Optical Networks and Communications
Transcript of 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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
Parts and Devices of Optical Communications
• Sources
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Τμήμα Πληροφορικής και Τηλεπικοινωνιών2
Source DetectorAmplifierFiber Fiber
• Silicon fibers for long distance transmissions
• Additional devices
– Amplifiers
– Filters
– Couplers, Isolators, Modulators etc.
• DetectorsFilter
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
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
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 Τηλεπικοινωνιών8
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
Attenuation Sources
1. Material Absorption loss
2. Coupling and splicing loss
3. Scattering loss
4. Bending loss
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Τμήμα Πληροφορικής και Τηλεπικοινωνιών9
Optical Communications &
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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
Optical Communications &
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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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
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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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
Receiver Sensitivity
• Fiber attenuation places an upper limit on– Transmission distance
– Bit rate
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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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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:
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
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B bits/sec
1
2
N
…
NB bits/sec
t1t2t3t4t5t6
t1t2t3t4t5t6
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Optical Communications &
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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
Optical Communications &
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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
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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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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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
Transmission Basics (2/2)
Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
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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
Optical Communications &
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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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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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• 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
Optical Communications &
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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
Optical Communications &
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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
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Optically dense medium (n1)
Optically thin medium (n2)
- Penetration depth in the cladding
- Goos–Haenchen sliding
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Ray Theory (3/6)
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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
Optical Communications &
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Ray Theory (4/6)
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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
Optical Communications &
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Ray Theory (5/6)
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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
Optical 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)
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
Types of Optical Fibers
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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
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SI–Fibern(r)
Radius a–a
nco
arn
arnrn
cl
co
,
,
ncl
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Single Mode Step-Index Fibers
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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)
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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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
Modes in Fibers (2/2)
Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Τμήμα Πληροφορικής και Τηλεπικοινωνιών45
Number of modes:
m (radial) = 7
n (azimuth) = 47
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Τμήμα Πληροφορικής και Τηλεπικοινωνιών50
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Τμήμα Πληροφορικής και Τηλεπικοινωνιών51
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
Total Intrinsic Loss
• Atomic resonances of fiber material
• Rayleigh scattering
Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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)
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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)
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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)
Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Τμήμα Πληροφορικής και Τηλεπικοινωνιών64
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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)
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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)
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
Chromatic Dispersion in Single-Mode SiO2 Fiber (6/6)
• Δλ = λ2 – λ1 – Δtg = tg(λ2) – tg(λ1)
– Δτg = L×Δtg
Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Τμήμα Πληροφορικής και Τηλεπικοινωνιών72
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)
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
Dispersion Control on Single-mode Fibers (1/2)
Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Τμήμα Πληροφορικής και Τηλεπικοινωνιών73
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Τμήμα Πληροφορικής και Τηλεπικοινωνιών74
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Τμήμα Πληροφορικής και Τηλεπικοινωνιών75
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
Dispersion-Shifted Fibers (2/4)
• Varying the refractive index profile of the fiber
Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
Dispersion-Shifted Fibers (3/4)• Changing the core diameter
Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
m×
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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
))
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
Non-Zero Dispersion-Shifted Fibers (2/3)• Multi-cladding or Dispersion Flattened Fibers
– Small core (~ 6 μm)
– Flat dispersion in a wide wavelength range
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~ 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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
Non-Zero Dispersion-Shifted Fibers (3/3)
• Multi-cladding or Dispersion Flattened Fibers
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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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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)
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~ 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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
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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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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
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– 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
Optical Communications &
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Inter-modal Dispersion in SI Fibers (1/4)
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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
Optical Communications &
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Inter-modal Dispersion in SI Fibers (2/4)
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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)
Optical Communications &
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Inter-modal Dispersion in SI Fibers (3/4)
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Lz = 0m z
core (nco)
cladding (ncl)
c
t
Light
source
(isotropic)
Pulse dispersion
at length z = L
t’
t3t2t1
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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)
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From the previous figures we derive the following equation
Optical Communications &
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Inter-modal Dispersion in GI Fibers (1/2)
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• 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
Optical Communications &
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Inter-modal Dispersion in GI Fibers (2/2)
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32
11
2
3
Selective beam stimulation with different propagation
angles (for characterization only)
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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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Total Dispersion
• In multimode fibers: mode dispersion has greater effect than intra-modal dispersion
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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:
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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
Optical Communications &
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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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• 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
Optical Communications &
Photonics Technology Laboratoryhttp://www.optcomm2.di.uoa.gr/
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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Ex
Ey
Ex
Ey
Propagation
direction (z)
Wave-front
Ex
Ey
Εx
Ey
Wave-frontLinear
polarization
Propagation
direction (z)
Circular
polarization
Optical Communications &
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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
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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
Optical Communications &
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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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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
Optical Communications &
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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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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
Optical Communications &
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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
Optical Communications &
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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
Optical Communications &
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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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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
Optical Communications &
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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
Optical Communications &
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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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