ECE 4105 Optical Fiber Communications Prof. Dr. Monir Hossen ECE, KUET Department of Electronics and Communication Engineering, KUET Modal Dispersion Material Dispersion Waveguide Dispersion Dispersion Management
ECE 4105
Optical Fiber Communications
Prof. Dr. Monir HossenECE, KUET
Department of Electronics and Communication Engineering, KUET
Modal Dispersion
Material Dispersion
Waveguide Dispersion
Dispersion Management
Dispersion in Optical Fibers
▪ When pulse of light proceeds
through the fiber, it widens in the
time domain (shown in Fig.) due to
a number of reasons.
▪ This spreading is called dispersion.
▪ Due to dispersion inter-symbol
interference may occur.
▪ This will limit the maximum rate of
data transmission.
Department of Electronics and Communication Engineering, KUET 2
Dispersion in Optical Fibers Cntd..❖Intermodal Dispersion:
In the case of multimode fiber, energy of the input pulses is
divided among many modes. Different modes travel at different
group velocities. This result in broadening of the input pulses
called intermodal or modal dispersion.
❖Intramodal Dispersion (chromatic dispersion):
When the input light contains a range of optical wavelengths,
i.e., not monochromatic, there may be propagation delay
differences between the different wavelengths in the transmitted
signal.
▪ Material Dispersion:
This dispersion arises because of the wavelength dependence of
the refractive index of the fiber material. In traveling a path the
longer wavelength light will go faster than the shorter
wavelength.Department of Electronics and Communication Engineering, KUET 3
The difference between the time of arrival of the slowest and
fastest moving waves is equal to the pulse broadening.
▪ Waveguide Dispersion:
It arises because the waveguiding of the fiber is dispersive, i.e.,
the normalized frequency, and hence vary with the wavelength
regardless of any refractive index variations of the medium.
▪ Profile Dispersion:
It arises because of the variation of the quantity with
wavelength. In other words, it depends on the fact that the
changes in refractive indices for core and cladding with
wavelength may not be same. This dispersion is negligibly
small.
Department of Electronics and Communication Engineering, KUET 4
Dispersion in Optical Fibers Cntd..
Department of Electronics and Communication Engineering, KUET 5
Inter-modal (mode) Dispersion▪ Multimode fibers exhibit modal dispersion that is caused by
different propagation modes travel at different group velocities:
1 1Path 1
Path 2core
cladding
cladding
L
s
1n
coree
cladding
cladding
/
/
v s t
v c n
=
=
1 2 1( ) /n n n = − 2 1(1 )n n= −
1 2 1cos / 1 /n n L s = = − =
1/ cos /(1 )s L L= = − max 1/ / (1 ) /T s v L c n= = − min
1/
LT
c n=
▪We know: 𝑛1𝑐𝑜𝑠𝜃1 = 𝑛2𝑐𝑜𝑠𝜃2
▪ This results in broadening of the input
pulses called intermodal dispersion:
𝛿𝑇 = 𝑇𝑚𝑎𝑥 − 𝑇𝑚𝑖𝑛
𝛿𝑇 = 𝑇𝑚𝑎𝑥 − 𝑇𝑚𝑖𝑛 =𝐿𝑛1
[𝐶 1 − ∆ ]−𝐿𝑛1𝐶
𝛿𝑇 =𝐿𝑛1𝐶
∆
1 − ∆≈𝐿𝑛1𝐶
∆
Department of Electronics and Communication Engineering, KUET 6
▪ Thus pulse broadening can be approximated by:
𝛿𝑇 ≅𝐿𝑛1∆
𝐶≈𝐿(𝑁𝐴)2
2𝑛1𝐶
▪ δTprovides an estimate of the maximum bit rate when assuming
no pulse overlap:
▪ Max. bit rate: 𝑩𝑻(𝒎𝒂𝒙) ≅𝟏
𝟐𝜹𝑻
▪ When all the rays over the range 𝟎 ≤ 𝜽 ≤ 𝜽𝒂 are excited
equally and all other dispersion effects are ignored, the root-
mean-square (RMS) pulse broadening can be obtained as:
▪ σprovides an estimate of the maximum bit rate when allowing
pulse overlap: Max. bit rate:
Inter-modal (mode) Dispersion Cntd..
cn
NAL
c
Ln
1
2
1
34
)(
32=
=
2.0(max) TB
Department of Electronics and Communication Engineering, KUET 7
Example
Department of Electronics and Communication Engineering, KUET 8
Problem
Department of Electronics and Communication Engineering, KUET 9
Pulse Broadening in a Graded-Index Fibers
Fig. (a) The refractive index profile, and (b) the sinusoidal paths of
meridional rays in a graded index fiber.
✓ For a power-law profile, the time spread is:
✓ Maximum δT actually occurs when: α = characteristic
refractive index
profile for fiber
Department of Electronics and Communication Engineering, KUET 10
✓ It is only about Δ/8 of step index result Δt = n12LΔ/(n2c0). For Δ
~ 1.3%, it achieves a time spread only 1/600 of that for a step
index fiber.
✓ Minimum RMS pulse broadening σ occurs when:
Pulse Broadening in a Graded-Index Fibers Cntd..
Department of Electronics and Communication Engineering, KUET 11
Department of Electronics and Communication Engineering, KUET 12
❖Material Dispersion:
✓ The velocity of light in a dielectric depends on the refractive
index. As the refractive index varies with wavelength, any light
wave consisting of several different wavelengths will travel at
different velocities, and so will arrive at their destination at
different times.
✓ δτ= difference in propagation times for two frequency. So
𝜹τ =𝜹τ
𝜹𝝀𝜹𝝀, where 𝜹𝝀 = Wavelength difference.
✓ If we consider unit length of fiber―
τ =𝟏
𝒗𝒈
now
Intramodal Dispersion Contd..
Department of Electronics and Communication Engineering, KUET 13
Intramodal Dispersion Contd..
Department of Electronics and Communication Engineering, KUET 14
Intramodal Dispersion Contd..
Ng = Group refractive index
If the source is characterized by spectral width 𝝙𝝀0, then
∆𝝉 =𝒅𝝉
𝒅𝝀𝟎∆𝝀𝟎
Department of Electronics and Communication Engineering, KUET 15
Intramodal Dispersion Contd..
is dimensionless
ps/nm/km
The negative sign shows the lowest wavelength arrives before the
highest wavelength.
Self-study: Examples; 3.6, 3.7 (Senior)
Department of Electronics and Communication Engineering, KUET 16
❖Waveguide Dispersion:
➢ The normalized propagation constant b is defined by:
➢ For guided modes 𝒏𝟏 >𝜷
𝒌𝟎> 𝒏𝟐, thus 1>b>0.
➢ As we have seen previously for step index fiber, b depends on
the value of the fiber.
➢ Normalized frequency,
[𝒏𝟏 𝐢𝐬 𝐯𝐞𝐫𝐲 𝐜𝐥𝐨𝐬𝐞 𝐭𝐨 𝒏𝟐]
Intramodal Dispersion Contd..
=
Department of Electronics and Communication Engineering, KUET 17
➢ Thus, ― true for all practical fiber.
➢ This equation implies that even if n1 and n2are independent of λ
(i.e., no material dispersion),𝒅𝜷
𝒅𝝎will depend on ω due to the
explicit dependence of b on V.
[we know group velocity, .]
➢ Assuming n1 and n2 are independent of λ―
➢ Since,
Intramodal Dispersion Contd..
Department of Electronics and Communication Engineering, KUET 18
➢ The time taken by a pulse to transverse length L of the fiber is
given by
➢ Where,
➢ Now for a source having a spectral width the corresponding
waveguide dispersion ―
Intramodal Dispersion Contd..
Department of Electronics and Communication Engineering, KUET 19
Intramodal Dispersion Contd..
where,
➢ Waveguide dispersion parameter,
➢ For design purposes, it is often used empirical formula ―
with A = 1.1428 and B = 0.996.
➢ A more accurate formula,
ps/km/nm.
and valid for
Example: 10.1, 10.2, 10.3, 10.4. (Ajoy Ghatak)
Department of Electronics and Communication Engineering, KUET 20
Dispersion in Multimode Fiber
▪ In multimode fiber, waveguide dispersion can be neglected.
▪ The total RMS pulse broadening σT is given by –
Here, σn is the RMS intermodal broadening and σm is the RMS
broadening due to material dispersion.
▪ RMS broadening due to material dispersion can be approximated by
With
Here, σλ is the RMS spectral width of optical source (nm) and DM is the
material dispersion parameter (ps.nm-1km-1).
Department of Electronics and Communication Engineering, KUET 21
✓ The pulse broadening in single-mode fibers results entirely from
intramodal or chromatic dispersion as only a single-mode is
allowed to propagate.
✓ Hence, the bandwidth is limited by the finite spectral width of
the source.
✓ The total RMS pulse broadening per unit length of fiber is given
by –
✓ In general the total dispersion parameter DT consists of three
components:
✓ With material dispersion parameter
Dispersion in Single-mode Fibers
PWMT DDDD ++=
Department of Electronics and Communication Engineering, KUET 22
✓ Waveguide dispersion parameter
✓ And profile dispersion parameter
✓ In the most practical cases, DP can be ignored.
Dispersion in Single-mode Fibers Contd..
Department of Electronics and Communication Engineering, KUET 23
✓ Material dispersion for pure silica goes through zero at a
wavelength near 1.27 µm.
✓ This zero material dispersion (ZMD) point can be shifted in
the wavelength the range from 1.2 to 1.4 µm by the addition of
suitable dopants (such as GeO2).
Material Dispersion Parameter
Department of Electronics and Communication Engineering, KUET 24
Material Dispersion Parameter
✓In the single-mode region (V ≤ 2.4), the normalized parameter
is always positive and has a maximum at V = 1.15 (step index fiber).
✓The waveguide dispersion parameter is always negative in the single-
mode region.
✓A change in the fiber parameters, such as the core radius, or in the
operating wavelength can alter the V and the waveguide dispersion
2
2 )(
dV
VbdV
Department of Electronics and Communication Engineering, KUET 25
Total Dispersion
✓ Here, λ0 is the zero dispersion wavelength (DT = 0).
Department of Electronics and Communication Engineering, KUET 26
CCITT Recommendations
❖CCITT => Consultative Committee for International
Telephone and Telegraph
✓For single-mode fibers optimized for operation at the
wavelength 1.3 µm.
✓Max DT < 3.5 ps.nm-1 km-1 for 1.285 µm ≤ λ ≤ 1.330
µm.
✓Max DT < 20 ps.nm-1 km-1 at λ = 1.55 µm.
Department of Electronics and Communication Engineering, KUET 27
Shift of Total Dispersion
❑ Methods to the zero dispersion wavelength to longer
wavelength:▪ Lowering the normalized frequency V
▪ Increasing the relative refractive index difference Δ
▪ Suitably doping the silica with germanium
Department of Electronics and Communication Engineering, KUET 28
❖Dispersion Shifted Fiber (DSF):Zero dispersion wavelength is shifted to 1.55 µm, where the
fiber has the lowest attenuation.
❖Dispersion Flattened Fiber (DFF)Low dispersion is maintained over a range of wavelengths
extending from 1.3 µm to 1.55 µm.
Various Types of Single-Mode Fibers
Department of Electronics and Communication Engineering, KUET 29
Various Types of Single-Mode Fibers
Contd..
❖ Nonzero Dispersion Shifted Fiber (NZ DSF):
A small dispersion remains in the C-band (1.525 – 1.565 µm) to
suppress nonlinear optical effects for DWDM application.
❖ Large Effective-Area Fiber (LEAF):
NZ DSF with a large effective core area for DWDM application
(Coming LEAF: 72 µm2, Standard NZ DSF: 55 µm2 )
Department of Electronics and Communication Engineering, KUET 30
Advanced Fiber Designs
Dispersion Compensating Fibers (DCF)
Fibers that have larger negative dispersion at the wavelength 1.55 µm
(up to -100 ps.nm-1 km-1):
Department of Electronics and Communication Engineering, KUET 31
Dispersion Management
To achieve low overall dispersion yet minimize nonlinear
wave mixing, which is important for high-bit-rate DWDM
systems.
Department of Electronics and Communication Engineering, KUET 32
Polarization Effects in Single-Mode Fibers
➢Practical single-mode fibers are not perfect circularly symmetric
structure, and therefore, do not generally maintain the polarization
state of the input light for more than a few meters.
➢The fundamental mode of a practical single-mode fiber may break
up into two nearly degenerate modes with orthogonal polarizations.
➢These two modes have different propagation constants, i.e., βx and
βy, and hence, travel at different velocities.
➢This gives rise to polarization mode dispersion (PMD), which can
limit the ultimate bandwidth of a single-mode fiber.
➢Modal Birefringence:
➢Beat Length:
kB
yx −=
BL
yx
B
=
−=
2
Department of Electronics and Communication Engineering, KUET 33
Polarization Effects in Single-Mode Fibers Cont..
B and LB are measures of deviation of the fiber from a
perfect circularly symmetric fiber. Typical single-mode
fibers have B ~ 10-6 – 10-7 or LB ~ 1 – 10 m.
❖ Polarization Mode Dispersion (PMD):
δτg = τgx – τgy
here, τgx – τgy is the group delays of the two polarization
modes.
❖ Typical single-mode fibers have δτg << 1 ps.km-1. PMD is
a serious consideration for 40 Gbps and above systems.
Department of Electronics and Communication Engineering, KUET 34
Special Optical Fibers ❖ High-Birefringence Fiber (Polarization-Maintaining
Fiber)
High-birefringence fibers can maintain linear polarization states
along the principal axes and find applications in interferometry and
polarimetric sensors.
Department of Electronics and Communication Engineering, KUET 35
Special Optical Fibers Cont..
❖ Stress-Induced Birefringence Fibers:
Department of Electronics and Communication Engineering, KUET 36
Special Optical Fibers Cont..
❖ Low-Birefringence Fiber:
▪ Low-birefringence fibers find application in magnetic field or
electric current sensing based on the detection of Faraday
rotation.
▪ They can be made by improving the conventional fabrication
method to reduce non-circularity and minimize asymmetric
stress.
▪ A more effective method of making a low-birefringence fiber is
by spinning a single-mode fiber during the fiber drawing
process. However, external perturbations (e.g., bending,
pressure) can re-introduce linear birefringence in the fiber.
Department of Electronics and Communication Engineering, KUET 37
Special Optical Fibers Cont..
❖Circularly Birefringent Fiber (Helical-Core Fiber):
▪ A circularly birefringence fiber preserves circular polarization
states. The fiber is useful for magnetic field or electric current
sensing.
▪ Its circular birefringence is insentitive to external perturbations.
▪A beat length of ~ 5 mm has been demonstrated.
Department of Electronics and Communication Engineering, KUET 38
Special Optical Fibers Cont..
❖ D-Shape Fiber:
▪By removing part of the cladding of a single-mode fiber,
one can probe into the evanescent field within the fiber to
form devices and sensors.
Department of Electronics and Communication Engineering, KUET 39
Special Optical Fibers Cont..
❖ Rare-Earth-Doped Fiber:
Many applications can be provided by introducing rare-earth ions
(e.g., erbium, neodymium) into a single-mode fiber.
➢ Fiber lasers and amplifiers
➢ Distributed temperature sensors based on absorption or
fluorescence
➢ Fibers with increased Verdet constant for electric current sensing
➢ Fibers with increased nonlinear optical coefficients
Department of Electronics and Communication Engineering, KUET 40
Special Optical Fibers Cont..
❖ Photonic Crystal Fiber / Microstructured Fiber:
Photonic crystal fibers are single-material fibers that offer many
unusual transmission characteristics that are being explored for
applications in fiber devices and sensors.
Department of Electronics and Communication Engineering, KUET 41
The Kerr Effect
➢The Kerr effect is due to the non-linear
response of the material.
➢Depending upon the type of input signal, the
Kerr-nonlinearity has three different effects
such as Self-Phase Modulation (SPM),
Cross-Phase Modulation (XPM) and Four-
Wave Mixing (FWM).
Department of Electronics and Communication Engineering, KUET 42
SPM: Self-Phase Modulation
➢ SPM is a fiber nonlinearity caused by the nonlinear index
of refraction of glass.
➢ The index of refraction varies with optical power level
causing a frequency chirp which interacts with the fiber’s
dispersion to broaden the pulse.
➢ The non-linear phase follows exactly the power shape of
the optical pulses.
➢ The frequency chirp is then proportional to the derivative
of the optical power. If pulses propagate under the non-
linear regime
Department of Electronics and Communication Engineering, KUET 43
XPM: Cross Phase Modulation
❑ In the case of multi-channel propagation at various
wavelengths, the different channels modulate
themselves via SPM but also each other via the fibre
index modulation.
❑ The efficiency of XPM depends on:
✓ The fibre chromatic dispersion
✓ Channel spacing
✓ Channel power
❑ XPM induces non-linear crosstalk.
Department of Electronics and Communication Engineering, KUET 44
FWM: Four Wave Mixing
❖ FWM: In the case of a multi–channel propagation and
under phase matching conditions, new frequencies are
generated in the fibre causing crosstalk and power
depletion.
❖ Under specific phase and wave vectors matching
conditions, four different waves will interact in the fibre
in a non-linear way.
❖ The easiest way to obtain FWM in a fibre is to propagate
two waves at angular frequencies ɷ1 and ɷ2 that will
create new waves at frequencies ɷ3 and ɷ4 such as:
ɷ1 + ɷ2 = ɷ3 + ɷ4
Department of Electronics and Communication Engineering, KUET 45
❑ This phenomenon is strongly dependent on
channel spacing and chromatic dispersion.
❑The generated waves may cause crosstalk if
they are at the same wavelength as incident
channels.
FWM: Four Wave Mixing Cont…
Department of Electronics and Communication Engineering, KUET 46
Thanks for Your Kind
Attention
Department of Electronics and Communication Engineering, KUET