ece 4105 optical fiber communications...ece 4105 optical fiber communications prof. dr. monir hossen...

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.


Dispersion in Optical Fibers Cntd..


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

∆


▪ 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


Example


Problem


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


✓ 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..


❖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..



Ng = Group refractive index

If the source is characterized by spectral width 𝝙𝝀0, then

∆𝝉 =𝒅𝝉

𝒅𝝀𝟎∆𝝀𝟎



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)


❖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]


=


➢ 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,



➢ 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 ―




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)


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).


✓ 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 ++=


✓ Waveguide dispersion parameter

✓ And profile dispersion parameter

✓ In the most practical cases, DP can be ignored.

Dispersion in Single-mode Fibers Contd..


✓ 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


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


Total Dispersion

✓ Here, λ0 is the zero dispersion wavelength (DT = 0).


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.


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


❖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


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 )


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):


Dispersion Management

To achieve low overall dispersion yet minimize nonlinear

wave mixing, which is important for high-bit-rate DWDM

systems.


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


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.


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.


Special Optical Fibers Cont..

❖ Stress-Induced Birefringence Fibers:



❖ 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.



❖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.



❖ 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.



❖ 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



❖ 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.


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).


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


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.


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


❑ 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…


Thanks for Your Kind

Attention

Department of Electronics and Communication Engineering, KUET

ece 4105 optical fiber communications...ece 4105 optical fiber communications prof. dr. monir hossen...

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