n depends on the material density n will get higher when the medium is compressed:

2 2( 1)( 2) 06

dn n nd n

Elasto-optic effect


The electrostriction

How uncharged bodies can beattracted by an electric field ?

A dielectric object in a non-uniform field feels a force toward regions of higher field strength.

2F E E E

Non-uniformitystrength

Inducedcharges

Forcestrength

126


The electrostrictionThe exact expression for the electrostrictive force is:

2( )2o rdF E

d

Electrostriction causes a material compression fromlower to higher field strengths.In optics the wave vibration is so fast that this mechanicalcompression will only feel the time-average fieldenvelope and the squared field can be straightforwardlyreplaced by the intensity: 221

2 o oI n c E

Replacing by all previously deduced expressions:2 2

2 2

2 ( 1)( 2)3o o

dn n nF I Ic d nc


The electrostriction

2212 o o

I nI n c EI n

Electrostriction can be seen like the reverse of the elasto-optic effect:

2 2

2 2

2 ( 1)( 2)3o o

dn n nF I Ic d nc

In nonlinear optics high intensities are required, so thatfocussed or guided beams are normally presenting a strong intensity gradient:Electrostrictive forces are important in dense mediaThey cause internal pressure and compressionDensity change causes a refractive index change

through elasto-optic effectThe net result is an intensity-dependent refractive

index n(I)

1I n dn n dn I

I n n d d I

128


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3rd order nonlinearity

In an optically isotropic medium the symmetry prohibits the presence of terms to an even power in the polarization expansion:

Nonlinear polarisation:

Let consider an incident wave :

3 34NLP E

( )Re e o

zj t n ct EE

( )23

3 ( )3 3

frequencysource

frequencysource

3 Re e

3Re e

o

o

zj t n cNL

zj t n c

E E

E

P

The 3rd harmonic generation is difficult to achieve, since the source term must propagate at the same velocity as the field term n=n3


3rd order nonlinearity

The frequency term will induce a change ∆ in the medium susceptibility:

using the intensity

that will cause the following change ∆n in the refractive index :

Optical Kerr effect: with

Typical value: n2 = 3.2 10-20 m2/W in silica optical fibres.

3233 6o o

NLo n c

E IPE

2

2o oc E

nI

2 2 2

32

32

o ocnn I n In n

2( )n I n n I

2 2 2

3

23o oc

nn

130


Physical origin of optical Kerr effectThe optical Kerr effect in amorphous dielectric materials (silica, soft glasses, etc…) has essentially 2 origins:

Eric L. Buckland and Robert W. Boyd, Opt. Lett. 22, 676-678 (1997)

1. The nonlinear response of the inducedmolecular dipoles in the material to the applied electric field, known as the electronic contribution.It is weak, but is always present and has no observed frequency limit(fast response)

2. The refractive index change due to the electrostriction induced by a gradient of intensity, known as the electrostrictive contribution.It is the dominant contribution (~1.5X larger), but is observed only in focussed beams and has a frequencylimit of approx. 300 MHz in standard optical fibres (slow response).


Nonlinear effective length

• Since the 3rd order nonlinearity is scaled by the intensity I and the intensitydecays during the propagation as a result of the linear loss , it is possible to define a fictitious effective length Leff that would result in the samenonlinear transformation for a lossless medium

0 0

1 1(0) ( ) (0)e (0) (1 e ) (1 e )L L

z L Leff effI L I z dz I dz I L

1 22 km in silica optical fibre (loss 0.2 dB/km)L

effL

132


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34


Nonlinear effective area

• In any guided mode or real light beam the intensity I shows a transversal distribution I(x,y) that is non-uniform. It is possible to define a fictitiouseffective area Aeff that would result in the same nonlinear transformationfor an uniform intensity distribution.

22

2

4

( , )( , ) ( , )

( , )o eff

F x y dxdyI x y I F x y A

F x y dxdy

280 m in standard single mode fibre (MFD 10 m)effA


III. Nonlinear effects in fibresB. Self- and cross-phase modulation

134


Cross phase modulation on CW light

• Let consider 2 CW optical waves propagating in 2 distinct modes(different frequency or direction or polarization)

• The nonlinear polarization induced by the superposition of the 2 fields is:

1 1 2 21 1 2 2

( ) ( )and, e , ej t k z j t k zz t E z t E E ERe Re

1 1

2 2

31 2

1 2 1

1 2 2

3

3 ( )1

3 ( )2

( , )

( , ) 2 ( , )

2 ( , ) ( , )

Term proport.to

Term proport.to

3 , ,

3 e ,

3 e ,

inefficient terms

NL

j t k z

j t k z

z t

z t z t

z t z t

z t z t

E E E z t

E E E z t

P E E

E

E

2 2

2 2

Re

Re


Cross phase modulation on CW light

• The effective refractive index experienced by each wave is:

• The effect of the other wave is doubled on the effective index!

• This causes spurious phase shifts in high precision phase sensitive systemsin case of power imbalance (gyroscope).

• This may be used to realize all-fibre "saturable absorber" and figure-8 lasers.

(1)1 2 1 2

(2)2 2 1 2

: ( 2 )

: (2 )

For wave

For wave

o

o

n n n I I

n n n I I

E

E

136


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35


Nonlinear optical loop mirror

• All-optical re-sharpening ofpulses

• Elimination of backgroundnoise

• Can be also transformed intoa switching element by anintense control beam

OscDet

PC

12 Km DSF

E2E1

[ Saturable absorber ]

Input OutputOscDet

PC

12 Km DSF

E2E1

[ Saturable absorber ][ Saturable absorber ]

InputInput Output

2

1cos12

T


Time-dependent self phase modulation

Frequencychirp

138


Nonlinear envelope equation

• Let express conveniently the field as a harmonic carrier term with a slowlymodulating envelope:

• Under the slowly-varying envelope approximation the wave equationincluding the 3rd order nonlinearity perturbation can be rewritten in asimplified form for the envelope:

• Let redefine a normalized envelope U expressed in a reference framemoving at the group velocity 1/1 given by the normalized time = t - 1z :

( )( , ) Re ( , ) e o oj t zz t A z t E

222

1 22 2A A j A A j A A

z t t

Nonlinear Schrödinger Equation

2( , ) e ( , )z

oA z P U z


Self phase modulation

• Assuming for simplication the absence of dispersion (2=0), the nonlinearSchrödinger equation for the normalized envelope takes the simple form:

• The general solution to this equation takes the following form in z=L:

• The spectrum of the pulsebroadens symmetricallyaround the centre wavelength.

2e zoU j P U U

z

2(0, )( , ) (0, ) e (0, )e o effNL j P L UjU L U U

Phase modulation

140


CUSO 09.03.2016

36


Self phase modulation

• This does not change the temporal distribution of the signal intensity, butmodulates the instantaneous frequency through the signal:

• When the signal intensity grows, the frequency shifts to the red,when the signal intensity decreases, the frequency shifts to the blue.

• Case of the Gaussian pulse:

2(0, )inst NL o effP L Ut t

2

2 22 2

2

(0, ) (0, )e eo oU U

2

22

2

4 einst o effo

oP L

t

I(t)(t)

Frequency chirp


Pulse compression

• The chirp in the instantaneousfrequency is similar to that caused bynormal dispersion, however with nopulse broadening.

Pulse compression after propagation ina medium showing anomalous groupvelocity dispersion (D > 0).

t

I(t)(t)

• Propagation through an optical fibrewith D > 0

• Reflection in a chirped fibre Bragggrating

• Pair of diffraction gratings

dl1

l2

l1

l1 > l2l2

142


Self phase modulation & Dispersion

• Anomalous dispersion (D > 0) and optical Kerr effect (n2 > 0) result in an inversed chirp on the instantaneous frequency.

Nonlinear + dispersivemedium

Nonlinearmedium

Dispersivemedium


P(t)

t

Dispersion

SPM

Solitons• With the adequate balance between power,

dispersion and duration, a pulse can remain undistorted

• Solitons are the only stationary solution of light propagation in nonlinear and anomalous-dispersive regime with 0:

with amplitude making a notable phase shift by SPM over the distance LGVD.

222

1 2

21

2

-, sech e GVD

zjL

oo

A A j A j A Az t t

t zA z t A

Io

sech2(t/to)

0 ttoto

22oo

A

2sech( )e et tt

144


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37


Solitons in transmission lines

• All intense pulses in a fibre evolve into solitonssooner or later Robust propagation regime inlong-haul high-capacity transmission systems


Imaging the soliton

Dispersive medium Dispersive + nonlinear medium

146


III. Nonlinear effects in fibresC. Modulation instability


Principle of Modulation Instability• What is the combined effect

of self phase modulation anddispersion on a smallamplitude fluctuation on aCW wave?

• The red shifted and blue-shifted components travel atdifferent speeds.

• In the anomalous dispersionregime the perturbation getsnarrower Modulation instability

• The wave eventually breaksup into a chaotic train ofsolitons.

148


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38


Principle of Modulation Instability• What is the combined effect

of self phase modulation anddispersion on a smallamplitude fluctuation on aCW wave?

• The red shifted and blue-shifted components travel atdifferent speeds.

• In the anomalous dispersionregime the perturbation getsnarrower Modulation instability

• The wave eventually breaksup into a chaotic train ofsolitons.

t

I

t

I

t

I

1550.0 1550.5 1551.0 1551.5Wavelength, nm


Experimental Modulation InstabilityP = 100 mWD = 0.025 ps·nm-1·km-1

1445 1450 1455 1460 1465-70

-60

-50

-40

-30

-20

-10

D=0.01 D=0.025

Det

ecte

d po

wer

(dB

m)

Wavelength (nm)

1445 1450 1455 1460 1465

-70

-60

-50

-40

-30

-20

-10

P=0.3 W P=0.1 W

Det

ecte

d po

wer

(dB

m)

Wavelength (nm)

1540 1545 1550 1555 1560 1565

-60

-50

-40

-30

-20

-10

0

Wavelength (nm)

Nor

mal

ized

spe

ctru

m (

dB)

This pulse break-up is at the heart of supercontinuumgeneration

150


Supercontinuum• Extreme modulational instability associated with other nonlinear effects

(Raman, solitons) leads to the generation of a broad continuous spectrumfrom a single frequency source

1400 1450 1500 1550 1600 1650

-60

-50

-40

-30

-20

-10

0

0.3 W 0.9 W 1.5 W 2.1 W

Nor

mal

ized

pow

er (

dB)

Wavelength (nm)

1445 1450 1455 1460 1465-30

-20

-10

0


Supercontinuum

• The physics of supercontinuum is quite complex as a result of the interplaybetween several nonlinear responses.

• Photonic crystal fibres make possible an advanced engineering of the dispersion and anomalous GVD in the visible

152


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39


Supercontinuum


III. Nonlinear effects in fibresD. 4-wave mixing and parametric amplification

154


Intuitive 4-wave mixing

E1

E2

|E1+E2|2

n

E1out


Four wave mixing

Anti-Stokes Stokes

Pumps

156


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Parametric amplification

• Let consider a nonlinear optical medium irradiated by an intense opticalwave at frequency P named pump. A weak signal wave at frequency Salso propagates in the medium.

• A partially degenerate four wave mixing can then be initiated with1=2=P and 3=S.

Assuming S<P four-wave mixing ofpump and signal will create a new wave atfrequency I=P+(P-S) called the idlerwave of the process that will grow.

I

S

P

I S

P

S

P

I

In turn the idler will combine with thepump through a partially degenerate fourwave mixing with 1=2=P and 3=I.The coupling of pump and idler willcontribute to the signal.

• It is possible to realize parametric oscillators (laser) by placing theamplifier in a closed loop configuration (cavity).


III. Nonlinear effects in fibresE. Stimulated Brillouin and Raman scatterings

158


Physics behind inelastic scatterings

• Oscillatory movement of theentire molecular chain.

• Classical wave, slow vibration transporting high momentum.

• Acoustic-like vibration.

• Vibrational oscillation inside themolecular chain.

• Quantum excited state, fastvibration with small momentum.

• Optical-like vibration.

k

Acousticbranch

Opticalbranch

In a solid state constituted of polyatomic molecules, the cohesive force between molecules allows a collective vibration into two distinct vibrational modes:

Energy-momentum diagram(dispersion curve)


Optical effect of inelastic scatterings

Optical branch: Raman scatteringHigh energy phononswith low momentumLarge spectral shift (~12 THz or 96 nm at o=1550 nm in SiO2) and non-strict phase matching.

Acoustic branch: Brillouin scatteringLow energy phononswith high momentumSmall spectral shift (~11 GHz or 0.07 nm at o=1550 nm in SiO2) and strict phase matching.

, k

V

´, k´

O OSi

h

h'

Ener

gy h h'

EVib=hR

160


CUSO 09.03.2016

41


Optical effect of inelastic scatterings

Optical branch: Raman scatteringHigh energy phononswith low momentumLarge spectral shift (~12 THz or 96 nm at o=1550 nm in SiO2) and non-strict phase matching.

Acoustic branch: Brillouin scatteringLow energy phononswith high momentumSmall spectral shift (~11 GHz or 0.07 nm at o=1550 nm in SiO2) and strict phase matching.

ANTI‐STOKES scatteringsSTOKES scatterings

Rayleigh scattering

Brillouin scattering Brillouin scattering

Raman scatteringRaman scattering


Spontaneous inelastic scatterings

Spontaneous inelastic scatterings are generated by thermal phonons The average number of phonons is governed by Bose-Einstein statistics

Spontaneous inelastic scatterings are purely thermally activatedand are thus linear processes.

n = 1

ehkT ‐ 1

• Anti-Stokes scattering annihilates a phonon Scattering coefficient is proportional to n

CAS ~ n = 1ehkT ‐ 1

• Stokes scattering creates a phonon Scattering coefficient proportional to +1n

CS ~ n + 1 = ehkT

ehkT ‐ 1

Stokes shift Average phonon number

Raman 13.2 THz 0.14 Anti-Stokes < StokesBrillouin 11 GHz 570 Anti-Stokes ~ Stokes

162


Spectral characteristics of inelastic scatterings

-40

-30

-20

-10

0

1525 1550 1575 1600 1625 1650 1675 1700

Wavelength, nm

Rayleigh scatteringat incident frequency

StokesRaman scattering

13 THz

2.75 THz

-30 -20 -10 0 10 20 30

-100

-95

-90

-85

-80

-75

-70

-65

Frequency, GHz

StokesBrillouin

Anti-StokesBrillouin

Rayleigh

11GHz

27 MHz

The linewidth of Brillouin scattering isruled by the acoustic loss (lifetime ~6ns)


Principle of Brillouin stimulated scattering

Interference +Electrostriction

Photoelasticity+ Diffraction

Pumpwave

Signalwave

Acousticwave

164


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42


Principle of Brillouin stimulated scatteringPump wave

Signal wave

Beat signalintensity

Acousticidler wave

Refractiveindex grating

Optical powertransfer


Principle of Brillouin stimulated scatteringPump wave

Signal wave

Beat signalintensity

Acousticidler wave

Refractiveindex grating

Optical powertransfer

Gain

166


Stimulated Raman scatteringFor a forward propagating pump and a backward signal the interaction isgoverned by the following set of coupled equations:

P PR P S P P

S

SR P S S S

dIg I I I

dzdI

g I I Idz

In absence of pump depletion:

(0)( ) (0)e R P eff Sg I L LS SI L I

(1 e ) /PLeff PL with

Nonlinear effective length

mW

1310Rg

1 W of pump power through 1 km of fibre

Net gain = 1.6


Cascaded Raman generation

• Each generated Stokes wave can act as a pump to generate an additional order

168


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Amplifiers based on stimulated scatterings

• Raman-based amplifiers are very attractive: large bandwidth, wavelengthflexibility and low noise. But: low gain high pump power

Pump

• Brillouin-based amplifiers also show a good wavelength flexibility and givea much higher gain, but very limited bandwidth and poor noise figure.


Brillouin limits the power handling capacity

Light in(continuous)

Amplifiedbackscattered

light

0

1

2

3

4

5

0 2 4 6 8 10 12 14 16

Opt

ical

pow

er (

mW

)

Input light (mW)

Loss

Light out

Brillouin mirror

16 effincrit

B eff

AP g L

Smith's model

170


IV. Distributed fibre sensing


Concept of distributed sensingThe fibre combines 2 functions: sensing element + signal propagation

1D

The sensor continuously informs about a large structure, that can be…

2D 3D

172


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Sensing using Scatterings in Optical Fibres

T, T,

• Scattering processes used for sensing applications▫ Rayleigh is a pure distributed reflection with a random amplitude.▫ Raman scattered magnitude is temperature dependent▫ Brillouin lines are spectrally temperature and strain sensitive


Distributed Sensors: ClassificationLinear

Elastic or InelasticBackscatterings

A small fraction of the scattered light is coupled

back into the fibre, similarto a continuously

distributed reflection.

Type ofinteraction

NonlinearParametric process

2 counterpropagatingwaves are coupledthrough a nonlinear

interaction involving a 3rd idler wave.

174


Spontaneous scattering-based sensors

Fibre under testDetection

Pulsed laser

Directionalcoupler

Lightpulse

P(z) = 12 vgr Po S(z) d (z) e- 2z

S(z) = 38o

n o(z)

2

: Recapture factor of the backscattered light (o: mode radius)

d(z) : Scattering coefficient

: Attenuation : Pulse temporal width

vgr : Group velocity


Spontaneous scattering-based sensors

Fibre under testDetection

Pulsed laser

Directionalcoupler

Lightpulse

0.00

0 10 20 30 40

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Res

pons

e

Distance (km)

The activating pulse necessarilyundergoes linear attenuation due to Rayleigh scattering.

The sensing scattering process must be smaller or equal to Rayleigh scattering. If not:

Larger depletion and reduced distance range

Biased measurements (pulse intensitycontains «sensing history»)

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Optical Time-Domain Analyzer

Single freq. laser

Sensing fibre

Oscilloscope

Amplitude EOM

Detector


Optical Frequency-Domain Analyzer

Single freq. laser

Sensing fibre

Spectrum Anal.

Amplitude EOM

Detector

1:1 equivalent to Time-Domain analysis!

178


Coherent Optical Frequency-Domain Analyzer

Single freq. laser

Sensing fibre

Spectrum Anal.Detector

Signal from different positions given different beat notes

t

i

t

Laser coherence length must be larger than distance range!


Optical Correlation-Domain Analyzer

Single freq. laser

Sensing fibre

Oscilloscope

Amplitude EOM

Detector

Delay line X Multiplication somewhere…

Each point can be addressed randomly and statically

Low frequency detection possible weak signals!

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CUSO 09.03.2016

46


Principle of Raman distributed sensing

• Anti-Stokes scattering annihilates a phonon Scattering coefficient is proportional to n

CAS ~ n = 1ehkT ‐ 1

• Stokes scattering creates a phonon Scattering coefficient proportional to +1n

CS ~ n + 1 = ehkT

ehkT ‐ 1

Based on the temperature dependence of Raman spontaneous scattering cross section, that is by essence thermally activated.

Temperature is evaluated by measuring the ratio between Anti-Stokes and Stokes intensities :

IASIS

= CAS IincCS Iinc

= ehkT


Raman distributed sensing

0

200

400

600

800

1000

1200

140010 15 20 25 30

Temperature (deg C)

Dep

th fr

om s

urfa

ce (m

)

Multimode Fiber

Stokes + Anti‐Stokes

Dét.

Dét.

Stokes

Anti‐Stokest

Pulsed Laser

Vertical temperature profile of the JindrichCoal mine in the Czech Republic based on 24-hr averaged data

• Fast & cost-effective solution for range up to 10km (Intermodal dispersion ~1 ns/km)

• < 1K temperature & 1m spatial resolutions.• Very sensitive to wavelength-dependent losses! Biased temperature measurement.

182


Brillouin distributed sensing

• Brillouin scattering is characterized by the Brillouin shift

• The Brillouin shift depends on the acoustic velocity of the medium, which is temperature and density dependent

Brillouin Frequency Shift:

B = 2nVA /

B(T,) depends ontemperature and density



• Temperature effects on the Brillouin scattering spectrum

Frequency Difference, GHz

0

1

Freq

uenc

yD

iffer

ence

, GH

z

12.72

12.76

12.80

12.84

12.88

Temperature, degC- 40 0 40 80

Bri

lloui

n G

ain,

x 1

0 -1

1m

/W

11.4 11.5 11.611.3 11.7

T= 30 degC

T= 90 degC

T= - 25 degC

Temp coeff . :

1 MHz/deg

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• Strain effects on the Brillouin scattering spectrumDeformation = L/L Density change

Freq

uenc

y D

iffer

ence

, GH

z

10.8

10.9

11.0

11.1

11.2

Deformation, %

0 0.2 0.4 0.6 0.8

Strain coeff . :

500 MHz/%

L = 0%L

L = 0.3%L

L = 0.5%L

Frequency Difference, GHz

0

1

2

3

12.9 13.0 13.112.8

Brill

ouin

Gai

n, x

10

-11

m/W

Effect of strain


Brillouin Optical Time-Domain Analysis

• Based on the use of a probe signal which wavelength is precisely controlled and scanned

Record probe intensitywhile its wavelength isscanned

186


Brillouin Optical Time-Domain Analysis

Inte

nsity


Strain distributed sensing

0 10 20 30 40

0

0.05

0.10

0.15

Position along the fibre, m

Elon

gati

on, %

0 10 20 30 40

0

0.05

0.10

0.15

Position along the fibre, m

Elon

gati

on, %

150 g

1.5 N

90 cm

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The refractive index effect

n(T)L

Integrated phase:2

2

Phase shift due to temperature:

{ {

Thermo-optic

coeficient

Thermalexpansioncoeficient

Equivalent refractive indexcoefficient

Identical effect for strain: T → xx

2

2 1

1


The refractive index effectThe frequency compensation:

1. Initial condition:

2. New phase due to T :

3. Compensation with :

2o

o

n Lc

2 1 1[1 ( ) ]o

dn dLnL Tc n dT L dT

2 ( ) 1 1[1 ( ) ]oo

dn dLnL Tc n dT L dT

Typical compensation in silica: 1.25 GHz/K & 60 MHz/

Classical implementations:Unbalanced

Mach-ZehnderInterferometer Fibre Bragg grating

The longer the exposed length, the higher the phase sensitivity!

190


Rayleigh-based sensing principle

• An optical pulse is use to interrogate the fiber• Backscattered light originated from the different scattering points

interfere, resulting in a zigzag-shaped trace.

fiber

optical frequency, refractive index and pitch

Coherent optical time-domain reflectometry


0 2 4 6 8 10 120

0.2

0.4

0.6

0.8

1

1.2

Distance [m]

Sign

al a

mpl

itude

[a.u

.]

frequency f0, temperature T0

Characteristic of Rayleigh traces

0 2 4 6 8 10 120

0.2

0.4

0.6

0.8

1

1.2

Distance [m]

Sign

al a

mpl

itude

[a.u

.]


frequency f0, temperature T0 - 26 mK

3

Temperature dependence

0 2 4 6 8 10 120

0.2

0.4

0.6

0.8

1

1.2

Distance [m]

Sign

al a

mpl

itude

[a.u

.]


0 2 4 6 8 10 120

0.2

0.4

0.6

0.8

1

1.2

Distance [m]

Sign

al a

mpl

itude

[a.u

.]


frequency f0 + 20 MHz, temperature T0

Frequency dependence

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49


Rayleigh-based sensing principle

,freq change

′ ∆ , ∆

Trace comparison, ∆ ∝ ∆

The similarity is determined by cross-correlation

, ∗ ′ ∆ , ∆ 4

0 2 4 6 8 10 120

0.2

0.4

0.6

0.8

1

1.2

Distance [m]

Sig

nal a

mpl

itude

[a.u

.]


0 2 4 6 8 10 120

0.2

0.4

0.6

0.8

1

1.2

Distance [m]

Sig

nal a

mpl

itude

[a.u

.]


frequency f0, temperature T0 - 26 mK

0 2 4 6 8 10 120

0.2

0.4

0.6

0.8

1

1.2

Distance [m]

Sig

nal a

mpl

itude

[a.u

.]

frequency f0, temperature T0frequency f0, temperature T0 - 26 mK

frequency f0+ 30 MHz, temperature T0 - 26 mK

, ∆temp change

The shape change induced bytemperature can be fullycompensated by the effect ofchanging optical frequency.


C-OTDR – Spectral measurementsSpectral cross-correlation

‐200 ‐150 ‐100 ‐50 0 50 100 150 200

‐0.2

0

0.2

0.4

0.6

0.8

1

1.2

Frequency shift (MHz)

Correlated

value

(a.u.)

Experimental dataQuadratic fitting

Frequency accuracy:▫ 3 MHz (2mK @ 300K)▫ 1k averages▫ Scanning step: 10 MHz▫ Time: 40s

Distance [m]

Freq

uency shift [M

Hz]

0 4 8 12 16 20 24

‐150

‐100

‐50

0

50

100

150

200

(b)

194


High spatial resolution distributed sensing

195

optical fibres - cuso...l.thévenaz ‐epfl ‐introduction to optical fibres, nonlinear effects...

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