FOT_MEng2004_FEUP

Fibre Optic TechnologyMestrado Eng. Electrotécnica e de Computadores

(2003/2005)

António Lobo Prof. Associado da UFP Prof. Convidado da FEUP

© A.Lobo (2004) 2

Course Topics

1. Optical Fibre: Basic Characteristics 2. Light Propagation in Fibres and Related Optical

Effects 3. Types of Optical Fibre 4. Passive Fibre Optic Devices 5. Active Fibre Optic Devices 6. Other Fibre Optic (Hybrid) Devices 7. Fibre Device Fabrication Techniques

© A.Lobo (2004) 3

Reading Material

Optical Fiber Communications G. Keiser, Optical Fiber Communications, 3rd Ed., McGraw-Hill (2000). J. M. Senior, Optical Fiber communications, Prentice Hall (1985). G. P. Agrawal, Non-Linear Fiber Optics, 2nd Ed., Academic Press (1995). H. Kolimbiris, Fiber Optics Communications, Pearson Prentice Hall (2004). Optical Fiber Technology K.T.V. Grattan and B.T. Meggitt, Optical Fiber Sensor Technology, Vol. 1 and 2, Chapman & Hall

(1995). B. Culshaw and J. Dakin, Optical Fiber Sensors: Principles and Components, vol.II, Artech House

(1988). B. Culshaw and J. Dakin, Optical Fiber Sensors: Components and Subsystems, vol.III, Artech House

(1997). R. Kashyap, Fiber Bragg Gratings, Academic Press (1999). C. Hentschel, Fiber Optic Handbook, HP Electronics Instruments Dept, ISBN:3-9801677-0-4. D. Derickson, Fiber Optic Test and Measurement, Hewlett-Packard Co., Prentice-Hall Publs. (1998). Jeff Hecht, Understanding Fiber Optics, 4th Ed., Pearson Prentice Hall (2002). General Optics E. Hecht, Optics, 4th Ed., Addison Wesley (2002) M. Born and E. Wolf, Principles of Optics, 7th Ed. Cambridge Univ. Press (1999). Other material Class notes and handouts with each of the class topics provided in this syllabus. Optical Fiber Sensors (OFS) Conference Proceedings. Optical Fiber Communications (OFC) Conference Proceedings.

© A.Lobo (2004) 4

Assessment to Final Grade

The grade is based on the following:

Final examination (50%) Home Assignments (20%) Term Paper Project (30%)

Examination is based on class lectures, reading assignments, homework problems and class handouts.

A Term Paper is required.

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Term Paper ProjectLISTING OF POTENTIAL SUBJECTS FOR TERM PAPER

(Paper is due May 29, 2004)

1. Optical fibre propagation in fibres 2. Non-linear optical fibre effect 3. High strength fibres 4. Fibre optic sensors (many choices here) 5. Environmental effects in fibres 6. Fibre optic cable designs 7. Wavelength division multiplexing devices 8. Fibre optic filters. 9. Fibre Bragg gratings 10. Microstructured Fiber Devices 11. Fibre optic modulators 12. Dispersion compensation devices 13. Plastic optical fibre for communications 14. Aging effects in fibre optics 15. Photonic crystal fibres 16. Active fibre optic devices in communications 17. Optical power propagation in fibres 18. Fibre Lasers 19. Long wavelength fibre applications 20. All-Fibre optic signal processing 21. Optical fibre technology for automotive applications 22. Optical fibre technology for biomedical applications 23. Optical fibre technology for environmental applications

© A.Lobo (2004) 6

Acknowledgements

Prof. David Jackson – Head of Applied Optics Group, School Physical Sciences, Univ. Kent (UK).

Prof. Philip Russell – Head of Optoelectronics Group, Univ. Bath & CTO of Blaze Photonics Ltd. (UK)

Prof. Govind Agrawal – Optical Communications Group, Univ. Rochester (USA).

Prof. Xiaoyi Bao – Fiber Optics Group, Univ. Ottawa (Canada).

Prof. Jose L. Santos – Head of UOSE, INESC Porto & FCUP, Univ. Porto (Portugal).

Dr. Adrian Podoleanu - Applied Optics Group, School Physical Sciences, Univ. Kent (UK).

Dr. David Webb – Photonics Research Group, Aston Univ. (UK).

Dr. Hector Guerrero – Lab. Optoelectronica, Dept. Ciencias Espacio, INTA (Spain).

Dr. Ralf Pechstedt, Bookham Technology Plc. (UK).

Prof. Y. J. Rao – Dept. optoelectronics Eng., Chongquing Univ. & General Manager of Chongqing Bao Tong Optical Fiber Technology Ltd. (China)

Dr. Christian Hentschel – Boeblingen Instruments Div., Hewlett-Packard GmbH (Germany).

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1. Optical Fibre: Basic Characteristics

Roman Times (Italy) Glass is drawn into fibers ?? (Venice) Decorative flowers made of glass fibers 1626 Snell (Holland) Snell’s Law 1713 Reaumur (France) Makes spun glass fibers 1841 Colladon (Swiss) Light guiding in jet of water of Geneva 1854 Tyndall (UK) Light guiding in a thin water jet 1880 Wheeler (USA) System of light pipes to illuminate homes 1888 Roth & Reuss (Austria) Bent glass to illuminate body cavities 1897 Rayleigh (UK) Analysis of waveguide 1926 Hansell (USA) Principles of fiber optic imaging bundle 1930 Lamm (Germany) Assembles first bundle of transparent fibers 1953-54 Heel (Holland) Simple bundles of clad fiber 1954 Hopkins, Kapany (UK) Image transmission w. unclad fiber bundles 1956 Curtiss (USA) Makes the first glass-clad fiber 1957 Hirschowitz & Curtiss (USA) First test fiber-optic endoscope in a patient 1960 Goubau & Christian (USA) Hollow optical guides w. periodic lenses

1.1 Historical Introduction

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1960 (May) Maiman et.al. (USA) First laser (ruby laser) 1960 (Dec.) Javan et.al. (USA) Operation of He-Ne laser 1961 Kapany and Snitzer (UK) Mode analysis of optical fiber – SingleMode Fiber 1962 Hall’s et. Al. (USA) Operation of semiconductor laser 1964 Goubau and Christian (USA) Light guide with periodic lenses 1966 Kao and Hockham (UK) Suggest that fiber loss could be <20 dB/km 1967 Kawakami (Japan) Proposes graded-index optical fiber 1970 Maurer, Keck, Schultz (USA) Fiber transmission loss 17dB/km @ 633 nm 1070-71 Dyot & Kapron (USA) Find pulse spreading lower at 1.2 to 1.3 µm 1972 Gambling et.al. (UK) Gigahertz bandwidth over 1km 1974 Kaiser & Astle (USA) Air-silica microstructured optical fiber 1975 Payne and Gambling (UK) Calculate zero material dispersion at 1.3 µm 1976 Horiguchi & Osanai (Japan) First fiber w. 0.47dB/km @ 1.2 µm & Open 3rd

Window @ 1.55 µm.


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1978 NTT (Japan) Makes SMF w. 0.2dB/km @ 1.55 µm 1981 British Telecom (UK) Transmits 140Mb/s in 49 km of SMF @ 1.3 µm 1987 Payne et.al.(UK) Develops EDFA @ 1.55 µm 1988 Mollenauer (USA) Soliton transmission on 4000 km of SMF 1991 Russell (UK) Proposes the Photonic Crystal optical fiber 1993 Nakazawa (Japan) Soliton signals over 180 million kms 1993 Mollenauer et.al.(USA) 10 Gbits through 11000 km of SMF using soliton system 1995-96 Russell et.al. (UK) Demonstrates the first Photonic Crystal optical fiber 1999 Cregan, Russell et.al. (UK) Demonstrates the Photonic Bandgap optical fiber


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1. Optical Fibre: Basic Characteristics1.2 Fibre Optic Physical Structure

Core (8-12 µm)

Cladding (125 µm)

Buffer Coating (250 ou 900 µm)

R. Maurer, P. Schultz, D.Keck (Corning Corp., 1970)

Human Hair ~ 70 µm

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1. Optical Fibre: Basic Characteristics1.2 Fibre Optic Physical Structure

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1. Optical Fibre: Basic Characteristics1.3 Index of Refraction and Index Difference

r ro o

cn

vεµ

ε µε µ

= = =

c = speed of light in vacuum (≈ 3×108 m/s) v = speed of light in medium

1

o o

cε µ

=

Permeability in vacuum = 4π×10-7 N s2/C2

Permitivity in vacuum = 8.854 ×10-12 C2/N m2

For most materials in the optical region: 1 r rnµ ε≈ ⇒ ≈

Substance nFused silica 1.458

Diamond 2.419

@ λ = 589.29 nm (Sodium D light)

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22

2 21 j

j j

An

λ

λ λ= +

−∑

Sellmeier’s Equation

Absorption Bands

Visible

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22 2

21 with jj j

j j

An b

bλ

λλ

= + =−∑

A1=0.6961663 b1=0.004629148

A2=0.4079426 b2=0.01351206

A3=0.8974994 b3=97.934062

Refractive index variation of fused silica

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1 2

1

for 1n nn−

Δ ≈ Δ≪

2 21 2

212

n nn−

Δ =

and 1 2n n>

Refractive Index Difference, also called Refractive Index Contrast

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1. Optical Fibre: Basic Characteristics1.4 Total Internal Reflection

1 1 2 2sin sinn nφ φ⋅ = ⋅Snell’s Law

Increasing θ1 progressively until θ2 = π/2 :

2

1

sin cnn

φ =

Critical angle

“Critical angle is the minimum angle necessary to obtain total internal reflection”

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1. Optical Fibre: Basic Characteristics1.5 Numerical Aperture and Acceptance Angle

2 21 2NA sino An n nθ= = −

Numerical Aperture (NA)

“Numerical Aperture express de ability of the fibre to collect light” or

“Numerical Aperture measures spreading of light from the end of the fibre”

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1. Optical Fibre: Basic CharacteristicsRelation between Numerical Aperture and Index Difference

1NA 2n≅ Δ

Fibre type NA ΔStep-Index SM 0.1 2×10-3

Graded-index MM 0.2 1×10-2

Step-index MM 0.3 2×10-2

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1. Using the Snell’s relation, how can you estimate the amplitudes of the optical rays?

2. “An optical ray at any angle θ less than the critical angle (θc) propagate along the fiber.” Is this true?

3. Definition of NA described before for singlemode fibre is frequently wrong! Why?

4. Why the index of refraction is frequency dependent?

Questions to think:

Light Propagation in Fibres and Related Optical Effects

FIBRE OPTIC TECHNOLOGY COURSE

António Lobo Prof. Associado (UFP)

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2. Light Propagation in Fibres and Related Optical Effects

2.1 The Wave nature of light. 2.2 Rays and Modes representation. 2.3 Mode Theory for fibres. 2.4 The Cut-off wavelength and V-number. 2.5 Singlemode and multimode fibre propagation. 2.6 Mode Field Diameter (MFD) 2.7 Phase velocity and group velocity. 2.8 Absorption and Scattering losses 2.9 Dispersion: Group delay and Material dispersion. 2.10 Chromatic Dispersion (CD). 2.11 Polarization effects and Birefringence. 2.12 Polarization Dependence Loss (PDL) 2.13 Polarization Mode Dispersion (PMD). 2.14 Non-linear Optical Effects

Stimulated Raman Scattering Stimulated Brillouin Scattering Four-Wave Mixing Self-Phase and Cross-Phase Modulation

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2.1 Wave Nature of the Light

Waves Electromagnetic radiation consisting of propagating electric and

magnetic fields (interference & diffraction)

Photons Quanta of energy (photoelectric effect)

The two views are related: the energy in a photon is proportional to the frequency of the wave.

DUAL NATURE

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Waves

[ ]( , ) cos ( v )Ar t k r tr

ψ " #= ⋅ ±% &' (

[ ]( , ) cos )x t A kx tψ ω= ⋅ ±

22

2

1v t

ψψ

∂∇ = ⋅

∂

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A Single Photon (“short” packet wave)

Photon Quanta of Energy: Photon (photoelectric effect)

E hν=

E → Energy of 1 photon in Joules (J) h → Planck’s constant: 6.626×10-34 J-s ν → frequency in Hz

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c → Speed of light = 2.9979 ×108 m/s; λ → Wavelength in meters; ν → Frequency in Hz n → Refractive index (vaccum=1.0000; standard air= 1.0003; silica fibre: 1.44 to 1.48)

c nλν=

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21o

o

S E B c E Bεµ

= × = ×! ! ! ! !y zE cB=

Poynting Vector

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2.2 Rays and Modes representation.

About Reflection (Fresnel Equations): E ⊥ Plane-of-Incidence

v

0

B k E

k E

= ×

=

!! !

! !i

cos( )

cos( )i oi r r

t ot t t

E E k r t

E E k r t

ω

ω

= −

= −

!! ! !i!! ! !i

ot oi orE E E= +! ! !

cos coscos cos

2 coscos cos

or i i t t

oi i i t t

ot i i

oi i i t t

E n nr

E n n

E nt

E n n

θ θ

θ θ

θ

θ θ

⊥

⊥

⊥

⊥

# $ −= =& '

+( )

# $= =& '

+( )

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About Reflection (Fresnel Equations): E || Plane-of-Incidence

cos coscos cos

2 coscos cos

or t i i t

oi i t t i

ot i i

oi i t t i

E n nr

E n n

E nt

E n n

θ θ

θ θ

θ

θ θ

" # −= =% &

+' (

" #= =% &

+' (

!

!

!

!

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Total Internal Reflection (case: ni > nt):θi ≥ θc sin t

ci

nn

θ =

Critical Angle:

2 2 2

2 2 2

2 2 2 2

2 2 2 2

cos sin

cos sin

cos sin

cos sint

t

i i i i t

i i i i t

i i i i t

i i i i t

n i n nr

n i n n

n in n nr

n in n n

θ θ

θ θ

θ θ

θ θ

⊥

− −=

+ −

− −=

+ −!

* * 1 e 0

1 r i tr r r r

I I IR

⊥ ⊥ "= =⇒ = =$

= %

! !

sint t i ii k xn n tt otE E e e θ ωβγ % &−( )= ∓" "

Evanescent wave:

Goos-Hänchen depth

1

04 2

xnλ

< Δ <Δ

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Total Internal Reflection (case: ni > nt):θi ≥ θc

*

2 2

1i i

r rr

r r e e− ΔΦ − ΔΦ

= =

= =

2 2 21

2 2 21

2

sintan

cos

sintan

cost

i i t

i i

i i i t

i

n nn

n n nn

θ

θ

θ

θ

−⊥

−

$ %−& 'ΔΦ =& '* +

$ %−& 'ΔΦ =& '* +

!

⊥ΔΦΔΦ!

21

i

t

nn=

=

Polarization TE → ΔΦ⊥

Polarization TM → ΔΦ||

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About Reflection (case: ni > nt): Phase-shiftstan t

pi

nn

θ =

Brewster Angle:

The component of electric field normal to plane-of-incidence undergoes a phase shift of π radians upon reflection when the incident medium has a lower index than the transmitting medium.

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11 2

2sin tan 1 ; is an integersin 2

kn a m mπφ

φ− $ %Δ

− − =' () *

Propagation Condition:

The optical field distribution that satisfies this phase matching condition is called MODE

Goos-Hänchen shift (ΔΦ⊥)

n1

n2

n2

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Formation of modes

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At angles for which the condition of self-consistently (i.e., as a wave reflects twice it duplicates itself) is satisfied, the two waves interfere and create a pattern that does not change with z direction.

z

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V

ξ

1 2V kn a= Δ

sin2φ

ξ =Δ

Single-mode condition

1.5712cV v π

< = =

Normalized frequency:

Propagation constant:

Dispersion Equation

1cos2

mV

πξ

ξ

− +=

(Slab Waveguide)

© A.Lobo (2004) 17


2.3 Mode Theory for fibres.

Coordinate SystemNotação

2

grad

div

rot

lap

f f

A A

A Af f

=∇

=∇

=∇×

=∇

! !i

! !

Cylindrical Coordinates (r,φ,z)

© A.Lobo (2004) 18



Maxwell´s Equations

0

BEtEB Et

E

B

µε µσ

ρ

ε

∂∇× = −

∂

∂∇× = +

∂

∇ =

∇ =

!!

!! !

!i!i

1

0

BE dl dStEB dl E dSt

E dS dV

B dS

µε µσ

ρε

∂⋅ = − ⋅

∂

' (∂⋅ = + ⋅) *

∂+ ,

⋅ = ⋅

⋅ =

∫ ∫∫

∫ ∫∫

∫∫ ∫∫∫

∫∫

!! !!

!! !! !

!!

!!

"

"

#

#

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Maxwell´s Equations (2)

0

BEtDH Jt

D

B

ρ

∂∇× = −

∂

∂∇× = +

∂

∇ =

∇ =

!!

!! !

!i!i

2 1

2 1

2 1

2 1

0

0

0

t t

t t

n n

n n

E E

H HD DB B

σ

− =

− =

− =

− =

! !

! !

Boundary Conditions

(for conductors)

o

o

D E E P

B H H M

J E

ε ε

µ µ

σ

= = +

= = +

=

! ! ! !

! ! ! !

! !

Constitutive Equations

© A.Lobo (2004) 20



22

2

22

2

0

0

EEtHHt

µε

µε

∂∇ − =

∂

∂∇ − =

∂

!!

!!

In dielectric, non-conducting media, σ = 0

Wave Equations (1)

22

2

22

2

0

0

E EEt tH HHt t

µε µσ

µε µσ

∂ ∂∇ − − =

∂ ∂

∂ ∂∇ − − =

∂ ∂

! !!

! !!

© A.Lobo (2004) 21



2 2 2

2 2 2

( ) ( ) 0

( ) ( ) 0

E r n k E r

H r n k H r

∇ + =

∇ + =

! !! !! !! !

Wave Equations (2)

Helmholtz Equations

22 2 2

2n kcω

µεω= =

Waves in photonics are often monochromatic, with a frequency that stays the same across the material boundaries, that is: ( , ) ( ) j tE r t E r e ω=

! !! !

© A.Lobo (2004) 22



Coordinate SystemNotação

2

grad

div

rot

lap

f f

A A

A Af f

=∇

=∇

=∇×

=∇

! !i

! !

Cylindrical Coordinates (r,φ,z)

© A.Lobo (2004) 23



( )

( )

( , ) ( , )

( , ) ( , )

j t z

j t z

E r t E r e

H r t H r e

ω β

ω β

φ

φ

−

−

=

=

! !!! !!

2 2 2

2 2 2

( ) ( ) 0

( ) ( ) 0

E r n k E r

H r n k H r

∇ + =

∇ + =

! !! !! !! !

2 2 22 2

2 2 2 2

2 2 22 2

2 2 2 2

1 1 ( , ) 0

1 1 ( , ) 0

z z z zz

z z z zz

E E E E n r k Er r r r zH H H H n r k Hr r r r z

φφ

φφ

∂ ∂ ∂ ∂+ ⋅ + ⋅ + + =

∂ ∂ ∂ ∂

∂ ∂ ∂ ∂+ ⋅ + ⋅ + + =

∂ ∂ ∂ ∂

The longitudinal component of the electric field does not change though either propagation or reflection at the cylindrical surface

© A.Lobo (2004) 24

Since the equations for Er and Eθ are coupled, we first solve for Ez (Hz is a solution of the same Helmholtz equation and its solutions have the same form ). We find all other field components form Ez and Hz using Mawell’s equations.

We look for solution of the form:



( , , ) ( ) ( ) ( )zE r z R r Z zφ φ= ⋅Φ ⋅

2 2 22 2 2

2 2 2 ( ) 0R R Zr r r knrr r zφ

∂ ∂ ∂ Φ ∂+ + + + =

∂ ∂ ∂ ∂

In the core we find: ( )( )( ) ( ) ( )

j z j z

j j

Z z ae bece de

R r gJ r hN r

β β

νφ νφ

ν ν

φ

κ κ

−

−

= +

Φ = +

= + 2 2 2( ) and 0,1, 2,...onkκ β ν= − =

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We can simplify these solutions noting that:

• Often we have only forward going waves, thus a =0. • The Neumann function Nν(κr) goes to minus infinity at r =0, so it is unphysical (h =0). Therefore Jν(κr) is the proper solution in the core.

© A.Lobo (2004) 26



2

2( ) j z ZZ z bez

β β− ∂= ⇒ = −

∂

2 22 2 2

2 2 0R Rr r r Rr r r

νκ# $∂ ∂

+ + − =' (∂ ∂ ) *

• Due to predominant propagation of the field along the z axis an oscillatory characteristic is assumed for the z dependence

• We need both the clockwise and counter-clockwise circulating exponentials that describe the φ dependence of the eigenmodes

22

2( ) j jce deνφ νφφ ν φφ

− ∂ ΦΦ = + ⇒ = −

∂

Bessel Equation

2 2 2( ) and 0,1, 2,...onkκ β ν= − =

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22

2 0rν

κ# $

− >& '( )

CASE 1: CORE

CASE 2: CLADDING

Modified Bessel functions

Bessel functions

22

2 0rν

κ# $

− <& '( )

( )

( )

j zz

j zz

E AJ r e

H BJ r e

νφ βν

νφ βν

κ

κ

−

−

=

=

( )

( )

j zz

j zz

E CK r e

H DK r e

νφ βν

νφ βν

γ

γ

−

−

=

=

A,B,C and D are constants determined by the boundary conditions

2 2γ κ= −

© A.Lobo (2004) 28



After some maths…. We get this “small” CHARACTERISTIC EQUATION for an optical fibre

( ) ( )

2' ' ' '2

1

2

2 21

( ) ( ) ( ) ( )1 1 1 1( ) ( ) ( ) ( )

1 1

o

J a K a J a K ana J a a K a a J a n a K a

n k a a

ν ν ν ν

ν ν ν ν

κ γ κ γ

κ κ γ γ κ κ γ γ

βν

κ γ

% &% & % &' (⋅ + ⋅ ⋅ ⋅ + ⋅ ⋅ =' ( ' (' (* +* + * +

, -% &. /= ⋅ +' (

' (. /* +0 12 2 2

12 2 2

2

( )

( )o

o

n k

n k

κ β

γ β

= −

= −

( ) ( )2 22V a aκ γ= + 2 21 2where oV k a n n= −

The characteristic equation is used with:

to find values for κ, γ, β and neff

© A.Lobo (2004) 29



About the Effective Index (neff)

A plane wave propagates with a phase term ejnkz, where k=2π/λo is the free-space wave-vector.

We can define an effective index for a guided wave that has a phase factor ejβz with:

2 eff

o

nπβ

λ≡

Then;

2 12 2

o o

n nπ πβ

λ λ< < 2 1effn n n< <

The effective index is an “average” index seen by the guided mode.

© A.Lobo (2004) 30



Meridional Modes (ν = 0)For modes that correspond to bouncing meridional rays, there is no φ dependence. The characteristic equation simplifies greatly. Modes are of two types – TE0µ (Ez=0) and TM0µ (Hz=0) with µ=1,2, …. The values κ, γ can be found graphically

Curves of the characteristic equation of the TE0µ and TM0µ modes

© A.Lobo (2004) 31



Skew Modes (ν ≠ 0)

Modes have both Ez≠0 and Hz≠0 and thus are called “hybrid” modes. The hybrid modes are labeled EHνµ and HEνµ depending on whether Ez or Hz is dominant. The values κ, γ can be found graphically

Curves of the characteristic equation of the HE1µ modes

© A.Lobo (2004) 32



Field Distributions in Optical Fibers (1)

1 0

1 0

0( )( )

0

r

r

EE J r

H J r

H

φ µ

µ

φ

κ

κ−

∼

∼

∼

∼

1 0

1 0

( )00( )

r

r

E J r

E

HH J r

µ

φ

φ µ

κ

κ

−∼

∼

∼

∼

TE Modes TM Modes

This Bessel function (J1) has a zero at the origin and one maximum in the core

© A.Lobo (2004) 33



Field Distributions in Optical Fibers (2)

1 21 1 21

1 21 1 21

( ) cos(2 ) ( )sin(2 )( )sin(2 ) ( ) cos(2 )

r rE J r H J rE J r H J rφ φ

κ φ κ φ

κ φ κ φ

−

− −

∼ ∼

∼ ∼HE21 Mode

This Bessel function (J1) has a zero at the origin and one maximum in the core

© A.Lobo (2004) 34



Linearly Polarized (LP) Modes

When the refractive index of the core n1 ≈ n2 , the characteristic equation (CE) can be simplified. This is called the “weakly guiding approximation”. The CE can be written in the unified form as:

1 1

( ) ( )( ) ( )

m m

m m

J a K aJ a K a

κ γ

κ κ γ γ− −

=

1 for TM and TE modes1 for EH modes 1 for HE modes

m ν

ν

→#$

= + →%$ − →'

LP modes can be constructed from sums of EH and HE modes that have the same propagation constant.

© A.Lobo (2004) 35



Linearly Polarized (LP) Modes

© A.Lobo (2004) 36


2.4 The Cut-off wavelength and V-number.

( ) ( )2 22V a aκ γ= +

2 2 21 2 1 2o oV k a n n k an= − = Δ

2 2 21

2 2 22

o

o

u a a k n

w a a k n

κ β

γ β

= = −

= = −

This is a dimensionless number that determines how many modes a fibre can support

2 222

2 2 21 2

( / )ok nwbV n n

β −= =

−

Normalized Propagation Constant*

2 21 2

2cutoff

an n

Vπ

λ = −

Cut-off Wavelength

* D. Gloge, “Weakly guiding fibers”, Applied Optics 10, 2252-2258 (1971)

© A.Lobo (2004) 37


2.4 The Cut-off wavelength and V-number.

min

1

2.405

3.7cutoff

V V

anλ λ

< =

> = Δ

Singlemode Condition

( )( ) 10log

( )straight

loop

PR

Pλ

λλ

" #= $ %$ %

& '

See recommendation ITU-T G.650

© A.Lobo (2004) 38


2.5 Singlemode and multimode fibre propagation.

2.405V ≤

Single-mode Condition

Sing

le-m

ode

Reg

ion

LP

Step-index singlemode fibre

© A.Lobo (2004) 39



2

2VM =

2 21 2NA n n= − 2 2 2 2

1 2sin n nπ θ πθ πΩ = ≈ = −

Numerical Aperture Solid Angle

Total number of Modes in the fibre (Step-index Fibre)

© A.Lobo (2004) 40



In the weakly guiding approximation, the big steps in this figure become perfectly vertival (eg. TE01, TM01 and HE21 have the same V at cutoff. Groups of modes with the same cutoff also have the same propagation constant.

Singlemode Condition

© A.Lobo (2004) 42



HE11 mode

Solid lines – E field Dashed lines – H field

With permission of C.D. Cantrell and D.M. Hollenbeck, “Fiberoptic Mode Functions: A Tutorial”, Erick Jonsson School of Eng. and Computer Science, Univ. Texas at Dallas, Course EE6314.

© A.Lobo (2004) 43




HE21 mode


© A.Lobo (2004) 44




TM01 mode TE01 mode


© A.Lobo (2004) 45



Optical Power in the Mode ( ) ( )* * *1 12 2z z r rS E H u E H E Hθ θ= × ⋅ = −! ! !

( )2 2

* *

0 0 0 0

12

a a

core z r rP S r dr d r E H E H dr dπ π

θ θφ φ= ⋅ ⋅ = − ⋅ ⋅∫ ∫ ∫ ∫

( )2 2

* *

0 0

12cladding z r r

a a

P S r dr d r E H E H dr dπ π

θ θφ φ∞ ∞

= ⋅ ⋅ = − ⋅ ⋅∫ ∫ ∫ ∫

22

2 2 21 1

( )( )1 1( ) ( )

1

core m

total m m

cladding core

total total

P K aaP V K a K a

P PP P

γκ

γ γ− +

$ %= − −& '

( )

= −

© A.Lobo (2004) 46



Optical Power in the Mode LPml

© A.Lobo (2004) 47


2.6 Mode Field Diameter (MFD).

Gaussian Beam (1)

2

( )rw

oE r E e! "−$ %& '=

2

2

( ) o

rw

oI r I e! "

− $ %& '=

© A.Lobo (2004) 48



Gaussian Beam (2)

1/ 22

2

( ) 1

( ) 1

oR

R

zw z w

z

zR z z

z

! "# $% &= + ' (% &) *+ ,

! "# $= +% &' () *% &+ ,

2o

Rw

zπ

λ=

2

owλ

πΘ =Divergence Angle:

Rayleigh Range:

for large ( )o

zz w z

wλ

π⇒ ≈

H. Kolgelnik and T. Li, “Laser beams and resonators”, Applied Optics 5, 1550-1566 (1966)

© A.Lobo (2004) 49



Petermann I Integral (Near-Field):

M. Artiglia et al, “Mode Field Diameter Measurements in Single-Mode Optical Fibers”, Journal of Lightwave Technology, Vol. 7, No. 8. (1989)

1/ 2

2 3

0

2

0

( )2 2

( )I

E r r drMFD

E r r dr

∞

∞

" #⋅% &

% &= ⋅% &

⋅% &% &' (

∫

∫

Petermann II Integral* (Far-Field):

1/ 2

3

2 ( )sin cos

( )sin cosII

I dMFD

I d

θ

θθ

θ

θ θ θ θλ

πθ θ θ θ

−

−

% &⋅( )

( )= ⋅( )

⋅( )( )* +

∫

∫*TIA/EIA FOTP-191, ITU-T G.650E

© A.Lobo (2004) 50



Near-Field Profiles

100X

40X

J. L. Guttman, “Mode-Field Diameter and “Spot Size” Measurements of Lensed and Tapered Specialty Fibers”, NIST Symposium on Optical Fiber Measurements, September 24-26, 2002

© A.Lobo (2004) 51



Far-Field Profiles

J. L. Guttman, “Mode-Field Diameter and “Spot Size” Measurements of Lensed and Tapered Specialty Fibers”, NIST Symposium on Optical Fiber Measurements, September 24-26, 2002

a.) Fiber #1 b.) Fiber #2

© A.Lobo (2004) 52



Petermann II Integral* (Far-Field):

1/ 2

3

2 ( )sin cos

( )sin cosII

I dMFD

I d

θ

θθ

θ

θ θ θ θλ

πθ θ θ θ

−

−

% &⋅( )

( )= ⋅( )

⋅( )( )* +

∫

∫(*TIA/EIA FOTP-191, ITU-T G.650E)

• Errors [1,2] • Obliquity Factor and Aperture Field

•Elliptical Fiber [3] • Radial Symmetry for Hankel Transform

• Field Within Fiber vs Field at Focus

[1] M. Young, “Mode-field Diameter of single-mode optical fiber by far-field scanning”, Applied Optics, Vol. 37, No. 24, August 1998 [2] R. C. Wittmann and M. Young, “Are the Formulas for Mode-Field Diameter Correct?”, NIST SOFM 1998 [3] M. Artiglia et al, “Mode Field Diameter Measurements in Single-Mode Optical Fibers”, Journal of Lightwave Technology, Vol. 7, No. 8. August 1989

© A.Lobo (2004) 53



1.5 6

1.619 2.8790.65w aV V

! "= + +# $% &D. Marcuse, Bell Systems Tech. Journal 56, 703-718 (1977)

Marcuse Model:

© A.Lobo (2004) 54



1.5 6

1.619 2.8790.65w aV V

! "= + +# $% &

For the best fit between a Gaussian function and the Bessel function in the core we can use the Marcuse Model:

Satisfying this condition gives about 96% overlap between the Gaussian and the Bessel function mode profiles. At the cut-off condition (V ≈ 2.405) we obtain:

1.1w a≈

© A.Lobo (2004) 55



1.5 6

1.237 1.4290.761w aV V

! "= + +# $% &

Other MFD models

1.5 6

1.289 1.0410.759w aV V

! "= + +# $% &

1.5 6

1.66 0.9870.616w aV V

! "= + +# $% &

( )1.5

1 for V>1

lnw a

V=Snyder and Sammut Model

Myslinski Model

Desurvire Model

Whitley Model

Several models have been developed to obtain better agreement with experimentally observed data (particularly gain factors → Erbium doped fibres)

© A.Lobo (2004) 56


2.7 Absorption and Scattering losses.

38 2

4

83R T B Fn p k Tπ

γ βλ

=

SCATTERINGNON-LINEAR

LINEAR • Rayleigh (diameter physical anomalies < λ/10) • Mie (diameter physical anomalies > λ/10)

• Brillouin (acoustic phonon → SBS)

• Raman (optical phonon → SRS)

n – refractive index of the material, βT – isothermal compressibility, p – photoelastic coefficient, TF – Solidification temperature, kB – Boltzman constant, L - the fibre length.

Rayleigh Scattering Coefficient

RLRayleighF e γ−=

Transmission Loss factor

© A.Lobo (2004) 57



ABSORPTION

INTRINSIC

INDUCED Curvature (micro and macrobending)

EXTRINSIC

Interaction of free electrons and the λ within the fibre material.

Impurities atoms in glass material (metal ions)

4.5823 [ ][ / ] 1.108 10

UVm

UV dB km Ce eλ

λ µλα −= = ×

48.4811 [ ][ / ] 4 10 m

IR dB km eλ µα −= ×

Urbach’s rule (empirical relationship) Macrobending (critical radius)21

2 21 2

34 ( )MMF

nRn nλ

π=

−

3

2 21 2

20 0.9962.748SMFcutoff

Rn n

λ λ

λ

−# $

= −% &% &− ' (

© A.Lobo (2004) 58


2.7 Absorption and Scattering losses.ATTENUATION

zdz

P P+dP

1 (0)( ) (0) ln [1/km or 1/m]

( )LdP PL P L P e

dz L P Lαα α− # $

= − ⇒ = ⇒ = & '( )

(0) (0)10log 10log 10 log 4.343

( ) ( )L LP Pe e L e

P L P Lα α α α

" #" #= ⇔ = = =% & ' (

' (

10 (0)[ / ] log

( )

[ / ] 4.343 [1/ ]

PdB kmL P L

dB km km

α

α α

" #= $ %

& '=

scattering absorption bendingα α α α= + +

© A.Lobo (2004) 60



Theoretically expected minimum attenuation

Governed by: 1. Rayleigh scattering at short λ 2. Multi-phonon absorption at long λ

© A.Lobo (2004) 61



Fibre λ (nm) α (dB/km) MMF-GI 850 2.5

SMF 1300 0.5SMF 1550 ≤0.25

F-POF (Fluorinated) 800 to 1340 60

ZBLAN 1550 0.02SMFF

(Fluoride glass)2300 0.005

Typical minimum attenuation values for several fibres

© A.Lobo (2004) 62


2.8 Phase velocity and group velocity.

phvω

β=g

dvdω

β=

11

gcvdnnd

λλ

=" #−% &' (

Group Velocity Phase Velocity

Guide Group Index (ng)

1ph

cvn

=

© A.Lobo (2004) 63


2.9 Dispersion: Group delay and Material dispersion.

1g

L d L dL Lv d c dk

β βτ β

ω= = = ⋅ =

Group Delay

1

o

dD

L dτ

λ= ⋅

Dispersion Parameter

Origin of the Dispersion: Frequency dependence of the mode index n(ω)

20 1 0 2 0

1( ) ( ) ( ) ( ) ...2

ncω

β ω ω β β ω ω β ω ω= = + − + − +

1

2 2 3 2

2 2 2 2 2

1 1

1 22

g

g

ndnnc d c v

dn d n d n d nc d d c d c d

β ωω

ω λβ ω

ω ω ω π λ

% &= + = =' () *

% &= + ⋅ ⋅' (

) *! !

© A.Lobo (2004) 64



21

22 2

2d c d nDd c dβ π λ

βλ λ λ

= = − − ⋅!Dispersion Parameter:

Group Velocity Dispersion (GVD): 12 2

1 1 g

g g

dvd dd d v v dβ

βω ω ω

# $= = = − ⋅' (' (

) *(Contains the information about the variation of the group velocity with wavelength)

2g g

d L d Lt L LDd v d v

δ δω β δω δλ δλω λ

% & % &= = ⋅ = = ⋅( ) ( )( ) ( )

* + * +

If a pulse with spectral width (Δδ) input to a fibre with length L, the output pulse broadening is:

Limitation on the bit rate:2

1 or 1t B t BL BLD

Bδ δ β δω δλ< = ⋅ ⋅ <

© A.Lobo (2004) 65



212

1 gmat

dn d nDc d c d

λ

λ λ= ⋅ = − ⋅

Material Dispersion

0gdndλ

=

Zero-dispersion wavelength = 1276 nm

Negative DmatPositive Dmat

© A.Lobo (2004) 66


2.10 Chromatic Dispersion (CD)

2 22

2 21 2

( / )ok nb

n nβ −

=−

Normalized propagation constant*:2

1 2

( / )ok nb

n nβ −

≅−

for small Δ

2 (1 )o o effk n b k nβ = + Δ =

* See D. Gloge, “Weakly guiding fibers”, Applied Optics 10, 2252-2258 (1971)

D. Gloge, “Dispersion in weakly guiding fibers”, Applied Optics 10, 2442-2445 (1971).

212

1 gmat

dn d nDc d c d

λ

λ λ= ⋅ = − ⋅

22

2

( )wg

n d VbD Vc dVλ

Δ= −

mat wgD D D= +

© A.Lobo (2004) 67



22

2

( )wg

n d VbD Vc dVλ

Δ= −

Waveguide Dispersion

© A.Lobo (2004) 68



Anomalous dispersionNormal dispersion

λD ≈ 1320 nm

© A.Lobo (2004) 69



Anomalous Dispersion (D > 0)

Normal Dispersion (D < 0)

© A.Lobo (2004) 70



P.K. Bachman et.al., “Dispersion-flattened single-mode fibres prepared with PCVD: Performance, limitations, design and optimization”, J. Lightwave Technology 4, 858-863 (1986)

© A.Lobo (2004) 71

0( ) ( )oD Sλ λ λ= −

40( ) 1

4oSD

λ λλ

λ

" #$ %= −' () *+ ,' (- .



Typical values for S0 are 0.092 ps/(km·nm2) for SMF, and between 0.06 and 0.08 ps/(km·nm2) for DSF

1( ) gdDL d

τλ

λ= ⋅

Slope (ps/km·nm2)

(See recommendation ITU-T G.652)

© A.Lobo (2004) 73

kh

v

kh

v


2.11 Polarization effects and Birefringence.

0 cos( )x x x xE e E t zω β φ= − +! !

0 cos( )y y y yE e E t zω β φ= − +! !

TOTAL x yE E E= +! ! !

nknλ

π==β2

x

y

POLARIZATION

© A.Lobo (2004) 74

timeh

v

timeh

v



-4 -2 2 4h,(V/m)

-3

-2

-1

1

2

3

v,(V/m)

0 0cos( ) cos( )TOTAL x x y yE e E t z e E t zω β ω β π= − + − +! ! !

LINEAR POLARIZATION

© A.Lobo (2004) 75



timeh

v

timeh

v-1 -0.5 0.5 1

h,(V/m)

-1

-0.5

0.5

1

v,(V/m)

0 sin( ) cos( )TOTAL x x yE E e t z e t zω β ω β# $= − + −& '! ! !

CIRCULAR POLARIZATION

© A.Lobo (2004) 76



timeh

v

timeh

v-2 -1 1 2

h,(V/m)

-4

-2

2

4

v,(V/m)ELLIPTICAL POLARIZATION

0 1 0 2sin( ) cos( )TOTAL x x y yE e E t z e E t zω β φ ω β φ= − + + − +! ! !

© A.Lobo (2004) 77



Birefringence effect of polarized light in the fibre

Birefringence

Beat Length

( )

or equivalently,2

( )

x y

x y

B n n

n nπ

βλ

= −

Δ = − 2BL B

π λ

β= =Δ

π/2 2π0 π/4 3π/4 π 5π/4 3π/2 7π/4

© A.Lobo (2004) 78



Jones Calculus* - applicable only to polarized waves (*) E. Hecht, “Optics”, 4Ed. Addison Wesley, Chapter 8, 2002.

A10

0

x

y

ix

in iy

E eE

E e

ϕ

ϕ

" #= $ %$ %& '

! xoutout

yout

EE

E! "

= # $% &

!

11 12

21 22

xout xin

yout yin

E Ea aE Ea a! " ! "! "

=# $ # $# $% &% & % &

00

0

11

x

x

x

iix

in xix

E eE E e

E e

ϕϕ

ϕ

" # " #= =$ % $ %

& '& '

!45º

1112

E ! "= # $

% &

!02 xixE e ϕ

Dividing both terms by:

© A.Lobo (2004) 79



Jones Matrixfrom E. Hecht, “Optics”, 4Ed. Addison Wesley, Chapter 8, 2002.

© A.Lobo (2004) 80



[from D.Derickson, “Fiber Optic Test and Measurement” Prentice Hall, Ch. 6 (1998)]

Measurement of the Jones Matrix of an optical element

© A.Lobo (2004) 81



Stokes Parameters – applicable to both totally or partially polarized light. The elements describe the optical power in particular reference polarization states.

0

1

2 45º 45º

3

total

LH LV

L L

RC LC

S IS I IS I IS I I

+ −

" # " #$ % $ %−$ % $ %=$ % $ %−$ % $ %

−$ % $ %& ' & '

2 2 21 2 3

0

S S SDOP

S+ +

=

© A.Lobo (2004) 82



Normalized Stokes Parameters

0

1

20

3

11 123

SSsSs SSs

! "! "# $# $# $# $ =# $# $# $# $# $% & % &

2 2 21 2 3DOP s s s= + +

© A.Lobo (2004) 83



Poincaré Sphere – graphical tool in real, 3D space that allows convenient description of polarized signals and of polarization transformations caused by propagation through devices.

© A.Lobo (2004) 84



Measurement of retardance θ of a near λ/4-wave retarder [from D.Derickson, “Fiber Optic Test and Measurement” Prentice Hall, Ch. 6 (1998)]

© A.Lobo (2004) 85



Twisting of a singlemode fibre [from Agilent HP8509C Application Note]

© A.Lobo (2004) 86



Muller Matrix – applicable to any degree of polarization.

00 01 02 030 0

10 11 12 131 1

20 21 22 232 2

30 31 32 333 3

out in

out in

out in

out in

m m m mS Sm m m mS Sm m m mS Sm m m mS S

! " ! "! "# $ # $# $# $ # $# $= ⋅# $ # $# $# $ # $# $

# $# $ # $& '& ' & '

© A.Lobo (2004) 87



Two polarization modes Ex , Ey of a singlemode fibre

© R. Ulrich, TU Hamburg-Harburg

© A.Lobo (2004) 88


2.11 Polarization effects and Birefringence.From K.T.V.Grattan & B.T. Meggitt, “Optical Fiber Sensor Technology”, Chapman & Hall (1995)

© A.Lobo (2004) 89


2.11 Polarization effects and Birefringence.From K.T.V.Grattan & B.T. Meggitt, “Optical Fiber Sensor Technology”, Chapman & Hall (1995)

© A.Lobo (2004) 90


2.12 Polarization Dependence Loss (PDL) .

Device Under Test (DUT)

Constant Power 100% Polarized

Time

Pmáx

Pmin

max

min

10 logdBPPDLP

! "= # $

% &

PDL measures the peak-to-peak difference in transmission for light with various states of polarization.

© A.Lobo (2004) 91


2.13 Polarization Mode Dispersion (PMD).

PMD is a fundamental property of singlemode optical fibre and components in which signal energy at a given wavelength is resolved into two orthogonal polarization modes of slightly different propagation velocity. The resulting difference in propagation time between polarization modes is called the differential group delay (Δτ).

g

L dLv d

n d nLc c d

βτ

ω

ω

ω

ΔΔ = =

Δ

Δ Δ% &= + ⋅( )* +

dL Ld

φ βφ β τ

ω ω

Δ= Δ → = = Δ

Δ

Also, Frequency-domain manifestation

© A.Lobo (2004) 92



PMD is characterized by the PMD-vector, Ω(ω), in Stokes space, around which an output state of polarization (SOP), s , rotates when the carrier frequency is changed.

' dSS Sdω

= =Ω×

!! !!

τΔ = Ω!

And the differential group delay (DGD) is:

© A.Lobo (2004) 93



CASE 1 - Ideal fibre section (βx = βy)

,

,

( ) x inin

y in

EE

Eω

" #= $ %& '

! ( )out in

j Lin

E J E

e Eβ

ω

−

$ % $ %= & ' & '

=

! ! !i!

0( )

0

j L

j L

eJ

e

β

βω

−

−

$ %= & '( )

!

0τΔ =

© A.Lobo (2004) 94



CASE 2 - linearly birefringent fibre section (βx ≠ βy)

,

,

( ) x inin

y in

EE

Eω

" #= $ %& '

!

0( )

0

x

y

j L

j L

eJ

e

β

βω

−

−

$ %= & '& '( )

!

2dL ndLnc

πτ

ω λ% &Δ = ⋅ Δ) *+ ,

≅ Δ ⋅

,

,

( )x

y

j Lx in

out j Ly in

e EE

e E

β

βω−

−

$ %= & '& '( )

!

© A.Lobo (2004) 95



CASE 3 - Birefringence axes aligned: PM fibre

0( )

0

x

y

j L

total j L

eJ

e

β

βω

−

−

$ %= & '& '( )

!

outout

dSS

dω=Ω×

!!!

Ω!τΔ = Ω

!

© A.Lobo (2004) 96



CASE 4 - Random orientation of birefringence axes aligned: standard long-length fibre

[ ] [ ] [ ] [ ] [ ] [ ]2 2 1 1total n nJ R J R J R J= ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅!

( )outout

dSS

dω

ω=Ω ×

!!!

© A.Lobo (2004) 97



• Frequency domain scenario: PMD vector and principal states of polarization (PSP)

1,20 if outoutout

dSS PSP

dω= =

!!

• Time domain scenario: Pulse splitting

© A.Lobo (2004) 98



• Frequency domain scenario : frequency dependence of PSP

0( ) ( ) ....ωω ω ωΩ =Ω +Ω Δ +! ! !

0

ddω

ω ωω

=

ΩΩ =

!!

1st order approximation is valid within “PSP-bandwidth”:

1PSPω

τΔ ≅

Δ• Time domain scenario: multi-path pulse transmission

[See J.L. Santos, Ph.D. Thesis, Chap.7, Univ. Porto, (1992)]

© A.Lobo (2004) 99



2

22

23

2 eτ

ατ

π α

Δ−Δ

⋅

with 8τ α πΔ =

Probability of finding DGD at value Δτ is given by the Maxwellian density distribution

© A.Lobo (2004) 100



Consequences of PMD DGD (Δτ) causes:

Pulse broadening Reduction of eye openings / increase in BER Additional power penalty Increase of outage probability

Instantaneous Δτ Is a random variable It varies due to environment (temnperature, strain) It can surpass its mean value by far

2PMD Lτ τΔ = Δ ∝

© A.Lobo (2004) 101


2.14 Non-linear Optical Effects.

Self-Phase Modulation (SPM) – pulses distiort as they propagate.

Cross-Phase Modulation (XPM) – pulses interfere with one another

Modulation Instability (MI) – CW beams break into pulses

Solitons – a nonlinear way of transmitting pulses

Four-Wave Mixing (FWM) Optical Kerr Effect – electric field imposed induces linear birefringence Stimulated Brillouin Scattering (SBS) – inelastic scattering from

acoustic phonons Stimulated Raman Scattering (SRS) – inelastic scattering from

molecular resonances Supercontinuum Generation (SG) – “white light” generation

Parametric Process

(light induced modulation)

Non-Parametric Process

Observed effect

© A.Lobo (2004) 102



Nonlinear optics is a result of anharmonic excitation of the medium. The induced polarization is given by:

( )0 1 2 3 ...P E EE EEEε χ χ χ= ⋅ + ⋅ + ⋅ +! ! ! ! ! ! !

where χ1, χ2, χ3 are 1st, 2nd, 3rd order susceptibilities. χ2 vanishes in centro-symmetric materials like glass, so the lowest-oder nonlinear term is χ3.

One manifestation of this is the nonlinear refractive index:

where n2K is the nonlinear Kerr coefficient and is directly related to χ3. In most glasses, n2 is positive, so the refractive index of the material increases at higher intensities. The value of n2K for SiO2 is ~3.2×10-20 m2W-1.

20 2Kn n n E= +

© A.Lobo (2004) 103



Nonlinear Coefficient (γ) – measure of the strength of the nonlinar response of a particular fibre at frequency ω0 with effective area Aeff and n2k known.

2 0K

eff

ncAω

γ =

Effective Length (Leff) – effective nonlinear length of a fibre with physical length L and loss given by α.

1 L

effeL

α

α

−−=

Nonlinear Length (LNL) – the fibre length required for nonlinear effects to become important, for a given peak pump power. Explicity, the length for development of a phase shift of unity. 0

1NLL Pγ=

Dispersion Length (Ld) – length over which the pulse length τ0 is significantly dispersed in a fibre with β2.

20

2dL

τ

β=

DEFINITIONS

© A.Lobo (2004) 104



λo

Rayleigh radiation (λo) Brillouin radiation (λo±0.08 nm)

Raman radiation (λo

±80 nm )

Scattering spectra of an optical fibre

Wavelength

Energy

Incident radiation (λo=1550 nm)

2 sB

o

nVn l=Anti-Stokes Stokes

Electrostriction Raman shift ≈ -13 THz @ 1.55 µm Brillouin shift ≈ -11 GHz @ 1.55 µm

© A.Lobo (2004) 105



2.14.1 Stimulated Raman Scattering (SRS)

(Spontaneous) Raman Scattering: a very small amount of light in any molecular is inelastic scattered. A lower-frequency photon is produced, and the extra energy goes into exciting a molecular vibrationsl or rotational mode.

Stimulated Raman Scattering (SRS): the lower-frequency radiation beats with the pump beam to provide a field beating at the Raman frequency. This drives the Raman oscillations directly, so that the shifted radiation experiences gain at the expense of the pump beam.

0PzS

SRS S S SdI g I I e Idz

α α−= −

The growth of the Stokes wave along the fibre in both spontaneous and stimulated emission may be expressed in the form:

Raman gain

© A.Lobo (2004) 106



2.14.1 Stimulated Raman Scattering (SRS)

16 effSRSth

SRS eff

kAP

g L≅

17 W km @ 1.55 µm

SRSth effP L⋅ ≈ ⋅

Relative polarization factor (1 ≤ k ≤ 2)

© A.Lobo (2004) 107



2.14.2 Stimulated Brillouin Scattering (SBS)

SBS Characteristics: Low power threshold Backward propagating Stokes wave Small Stokes shift (low phonon energy) Acoustic phonon lifetime is long (10ns), so gain bandwidth is narrow. Need narrow linewidth pump source for efficient excitation.

21 1 pump effSBSth

B SBS eff

AP

g Lν

ν

Δ# $≅ +& 'Δ( )

0.03 W km @ 1.55 µm

SBSth effP L⋅ ≈ ⋅

Electrostriction

© A.Lobo (2004) 108



2.14.3 Four-Wave Mixing (FWM)

26

34 2 2

31024( ) eff Lij FWM i j

eff

LP L PP e

n c Aαχπ

ηλ

−' (' (

= ⋅* +* + * +, - , -see A.R. Chraplyvy, Journal Lightwave Technology 8, 1548-1557 (1990).

© A.Lobo (2004) 109



2.14.4 Self-Phase (SPM) and Cross-Phase Modulation (XPM)

Kerr nonlinearityLinear regime

2

effSPMth

K eff

AP

n Lλ

π≅

1.5 W km @ 1.55 µm

SPMth effP L⋅ ≈ ⋅

( )22SPM Kdn Edt

νΔ ∝

© A.Lobo (2004) 110



2.14.4 Self-Phase (SPM) and Cross-Phase Modulation (XPM)

( )20 22

0 2

22

K

K

nL L n n En n n E

πφ π

φλλ

$= %⇒ = +'

%= + (

( )

0 0

20 2

' '

2' K

ddt

L dn Edt

φω ω ω ω ω

πω ω

λ

= + ⇔ = + ⇒

⇒ = +

( )

( )

20

20

0 ' ( )

0 ' ( )

K

K

d E tdtd E tdt

ω ω ω

ω ω ω

> ⇒ = −

< ⇒ = +

Pulse is CHIRPED

© A.Lobo (2004) 111



Limitations over WDM Limitations on the channel power imposed by four nonlinear effects (assumed λ=1.55 µm and fibre loss of 0.2 dB/km)

see A.R. Chraplyvy, Journal Lightwave Technology 8, 1548-1557 (1990).

© A.Lobo (2004) 112



Soliton Propagation2

0 2

3.11

FWHM

PT

β

γ!

Fundamental soliton peak power

Types of Optical Fibre



© A.Lobo (2004) 2

3. Types of Optical Fibre

3.1 Optical Fibre Fabrication. 3.2 Standard Singlemode Fibre. 3.3 Step-Index and Graded-Index Multimode Fibre. 3.4 Dispersion Shifted Fibre. 3.5 Dispersion Flattened Fibre. 3.6 Non-Zero Dispersion Shifted Fibre. 3.7 Dispersion Compensating Fibre. 3.8 E-Band Fibre. 3.9 Polarization Maintaining Fibres: PANDA, Bow-Tie, Elliptical and Side-Hole types. 3.10 Rare-Earth Doped Fibres: Erbium, Ytterbium, Neodymium, Praseodymium. 3.11 Long Wavelength Fibres (Fluoride and Chalcogenide). 3.12 Plastic Fibre. 3.13 Hollow Fibre. 3.14 Photonic Crystal Fibre.

© A.Lobo (2004) 3


3.1 Optical Fibre Fabrication Fibre Drawing (Double-Crucible Method)

Cabelte S.A.

© A.Lobo (2004) 4


3.1 Optical Fibre Fabrication

Modified Chemical Vapour Deposition (MCVD)

Prof. J. Knight, Optoelectronics Group, Dept. Physics, University of Bath (UK) & Blaze Photonics Ltd. (UK)

© A.Lobo (2004) 5


3.2 Standard Singlemode Fibre (SMF)

Generally standard singlemode fibre, have a step-index refractive profile. Main disadvantages: coupling difficulties with incoherent optical sources (like LEDs), small NA One of the most advanced commercial singlemode fibres: SMF-28 (by Corning)

Main Characteristic (Measurement methods comply with ITU-T G.650 and IEC 793-1) Attenuation coefficient: ≤0.40 dB/km @ 1310 nm , ≤0.3 dB/km @ 1550 nm NA = 0.13 Cut-off wavelength: < 1260 nm Core diameter: 8.3 µm MFD: 9.30±0.50 µm @ 1310 nm, 10.50 ±1.00 µm @ 1550 nm Zero dispersion wavelength: 1301.5 nm ≤ λ0D ≤ 1321.5 nm Zero dispersion slope (So): 0.092 ps/nm2#km PMD (máx): ≤ 0.2 ps/√km Refractive index difference (Δ): 0.36% Effective group index refraction (Ng): 1.4675 @ 1310 nm, 1.4681 @ 1550 nm

© A.Lobo (2004) 6



SMF-28

From Plasma Optical Fiber B.V. (Eindhoven)

© A.Lobo (2004) 7



Depressed cladding 1300 nm Optimized SMF

© A.Lobo (2004) 8


3.3 Step-Index (SI-MMF) and Graded-Index Multimode Fibre (GI-MMF)

SI-MMF are very similar to step-index SMF, but differ in their core diameter. SI-MMF have fibre core diameters around 50 to 62.5 µm, and cladding with 125 µm. GI-MMF are defined by a progressive decrease of refractive index from the centre of the core with

radius a toward the cladding, while still maintaining the fundamental relationship: n1 > n2. Different modes can interfere with each other generating modal noise. Refractive index profiles difficult to realize in practice → expensive and some flutctuations from

ideal profile are inevitable.

1( ) 1 2yrn r n

a! "= − Δ% &' (

Where y is the core characteristic refractive index profile: y = ∞ for step-index profile y = 1 for triangular profile y = 2 for parabolic profile


© A.Lobo (2004) 9


3.4 Dispersion Shifted Fibre (DSF)

DSF is a singlemode fibre with very low dispersion at 1550 nm operating wavelength. Main Characteristics (Measurement methods comply with ITU-T G.650 and IEC 793-1) Attenuation coefficient: ≤0.25 dB/km @ 1550 nm Cut-off wavelength: ≤ 1260 nm NA = 0.17 Core diameter: 8.3 µm MFD: 8.10 ±0.65 µm @ 1550 nm Zero dispersion wavelength: 1535 nm ≤ λ0D ≤ 1565 nm Zero dispersion slope (So): 0.085 ps/(nm2·km) Total dispersion coefficient: ≤ 2.7 ps/(nm·km) PMD (máx): ≤ 0.5 ps/√km

© A.Lobo (2004) 10


3.5 Dispersion Flattened Fibre (DF-SMF)

DF-SMFF is a singlemode fibre with very low dispersion simultaneously at 1330 nm and 1550 nm operating wavelengths.

Main Characteristics Attenuation coefficient: ≤0.5 dB/km @ 1310 nm , ≤0.3 dB/km @ 1550 nm Dispersion coefficient: ≤3.5 ps/(nm·km) @ 1310 nm , ≤ 3.5 ps/(nm·km) @ 1550 nm


© A.Lobo (2004) 11


3.6 Non-Zero Dispersion Shifted Fibre (NZ-DSF)

NZ-DSF is a singlemode fibre specially designed for Dense Wavelength Division Multiplexing (DWDM) technology. Non-linear effects such as Four-Wave Mixing (FWM) are minimized, by moving the zero-dispersion wavelength outside the band used by EDFAs..

Main Characteristics Dispersion coefficient: -3.5 to -0.1 ps/(nm·km) over the range 1530 to 1560 nm PMD: ≤ 0.5 ps/√km Attenuation coefficient: ≤0.25 dB/km @ 1550 nm

From Corning Corp.

© A.Lobo (2004) 13



Large Area NZ-DSF Fibre nonlinearities are inversely proportional to the core effective area, and so, increasing the effective area will ultimately reduce nonlinearities through the reduction of light density propagating along the core. The large effective area NZ-DSF is based on a triangular core and raised index ring. Corning Corp. developed the LEAF NZ-DSF with a effective area of 72 µm2 as compared with to 55 µm2 standard NZ-DSF.

Shifts the zero dispersion wavelength to the 1550 nm range

Enhances the cross-sectional effective area while simultaneously achieving a relative low bending loss

Refractive Index Profile

© A.Lobo (2004) 14



Large Area NZ-DSF

2K input

eff

n LPNonlinearity

A→

From Corning Corp.

© A.Lobo (2004) 15



Increasing the optical power on a SMF (G.652)

10,6 10,7 10,8 10,9 11,0 11,1 11,2

-45

-40

-35

-30

-25

-20

-15

-10

ν[email protected]ºC

νBrillouin

Opt

ical P

ower

(dBm

)

Frequency Shift (GHz)

VOA=6dB

9,0 9,5 10,0 10,5 11,0 11,5 12,0-45

-40

-35

-30

-25

-20

-15

-10

-5

0

VOA=5dB ν[email protected]ºC

νBrillouin

Opt

ical P

ower

(dBm

)

Frequency Shift (GHz)

With permission of M. Melo and M.O. Berendt, Multiwave Networks Lda.. (Portugal)

© A.Lobo (2004) 16


3.7 Dispersion Compensating Fibre (DCF)

DCF is a singlemode fibre with very high waveguide dispersion. The overall dispersion of this fibre is opposite in sign and much larger in magnitude than that of standard fibre, so they can be used to cancel out or compensate the dispersion in SMF.

Main Characteristics Dispersion coefficient (typ.): -80 to -150 ps/(nm·km) @ 1550 nm Dispersion slope: -0.40 ps/(nm2·km) @ 1550 nm PMD: 0.25~0.5 ps/√km Attenuation: ≤0.55 dB/km @ 1550 nm

ab

From Fujikura Technical Review, 2001

© A.Lobo (2004) 17


3.8 E-Band Fibre (E-SMF)

E-SMF is a singlemode fibre specially designed for the Extend-Band (or E-Band) transmission window, which is located at the wavelength range region from 1360 nm to 1460 nm, but with possibility to operate also in the other bands, such as, C-band.

Main Characteristics: Attenuation (máx): 0.35 dB/km @ 1310 nm , 0.31 dB/km @ 1385 nm, 0.22 dB/km @ 1550 nm Zero dispersion wavelength: 1300 nm ≤ λ0D ≤ 1322 nm Zero dispersion slope (So): 0.092 ps/nm2#km PMD (typ.): ≤ 0.08 ps/√km

Commercial Examples: Corning SMF-28e® fibre → Corning Corp. AllWave® fibre → Lucent Technologies Inc. LightScope ZWP™ fibre → CommScope Inc. TeraSPEED ™ fibre → Avaya Inc. BBG ® -SMF-WF fibre → Hitachi Cable Ltd.

DEFINITION OF SIGNAL WAVELENGTH BAND (ITU-T)

Band Name Wavelength (nm)

O-band (Original) 1260 - 1360

E-band (Extended) 1360 - 1460

S-band (Short Wavelength) 1460 - 1530

C-band (Conventinal) 1530 - 1565

L-band (Long Wavelength) 1565 - 1625

U-band (Ultralong Wavelength) 1625 - 1675

© A.Lobo (2004) 18


3.8 E-Band Fibre (E-SMF)

SMF

E-SMF (5th window)

“water peak” around 1385 nm

© A.Lobo (2004) 19


3.9 Polarization Maintaining Fibre (PMF)

PMF is a singlemode fibre specially designed to maintain the state of polarization (SOP) of guided polarized light. In the most common optical fiber telecommunications applications, PM fiber is used to guide light in a linearly polarized state from one place to another.

Commercial Types: PANDA fibre BowTie fibre Elliptical shape (core or cladding ) fibre D-shaped fibre Side-Hole fibre Side-Pit fibre Spun fibre

2 ( )F SL n nπφ

λΔ = Δ −

Birefringence (typ.): 2×10-4 to 7 ×10-4

© A.Lobo (2004) 20


3.9 Polarization Maintaining Fibres (PMF) Fast axis

Slow axis

Bow Tie PANDA Side-Hole

Elliptical Stressed Cladding D-shaped

Elliptical CoreElliptical Core

© A.Lobo (2004) 21


3.10 Rare-Earth Doped Fibres.

For more details see: www.webelements.com

Erbium (Er) Ytterbium (Yb) Neodymium (Nd) Praseodymium (Pr) Thulium (Tm) Holmium (Ho)

Lanthanides are best characterized by observation that they possess incomplete inner 4f levels and, to a large extent, they form ions that exist solely in the 3+ state. This state is formed by the removal of two outer 6s electrons and one inner 4f electron.

What are Rare Earth Ions?

© A.Lobo (2004) 22



Optical properties of the Rare Earth Ions

Fluorescence Up-Conversion

© A.Lobo (2004) 23



Erbium Doped Fibre (ErDF)ABSORPTION BANDS: 520 nm 650 nm 800 nm 980 nm (free from excited-state absorption ESA) 1480 nm

© A.Lobo (2004) 24



Neodymium Doped Fibre (NdDF)ABSORPTION BANDS: 520 nm 590 nm 820 nm

© A.Lobo (2004) 25



Thulium Doped Fibre (TmDF)ABSORPTION BANDS: 520 nm 590 nm 820 nm

© A.Lobo (2004) 26



Holmium Doped Fibre (HoDF)

Pumped at 640 nm

© A.Lobo (2004) 27



Praseodymium Doped Fibre (PrDF)

© A.Lobo (2004) 28



Ytterbium Doped Fibre (YbDF)ABSORPTION BANDS: 520 nm 590 nm 840 nm

This transition is significantly broadened

© A.Lobo (2004) 29


3.11 Long Wavelength Fibres (Fluoride and Chalcogenide).

Fluorozirconate fibers transmit light between 0.4 and 5 µm. Silver Halide compounds fiber (AgBrCl) transmit light between 3 and 16 µm. Synthetic crystalline sapphire (Al2O3) can transmit light between 0.5 and 3.1 µm

© A.Lobo (2004) 30


3.12 Plastic Fibre (POF).

Fluorinated POF characteristics: Attenuation: <150 dB/km @ 650 nm 1.5 mm diameter NA: 0.4 Index profile: Step-index and also GI-index

PMMA – Polymethyl Metacrylate

© A.Lobo (2004) 31


3.13 Hollow Fibre (HOF).

Hollow optical fiber with an inner core ring

Hollow silica tube filled with HCBD (hexachlorobutadiene) D. N. Payne and W. A. Gambling, Electronics Letters, vol. 8, p374, 1972

K. Oh, FOR Lab., Dept. of Information and Communications Kwangju Institute of Science and Technology (K-JIST)

© A.Lobo (2004) 32


3.13 Hollow Fibre (HOF).

K. Oh, FOR Lab., Dept. of Information and Communications Kwangju Institute of Science and Technology (K-JIST)

S. Choi, K. Oh, W. Shin, U. C. Ryu, Electron. Lett., vol. 37, no.13 , pp.823-825, Jun. 2001.

New type of Mode Coupler based on tapered HOF

© A.Lobo (2004) 33


3.14 Photonic Crystal Fibre (PCF).

Stack-and-Draw Fabrication Process


© A.Lobo (2004) 34



How can one make this….?

Differential Pressure !


© A.Lobo (2004) 35



Extrusion (Soft glass)


© A.Lobo (2004) 38



Prof. P.St Russell, Head of Optoelectronics Group, Dept. Physics, University of Bath (UK) & CSO of Blaze Photonics Ltd. (UK)

Endlessly SMF PM fibre

Multicore PCF

Highly Nonlinearity PCF

Hollow Core PCF Hollow Core Visible PCF

© A.Lobo (2004) 39



Random Hole Fibre (RHOF)

Virginia Polytechnic Institute and State University , USA

High NA PCF

Crystal Fiber A/S (Denmark)

High NA Yb-Doped PCF

Crystal Fiber A/S (Denmark)

Passive Fibre Optic Devices



© A.Lobo (2004) 2

4. Passive Fibre Optic Devices

4.1 Directional Couplers: Splitters and Combiners. 4.2 WDM Couplers. 4.3 Tap Couplers 4.4 Biconical Fibre Filter. 4.5 Fibre Bragg Gratings. 4.6 Long Period Fibre Gratings. 4.7 Gain Equalizing Filters. 4.8 Mach-Zehnder and Michelson Filters (Interleavers). 4.9 Fibre Ring Filters. 4.10 Fibre Fabry-Perot Filters. 4.11 Fibre Polarizer. 4.12 Fibre Depolarizer. 4.13 Fibre Polarization Controller. 4.14 Fibre Optic Attenuator.

© A.Lobo (2004) 3


4.1 Directional Couplers: Splitters and Combiners

Directional Coupler. Theory of Coupled Modes


Between the waveguides 1 and 2 optical power is coupled continuously back and forth (in both directions, 1→2 and 2→1). This results in a periodic spatial variation of the powers Pi(z) in the waveguides (i=1,2) with a periodicity Lc (coupling length)

© A.Lobo (2004) 4



Theory of Coupled Modes: The coupled pendulums

© A.Lobo (2004) 5



Directional Coupler: Coupled Mode Theory (*)

Coupled Wave Equations:

and

2 1

2 1

( )112 2

( )221 1

j z

j z

dA j A edzdA j Aedz

β β

β β

κ

κ

− −

+ −

= −

= − 12 21κ κ κ= =

(*) for more detailed analysis see K. Okamoto, Fundamentals of Optical Waveguides, Academic Press (2001) – Chap.4

mode coupling coeff. (coupler with geometric symmetry)

Solutions assumed in the form: (for codirectional couplers: β1>0, β2>0)

1 1 1

2 2 2

( )

( )

jqz jqz j z

jqz jqz j z

A z a e a e e

A z a e a e e

δ

δ

+ − − −

+ − −

⎡ ⎤= +⎣ ⎦⎡ ⎤= +⎣ ⎦

With initial conditions:

1 1 1

2 2 2

(0)

(0)

a a Aa a A

+ −

+ −

+ =

+ =2 1( )2

β βδ −=and

2 2q κ δ= +

© A.Lobo (2004) 6



Directional Coupler: Coupled Mode Theory(*)

Substituting the assumed solutions into the coupled wave equations and applying the initial conditions, we obtain:

(*) for more detailed analysis see K. Okamoto, Fundamentals of Optical Waveguides, Academic Press (2001) – Chap.4

1 1 2

2 1 2

( ) cos( ) sin( ) (0) sin( ) (0)

( ) sin( ) (0) cos( ) sin( ) (0)

j z

j z

A z qz j qz A j qz A eq q

A z j qz A qz j qz A eq q

δ

δ

δ κ

κ δ

−⎡ ⎤⎛ ⎞= + −⎢ ⎥⎜ ⎟

⎝ ⎠⎣ ⎦⎡ ⎤⎛ ⎞

= − + −⎢ ⎥⎜ ⎟⎝ ⎠⎣ ⎦

© A.Lobo (2004) 7



Directional Coupler: Coupled Mode Theory

For the most practical case, in which light is coupled into waveguide 1 only at z=0, we have the conditions of A1(0)=Ao and A2(0)=0. Then the optical power flow along the z-direction is given by:

21 2

1 2

22 2

2 2

( )( ) 1 sin ( )

( )( ) sin ( )

o

o

A zP z F qz

A

A zP z F qz

A

= = −

= =

2 1( )2

β βδ −=

2 2q κ δ= +

( )2

21

1F

qκ

δκ

⎛ ⎞= =⎜ ⎟⎝ ⎠ +

Power-coupling efficiency

© A.Lobo (2004) 8



Directional Coupler

0 1 2 3 4 5 60

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 60

0.2

0.4

0.6

0.8

10 1Fδ = ⇒ = 0.5Fδ κ= ⇒ =

P1 P1

P2 P2

Normalized distance (qz) Normalized distance (qz)

For 50% coupling it is a necessary condition that δ ≤ κ

2 22 2cL q

π πκ δ

= =+

Coupling Length:

Lc

Lc/2

Nor

mal

ized

Pow

ers

© A.Lobo (2004) 9



Directional Fibre Coupler

Side-Polished coupler (adjustable CR)

Fused coupler (fixed CR, possibly λ-dependent)


© A.Lobo (2004) 11



Combiner

Splitter

© A.Lobo (2004) 12



1

3

(dB) 10logPCRP

⎛ ⎞= ⎜ ⎟

⎝ ⎠

Coupling Ratio (CR)

By varying the parameters δ and κ it is possible to adjust CR in a very wide range.

© A.Lobo (2004) 13


4.2 WDM Couplers.


Normal -3dB coupler at 1550 nm has interaction coupling length is typically 0.9 mm, whereas for a WDM coupler that length can be from 100 to 500 mm.

Lc is depends on the optical wavelength λ

© A.Lobo (2004) 14


4.3 Tap Couplers.

Tap Coupler Pin (95 to 99%) Pin

(5 to 1%) Pin Used for monitor

© A.Lobo (2004) 15


4.4 Biconical Fibre Filter.

n1

n2

n3

Refraction Index Profile

Core

Int. Cladding

Ext. Cladding

Biconical Filter

1487 1507 1527 1547 1567 1587

-68

-66

-64

-62

-60

Tra

nsm

itted

Pow

er (d

Bm

)

Wavelength (nm)

Depressed-cladding fibre

1 21 sin (2 fT m π λ λ⎡ ⎤⎛ ⎞≈ + −⎜ ⎟⎢ ⎥Λ⎝ ⎠⎣ ⎦

A.B. Lobo Ribeiro, Ph.D. thesis, FCUP (1996)

•  A.C. Boucouvalas, J. Lightwave Technol. 3, 1151-1158 (1985). •  A.C. Boucouvalas and G Georgiou, IEE Proc. 134, Pt.J, 191-195 (1987)

© A.Lobo (2004) 16


4.5 Fibre Bragg Grating.

2B effnλ = Λ

Periodic refraction index change

Bragg Condition

© A.Lobo (2004) 17



4

2 effnλΛ =

λ1 λ2 λ3 λ4 λ1 λ2 λ3

λ4

2( ) coseff zn z n n zπδ ⎛ ⎞= + ⎜ ⎟Λ⎝ ⎠

4 2 effnλ = Λ

2tanh zpeak

B

L nR π δλ

⎛ ⎞⋅= ⎜ ⎟⎝ ⎠

222

2B z

Beff B

L nn Lλ π δλ π

λ⎛ ⎞

Δ = + ⎜ ⎟⎝ ⎠

L Peak Reflectivity

Stop-Band Width (FWHM)

Rpeak

ΔλB

© A.Lobo (2004) 18



Fibre Bragg Grating: Coupled Mode Theory(*)

(*) for more detailed analysis see R. Kashyap, Fiber Bragg Gratings, Academic Press (1999) – Chap.4

2 22

2 2 2

sinh ( )( )

cosh ( )

LR

Lα

λ ρα β

Ω= =

Ω −Δ

2 2

2

2

z

eff

eff

nn

n

π δ

α β

π πβλ

⋅Ω =Λ

= Ω −Δ

⎛ ⎞ ⎛ ⎞Δ = −⎜ ⎟ ⎜ ⎟Λ⎝ ⎠⎝ ⎠

2 (arg )( )2

dc d

λ ρτ λπ λ

= −

L = 20 mm

sinh( )sinh( ) cosh( )

LL i L

αρβ α α α

−Ω=Δ −

Group delay:

Reflectivity:

ΩL = 4

© A.Lobo (2004) 19



Chirped Fibre Bragg Grating (CFBG)


2chirp eff chirpnλΔ = ΔΛ 0( ) 2( ) G

chirp g

Lv

λ λτ λλ−≈ ⋅

Δ

λ1 λ2 λ3

Pulse compression after CFBG

λ1

λ2

λ3

In most fibre at 1550 nm, short wavelength light tends to travel faster

Λ

L

© A.Lobo (2004) 20





Uniform Grating

Chirped Grating

Chirped Grating with Apodization

( )( ) cos ( )eff zn z n n z zδ κ= + ⋅δnz

z

© A.Lobo (2004) 21


4.6 Long-Period Fibre Grating.

LPG promotes coupling between the propagating core mode and co-propagating cladding modes

ΛLPG

, ,( )LPG i eff clad i LPGn nλ = − Λ

The long-period grating (LPG) has a period typically in the range 100 µm to 1 mm

L = 10mm, ΛLPG = 450 µm (SMF-28 fibre)

© A.Lobo (2004) 22



2FBG effnλ = Λ , ,( )LPG i eff clad i LPGn nλ = − Λ

© A.Lobo (2004) 23



Concatenated LPGs

© A.Lobo (2004) 24


4.7 Gain Equalizing Filter.

© Teraxion Inc.

Gain Flattening Filter (GFF) with Concatenated Chirped-FBG (*)

(*) M. Rochette, M. Guy, S. LaRochelle, J. Lauzon and F. Trépanier, Photonics Technology Letters 11, 536-538 (1999).

© A.Lobo (2004) 25



K. Mizuno et.al., Furukawa Review no.19, 53-58 (2000).

© A.Lobo (2004) 26



Comparison of GFF technologies

Source: Teraxion Inc.

© A.Lobo (2004) 27


4.8 Mach-Zehnder and Michelson Filters (Interleavers).

0 1 2 3 4

0

1

0 4π3π2ππ

λ/2

Pontos dequadratura

Iout/Iin

φ (radianos)

high sensitivity

points

Mach-Zehnder Michelson

1 21 2

1 2

2( ) 1 ( ) cos

( )out

I II I I

I Iγ τ φ

⎡ ⎤= + ⋅ ± ⋅⎢ ⎥

+⎢ ⎥⎣ ⎦

2 n Lπφλ

= Δ

1 2L L LΔ = − 1 22( )L L LΔ = −

© A.Lobo (2004) 28



Optical interleavers

•  Channel spacing management via optical interferometry (e.g., Michelson, Mach-Zehnder) e.g. from 25 GHz to 50 GHz, or vice versa. •  Interleavers are needed in density populated WDM systems with 2.5 Gbit/s, 10 Gbit/s and even 40 Gbit/s transmitter/receivers

© A.Lobo (2004) 29



Cascaded Mach-Zehnders: 16-Channel Frequency Selector

0 1 2 3 4 5 6

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 60

0.2

0.4

0.6

0.8

1

MZ1

ΔL 2ΔL 4ΔL 8ΔL

MZ2 MZ3

MZ4

© A.Lobo (2004) 30



Cascaded Mach-Zehnders: 1×4 Demultiplexer

0 1 2 3 4 5 60

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 60

0.2

0.4

0.6

0.8

1

MZ1

ΔL

MZ2

MZ3

ΔL/2

ΔL/2

λ1, λ2, λ3, λ4 λ1

λ3

λ2

λ4

© A.Lobo (2004) 31


4.9 Fibre Ring Filter.

Ring (direct coupled)

0 180 360 540 720

0

1

4π3ππ 2π0

k = 0.5

k = 0.2

k = 0.1

Iout/Iin

φ (radianos)

2

2 2(1 ) 14(1 )sin ( / 2)out in

kI I

k kδ

φ⎡ ⎤

= − −⎢ ⎥− −⎣ ⎦2(1 ) Lk e αδ −= −

Ring: Direct coupled

Phase (!)

Nor

mal

ized

Tra

nsm

itted

Pow

er

k - power coupling coefficient of the coupler (1-δ) – power coupling loss of the coupler α – attenuation coeff. of the fibre ring L – ring length

Iin Iout

© A.Lobo (2004) 32 0 180 360 540 720

0

1

(a) Acoplamento Cruzado

k = 0.5

k = 0.8

k = 0.9

Iout

/Iin

φ (radianos)4π3π2ππ0



2

2 2

(1 )(1 ) 1(1 ) 4 sin ( / 2 / 4)out in

kI I

k kδ

φ π⎡ ⎤−= − −⎢ ⎥− − −⎣ ⎦

2(1 ) Lk e αδ −= −

Phase (!)

Nor

mal

ized

Tra

nsm

itted

Pow

er

Ring (cross-coupled)

Ring: Cross-coupled

•  An advantage of this configuration is that the entire ring can be made of one fibre, i.e., without cutting and splicing the fibre

Iin

Iout

© A.Lobo (2004) 33



Fibre Ring Filter: Sagnac Interferometer (*)

(*) X. Fang, H.Ji, C.T. Allen, K. Demarest and L. Pelz, IEEE Photonics Technology Letters 9, 458-460 (1997).

PMF

SMF

3 dB

0 10 20 30 40 50 600

0.2

0.4

0.6

0.8

1

2( ) sin2

out

in

II

φγ τ ⎛ ⎞= ⋅ ⎜ ⎟⎝ ⎠

Phase (!)

Nor

mal

ized

Tra

nsm

itted

Pow

er

Iin

Iout

© A.Lobo (2004) 34


4.10 Fibre Fabry-Perot Filter.

L

M M

0 180 360 540 720

0

1

4π3π2ππ0

R = 80%

R = 50%

R = 25%

R = 4%

Iout/Iin

φ (radianos)

Nor

mal

ized

Tra

nsm

itted

Pow

er

Phase (!)

2

2

2

11

21 sin1 2

ART

RR

φ

⎛ ⎞−⎜ ⎟−⎝ ⎠=⎛ ⎞ ⎛ ⎞+ ⎜ ⎟ ⎜ ⎟− ⎝ ⎠⎝ ⎠

T

2

2

4 1 sinnLn

π θφλ

−=

For normal incidence: θ = 0º

1FSR RFinesseFWHM R

π= =−

A – Absorption loss of the mirror R – Reflectivity of the mirror

For more detailed analysis see E. Hecht, Optics, 4ed. Chap.9.

FSR

© A.Lobo (2004) 35


4.10 Fibre Fabry-Perot Filter.

www.micronoptics.com

© A.Lobo (2004) 36


4.11 Fibre Polarizer.

Surface Plasmon Polarizer A Surface plasmon is an electromagnetic wave that propagates along the interface of two materials, one of which has a negative dielectric constant. The plasmon is a transverse magnetic effect and exhibits the property of strongly attenuating one polarization component from an optical beam while the other polarization is unaffected. Thus only the TM polarization is coupled to the plasmon and the TE polarization is unaffected.



TMo Plasmonβ β=Phase-Matching Condition

© A.Lobo (2004) 37


4.11 Fibre Polarizer.

Surface Plasmon Polarizer

Thin-film metal layer

Fibre Core

Silica Block

Optical Fibre

Fibre Cladding

~50 nm

P. Perumalsamy, In-Line Fiber Polarizer, M.Sc. Thesis, Virginia Polythecnic Institute, Virgina, USA (1998).

© A.Lobo (2004) 38


4.12 Fibre Depolarizer.

#1 #2 #n

Depolarization occurs by averaging over many different polarization states of the recirculating beams. Advantages are: •  All-fibre SMF device •  Low cost structure •  Insensitive to input polarization state •  Infinitesimal DOP is possible with increasing numbers of cascaded fibre rings

(*) B. Paisheng and C. Lin, Electronics Letters 34, 1777-1778 (1998).

Passive Fibre Depolarizer

3 dB

© A.Lobo (2004) 39


4.13 Fibre Polarization Controller.

Fibre Coil Polarization Controller (*)

(*) H.C. Lefevre, Electronics Letters 16, 778-780 (1980). A.B. Lobo Ribeiro, M.Sc. Thesis, Univ. Kent, UK (1992).

20.836( , ) r N mR m Nλ⋅ ⋅ ⋅=

R – radius of the coil r – nominal radius of the fibre (2r =125 µm, standard SMF) N – number of turns of fibre on the coil m –fractional-wave order (m=2, 4 or 8) to get a λ/m wave plate λ – wavelength of the light

Free-space optics approach

Fibre optic approach

© A.Lobo (2004) 40



Fibre Squeezer Polarization Controller(*): The PolaRITE TM

(*) www.generalphotonics.com Babinet Compensator: see E. Hecht, Optics, 4ed. Chap.8.

Free-space optics approach (Babinet-Soleil compensator)

Fibre optic approach (PolaRITE TM)

1 22 ( ) o ed d n nπϕλ

Δ = − ⋅ −

© A.Lobo (2004) 41



PM Fibre Twist Polarization Controller(*)

(*) www.fiberpro.com

PMF

SMF SMF

Free-space optics approach (with λ/4-wave plates)

•  No Fiber Squeezing •  No Damage on Fiber Jacket

TWIST

© A.Lobo (2004) 42


4.14 Fibre Optic Attenuator.

Pin Pout ( ) 10 log 10in

out

PIL dB ODP

⎛ ⎞= ⋅ = ×⎜ ⎟

⎝ ⎠

OD : Optical Density

For example: An attenuator with optical density of 2, has a 20 dB ILoss

Standard SMF Standard SMF

Air Gap

λ = 1300 nm

Fresnel reflection 3.5% → return loss of 14.5 dB

( ) 10 log in

back

PRL dBP

⎛ ⎞= ⋅ ⎜ ⎟

⎝ ⎠

Pback

More accurate analysis based on electric fields: INTERFERENCE ANALYSIS

© A.Lobo (2004) 43


4.14 Fibre Optic Attenuator.

Standard SMF Standard SMF

Absorbing SMF (GeAl core+Rare Earth ions)

S. Chia, AMP Journal of Technology 5, 19-23 (1996) from AMP Inc.

Response of insertion loss to temperature cycling between -40ºC and 85ºC of five individual samples of a 5 dB OA measured at 1550 nm.

± 0.30 dB

5 dB attenuator.

Active Fibre Optic Devices



© A.Lobo (2004) 2

5. Active Fibre Optic Devices

5.1 Thermally Tunable Fibre Filter and Modulator. 5.2 Twin-Core Fibre Switch. 5.3 Acousto-Optic Tunable Fibre Filter. 5.4 Piezoelectric Tunable Fibre Filter. 5.5 Acousto-Optic Fibre Modulator. 5.6 Piezoelectric Fibre Modulator. 5.7 Electric Poling Fibre Modulator. 5.8 Fibre Amplifier.

© A.Lobo (2004) 3


5.1 Thermally Tunable Fibre Filter and Modulator.

Temperature-induced optical phase shifts in fibres (*)

(*) N. Lagakos, J.A. Bucaro and J. Jarzynski, Applied Optics 20, 2305-2308 (1981).

1z

T

L n n nTL n n T nρ

φ εφΔ Δ Δ ∂ Δ⎛ ⎞ ⎛ ⎞= + = + ⋅Δ +⎜ ⎟ ⎜ ⎟∂⎝ ⎠ ⎝ ⎠

2 nLπφλ

=

εz , εr – Axial (z) and radial (r) strains in the core. ρ – core density. n – effective refractive index p11 , p12 – are the Pockels coefficients of the core.

[ ]2

11 12 121 1 ( )

2z r zn n p p p

T n T Tρ

φ ε ε εφ

⎧ ⎫Δ ∂⎛ ⎞= + − + +⎨ ⎬⎜ ⎟Δ ∂ Δ⎝ ⎠ ⎩ ⎭

5 -10.7 10 CbareT

φφ

−Δ = ×Δ

o

5 -11.7 10 CjacketT

φφ

−Δ = ×Δ

o

© A.Lobo (2004) 4



Optical phase sensitivity of the fibre due to a physical parameter

2X

n L nSL X L X Xφ π

λΔ ∂ ∂⎡ ⎤= = ⋅ +⎢ ⎥Δ ∂ ∂⎣ ⎦

Physical Parameter (X) Sensitivity (SX)

Axial Deformation (ε) 107 rad m-1 strain-1

Temperature (T) 100 rad m-1 °C-1

Hydrostatic Pressure (P) 5*10-5 rad m-1 Pa-1

(For a wavelength of 850 nm)

© A.Lobo (2004) 5



Temperature-induced optical phase shifts in metal coated fibres (*)

(*) C.T. Shyu and L. Wang, J. Lightwave Technology 12, 2040-2048 (1994).

Standard SMF Standard SMF Metallic film

2( )o nT T I R hAt t V cρ

∂ − − Θ∂Θ= =∂ ∂ ( )

2/( ) 1 tnI Rt e

hAτ−Θ = −

( )2

/( ) 1 tnI Rt ehA

τβφ −Δ = −R – Electrical resistance of the metallic film. ρ , c – density and specific heat of the fibre (respectively). V , A – volume and surface area of the metallic film. k – thermal conductivity of the film h – heat transfer coefficient

In

cVhAρτ =

Tφβ Δ=

Δ→ Fibre glass material

© A.Lobo (2004) 6



Temperature-induced optical phase shifts in metal coated fibres (*)

(*) C.T. Shyu and L. Wang, J. Lightwave Technology 12, 2040-2048 (1994).

gold coating

In

Coating length: 3 cm Resistance: 60.6 Ω

© A.Lobo (2004) 7



Thermally fibre modulator (*)

(*) - C.T. Shyu and L. Wang, J. Lightwave Technology 12, 2040-2048 (1994). - B.J. White et. al., J. Lightwave Technology 5, 1169-1174 (1987).

Metallic film

In cos (ωt)

Test current

Detected optical signal

Predicted signal

100 Hz

© A.Lobo (2004) 8



Thermally tunable fibre Bragg grating filter (*)

1 1BX

B

nSX X X n X

λλΔ ∂Δ ∂= = ⋅ + ⋅Δ ∂ ∂

Physical Parameter (X) Sensitivity (SX)

Axial Deformation (ε) 0.78×10-6 µs t r a i n

-1

Temperature (T) 8×10-6 °C-1

Hydrostatic Pressure (P) 2.7×10-6 MPa-1

2B nλ = Λ

B

X

© A.Lobo (2004) 9

0.0 0.1 0.2 0.3150

200

250

300

350

400

Time (min.)

I s (mA

)

Vaplicado

0.8

0.9

1.0

1.1

1.2

1.3

1.4

(a)

Vout /V

ref




(*) P.M. Cavaleiro, F.M. Araújo and A.B.Lobo Ribeiro, Electronics Letters 34, 1133-1135 (1998)

silver film

In

SMF fibre with FBG

0.0 0.5 1.0 1.5 2.0 2.5 3.0835.2

835.4

835.6

835.8

836.0

836.2

836.4

836.6

Bra

gg W

avel

engt

h (n

m)

Electrical current - squared (A2)


© A.Lobo (2004) 10




(*) L.Lin et. al., IEEE Photonics Technology Letters 15, 545-547 (2003)

Ti-Pt-Ni metal alloyed coating (2 µm)

In

SMF fibre with FBG


© A.Lobo (2004) 11

11.2 nm

Wavelength (nm)

Opt

ical

Pow

er (d

Bm

)



Thermally tunable fibre Bragg grating (*): Laser Application

(*) J.J. Pan et.al., Lightwaves 2020 Inc., US Pat.6018534

0.009 nm/ºCB

TλΔΔ

;

0.16 nm/ºCB

DFBTλΔΔ

;

© A.Lobo (2004) 12


5.2 Twin Core Fibre Switch.

Twin Core Fibre (*)

(*) - P.J. Severin, in Proc. SPIE vol.1314 – Fiber Optics 90, 348-364 (1990). - R. Romaniuk, J. Dorosz, in Proc. SPIE vol.4887 (2001)

2 21

2 22

( ) 1 sin

( ) sin

o

o

P z kzF

P F

P z kzF

P F

⎛ ⎞= − ⎜ ⎟⎝ ⎠⎛ ⎞= ⎜ ⎟⎝ ⎠

22 1

1

12

F

kβ β

=−⎛ ⎞+ ⎜ ⎟⎝ ⎠

Power-coupling efficiency:

Cladding (125 µm)

4 µm

Cores (10 µm)

© A.Lobo (2004) 13



Twin Core WDM coupler/filter (*)

1530 1535 1540 1545 1550 1555 15600

0.2

0.4

0.6

0.8

1

Wavelength [nm]

Nor

mal

ized

Pow

ers

P1

P2

(*) twin core fibre sample provided by Prof. P.J. Severin (Philips Eindhoven)

L = 20 cm

P2

P1 Po

Cores: 9 µm Cores separation: 2 to 5 µm Cladding: 100 µm

© A.Lobo (2004) 14

1530 1535 1540 1545 1550 1555 15600

0.2

0.4

0.6

0.8

1



(*) twin core fibre sample provided by Prof. P.J. Severin (Philips Eindhoven)

P1 Po

Piezoelectric Transducer

V

Wavelength [nm]

Nor

mal

ized

Pow

er (P

1 /P o

)

Length variation of 100 µm on 20 cm

© A.Lobo (2004) 16


5.3 Acousto-Optic Tunable Fibre Filter.

FREQUENCY SHIFTER

Optical Frequency ωo

Optical Frequency ωo ± ωac

Acoustic Frequency ωac

( Acoustic frequency (ωa) can be generated electrically or optically)

sin2 4

o o acB B

ac acVλ λ ω

πΘ = ⇒Θ ≅

Λ

Diffracted beam angle at:

For more information see: www.brimrose.com

© A.Lobo (2004) 17



(*) W. P. Risk, R. Youngquist, R.C. Kino, H.J. Shaw, Optics Letters 9, 309 (1984)

Surface Acoustic Wave (SAW) device (*)

(Used to produce surface acoustic waves)

cos SAW a

a B B

Vf L L

ΛΘ = =Phase-matching condition:

Velocity of the SAW

Fibre beat length

SAW wavelength

© A.Lobo (2004) 18



Flexure-wave fibre device (*)

(*) B.Y. Kim, J.N. Blake, H.E. Engan, H.J. Shaw, Optics Letters 11, 389-391 (1986).

York HB600 fibre (HiBi fibre), with beat length of 1.5 mm and an acoustic frequency of ~0.2 MHz, producing a frequency shift of ~790 kHz

© A.Lobo (2004) 19




(*) T. E. Dimmick, G. Kakarantzas, T. A. Birks, and P. St. J.Russell, in Proc. OFC‘2000, FB4 pp.25-27, 2000.

11 21

2ac

HE HE

πβ β

Λ =−Resonance condition:

© A.Lobo (2004) 20




(*) T. E. Dimmick, G. Kakarantzas, T. A. Birks, and P. St. J.Russell, in Proc. OFC‘2000, FB4 pp.25-27, 2000.

Filter bandwidth 0.8 ac

Lλλ

ΛΔ =

2.9 nm bandwidth

(4 cm)

< 10 cm

© A.Lobo (2004) 21

1.53 1.54 1.55 1.56 1.57

0.2

0.4

0.6

0.8

1


5.4 Piezoelectric Tunable Fibre Filter.

L

M M

PZT Optical fibre

A = 0 R = 95 % L = 20 µm ΔL = +1 µm 2

2

2

11

21 sin1 2

ART

RR

φ

⎛ ⎞−⎜ ⎟−⎝ ⎠=⎛ ⎞ ⎛ ⎞+ ⎜ ⎟ ⎜ ⎟− ⎝ ⎠⎝ ⎠

FSR ≈ 60 nm FWHM ≈ 2 nm Finesse ≈ 30

Wavelength (µm)

Tran

smitt

ance

Tunable Fibre FP Filter

© A.Lobo (2004) 23



Strain-induced optical phase shifts in fibres (*)

(*) A. Bertholds, R. Dändliker, J. Lightwave Technology 5, 895-900 (1987).

( )2T const

n L nLπφλ=

Δ = Δ +Δ2 nLπφλ

=

εz , εr – Axial (z) and radial (r) strains in the core (εr= ν εz) ν – Poisson ratio (=0.17 for silica). n – effective refractive index (= 1.456 at λ=1550 nm) p11 , p12 –Pockels coefficients of the core (p11=0.121 , p12=0.27 for silica)

[ ]2

11 12 122 ( )

2z r znnL p p pπφ ε ε ε

λ⎧ ⎫

Δ − + +⎨ ⎬⎩ ⎭

;

6 -1 -14 10 rad m strainLφε

Δ ≈ × ⋅ ⋅Δ

for λ = 1550 nm

© A.Lobo (2004) 24



PZT PZT FBG

(*) A. Iocco, H.G. Limberger, R.P. Salathé, Electronics Letters 33, 2147-2148 (1997).

Tunable FBG Filter (*)

© A.Lobo (2004) 26


5.5 Acousto-optic Fibre Modulator.

All-fibre AO Frequency Shifter (*)

(*) D.O. Culverhouse et.al., IEEE Photonics Tech. Letters 8, 1636-1637 (1996).

© A.Lobo (2004) 27


5.5 Acousto-optic Fibre Modulator.

ZnO-Coated Optical Fibre AO Phase Modulator(*)

(*) A. Roeksabutr and P.L. Chu, J. Lightwave Technology 16, 1203-1211 (1998).

311 12( ) rn l p pπφ ε

λΔ ≈ +

Optical phase shift:

Max. phase shift (exp):~700 mrads @ 670 MHz

© A.Lobo (2004) 28

r R


5.6 Piezoelectric Fibre Modulator.

3211 12

12

(1 ) ( )42 2

effeff

n p p rNC n pV R

νφ πλ

⎧ ⎫+ +Δ ⎪ ⎪⎡ ⎤= + −⎨ ⎬⎢ ⎥⎣ ⎦⎪ ⎪⎩ ⎭(rad/volt)

for more details see: G. Martini, Optical & Quantum Electronics 19, 179 (1987).

N – number of fibre turns wrapped on the PZT ν – Poisson ratio of silica (0.17) p11 , p12 –Pockels coefficients of the fibre core C – radial displacement of PZT per unit of voltage (p.ex. C≈0.61 nm/V for a PZT-5H)

© A.Lobo (2004) 30



(*) M.N. Zervas and I.P. Giles, Optics Letters 13, 404-406 (1988).

Fibre-Loop Phase Modulator(*)

2phase

resonanceloop

Vf

L=

Resonance Frequency of the loop

As the advantage to remove the phase shift dependence on the PZT characteristics

© A.Lobo (2004) 31


5.7 Electric Poling Fibre Modulator.

The fibre is 127 mm diameter with two holes of 45 mm diameter. The optical fibres are thermally poled at around 250°C with an electric field in the order of 4kV. The electrodes are inserted to lengths in excess of 20 cm.

(150 VAC at 4.5 kHz) EO coefficient can be calculated. EO coefficients of ~0.2 pm/V have been measured in 1.55 µm silica single mode fibres (for a LiNbO3: 7~30 pm/V)

See: Applied optics Group, Univ. Kent, Canterbury (U.K.) - www.kent.ac.uk/physical-sciences/aog

4.5 kHz

22

2NL Kn L Eπφ

λΔ =

n2K ≈ 3.2×10-20 m2/W

22eff o Kn n n E= + 2 11

2 for 10 V/mK on E n E≈ ≈

© A.Lobo (2004) 32


5.8 Fibre Amplifier.

Gain (EDFA)

Power Supply (PUMP)

IN

OUT

FEEDBACK (Resonant Cavity)

FIBER LASER

© A.Lobo (2004) 33


5.8 Fibre Amplifier.

S-Ring Fibre Laser (*)

(*) O.G. Okhotnikov, A.B.Lobo Ribeiro, J.A.R. Salcedo, Applied Physics Letters 63, 2726-2728 (1993).

Fibre Optic (Hybrid) Devices



© A.Lobo (2004) 2

6. Fibre Optic (Hybrid) Devices

6.1 Fibre Beam Collimator/Expander. 6.2 Thin-Film Fibre Filters and Couplers. 6.3 Faraday Rotator Mirror. 6.4 Fibre Isolator. 6.5 Fibre Circulator. 6.6 Fibre Interleavers (Fabry-Perot and Michelson Interferometers). 6.7 Wavelength Locker. 6.8 Add/Drop Multiplexer. 6.9 Dispersion Compensator. 6.10 Array Waveguide Grating (AWG). 6.11 MEMS based Devices.

© A.Lobo (2004) 3

GRIN Lens Conventional Aspherical Lens


6.1 Fibre Beam Collimator/Expander.

•  The index of refraction within the lens material varies gradually •  Dramatically reduced need for tightly-controlled surface curvatures •  Simple and compact lens geometry.

GRaded-INdex Lens (GRIN lens) (*)

(*) www.nsgamerica.com www.grintech.de

© A.Lobo (2004) 4



GRIN lens

no – Refractive index at the optical axis A – squared gradient constant r – radial position of the lens

2( ) 12oA

n r n r⎛ ⎞= −⎜ ⎟⎝ ⎠

2z APπ

=

Lens Length (z) and Pitch (P)

© A.Lobo (2004) 5



21

2

cos( ) sin( )1sin( ) cos( )

o

o o

l n A z A z Al

n A l n A z A z A+= ⋅−

In the case of collimating from a laser diode, LED, or fiber, there is only a variable distance (l), which is the distance from the source to the GRIN lens.

1 1tan( )o

ln A z A

= ⋅

2l →∞

© A.Lobo (2004) 7



Thermally-diffused Expanded Core (TEC) fibres

americas.kyocera.com www.totoku.com www.kadencephotonics.biz

© A.Lobo (2004) 8


6.2 Thin-Film Fibre Filters and Couplers.

•  Principle of thin film filter is based on multiple reflection from two surfaces => Fabry-Perot filters •  Assume two partially reflective parallel surfaces

•  Light is partially reflected back and forth within the cavity •  The output is the result of superposing many reflected beam •  Light that the cavity-length is an integer number their wavelengths add constructively at the output => resonant wavelengths •  Multiple wavelength can satisfy the constructive interference => their frequency distance defines as free spectral range

© A.Lobo (2004) 9



(glass) - (High index) - (Low index) – (air)

•  For H-layers: Zirconium dioxide (n = 2.1) or Titanium dioxide (n = 2.40) or zinc sulfide (n = 2.32).

•  For L-layers: Magnesium fluoride (n = 1.38) or Cerium fluoride (n = 1.63).

For more information see: E. Hecht, Optics, 4.ed, Chap.9

© A.Lobo (2004) 12

When the direction of propagation of light is altered by a medium, a new orthonormal coordinate bases for the polarisation must be defined, where ez is the new direction of propagation.


6.3 Faraday Rotator Mirror (FRM).

Jones Matrix on backward propagation direction

( ) ( ), , , ,x y z x y ze e e u u u= −

For a reciprocal system the Jones matrix is the transpose of the matrix for the forward direction.

[ ] 1 4

3 2forward

m mM

m m⎡ ⎤

= ⎢ ⎥⎣ ⎦

[ ] [ ] 1 3

4 2

T

backward forward

m mM M

m m⎡ ⎤

= = ⎢ ⎥⎣ ⎦

[ ] [ ]Tx xM M=

[ ] [ ]Tx xM M≠Nonreciprocal element

Reciprocal element (for example: mirror, half-wave plate)

(for example: Faraday rotator mirror)

© A.Lobo (2004) 13



Jones Matrices of some reflectors (*)

[ ] 1 00 1mirror

M⎡ ⎤

= ⎢ ⎥⎣ ⎦

[ ] 1 00 1loop

M⎡ ⎤

= ⎢ ⎥−⎣ ⎦

[ ] 0 11 0FRM

M ⎡ ⎤= ⎢ ⎥−⎣ ⎦

180º phase shift

rotation by 90º

(a)

(b)

(c)

(*) M.O. van Deventer, Fundamentals of Bidirectional Transmission over a Single Optical Fibre, Kluwer Academic Press (1996).

© A.Lobo (2004) 14



[ ] [ ] [ ] [ ]cos45º sin 45º 1 0 cos45º sin 45º 0 1sin 45º cos45º 0 1 sin 45º cos45º 1 0

FRM FR mirror FRM M M M= =

⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤= =⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥− − −⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦

g g

g g

( )L

V B dlθ λ= ⋅∫rr

Verdet constant For example, Faraday rotation @ λ=1310 nm: •  Pure silica fibre is ~2.2 degree/m •  Pure YIG crystal is ~22000 degree/m

(YIG crystal) θ = 45º

The Faraday Effect (*)

For more information see: E. Hecht, Optics, 4.ed, Chap.8

© A.Lobo (2004) 16


6.4 Fibre Isolator.

θ = 45º

Fibre isolator using Faraday effect (*)

(*) C Hentschel, Fiber Optics Handbook, Hewlett-Packard (1989).

© A.Lobo (2004) 17


6.4 Fibre Isolator.

Fibre isolator using λ/4-Wave plate (*)

(*) C Hentschel, Fiber Optics Handbook, Hewlett-Packard (1989).

© A.Lobo (2004) 18


6.5 Fibre Circulator. Polarisation Beam Splitter (PBS)

λ/2-wave rotator

Port 1

Port 2

(Port 3)

(Port 4)

FR λ/2 WP

© A.Lobo (2004) 19


6.6 Fibre Interleaver (Fabry-Perot and Michelson Interferometers).

Optical interleavers

•  Channel spacing management via optical interferometry (e.g., Michelson, Mach-Zehnder) e.g. from 25 GHz to 50 GHz, or vice versa. •  Interleavers are needed in density populated WDM systems with 2.5 Gbit/s, 10 Gbit/s and even 40 Gbit/s transmitter/receivers

© A.Lobo (2004) 20



Optical interleaver using Birefringence

Polarized Input Beam

Birefringent Crystal

PBS

21 ( ) cos ( )

2in

out x yI

I n n Lcπγ τ ν⎧ ⎫⎡ ⎤= ⋅ ± ⋅ −⎨ ⎬⎢ ⎥⎣ ⎦⎩ ⎭

where =integer( )mx y

cm mn n L

ν =−

ν1 ν3 ν5 ν7 ν9 ν11 ν13

ν2 ν4 ν6 ν8 ν10 ν12

© A.Lobo (2004) 21



Optical interleaver using Michelson interferometer

BS

1 22

1 ( ) cos ( )2in

outI

I n L Lcπγ τ ν⎧ ⎫⎡ ⎤= ⋅ + ⋅ −⎨ ⎬⎢ ⎥⎣ ⎦⎩ ⎭

1 22 ( )cFSR

n L L=

−

ν1 ν3 ν5 ν7 ν9 ν11 ν13

mirror

mirror

L2

L1

© A.Lobo (2004) 22



Optical interleaver using Gires-Tournois etalon

•  Front mirror reflectivity R1<1

•  Rear mirror reflectivity R2=1

•  Etalon reflectivity R=1 for all λ

•  Phase shift is a periodic function of frequency with:

•  nd can be chosen so that FSR coincides with ITU grids

•  ULE glass cab be used as spacer

2cFSRnd

=

© A.Lobo (2004) 23



Gires-Tournois cavity (www.accumux.com)

R<1 Ro=1

d

( )12 tan tanσ φ−Φ = 02 21 ( 1)sinστ τ

σ φ=

+ −

11

RR

σ +=−

2 ndπφλ

=

τ0 is the roundtrip flight time inside the cavity

© A.Lobo (2004) 24



Michelson interferometer with GTI-mirrors

BS

L2

L1

GTI-mirrors

1 2 1 22

1 ( ) cos ( )2in

outI

I L Lcπγ τ ν φ φ⎧ ⎫⎡ ⎤= ⋅ + ⋅ − + −⎨ ⎬⎢ ⎥⎣ ⎦⎩ ⎭

•  Giles-Tournois etalons are employed as phase dispersive mirrors

•  With proper choices of the front mirror reflectivities, flat-top passbands can be obtained

•  The cavity spacing must match with the optical path difference (ΔL)

•  Channel isolation of better than 35dB can be achieved

(*) for more information see: www.accumux.com

© A.Lobo (2004) 27


6.8 Add/Drop Multiplexer.

λ1 λ2 λ3 λ4

λ3

λ1 λ2 λ3 λ4

•  Thin Film Filters

•  WDM Couplers

•  Fibre Gratings

•  Fixed OADM

•  Reconfigurable OADM

© A.Lobo (2004) 28



Filter reflects i Add / Drop

Dielectric thin-film filter design

Common Passband

Circulator with FBG design

Add i Drop i

LW Technology (Passive Components) © Copyright 1999, Agilent Technologies


© A.Lobo (2004) 29



Planar Tunable Add/Drop MUX

COBNET Consortium –European Project AC069-ACTS program (http://ica1www.epfl.ch/COBNET/)

ADD λi

Drop λj

Input λ1+...+ λj +...+ λn

Output λ1+...+ λi +...+ λn

© A.Lobo (2004) 30


6.9 Dispersion Compensator.



λ1 λ2 λ3

λ1 λ2

λ3

In this case, the longest wavelength (λ3) arrive first

Grating spacing increases

λ1< λ2 < λ3 Delay is largest for λ3

© A.Lobo (2004) 32



Thermally Tunable CFBG + Circulator

©B.J. Eggleton, Optical Fiber Research Dept., Bell Labs., Lucent Technologies

© A.Lobo (2004) 33



Thermally Tunable CFBG + Circulator

Nielsen, Eggleton,Rogers et.al., Lucent Technologies (ECOC 1999) Rx

Tx 40 Gb/s 0-10 dBm

120 km Truewave

PMD<0.5 ps Ripple<1.0 dB @ 10-9 BER

© A.Lobo (2004) 34



Gires-Tournois etalon

R<1 Ro=1

d

02 21 ( 1)sinστ τ

σ φ=

+ −

2 2

22 2

4 ( 1)sin(2 )

1 ( 1)sin

dDLc

τ π σ σ φλ λ σ φ∂ −⎛ ⎞= = ⋅⎜ ⎟∂ ⎝ ⎠ ⎡ ⎤+ −⎣ ⎦

see www.accumux.com

Frequency (THz)

Dis

pers

ion

(ps/

nm)

Group Delay

© A.Lobo (2004) 35


6.10 Array Waveguide Grating (AWG).


sin sin om o m

ngλϑ ϑ− =

Planar Grating

m = 0, ±1, ±2,….= diffraction order

© A.Lobo (2004) 37



Grating equation:

sinn L d mθ λ⋅Δ + =ΔL – path difference between

neighbouring guides d – distance between guides n – refractive index m – integer λ – wavelength θ – angle of diffraction

ΔL >> λ to achieve high order diffraction

© A.Lobo (2004) 38



Spectral Resolution:

mNλλΔ =

number of guides in the array

Δλ = 0.8 nm (~100 GHz) @ 1550 nm, mN must > 1940

© A.Lobo (2004) 40


6.10 Array Waveguide Grating (AWG). AWG INPUT SIDE

AWG OUTPUT SIDE (analogous to Youngs experiment)

© A.Lobo (2004) 42



1a 3a

2a 4a

1b 3b 2b 4b

1c 3c

2c 4c

1d 3d 2d 4d

1a

3c 2d 4b

1b 3d 2a

4c

1c 3a 2b 4d

1d

3b 2c 4a

Rows .. .. translate into .. .. columns

© A.Lobo (2004) 43



COBNET Consortium –European Project AC069-ACTS program (http://ica1www.epfl.ch/COBNET/)

Input λ1+ λ2 +...+ λn

Outputs

λ1 λ2

λn

Planar MUX

© A.Lobo (2004) 44


6.11 MEMS based Devices.

•  NxN Switches (very large N) •  Variable optical attenuators •  Wavelength Add/Drop

MEMS : Micro Electro-Mechanical Systems

© A.Lobo (2004) 46



Optical Cross-Connect (OXC) – Lucent WaveStar

•  1024 x 1024 prototype

•  Thin film silicon MEMS design

Fibre Device Fabrication techniques



© A.Lobo (2004) 2

7. Fibre Device Fabrication Techniques

7.1 Fibre Bragg Gratings Fabrication. 7.2 Fibre Couplers Fabrication. 7.3 Special Fibre Devices.

© A.Lobo (2004) 3


7.1 Fibre Bragg Grating Fabrication.

Fabricação do Sensor de BRAGG (“GRATING”)

Multiwave Networks Portugal, Lda.

Reflectivity 0 – 100% Spectral width: 50 – 500 pm Wavelength 1520 – 1570 nm

•  D.A. Jackson, A.B. Lobo Ribeiro, L. Reekie and J.L. Archambault, Opt. Lett. 18, 1192-1194 (1993). •  F.M. Araújo, J.M. Sousa and A.B. Lobo Ribeiro, 9ª Conf. Nac. Física, pp.182-183 (1994).

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