Optical Networks and Communications

113
Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών Τμήμα Πληροφορικής και Τηλεπικοινωνιών Optical Communications & Photonics Technology Laboratory http://www.optcomm2.di.uoa.gr/ Optical Networks and Communications Silicon Optical Fibers Professor Syvridis Dimitris

Transcript of Optical Networks and Communications

Page 1: Optical Networks and Communications

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών

Optical Communications &

Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/

Optical Networks and

Communications

Silicon Optical FibersProfessor Syvridis Dimitris

Page 2: Optical Networks and Communications

Optical Communications &

Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/

Parts and Devices of Optical Communications

• Sources

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών2

Source DetectorAmplifierFiber Fiber

• Silicon fibers for long distance transmissions

• Additional devices

– Amplifiers

– Filters

– Couplers, Isolators, Modulators etc.

• DetectorsFilter

Page 3: Optical Networks and Communications

Optical Communications &

Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/

Parts and Devices of Optical Communications

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών3

Source DetectorAmplifier

Filter

Fiber Fiber

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Optical Communications &

Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/

Optical Fibers - Contents

• Introduction

• Fading in SiO2 optical fibers

• Receiver sensitivity and power budget

• Multiplexing techniques in optical networks

• Light propagation in optical fibers

• Types of optical fibers

• Fading and attenuation in multi-mode and single-mode optical fibers

• Chromatic dispersion in single mode silica fibers

• Mode dispersion

• Total dispersion, Scenarios

• Control of the slope of chromatic dispersion

• Polarization dispersion in single mode fibers - Troubleshooting

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών4

Page 5: Optical Networks and Communications

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Advantages of Optical Fibers

• High carrier frequency → Modulation of larger bandwidth (> 10 GHz)

• Low losses / attenuation (< 0.3 dB/km) as a function of wavelength

– Coverage of longer distances without any repeater (> 50km)

• Small diameter (125 µm)– Less material / weight

– Light and relatively flexible cable

• High tolerance against interference from electromagnetic waves– No need for shielding

• No interference to the external environment

• Electrical insulation– Νo troubles with groundings / potential differences

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Communication

networks

Underwater

cables

Systems on ships and

airplanes

Computer systems / Data

transmission

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Disadvantages of Optical Fibers

• Small diameter: connection difficulties

– Solved by plastic optical fibers (from polymers), but not satisfactorily as they incur large losses

• Additional lines for power supply at remote locations where there are additional devices, such as amplifiers

• Fiber sensitivity to hydrogen, water and ionizing radiation →increased losses

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Τμήμα Πληροφορικής και Τηλεπικοινωνιών6

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Structure of Optical Fibers

• Core and cladding are important for light transmission

• Higher refractive index for the core

• Fiber diameters: 50 – 1000 µm, depending on application– Typical cladding diameter:125

μm

• Difference of refractive indexes between core and cladding 1% or a little more

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• Single Mode (SM) Fibers: Fibers

that allow propagation of only one

transverse mode

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Optical Fibers - Contents

• Introduction

• Fading in SiO2 optical fibers

• Receiver sensitivity and power budget

• Multiplexing techniques in optical networks

• Light propagation in optical fibers

• Types of optical fibers

• Fading and attenuation in multi-mode and single-mode optical fibers

• Chromatic dispersion in single mode silica fibers

• Mode dispersion

• Total dispersion, Scenarios

• Control of the slope of chromatic dispersion

• Polarization dispersion in single mode fibers - Troubleshooting

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών8

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Attenuation Sources

1. Material Absorption loss

2. Coupling and splicing loss

3. Scattering loss

4. Bending loss

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1. Material Absorption Loss (1/2)

• Extrinsic losses

– Atomic resonances of external particles in the fiber

– Light absorption from Ο–Η bonds

• Fundamental resonance frequency: 1.1×1014 Hz / 2.72 μm

• Absorption peaks at wavelengths 2.72/(k+1) μm

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0.6 0.8 1.41.2

10

1

102

103

104

dB/km

μm1.0

1st

harmonic

2nd

harmonic3rd

harmonic

0.68 0.91 1.36

Interaction between O–H bonds

and SiO2 fiber

1.24

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1. Material Absorption Loss (2/2)

• Intrinsic losses– Atomic resonances of fiber material

– Occurs in both infrared and ultraviolet ranges

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0.7 0.8 0.9 1.1 1.3 1.41.0 1.5

0.1

0.03

0.3

1

3

10

dB/km

Infrared

absorption

μm2.0

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2. Coupling and Splicing loss

• Extrinsic loss

– Misalignment in the core center

– Tilt of a fiber

– End face quality

• Intrinsic loss

– Core ellipticity

– Mismatch in refractive index

• Typical values:

– Coupling loss: 0.2 dB

– Splicing loss: 0.05 dB

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών12

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Optical Communications &

Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/

Optical Fibers - Contents

• Introduction, advantages/disadvantages, structure of optical fibers

• Fading in SiO2 optical fibers

• Receiver sensitivity and power budget

• Multiplexing techniques in optical networks

• Light propagation in optical fibers

• Types of optical fibers

• Fading and attenuation in multi-mode and single-mode optical fibers

• Chromatic dispersion in single mode silica fibers

• Mode dispersion

• Total dispersion, Scenarios

• Control of the slope of chromatic dispersion

• Polarization dispersion in single mode fibers - Troubleshooting

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών13

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Receiver Sensitivity

• Fiber attenuation places an upper limit on– Transmission distance

– Bit rate

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

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• Receiver sensitivity: A certain minimum received power required

in a communication system in order to achieve a specified

performance

• In digital transmission, performance is based on the Bit Error Rate

(BER)– Typical required BER values:10–9 or 10–12

• If the received power is lower than the minimum required power,

the system will perform unsatisfactorily or may even be

inoperational

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Power Budget

• Transmitted power is restricted to a few mW to– Prevent overheating

– Avoid undesirable nonlinearities

– Reduce power consumption

• Power Budget: The upper limit for allowable power loss from transmission– Depends on required received power and available transmission power

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Ptx : Transmitted power,

Pmin : Minimum required receiving power (sensitivity)

• The total power loss in a transmission line must be bellow the power

budget

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Transmission Distance

• As the bit rate increases– ↑ signal bandwidth ↑ receiver bandwidth Signal power should be proportionally

increased, to maintain SNR

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• If a fiber is L km long and its attenuation is afiber dB/km, the total attenuation is

(afiber L) dB

• afiber L [dB] + other loss ≤ Power Budget [dB]

• Sensitivity is linearly proportional to the transmission bit rate (bits/sec)

• Maximum transmission distance:

Page 17: Optical Networks and Communications

Optical Communications &

Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/

Optical Fibers - Contents

• Introduction, advantages/disadvantages, structure of optical fibers

• Fading in SiO2 optical fibers

• Receiver sensitivity and power budget

• Multiplexing techniques in optical networks

• Light propagation in optical fibers

• Types of optical fibers

• Fading and attenuation in multi-mode and single-mode optical fibers

• Chromatic dispersion in single mode silica fibers– Control of chromatic dispersion

– Chromatic dispersion and nonlinear effects

• Mode dispersion

• Total dispersion, Scenarios

• Control of the slope of chromatic dispersion

• Polarization dispersion in single mode fibers - Troubleshooting

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών17

Page 18: Optical Networks and Communications

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Multiplexing Techniques• Need for multiplexing: Transmits data at higher rates over a single fiber

• 2 fundamental multiplexing techniques:

– Time Division Multiplexing (TDM)

– Wavelength division multiplexing (WDM)

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• ONU: Optical Network Unit

• OLT: Optical Link Terminal

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Time Division Multiplexing• The multiplexer typically interleaves the lower-speed streams to obtain the higher-speed

stream

• Optical Time Division Multiplexing (OTDM): Performs optical multiplexing and

demultiplexing Increases TDM transmission rates

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

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B bits/sec

1

2

N

NB bits/sec

t1t2t3t4t5t6

t1t2t3t4t5t6

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Wavelength Division Multiplexing

• Simultaneous data transmission at multiple carrier wavelengths over a fiber

• These wavelengths do not interfere with each other provided they are kept

sufficiently far apart

• Virtual fibers: It makes a single fiber look like multiple “virtual” fibers, with each

virtual fiber carrying a single data stream

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

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1

2

N

B bits/secλ1

λ2

λ3

B bits/sec

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Wavelength Bands

• WDM uses multiple wavelength bands inside a fiber

• The wavelengths and frequencies used have been standardized by ITU

• ITU has standardized fixed channel spacing in the frequency domain (not in the wavelength domain)

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193.3 193.2 193.1 193.0 192.9

1550.918 1551.721 1552.524 1553.329 1554.134

Frequency (THz)

Wavelength (nm)

100 GHz100 GHz ……

Signal Bandwidth

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WDM types in optical communications• Coarse WDM – CWDM

– Suitable for low-cost, low-rate and short-range applications

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• Dense WDM – DWDM

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ITU Assigned Wavelength Bands

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1260λ (nm)

O-Band E-Band S-Band C-Band L-Band

1360 1460 1530 1565 1625

Original Band

Single Channel

and Coarse WDM

Extended Band

Coarse WDM

Short Band

Future band

for Dense

WDM

Conventional Band

Dense/Coarse WDM

Long Band

Upcoming band

for Dense WDM

With the rise in demands, the need for a new band (U

band) in the range of 1625 - 1675 nm has emerged

Page 24: Optical Networks and Communications

Optical Communications &

Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/

Optical Fibers - Contents

• Introduction, advantages/disadvantages, structure of optical fibers

• Fading in SiO2 optical fibers

• Receiver sensitivity and power budget

• Multiplexing techniques in optical networks

• Light propagation in optical fibers

• Types of optical fibers

• Fading and attenuation in multi-mode and single-mode optical fibers

• Chromatic dispersion in single mode silica fibers

• Mode dispersion

• Total dispersion, Scenarios

• Control of the slope of chromatic dispersion

• Polarization dispersion in single mode fibers - Troubleshooting

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών24

Page 25: Optical Networks and Communications

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Transmission Basics (1/2)

• Wavelength: λ

• Frequency: f

• Light speed in space: c = 3×108 m/s– Lower inside the fiber

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Τμήμα Πληροφορικής και Τηλεπικοινωνιών25

fc

ccf

ΔΔ

ΔΔΔ

2

22

λλ

λλ

λλ

Differentiating

by λ

λλ cffc

Optical bandwidth depends

on the bit rate (R, in bits/sec)

and the applied modulation

scheme (e.g. M-ASK, M-

PSK)

E.g. For λ = 1550 nm,

f = c/λ = 3×108 m/s / 1550 nm ≈ 193.55 THz

2Δ 2f R log M

Page 26: Optical Networks and Communications

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Transmission Basics (2/2)

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Τμήμα Πληροφορικής και Τηλεπικοινωνιών26

time

A

10

T 2T

Signal in time domain

Bit Rate = 1/T [bits/sec]

frequency

ASignal in

frequency domain

Power spectrum: Set

of frequencies where

the energy of the

signal is spread

Signal bandwidth (Hz)

A0

Page 27: Optical Networks and Communications

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Optical Signal Bandwidth• The signal bandwidth needs to be sufficiently smaller than the channel spacing

– Otherwise we would have undesirable interference between adjacent channels and

distortion of the signal itself

• The usable bandwidth of optical fiber in primary bands used for optical

communication is approximately:

– 80 nm at 1.3 μm wavelength band

– 180 nm at 1.55 μm wavelength band

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Τμήμα Πληροφορικής και Τηλεπικοινωνιών27

about 35,000 GHz!

Occupied Channel

Bandwidth Guardband

Channel

Spacing

λ3λ2λ1

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Light Propagation in Optical Fibers (1/2)

• Single mode fibers (SMFs): Only one

mode/ray/path in which light can propagate

• To conceptualize propagation in a single-

mode fiber we treat the light as a single

beam

• In a medium with constant n, a narrow light

beam tends to spread due to diffraction

the beam width will increase as light

propagates

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• The diffraction effect can be counteracted by focusing the light with a lens

– E.g. Use of a chain of convex lenses that bring the beam back to size periodically

– This allows the beam to be guided in the medium and go long distances with low loss

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Light Propagation in Optical Fibers (2/2)

• Single-mode fiber is an optical waveguide

– Best described with the use of wave theory approach

• Explains the physics of how optical signals propagate through fiber

• More general and exact

• Applicable for all values of the fiber radius

• Use of Maxwell’s equations for the electromagnetic field

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Τμήμα Πληροφορικής και Τηλεπικοινωνιών29

A light wave propagates

in the core of the fiber

It may have different electromagnetic field

distributions in the cross-section of the fiber

Each field distribution that meets the Maxwell equations and the boundary

condition at the core-cladding interface is called a transverse or propagation

mode

• Fibers that allow propagation of multiple transverse modes are called Multi-

Mode Fibers (MMFs)– Best described with the use of ray theory approach

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Wave Theory (1/2)

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– i : index to propagation mode ψi

– Ai(r,φ) : transverse field distribution

– βzi : z-axis propagation constant

• For circular waveguides, the wave function of a propagation mode can be expressed as

Ψ

zi

j ωt β z

i ir,φ,z A r,φ e

Page 31: Optical Networks and Communications

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Wave Theory (2/2)

• Group velocity (ug,i) of a mode i expresses how fast the power of a light signal propagates

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Τμήμα Πληροφορικής και Τηλεπικοινωνιών31

• Group refractive index (nco,g)

• Phase velocity (up,i) expresses how fast the phase of a light signal changes

• Each propagation mode has a different propagation delay Broader pulse at the fiber end

g ,i

z ,i

ωu

β

p ,i

z ,i

ωu

β

co

co,g co

nn n ω

ω

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Ray Theory (1/6)

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From optically thin to optically

dense medium

From optically dense to

optically thin medium

n2 > n1

n1

βa

b

b b

a a

α α

α

a

Total

reflection

b

a

β

θ

θc

b

a

n2 < n1

n1

βcαc

Snell’s reflection law: βα 21 sinnsinn

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Ray Theory (2/6)• Good approximation when λ << core’s diameter

• Total reflection

• Special refraction case with ideal materials (no loss): – No energy or power loss

– 100 % refflection

• However, there are losses and fading because of the material

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών33

Optically dense medium (n1)

Optically thin medium (n2)

- Penetration depth in the cladding

- Goos–Haenchen sliding

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Ray Theory (3/6)

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

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core (nco)

cladding (ncl)

θc θ

θ

• Critical angle of total reflection: θc = acos(ncl/nco)

Total reflection

in SI fibers

• Meridional rays: θ< θc waveguide with low loss

• Different angles will have different propagation times in a fiber with length L → Dispersion

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Ray Theory (4/6)

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Τμήμα Πληροφορικής και Τηλεπικοινωνιών35

core (nco)

cladding (ncl)

θc

αmax: acceptance angle or critical angle of meridional rays acceptance cone

Numerical Aperture (NA)

d

Δ22

A

2

22

clclclcocl

clcoclcoclcomax

nnnnn

nnnnnnasin

N

The smaller the NA, the fewer The smaller the NA, the fewer

the propagation modes

Page 36: Optical Networks and Communications

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Ray Theory (5/6)

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

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core (nco)

cladding (ncl)

c

αmax

1,

2412

2

22

maxmax

maxmax

aasin

asinacosdareacone

π

ππΩ

Solid Angle

d

So, Ω = π×ΝΑ2

Page 37: Optical Networks and Communications

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Ray Theory(6/6)

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Meridional Rays:

• The rays either propagate on the fiber axis or across it – Note: for the theoretical definition of NA, we consider

only the meridional rays

Skew Rays:• They do not cross the optical axis

• They do not propagate parallel to the axis

Helical Rays:

• Helical propagation around the fiber axis – Special case of skew rays (GI fibers only)

Page 38: Optical Networks and Communications

Optical Communications &

Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/

Optical Fibers - Contents

• Introduction, advantages/disadvantages, structure of optical fibers

• Fading in SiO2 optical fibers

• Receiver sensitivity and power budget

• Multiplexing techniques in optical networks

• Light propagation in optical fibers

• Types of optical fibers

• Fading and attenuation in multi-mode and single-mode optical fibers

• Chromatic dispersion in single mode silica fibers

• Mode dispersion

• Total dispersion, Scenarios

• Control of the slope of chromatic dispersion

• Polarization dispersion in single mode fibers - Troubleshooting

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών38

Page 39: Optical Networks and Communications

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Types of Optical Fibers

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Τμήμα Πληροφορικής και Τηλεπικοινωνιών39

Type

Graded-Index

(GI) fiber

Ray propagationRefractive

index profile

Step-Index (SI)

fiber

Single mode

(SM) fiber

n

r

n

r

n

r

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Step-Index Fibers

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών40

SI–Fibern(r)

Radius a–a

nco

arn

arnrn

cl

co

,

,

ncl

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Single Mode Step-Index Fibers

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών41

n(r)

Radiusa–a

nco

arn

arnrn

cl

co

,

,

ncl

• Key design: core with small diameter

• Cutoff wavelength (λc):

– The wavelength above which there is

only one single transverse mode

222clcoc nn

V

παλ

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Graded-Index Fibers (1/2)

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών42

GI–Fiber

n(r)

Radius

g: exponent of the refractive index profile

a–a

ncl

n0

arn

ara

rnrn

cl

g

,

,210 Δ

coclcoclclco nnnnnn Δ

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Graded-Index Fibers (2/2)

• Rays traversing the shortest path through the center of the core encounter the highest refractive index and travel slowest

– Whereas rays traversing longer paths encounter regions of lower refractive index and travel faster

• GI fibers can– «equalize» the propagation delays of different rays

– reduce dispersion in the fiber

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών43

GI fiber:

amax(r)

amax(0)

cladding (ncl)

core (nco(r))

22NA clmax nrnrasin

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Transverse Modes in Fibers (1/2)

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών44

LPnm

0 1 2 3 4 5

1

2

3

n: azimuth mode number (φ)

m:

rad

ial

mod

e n

um

ber

(r)

Near-field light intensity profiles of the lowest order modes

LP: Linear Polarized mode

designation

SMF

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Modes in Fibers (2/2)

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών45

Number of modes:

m (radial) = 7

n (azimuth) = 47

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Optical Fibers - Contents

• Introduction, advantages/disadvantages, structure of optical fibers

• Fading in single-mode SiO2 optical fibers

• Receiver sensitivity and power budget

• Multiplexing techniques in optical networks

• Light propagation in optical fibers

• Types of optical fibers

• Fading and attenuation in multi-mode and single-mode optical fibers

• Chromatic dispersion in single mode silica fibers– Control of chromatic dispersion

– Chromatic dispersion and nonlinear effects

• Mode dispersion

• Total dispersion, Scenarios

• Control of the slope of chromatic dispersion

• Polarization dispersion in single mode fibers - Troubleshooting

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών46

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Attenuation Sources

1. Material Absorption loss

2. Coupling and splicing loss

3. Scattering loss

4. Bending loss

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών47

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3. Scattering Loss (1/3)

• Rayleigh scattering– Linear Scattering

– Partial power of a propagation mode is transferred to the radiation mode due to inhomogeneity of refractive index

– Loss: aR = cR×(1/λ4) [dB/km]• cR: Rayleigh scattering coefficient ( (dB/km)×μm4 )

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών48

0.7 0.8 0.9 1.1 1.3 1.41.0 1.5

0.1

0.03

0.3

1

3

10

dB/km

μm2.0

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3. Scattering Loss (2/3)

Rayleigh scattering coefficient

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών49

0.30 0.35 0.55 0.65 0.70 0.750.60 0.80

0.85

0.80

0.90

1.00

1.05

1.10

Rayle

igh

sca

tter

ing c

oef

fici

ent

( (d

B/k

m)×μ

m4

)

Pure silica

core fiber

0.40 0.45 0.50Relative index difference (%)

GeO2– doped

fibers

λ = 1550 nm

λc = 1.1 μm

λc = 1.3 μm

λc = 1.5 μm

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3. Scattering Loss (3/3)

• Mie scattering

– Linear scattering

– A partial power of a propagation mode is transferred to the radiation mode due to inhomogeneity of waveguide surface

• Brillouin and Raman scattering

– Nonlinear scattering

– Caused by thermal molecular vibrations

– A partial power of a propagation mode is transferred to a mode of a different frequency

– Require large incident power:

• Brillouin: 100 mW

• Raman: 1 W

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Τμήμα Πληροφορικής και Τηλεπικοινωνιών50

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4. Bending loss

• Losses at bends and curves because of light escaping the medium and evanescent modes generated

• Not significant unless the bending curvature is in the order of 1mm-1

or larger

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Τμήμα Πληροφορικής και Τηλεπικοινωνιών51

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Total Intrinsic Loss

• Atomic resonances of fiber material

• Rayleigh scattering

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Τμήμα Πληροφορικής και Τηλεπικοινωνιών52

0.7 0.8 0.9 1.1 1.3 1.41.0 1.5

0.1

0.03

0.3

1

3

10

dB/km

μm

Infrared

absorption

2.0

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Total Fiber attenuation

• Extrinsic absorption due to O-H bonds varies with the fiber manufacturing process

• Preferred windows: 850 nm, 1310 nm and 1550 nm

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών53

0.7 0.8 0.9 1.1 1.3 1.41.0 1.5

0.1

0.03

0.3

1

3

10

dB/km

μm2.0

Infrared

absorption

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Optical Fibers - Contents

• Introduction, advantages/disadvantages, structure of optical fibers

• Fading in single-mode SiO2 optical fibers

• Receiver sensitivity and power budget

• Multiplexing techniques in optical networks

• Light propagation in optical fibers

• Types of optical fibers

• Fading and attenuation in multi-mode and single-mode optical fibers

• Chromatic dispersion in single mode silica fibers

• Mode dispersion

• Total dispersion, Scenarios

• Control of the slope of chromatic dispersion

• Polarization dispersion in single mode fibers - Troubleshooting

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών54

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Dispersion

• 4 kinds of fiber dispersion:– Material Dispersion

– Waveguide Dispersion

– (Inter-)Modal Dispersion

– Polarization Mode Dispersion (PMD)

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών55

Intra-modal Dispersion

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Material Dispersion (1/2)• The refractive index of SiO2 is wavelength dependent

Different spectral components travel at different speeds

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών56

λ1 λ2 λ3

λ1

λ2

λ3

λ1 λ3λ2 λ1 λ3

λ2

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Material Dispersion (2/2)

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών57

1.31.21.1 1.61.51.4 1.7

20

10

0

–10

–20

Mate

rial

Dis

per

sion

(ps/

(nm×

km

))Dmaterial

1276 nm

λ (μm)

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Waveguide Dispersion (1/2)• The light energy of a mode propagates partly in the core and

partly in the cladding– Power distribution of a mode is a function of wavelength: the

longer the wavelength, the more power in the cladding

– Cladding and core are of different material Different refractive indexes Light will travel at different speeds

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών58

nco

ncl

Light

Slower at the

core

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Waveguide Dispersion (2/2)

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών59

1.31.21.1 1.61.51.4 1.7

30

20

10

0

–10

–20

Waveg

uid

e D

isp

ersi

on

(ps/

(nm×

km

))

Dwaveguide

λ (μm)

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1izg ,i

int ra

g ,i

β λt λD

λ λ u λ ω

Intra-Modal Dispersion (1/7)• For a propagation mode i

– Group velocity is frequency dependent

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών60

Chromatic

Dispersion

Total Intra-

modal

Dispersion

Group Velocity

Dispersion

tg,i(λs) is the unit distance propagation delay at the central wavelength λs

Unit Propagation Delay 1/ug,i Group Propagation Time

...tt

tti,g

s

i,g

ssi,gi,g

2

2

2

2

1

λ

λλλ

λ

λλλλλ

Rate of change of group

propagation time by

wavelength

Taylor series

expansion at a

given wavelength λ

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Intra-Modal Dispersion (2/7)

• The Unit Propagation Delay will become

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών61

If we keep only the first two terms

λ

λλλλλλ

raint

sraintssi,gi,g

DDtt

2

2

1

rainti,graintssi,gi,g DtDtt λλλλλ ΔΔ

Δtg,i is the pulse width increase due to intra-modal dispersion

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1 1i i iz z zco,g co,g

int ra co,g

co co co

β β βn nD n

c λ β c λ β c λ β

Intra-Modal Dispersion (3/7)

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Τμήμα Πληροφορικής και Τηλεπικοινωνιών62

Dmaterial Dwaveguide+

co

z

g,coco

co

zz

raintiii n

cD

β

β

λω

β

β

β

λω

β

λ

1With

c

n g,coco ω

β

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co

co,g co

nn n λ

λ

Intra-Modal Dispersion (4/7)

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών63

andλλ

πω

λ

πω d

cd

c2

22Because

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Intra-Modal Dispersion (5/7)

• Dmaterial :

– independent of the propagation mode

– solely depends on the wavelength dependence of nco

• Dwaveguide

– depends on the propagation mode i

• determined by the optical waveguide structure

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Τμήμα Πληροφορικής και Τηλεπικοινωνιών64

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co

co,g co

nn n λ

λ

Intra-Modal Dispersion (6/7)

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών65

0.5 0.75 1.25 1.75 2.01.0 1.5 λ (μm)1.440

1.445

1.450

1.455

1.460

1.465

1.470

1.475

1.480

1.485

1.490

nco(λ)

nco,g(λ)

7.9 Mol–% GeO2

0 Mol–% GeO2

(Pure SiO2)

7.9 Mol–% GeO2

0 Mol–% GeO2

(Pure SiO2)

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Intra-Modal Dispersion (7/7)

• The group refractive index is reduced,– “fast” until 1000 nm

– “slowly” from 1000 nm and thereafter

– Dmaterial is negative but ascending

• The refractive index is increased– Dmaterial is positive

and ascending

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Τμήμα Πληροφορικής και Τηλεπικοινωνιών66

0.5 0.75 1.25 1.75 2.01.0 1.5 λ (μm)1.440

1.445

1.450

1.455

1.460

1.465

1.470

1.475

1.480

1.485

1.490

Gro

up

ref

ract

ive

inte

xn

co,g

(λ)

Dmaterial = 0

λ 1276 nm

Silicon dioxide fiber

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Chromatic Dispersion in Single-Mode SiO2 Fiber (1/6)

D = Dmaterial + Dwaveguide

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών67

1.31.21.1 1.61.51.4 1.7

30

20

10

0

–10

–20

Ch

rom

ati

c D

isp

ersi

on

D (

ps/

(nm×

km

))

Dwaveguide

Dmaterial

Total Intra-

modal

Dispersion (D)

1310 nm

λ (μm)

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Chromatic Dispersion in Single-Mode SiO2 Fiber (2/6)

• Group velocity dispersion parameter β2 = 2βzi/ω2

– β2 = 0: zero-dispersion wavelength

– β2 < 0: anomalous chromatic dispersion

– β2 > 0: normal chromatic dispersion

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Τμήμα Πληροφορικής και Τηλεπικοινωνιών68

2

2

22 2 2

1

2

2 2

i i

i

z zg ,i

int ra

z

β βt λD

λ λ ω ω ωλ

πc

βπc πcβ

λ ω λ

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Chromatic Dispersion in Single-Mode SiO2 Fiber (3/6)

• For wavelengths smaller than 1310 nm, D is negative and ascending

• Unit Propagation Delayis descending as a function of wavelength

• If λ1 < λ2 < 1310 nm, λ2will travel a certain fiber length with less delaythan λ1

– λ2 will reach the fiber endearlier

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών69

1.31.21.1 1.61.51.4 1.7

30

20

10

0

–10

–20

Ch

rom

ati

c D

isp

ersi

on

D (

ps/

(nm×

km

))

Total Intra-modal

Dispersion (D)

1310 nm

λ (μm)

Normal

Dispersion,

β2 > 0

Anomalous

Dispersion,

β2 < 0

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Chromatic Dispersion in Single-Mode SiO2 Fiber (4/6)

• For wavelengths greater than 1310 nm, D is positive and ascending

• Unit Propagation Delayis ascending as a function of wavelength

• If 1310 nm < λ1 < λ2, λ1will travel a certain fiber length with less delaythan λ2

– λ1 will reach the fiber end earlier

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών70

1.31.21.1 1.61.51.4 1.7

30

20

10

0

–10

–20

Ch

rom

ati

c D

esp

ersi

on

D (

ps/

(nm×

km

))

Total Intra-modal

Dispersion (D)

1310 nm

λ (μm)

Normal

Dispersion,

β2 > 0

Anomalous

Dispersion,

β2 < 0

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Chromatic Dispersion in Single-Mode SiO2 Fiber (5/6)

• Pulsed signal with Δλ = λ2 – λ1

– Δtg = tg(λ2) – tg(λ1)

– Δτg = L×Δtg

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών71

1.31.21.1 1.61.51.4 1.7

30

20

10

0

–10

–20

Ch

rom

ati

c D

isp

ersi

on

D (

ps/

(nm×

km

))

λ (μm)

Normal

Dispersion,

β2 > 0

Anomalous

Dispersion,

β2 < 0

λ1 < λ2 ≈ 1310 nm

λ1λ2λ1, λ2 t t’

Δtg≈ 0

λ1 < λ2 < 1310 nm

λ1λ2λ1, λ2 t t’

Δtg < 0

1310 nm < λ1 < λ2

λ1 λ2λ1, λ2 t t’

Δtg > 0

λ1 λ2 λ1 λ2

λ1

λ2

Total Intra-

modal

Dispersion

(D)

1310 nm

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Chromatic Dispersion in Single-Mode SiO2 Fiber (6/6)

• Δλ = λ2 – λ1 – Δtg = tg(λ2) – tg(λ1)

– Δτg = L×Δtg

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λ1 < λ2 ≈ 1310 nm

λ1λ2λ1, λ2 t t’

Δtg≈ 0

λ1 < λ2 < 1310 nm

λ1λ2λ1, λ2 t t’

Δtg < 0

1310 nm < λ1 < λ2

λ1 λ2λ1, λ2 t t’

Δtg > 0

1.31.21.1 1.61.51.4

Un

it P

rop

agati

on

Del

ay (

t g)

(Qu

ali

tati

ve

Imagin

g)

1310 nm

Normal

Dispersion,

β2 > 0

Anomalous

Dispersion,

β2 < 0

λ1 λ2 λ1 λ2

λ1

λ2

1.7 λ (μm)

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Dispersion Control on Single-mode Fibers (1/2)

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Dispersion Control on Single-mode Fibers (2/2)

• We do not have much control over the material dispersion– Can be varied slightly by doping the core and cladding regions of the fiber

• We can vary the waveguide dispersion considerably so as to– shift the zero-dispersion wavelength into the 1.55 μm band

– or compensate for the dispersion occurring at 1.55 μm band

• Generally, the impact of chromatic dispersion can be reduced by:– External modulation in conjunction with DFB lasers → in high-speed

systems

– Fibers with zero or small chromatic dispersion → (Non-Zero) Dispersion Shifted Fibers (DSF) that have a small chromatic dispersion value in the C-band

– Chromatic dispersion compensation → when external modulation alone is not sufficient

– Chirped Fiber Bragg Grating (special design of Bragg grating filters)• Introduces different delays at different frequencies

• Ideally suited to compensate for individual wavelengths rather than multiple wavelengths

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Dispersion-Shifted Fibers (1/4)

• Dispersion-Shifted Fiber (DSF): Fiber with zero

dispersion at 1550 nm– Chromatic dispersion at 1550 nm band is at most 6

ps/(nm×km)

– Typically zero dispersion at 1550 nm

• The waveguide dispersion can be varied by– varying the refractive index profile of the fiber

– changing the core diameter

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Dispersion-Shifted Fibers (2/4)

• Varying the refractive index profile of the fiber

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Τμήμα Πληροφορικής και Τηλεπικοινωνιών76

Trapezoidal or triangular variation of

the refractive index in the core

Step variation of the refractive index

in the cladding

single-mode fiber with zero dispersion in the 1550 nm band

~ 6 μm

~ 120 μm

Dispersion shifted fiber

r = 0

+

~ 10 μm

~ 120 μm

nco

ncl

Standard single-mode fiber

r = 0

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Dispersion-Shifted Fibers (3/4)• Changing the core diameter

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Τμήμα Πληροφορικής και Τηλεπικοινωνιών77

~ 6 μm

~ 120 μm

Dispersion shifted fiber

r = 0

~ 10 μm

~ 120 μm

nco

ncl

Standard single-mode fiber

r = 0

~ 6 μm

~ 120 μm

Dispersion shifted fiber

~ 5 μm

~ 120 μm

Dispersion shifted fiber

n’co

ncl

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Dispersion-Shifted Fibers (4/4)

• Typical single-mode fiber

• Dispersion-shifted fiber

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών78

1.31.21.1 1.61.51.4 1.7

30

20

10

0

–10

–20

Ch

rom

ati

c D

isp

ersi

on

D

(p

s/(n

km

))

Dwaveguide

Dmaterial

1310 nm

λ (μm)

α = 4.0 μm

α = 2.5 μm

α = 2.0 μm

1550 nm

α = 2.5 μm

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Non-Zero Dispersion-Shifted Fibers (1/3)• Non-Zero Dispersion Shifted Fibers (NZ–DSF): Dispersion shifted fibers with

non-zero dispersion at 1550 nm– More specifically, dispersion is small and non-zero in the C band

– Chromatic dispersion can be either positive or negative in the C band

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών79

154015201500 1600158015601480 λ (μm)

0

–2

–4

–6

6

4

2

C band

1620

L band

Ch

rom

ati

c D

isp

ersi

on

D (

ps/

(nm×

km

))

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Non-Zero Dispersion-Shifted Fibers (2/3)• Multi-cladding or Dispersion Flattened Fibers

– Small core (~ 6 μm)

– Flat dispersion in a wide wavelength range

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών80

~ 6 μm

~ 120 μm

Dispersion-flattened fiber

r = 0

~ 10 μm

~ 120 μm

nco

ncl

Typical single-mode fiber

r = 0

~ 6 μm

~ 120 μm

Dispersion-flattened fiber

Doubly

clad

Quadruply

clad

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Non-Zero Dispersion-Shifted Fibers (3/3)

• Multi-cladding or Dispersion Flattened Fibers

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών81

1.31.21.1 1.61.51.4 1.7

30

20

10

0

–10

–20

Ch

rom

ati

c D

isp

ersi

on

D (

ps/

(nm×

km

))

Total

Dispersion (D)

1310 nm

λ (μm)

Dispersion-

flattened fibers

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Dispersion Compensating Fibers (1/2)

• Dispersion Compensating Fibers (DCFs): Fibers with very large

chromatic dispersion of the opposite sign

– Compensates for the accumulated chromatic dispersion on a lengthy link

• Known as depressed cladding fibers

• DCF chromatic dispersion coefficient: –100 ~ –300 ps/(nm×km)

• Better suited to simultaneously compensate over a wide range of wavelengths

• Introduces additional loss

• Relatively more vulnerable to non-linear effects

• Terrestrial systems: positive chromatic dispersion with negative chromatic dispersion compensation

• Submarine systems: negative chromatic dispersion with positive chromatic dispersion compensation

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Dispersion Compensating Fibers (2/2)

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών83

~ 5 μm

~ 120 μmDCF

r = 0

~ 10 μm

~ 120 μm

nco

ncl

Standard single-mode fiber

r = 0

The core radius of a DCF fiber is considerably

smaller than that of standard single-mode fiber but

has a higher refractive index

Large negative chromatic

dispersion

The core is surrounded by a

ring of lower refractive

index, which is in turn

surrounded by a ring of higher

refractive index

Negative chromatic

dispersion slope, an

important characteristic

for chromatic dispersion

compensation

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Chromatic dispersion map• Describes the variation of accumulated chromatic dispersion with distance

• Includes the diagrams of– Chromatic dispersion coefficients (ps/(nm×km)) of the used fiber segments, in

relation to the distance

– Accumulated dispersion (ps/nm) in relation to the distance

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών84

T …Standard SMF DCF Standard SMF DCF

length

Local Chromatic

Dispersion (ps/(nm×km))

Chromatic dispersion

coefficients of each

fiber segment

length

Accumulated

Dispersion (ps/nm)

For the specific

transmission

wavelength, DCF

fully compensates for

the dispersion

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Optical Fibers - Contents

• Introduction, advantages/disadvantages, structure of optical fibers

• Fading in single-mode SiO2 optical fibers

• Receiver sensitivity and power budget

• Multiplexing techniques in optical networks

• Light propagation in optical fibers

• Types of optical fibers

• Fading and attenuation in multi-mode and single-mode optical fibers

• Chromatic dispersion in single mode silica fibers

• Mode dispersion

• Total dispersion, Scenarios

• Control of the slope of chromatic dispersion

• Polarization dispersion in single mode fibers - Troubleshooting

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Inter-modal Dispersion

• Caused by different propagation delays of different propagation modes

• Each mode has different βzi

different group velocity (ug,i)

different propagation delay

• Modal dispersion can be defined as

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών86

– τg,max: the maximum unit group propagation delay

– τg,min: the minimum unit group propagation delay

• Modal dispersion is expressed in ps/km

1 1int ra g ,max g ,min

g ,min g ,max

D τ τu u

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Inter-modal Dispersion in SI Fibers (1/4)

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών87

core (nco)

cladding (ncl)

c

At a time t*

Lz = 0m

All angles have equal velocity

z

Light

source

(isotropic)

t

z3z2z1

z3 < z2 < z1

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Inter-modal Dispersion in SI Fibers (2/4)

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών88

L3 > L2 > L1 (geometric paths)

L1 = Lmin = LFiber

L3 = Lmax = LFiber / cos(c) = LFiber / (ncl/nco)

Lz = 0m z

core (nco)

cladding (ncl)

c

t

Light

source

(isotropic)

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Inter-modal Dispersion in SI Fibers (3/4)

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών89

Lz = 0m z

core (nco)

cladding (ncl)

c

t

Light

source

(isotropic)

Pulse dispersion

at length z = L

t’

t3t2t1

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1 1 12 3

Δ

3 3Δ

1 1Δ 1 1

Δ

co comax min modal

co comodal fiber fiber

cl co

co cl co cofiber fiber modal fiber

cl

c

n nt t t

c c

n nt L L

co

tt t Lt t

s c n n c

n n n nL L D L

n c

L

c

θ

�����

Inter-modal Dispersion in SI Fibers (4/4)

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών90

From the previous figures we derive the following equation

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Inter-modal Dispersion in GI Fibers (1/2)

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών91

• Different geometric paths : L1 < L2 < L3

• Different velocities on paths 2 and 3– Faster near the core-cladding boundary: n(r) < n(0)

• Almost similar paths: n(0) × L1 ≈ nmean,2 ×L2 ≈ nmean,3 × L3

• Δt modal = tmax – tmin = L × Δτmodal = L × Δ2/2 × τg– τg = n(0)/c: normalized time delay

– Δ: (relative) difference of refractive indexes

t

Pulse

dispersion at

length z = Lt’

t3t2t1

Light

source

(isotropic)

At a time t*

z3 ≈ z2 ≈ z1

Lz = 0m z

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Inter-modal Dispersion in GI Fibers (2/2)

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών92

32

11

2

3

Selective beam stimulation with different propagation

angles (for characterization only)

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Optical Fibers - Contents

• Introduction, advantages/disadvantages, structure of optical fibers

• Fading in single-mode SiO2 optical fibers

• Receiver sensitivity and power budget

• Multiplexing techniques in optical networks

• Light propagation in optical fibers

• Types of optical fibers

• Fading and attenuation in multi-mode and single-mode optical fibers

• Chromatic dispersion in single mode silica fibers

• Mode dispersion

• Total dispersion - Types

• Control of the slope of chromatic dispersion

• Polarization dispersion in single mode fibers - Troubleshooting

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Τμήμα Πληροφορικής και Τηλεπικοινωνιών93

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Total Dispersion

• In multimode fibers: mode dispersion has greater effect than intra-modal dispersion

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Τμήμα Πληροφορικής και Τηλεπικοινωνιών94

Total dispersion is expressed inps/km

• Fiber bandwidth is defined as

L: distance

Intra-modal

Dispersion

Inter-modal

Dispersion

Total

Dispersion

2 2 2 2Δtotal int ra mod al

D D λ D

1fiber

total

BD L

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Dispersion Limit (1/2)

• Dispersion limit: upper bound for the transmission distance at a given bit rate

• T0: pulse width (equal to the bit period)

• R: bitrate

• Received pulse has width T’ > T0 Inter-Symbol Interference (ISI) increase of the BER

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T0

T’

Transmitted signal

Received signal

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Dispersion Limit (2/2)• As a rule of thumb, the BER will not be

degraded significantly if:

• Pulse broadening is not caused by fiber dispersion alone:

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών96

R

TLDT'TT total

1

4

1

4

00 Δ

2222LDT totalrt ττΔ

2

222 1

4

1

R

LDtotalrt ττ

– τt : rise time of the light source

– τr : rise time of the receiver

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Input Conditions and Ray Conversion in Multimode Fibers

• Problems– Selective stimulation

– Mode Dependent Attenuation

– Delay and pulse spreading depending on the mode

– Ray (mode) conversion along the fiber due to scattering

• Notes– Rays with greater propagation angle suffer from higher attenuation

– After a certain distance, a steady state will be imposed

– But there will be changes in interconnections

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core

cladding

Ray afterwards Ray afterwards

Ray conversion and power transfer

in other modes

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Modal Dispersion at Longer Distance

• Mode coupling: power transfer among propagation modes

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Τμήμα Πληροφορικής και Τηλεπικοινωνιών98

• Depending on the current propagation mode that is activated due to power transfer, photons travel– sometimes faster – large group velocity

– and sometimes slower – small group velocity

• This speed variation makes the dispersion only proportional to the square root of the total length when the length is greater than the coupling length

• Coupling length (Lc): critical length above which the total dispersion in a multimode fiber is not proportional to the length linearly but to its square root– For L < Lc, dispersion is linearly proportional to the distance

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Optical Fibers - Contents

• Introduction

• Light propagation in optical fibers

• Multiplexing techniques in optical networks

• Types of optical fibers

• Attenuation in optical fibers

• Receiver sensitivity and power budget

• Chromatic dispersion in single mode silica fibers

• Mode dispersion

• Total dispersion

• Polarization dispersion in single mode fibers

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Polarization• Transverse electric field: The electric field associated with an electromagnetic

wave does not have any component along the z direction

• A wave is decomposed into two waves with polarizations perpendicular to each other

– Components with same phase linearly polarized wave

– Components with phase difference of π/2 circularly polarized wave

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Τμήμα Πληροφορικής και Τηλεπικοινωνιών100

Ex

Ey

Ex

Ey

Propagation

direction (z)

Wave-front

Ex

Ey

Εx

Ey

Wave-frontLinear

polarization

Propagation

direction (z)

Circular

polarization

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State Of Polarization (SOP)

• State of polarization (SOP) of a wave is characterized by the relative phase and the amplitudes of the two perpendicular polarizations– Refers to the distribution of light energy among the two polarization modes

• For the fundamental mode of a single-mode fiber: Ez << Ex or Ey(the transverse component)– The electric field associated with the fundamental mode can effectively be

assumed to be a transverse field

– Each of the two components of the electric field, Ex and Ey, is linearly polarized along the x and y axis respectively

– The two axes are perpendicular to each other and the two components are orthogonally polarized

– Any linear combination of these two linearly polarized fields is also a fundamental mode

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Polarization in Ideal Circular Fibers

• Circular fiber: Two perpendicularly polarized waves have the same propagation constant and refer to the fundamental mode

• Ideal, perfectly circularly symmetric fiber: The polarization state of the wave stays the same throughout the propagation– The fiber is still termed single mode, because these two

polarization modes are degenerate

– Although the energy of a pulse is divided between these two polarization modes, since they have the same propagation constant, it does not give rise to pulse spreading by dispersion

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Polarization in Practical Fibers• A practical fiber has a slight and random ellipticity along its

axis– As the waves propagate, their propagation constants fluctuates

– The polarization state at the end of propagation is different from the initial one

• One intuitive way to maintain polarization is to make the fibers as circular as possible

• Birefrigence: characterizes the circular symmetry of a fiber– Expresses the fact that the two orthogonally polarized modes have slightly

different propagation constants

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Πληροφορικής και Τηλεπικοινωνιών103

x y

x y

β βB n n

k

• k = ω/c = 2π/λ

• βx, βy : propagation constants of the two perpendicular polarizations

• nx, ny : corresponding effective refractive indices

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Polarization Mode Dispersion (PMD) (1/5)

• PMD arises due to the fiber birefringence– The transmitted pulse consists of a “fast” and a “slow”

polarization component

– The PMD effect is much weaker than other pulse spreading cases

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Τμήμα Πληροφορικής και Τηλεπικοινωνιών104

Assumption: the propagation constants of

the two polarizations are fixed throughout

the length of the fiber

Time

Initial pulse

no PMD

Propagation

through the fiber Time

Broader pulse due to

PMD

x

yz

The horizontal polarization component

travels slower than the vertical one

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Polarization Mode Dispersion (PMD) (2/5)

• For propagation constants with fixed value– Δβ: difference in propagation constants

– Δτ = Δβ/ω: time spread due to PMD• Typical PMD value: 0.5 ps/km

• The assumption of fixed propagation constants for each polarization mode is unrealistic for fibers of practical lengths since the fiber birefringence changes over the length of the fiber

• Origin of PMD: – Inside the fiber: Different polarizations travel with different group velocities,

since the fibers are not structurally perfect

– Individual components used in the network

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Polarization Mode Dispersion (PMD) (3/5)

• The distribution of signal energy over the different SOPs changes slowly with time, because of temperature and other environmental changes The PMD penalty varies with time

• PMD effects are not that bad: the time delays in different segments of the fiber vary randomly and tend to cancel each other

• Time-averaged differential time delay between the two orthogonal SOPs:

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Τμήμα Πληροφορικής και Τηλεπικοινωνιών106

PMDΔτ D L Dependence on the square

root of the link length

– Δτ: Differential Group Delay (DGD)

– L: link length

– DPMD: fiber PMD parameter, measured in ps/km1/2

• Typical fibers: 0.5 – 2 ps/km1/2

• Carefully constructed new links: 0.1 ps/km1/2

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Polarization Mode Dispersion (PMD) (4/5)

• In reality, SOPs vary slowly with time the actual DGD Δτ is a random variable– Assumed to have a Maxwellian probability density function

The square of DGD is modeled by the exponential distribution

– The larger the DGD, the larger the negative effect of PMD• The power penalty due to PMD is proportional to Δτ2 obeys an

exponential distribution

• PMD gives rise to Inter-Symbol Interference (ISI) due to pulse spreading

• Equalization to overcome ISI and compensate for PMD can be carried out in the electronic domain– More difficult as the bit rate increases

– At bit rates of 40 Gbit/s, optical PMD compensation must be used

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Polarization Mode Dispersion (PMD) (5/5)

• PMD also depends on whether RZ or NRZ modulation is used– RZ modulation: the use of short pulses enables more PMD to be

tolerated

• Polarization-dependent loss (PDL): the loss through the component depends on the state of polarization– Accumulate in a system with many components in the

transmission path

• The state of polarization fluctuates with time The SNR at the end of the path will fluctuate with time Careful attention to maintain the total PDL on the path within acceptable limits

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Optical PMD compensation

• Splits the received signal into its fast and slow polarization components

• Delays the fast component so that the DGD between the two components is compensated

• The delay that must be introduced in the fast component must be estimated in real time from the properties of the link

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Time Time

Fast

component

Slow

component

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Polarization Maintaining Fibers (1/4)• Single Polarization or Differential Polarization Fibers: Maintain polarization

by introducing a differential mechanism that cuts off one of the polarizations– Introduces a large enough Β

– nx and ny in the core are different and the two polarizations have different cutoff wavelengths

• In a single-mode fiber, even when a large B is introduced, both polarizations can still propagate

• To suppress one polarization, proper core index profile is used, which, under certain conditions, cuts off the x-polarization completely

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Fiber core

nco

ncl

Core and cladding

refractive indices of a

typical single-mode fiber

r = 0

Single polarization

fiber

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Polarization Maintaining Fibers (2/4)• Two Polarization or Linearly Birefringent Fibers: When the birefringence is

large enough, coupling from one polarization to another is difficult– The polarization state can be maintained if only one polarization is transmitted initially

• To characterize mode coupling in polarization-maintaining fibers, parameter h is introduced

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Τμήμα Πληροφορικής και Τηλεπικοινωνιών111

10 1010 10x

y

Plog log tan hL

P

– Py: power of the initial polarization after a transmission distance L

– Px: coupled power of the other polarization

• Problem 1 (important): The entire system should be equipped with these special fibers and the already installed fibers should be replaced

• Problem 2: The transmitted SOP must be settled in such a way that it will adapt to one of the two degenerate modes

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Polarization Maintaining Fibers (3/4)

• Large birefringence is introduced through mechanical stress

• Maintaining polarization of the optical waves as they are propagating– Critical for coherent systems, where the polarization of the received light

affects the performance

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Outer cladding

Borosilicate cladding

Silica core Silica core

Elliptically

deformed

claddingElliptically deformed core

Panda or

Bow-tie

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Optical Communications &

Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/

Polarization Maintaining Fibers (4/4)

• GE: Geometrical Effect

• SE: Stress Effect

• HB: High Birefrigence

• SP: Single Polarization

Types Names B h (1/m) Loss (dB/km)

HB with GE Elliptical core 4.2×10–4 30×10–6 85

HB with SE Elliptical cladding 7.2×10–4 1.2×10–6 5

Elliptical jacket 3.0×10–4 1.0×10–6 0.8

Panda 3.0×10–4 0.5×10–6 0.25

Panda, SP 5.9×10–4 (44 dB) 0.3

Bow-tie 4.8×10–4 – 3.6

Bow-tie, SP 6.7×10–4 (42 dB) 1.0

Flat-clad 2.5×10–4 5.9×10–6 2.6

Flat-clad, SP 4.7×10–4 (34 dB) 1.0

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