chapter 2 optical fiber (10!12!12)1

7/27/2019 Chapter 2 Optical Fiber (10!12!12)1

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Chapter Goals

Describe the details of Geometrical-Optics: Step-Index Fiber,

Graded-Index Fibers

Describe Refraction and Reflection rays

Derive Total Internal Reflection Conditions

Determine Numerical Aperture

Describe propagation rays in Multi-Mode Step-Index Fiber and

in Multi-Mode Graded-Index Fiber

Determine BL product Limitation of Graded-Index Fiber


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Determine Dispersion in Single-Mode Fibers: Group-Velocity,

Material, Waveguide, Higher-Order, Polarization-Mode

Determine Fiber Losses: Attenuation Coefficient, Material

Absorption, Rayleigh Scattering, Waveguide Imperfections.

Describe Fiber Manufacturing: Design Issues, Fabrication

Methods, Cables

Investigate Dispersion Compensation in Fiber by OptiWave


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Geometrical-Optics Description


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Geometrical-Optics Description

MM-SI Fiber

n2

n2

n1

1MM-GI Fiber

1n2

n2

n1

SM Fiber

n2

n2

n1


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Refraction and Reflection


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Refraction and Reflection

n1

n2

reflectedray

refracted

ray

1

2

1

incident

ray

2211 sin.sin. nn

Assuming: 21 nn Laws Snell:


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Total Internal Reflection

n1

n2refracted

ray

reflected

ray

c 1 1

22

increasethenincrease 21

anglecriticaln

ncc :,sin

1

2

221 thenc

Total Internal Reflection conditions?


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Total Internal Reflection Conditions

n1

n2refracted

ray

reflected

ray

c 1 1

22

Conclusion: The total reflection occurs when:

cwithraysall

nn

1

21


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Numerical Aperture (NA) of the Fiber

)(sin2

2

2

10 nnnNA i

In analogy with lenses, is known as

the numerical aperture(NA) of the fiber. It represents

the light-gathering capacity of an optical fiber.


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Numerical Aperture (NA) of the Fiber


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07.1146.1 22222

1 nnNA

0.209145.1465.1 22222

1 nnNA

Example 1

Determine Numerical Aperture of the Fiber?

(i) n1= 1.46 and n2= 1 (air)

(ii) n1= 1.465 and n2 = 1.45.

Application of Eq:

(i)

(ii)

)(sin 222

10 nnnNA i


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Numeric Aperture (NA) of the Fiber


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Numeric Aperture (NA) of the Fiber

)(sin 222

10 nnnNA i

1

21

n

nn

?21 nNA

With

Demonstrate:


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Typical Numerical Aperture values

of the MM Fiber


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Example 2

Determine BL of the MM-SI fiber which has these

parameters as follows: n1 = 1.5 and n2 = 1?

Determine Bit rate transferred through this fiber which

has length of 10 km?

BL < n2c/n12


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Answer 2

This condition provides a rough estimate of a fundamental

limitation of step-index fibers. Consider an unclad glass

fiber with n1 = 1.5 and n2 = 1 BL < 400 (kb/s)-km.

Rb40 kb/s over L 10 km. Considerable improvementoccurs for cladded fibers with a small index step.

Most fibers for communication applications are designed with

< 0.01. As an example,BL < 100 (Mb/s)-km for= 2

103. Rb10 Mb/s over L 10 km and may be suitable for

some local-area networks.


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Multimode Graded-Index Fiber


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The quantity T /L, where T is the maximum

multipath delay in a fiber of length L, is found to vary

considerably with .

Figure 2.4 shows this variation for n1 = 1.5 and =

0.01. The minimum dispersion occurs for

= 2(1 ) and depends on as

T/L = n12 /8c.

Limitation BL


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The limiting bit ratedistance product is obtained by

using the criterion T < 1/B and is given by

BL < 8c/n12.

The right scale in Fig. 2.4 shows theBLproduct as a

function of . Graded-index fibers with a suitably

optimized index profile can communicate data at a bit

rate of 100 Mb/s over distances up to 100 km.

Limitation BL


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Figure 2.4: Variation of intermodal dispersion T /L

with the profile parameter for a GI fiber. The scale on

the right shows the corresponding BL product.


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Example 3

Determine BL of the MM-GI fiber which has these

parameters as follows: n1 = 1.5 and = 0.01.

Determine Bit rate is transferred through this MM-GI

fiber which has length of 10 km?

Compare this BL with that of MM-SI fiber which was

investigated in example 2?

BL < 8c/n12


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Single Mode Step-Index Fiber


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E & H: the electric & magnetic field vectors,

D & B: the corresponding flux densities.

The constitutive relations:

D = 0

E + P, (2.2.5)

B = m0 H + M, (2.2.6)

0 : the vacuum permittivity,

m0 : the vacuum permeability,P & M: the induced electric & magnetic polarizations


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Review Related Equations


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-


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)(

0 ),(ztj

eHH

)(

0 ),(

ztj

eEE

Analysis in Cylindral Coordinates


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SMF Condition

2.405


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or


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The single-mode condition: V


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Example:

One SMF has n1 = 1,505 and n2 = 1,502

at = 1300 nm.

+ NA?

+ Determine core radius of the ?


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Kinds of Dispersion in Fiber

Total Dispersion

Mode Dispersion

Material Dispersion Waveguide Dispersion

SMF

MMF

Polarisation Mode

Dispersion

Chromatic Disp.or

Group Velocity Disp


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P l Sh di t


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Pulse Shapes versus distance


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Fiber Dispersion


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Example 2

Determine BL of the SM fiber which has these

parameters as follows: Spectrum width of optical

pulse: f = 12.5 GHz, =1.55 mm, and D =

19ps/nm.km

Determine Bit rate is transferred through this fiber

which has length of 50 km?


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d

ndnng


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For pure silica these parameters are found to beB1 =

0.6961663,B2 = 0.4079426,B3 = 0.8974794, 1 = 0.0684043

mm,2 = 0.1162414 mm, and 3 = 9.896161 mm, where j =

2c/j with j = 13.

The group index ng = n + (dn/d ) can be obtained by

using these parameter values


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Index n1 shape of DCF


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d

dn

cd

dnD

gg

M

22

2

12

dV

Vbd

d

dn

dV

VbVd

n

nD

gg

W

)()(2 22

2

2

22

2

(2.100)

Two parts of Chromatic Dispersion of SMF


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Attenuation versus Wavelength


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2000s

Water

spike



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Typical loss value of optical components


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Typical loss value of optical components

Gain in the small signal regime of EDFAs

Splice loss between two identical fibres

Loss of a 10% tap coupler

Isolator, 1480/1550 nm multiplexer

Linear

1000

10

0.977

0.955

0.90.5

Decibel

+30 dB

+10 dB

-0.1 dB

-0.2 dB

-0.5 dB-3.0 dB

Ga

in

Loss

Gain with saturating input signal

Cable fiber loss per km

Bulk optical filter


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Material Absorption


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Material absorption can be divided into two kinds:

+ Intrinsic absorption losses correspond to absorption by

fused silica (material used to make fibers)

+ Extrinsic absorption is related to losses caused by

impurities within silica.

Any material absorbs at certain wavelengths

corresponding to the electronic and vibrational resonances

associated with specific molecules. For silica (SiO2) molecules, electronic resonances occur

in the ultraviolet region (< 0.4 mm),

Material Absorption


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whereas vibrational resonances occur in the infrared region

(> 0.7mm).

Because of the amorphous nature of fused silica, these

resonances are in the form of absorption bands whose tails extend

into the visible region.

Extrinsic absorption results from the presence of impurities.

Metal impurities such as Fe, Cu, Co, Ni, Mn, and Cr absorb

strongly in the wavelength range 0.61.6 mm.


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Their amount should be reduced to below 1 part per billion

to obtain a loss level below 1 dB/km. Such high-purity silica

can be obtained by using modern techniques.

The main source of extrinsic absorption in state-of-the-art

silica fibers is the presence of water vapors.

A vibrational resonance of the OH ion occurs near 1.4 mm

Its harmonic and combination tones with silica produce


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Its harmonic and combination tones with silica produce

absorption at the 1.39, 1.24, and 0.95 mm wavelengths. The three

spectral peaks seen occur near these wavelengths and are due tothe presence of residual water vapor in silica.

Even a concentration of 1 part per million can cause a loss of

about 50 dB/km at 1.39 mm.

The OH ion concentration is reduced to below 10 8 in

modern fibers to lower the 1.39 mm peak below 1 dB. In a new

kind of fiber, known as the dry fiber, the OH ion concentration is

reduced to such low levels that the 1.39 mm peak almost

disappears.


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Rayleigh Scattering

Rayleigh scattering is a fundamental loss mechanism

arising from local microscopic fluctuations in density.

Silica molecules move randomly in the molten state and

freeze in place during fiber fabrication.

Density fluctuations lead to random fluctuations of the

refractive index on a scale smaller than the optical

wavelength .

Light scattering in such a medium is known asRayleigh

scattering.


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Cable Construction

Cross Section of a Fiber Cable


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Cross Section of a Fiber Cable


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Cable Construction

Inside Plant Ribbon-Cable System


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Cross Section of Armored Outside-Plant Cables


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Cross Section of Armored Outside Plant Cables


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Complete Compensation D1L1=D2L2, Rb=2.5 GB/s


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Complete Compensation D1L1=D2L2 Rb=5 GB/s


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Uncomplete Compensation D1L1D2L2 Rb=5 Gb/s


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chapter 2 optical fiber (10!12!12)1

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