From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 65
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 65
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Chapter 2 Dielectric Waveguides and Optical Fibers
Charles Kao, Nobel Laureate (2009)Courtesy of the Chinese University of Hong Kong
Propagation losses in optical fibers
S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education© 2013 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is prote cted by Copyright and written permission should be obtained from the
publisher prior to any prohibited reproduction, sto rage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photo copying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearso n Education, Inc., Upper Saddle River, NJ 07458.
21-Fev-2017
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 66
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 66
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Light Attenuation
Attenuation = Absorption + Scattering
Attenuation coefficient α is defined as the fractional decrease in the optical power per unit distance. α is in m-1.
Pout = Pinexp(−αL)
=
out
indB log10
1
P
P
Lα ααα 34.4
)10ln(
10dB ==
The attenuation of light in a medium
21-Fev-2017
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 67
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 67
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Attenuation in Optical Fibers
Attenuation vs. wavelength for a standard silica based fiber.
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 68
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 68
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Lattice Absorption (Reststrahlen Absorption)
EM Wave oscillations are coupled to lattice vibrations (phonons), vibrations of the ions in the lattice. Energy is transferred from the EM wave to these lattice vibrations.
This corresponds to “Fundamental Infrared Absorption” in glasses
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 69
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 69
JF, SCO 1617 Rayleigh Scattering
Rayleigh scattering involves the polarization of a small dielectric particle or a regionthat is much smaller than the light wavelength. The field forces dipole oscillations inthe particle (by polarizing it) which leads to the emission of EM waves in "many"directions so that a portion of the light energy is directed away from the incident beam.
αR ≈ 8π 3
3λ4 n2 −1( )2βTkBTf
βΤ = isothermal compressibility (at Tf)
Tf = fictive temperature (roughly thesoftening temperature of glass) wherethe liquid structure during the coolingof the fiber is frozen to become theglass structure
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 70
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 70
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Attenuation in Optical Fibers
Attenuation vs. wavelength for a standard silica based fiber.
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 71
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 71
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Low-water-peak fiber has no OH- peak
E-band is available for communications with this fiber
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 72
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 72
JF, SCO 1617
Chapter 2 Dielectric Waveguides and Optical Fibers
Charles Kao, Nobel Laureate (2009)Courtesy of the Chinese University of Hong Kong
Dispersion in optical fibers
S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education© 2013 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is prote cted by Copyright and written permission should be obtained from the
publisher prior to any prohibited reproduction, sto rage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photo copying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearso n Education, Inc., Upper Saddle River, NJ 07458.
21-Fev-2017
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 73
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 73
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(a) A sine wave is perfectly coherent and contains a well-defined frequency υo. (b) A finite wave train lasts for a duration ∆t and has a length l. Its frequency spectrum extends over ∆υ = 2/∆t. It has a coherence time ∆t and a coherence length λ. (c) White light exhibits practically no coherence.
Spectral width Pulse duration(Temporal and Spatial Coherence)
21-Fev-2017
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 74
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 74
JF, SCO 1617 Spectral width Pulse duration(Temporal and Spatial Coherence)
t∆≈∆ 1υ FWHM spreads
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 75
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 75
JF, SCO 1617 Spectral width Pulse duration(Temporal and Spatial Coherence)
(a) Two waves can only interfere over the time interval ∆t. (b) Spatial coherence involves comparing the coherence of waves emitted from different locations on the source. (c) An incoherent beam
c
(a)
Time
(b)
A
B
∆ tInterference No interferenceNo interference
Space
c
P
Q
Source
Spatially coherent source
An incoherent beam(c)
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 76
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 76
JF, SCO 1617 Spectral width Pulse duration(Temporal and Spatial Coherence)
∆t = coherence time
l = c∆t = coherence length
For a Gaussian light pulse
Spectral width Pulse duration
t∆≈∆ 1υ
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 77
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 77
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Temporal and Spatial Coherence
∆t = coherence time
l = c∆t = coherence lengthNa lamp, orange radiation at 589 nm has spectral width ∆υ ≈5´1011 Hz.
∆t ≈ 1/ ∆υ = 2´10-12 s or 2 ps,
and its coherence length l = c∆t,
l = 6´10-4 m or 0.60 mm.
He-Ne laseroperating in multimode has a spectral width around 1.5´109 Hz, ∆t ≈ 1/∆υ = 1/1.5´109 s or 0.67 ns
l = c∆t = 0.20 m or 200 mm.
t∆≈∆ 1υ
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 78
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 78
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Intermode Dispersion (MMF)
∆τL
≈ n1 − n2
c
Group Delay τ = L / vg
(Since n1 and n2 are only slightly different)
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 79
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 79
JF, SCO 1617 Intermode Dispersion (MMF)
maxmin gg vvLL −=∆τ
∆τL
≈ n1 − n2
c∆τ/L ≈ 10 − 50 ns / km
Depends on length!
=≈
1
2
11min sin
n
n
n
c
n
ccθgv
−=∆
2
121 )(
n
n
c
nn
L
τ
θc θcTE0
TEhighest
1max n
c≈gv
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 80
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 80
JF, SCO 1617 Intramode Dispersion (SMF)
Group Delay τ = L / vg
Group velocity vg depends on
Refractive index = n(λ) Material Dispersion
V-number = V(λ) Waveguide Dispersion
∆ = (n1 − n2)/n1 = ∆(λ) Profile Dispersion
Dispersion in the fundamental mode
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 81
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 81
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Material Dispersion
Emitter emits a spectrum∆λ of wavelengths.
Waves in the guide with different free space wavelengths travel at different groupvelocities due to the wavelength dependence ofn1. The waves arrive at the end of thefiber at different times and hence result in a broadened output pulse.
∆τL
= Dm∆λ Dm = Material dispersion coefficient, ps nm-1 km-1
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 82
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 82
JF, SCO 1617 Intramode Dispersion (SMF)Chromatic dispersion in the fundamental mode
λ1
vg1
vg2
∆λ = λ2 − λ1
λ2 τg1 τg2
τ
∆λ
δ(t)
∆τ
∆τ = τg1 − τg2
λτ
Ld
dD =
DispersionChromatic spread
Definition of Dispersion Coefficient
λτ
∆∆=
LD
OR
λτ ∆=∆ DLOutput pulse
dispersed
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 83
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 83
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Material Dispersion
∆τL
= Dm∆λ
Dm = Material dispersion coefficient, ps nm-1 km-1
Cladding
CoreEmitter
Very shortlight pulse
vg(λ1)Input
Outputvg(λ2)
vg = c / Ng
Depends on the wavelengthGroup velocity
−≈
2
2
λλ
d
nd
cDm
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 84
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 84
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b = (β /k)2 − n22
n12 − n2
2
Wave guide dispersion
b hence β depend on V and hence on λ
Normalized propagation constant
k = 2π/λ
2996.0
1428.1
−≈V
b( ) 2/122
21
2nn
aV −=
λπ
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 85
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 85
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Waveguide Dispersion
Waveguide dispersionThe group velocity vg(01) of the fundamental mode depends on the V-number, which itself depends on the source wavelength λ, even if n1 and n2 were constant. Even if n1 and n2 were wavelength independent (no material dispersion), we will still have waveguide dispersion by virtue of vg(01) depending on V and Vdepending inversely on λ. Waveguide dispersion arises as a result of the guiding properties of the waveguide which imposes a nonlinear ω vs. βlm relationship.
∆τL
= Dw∆λ Dw = waveguide dispersion coefficient
Dw depends on the waveguide structure, ps nm-1 km-1
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 86
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 86
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Chromatic Dispersion
Material dispersion coefficient (Dm) for the core material (taken as SiO2), waveguide dispersion coefficient (Dw) (a = 4.2 µm) and the total or chromatic dispersion coefficient Dch (= Dm + Dw) as a function of free space wavelength, λ
∆τL
= (Dm + Dw)∆λ
Chromatic = Material + Waveguide
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 87
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 87
JF, SCO 1617 What do Negative and Positive Dm mean?
λ1
12
λ2
t
λ1 vg1
vg2λ2
t
∆λ = λ2 − λ1
1 2
λ1 λ2
Positive Dm
Ng2 > Ng1
∆τ = Positive
t
λ1vg1
vg2λ2
t
Negative Dm
Ng2 < Ng1
∆τ = Negative
Negative Dm
Positive Dm
Dm
λτ
∆∆=
LDm
Silica glass ∆τ
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 88
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 88
JF, SCO 1617
∆=2
22 )(
dV
bVdV
c
nDw λ
Waveguide Dimension and Chromatic Dispersion
22
025.0
cnaDw
λ−≈
22
11
)]µm([
)µm(76.83)kmnmps(
naDw
λ−≈−−
Waveguide dispersion depends on the guide properties
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 89
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 89
JF, SCO 1617
Profile Dispersion
Group velocity vg(01) of the fundamental mode depends on ∆, refractive index difference.
∆ may not be constant over a range of wavelengths: ∆ = ∆(λ)
∆τL
= Dp∆λ Dp = Profile dispersion coefficient
Dp < 0.1 ps nm-1 km-1
Can generally be ignored
NOTE
Total intramode (chromatic) dispersion coefficient Dch
Dch = Dm + Dw + Dp
where Dm, Dw, Dp are material, waveguide and profile dispersion coefficients respectively
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 90
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 90
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Chromatic Dispersion
λτ ∆=∆chD
L
−=4
00 14 λ
λλSDch
Dch = Dm + Dw + Dp
S0 = Chromatic dispersion slope at λ0
Chromatic dispersion is zero at λ = λ0
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 91
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 91
JF, SCO 1617
L+∆
+∆
=−=∆ 22
2
0 )(!2
1)()()(
00
λλτλ
λτλτλττ
λλ d
d
d
d
Is dispersion really zero at λ0?
The cause of ∆τ is the wavelength spread ∆λ at the input
∆τ = f(∆λ)
chDLd
d =∆λτ
( )( ) ps01.1nm2kmnmps090.02
km1)(
221-2-2
0 ==∆=∆ λτ SL
0Sd
dDch =λ
20 )(
2
1)]([
0
λλτ
λλλτ
λ
∆
+∆=∆d
d
d
dLDch
= 0
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 92
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 92
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Polarization Dispersion
n different in different directions due to induced strains in fiber in manufacturing, handling and cabling. δn/n < 10-6
LDPMD=∆τDPMD = Polarization dispersion coefficient
Typically DPMD = 0.1 − 0.5 ps nm-1 km-1/2
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 93
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 93
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Self-Phase Modulation Dispersion : Nonlinear EffectAt sufficiently high light intensities, the refractive index of glass n′ is
n′ = n + CI
where C is a constant and I is the light intensity. The intensity of light modulates its own phase.
What is the optical power that will give ∆τ/L ≈ 0.1 ps km-1?
Take C = 10-14 cm2 W-1
∴ ∆I ≈ (c/C)(∆τ/L) = 3×106 W cm-2
or ∆n ≈ 3×10-6
Given 2a ≈ 10 µm, A ≈ 7.85×10-7 cm2
∴ Optical power ≈ 2.35 W in the core
c
IC
L
∆≈∆τ
In many cases, this dispersion will be less than other dispersion mechanisms
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 94
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 94
JF, SCO 1617 Nonzero Dispersion Shifted Fiber
For Wavelength Division Multiplexing (WDM) avoid 4 wave mixing: cross talk.
We need dispersion not zero but very small in Er-amplifer band (1525-1620 nm)
Dch = 0.1 − 6 ps nm-1 km-1.
Nonzero dispersion shifted fibers
Various fibers named after their dispersion
characteristics. The range 1500 - 1600 nm is only
approximate and depends on the particular
application of the fiber.
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 95
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 95
JF, SCO 1617 Dispersion Flattened Fiber
Dispersion flattened fiber example. The material dispersion coefficient (Dm) for thecore material and waveguide dispersion coefficient (Dw) for the doubly clad fiberresult in a flattened small chromatic dispersion between λ1 and λ2.
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 96
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 96
JF, SCO 1617 Nonzero Dispersion Shifted Fiber: More Examples
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
-0.1-25 -15 -5 15 2550
Radius (µm)
Refractive Index change (%)
Nonzero dispersion shifted fiber (Corning)
Fiber with flattened dispersion slope
(schematic)
0.6%
0.4%
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 97
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Commercial Fibers for Optical Communications
Fiber Dch
ps nm-1 km-1
S0
ps nm-2 km-1
DPMD
ps km-1/2
Some attributes
Standard single mode, ITU-T G.652
17
(1550 nm)
≤ 0.093 < 0.5
(cabled)
Dch = 0 at λ0 ≈ 1312 nm, MFD = 8.6 - 9.5 µm at 1310 nm. λc ≤1260 nm.
Non-zero dispersion shifted fiber, ITU-T G.655
0.1 − 6
(1530 nm)
< 0.05 at 1550 nm
< 0.5
(cabled)
For 1500 - 1600 nm range. WDM application
MFD = 8 − 11 µm.
Non-zero dispersion shifted fiber, ITU-T G.656
2 − 14 < 0.045 at 1550 nm
< 0.20
(cabled)
For 1460 - 1625 nm range. DWDM application. MFD = 7 − 11 µm (at 1550 nm). Positive Dch. λc
<1310 nmCorning SMF28e+
(Standard SMF)
18
(1550 nm)
0.088 < 0.1 Satisfies G.652. λ0 ≈ 1317 nm, MFD = 9.2 µm (at 1310 nm), 10.4 µm (at 1550 nm); λc ≤ 1260 nm.
OFS TrueWave RS Fiber 2.6 - 8.9 0.045 0.02 Satisfies G.655. Optimized for 1530 nm - 1625nm. MFD = 8.4 µm (at 1550 nm); λc ≤1260 nm.
OFS REACH Fiber 5.5 -8.9 0.045 0.02 Higher performance than G.655 specification. Satisfies G.656. For DWDM from 1460 to 1625 nm. λ0 ≤ 1405 nm. MFD = 8.6 µm (at 1550 nm)
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 98
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 98
JF, SCO 1617 Single Mode Fibers: Selected Examples
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 99
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 99
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Dispersion Compensation
Total dispersion = DtLt + DcLc = (10 ps nm-1 km-1)(1000 km) +
(−100 ps nm-1 km-1)(80 km)
= 2000 ps/nm for 1080 km
Deffective = 1.9 ps nm-1 km-1
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 100
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 100
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Dispersion Compensation
Dispersion D vs. wavelength characteristics involved in dispersion compensation. Inverse dispersion
fiber enables the dispersion to be reduced and maintained flat over the communication
wavelengths.
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 101
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 101
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Dispersion Compensation and Management
� Compensating fiber has higher attenuation. Doped core. Need shorter length
� More susceptible to nonlinear effects.Use at the receiver end.
� Different cross sections. Splicing/coupling losses.
� Compensation depends on the temperature.
� Manufacturers provide transmission fiber spliced to inverse dispersion fiber for a well defined D vs. λ
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 102
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 102
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Dispersion and Maximum Bit Rate
B ≈ 0.5∆τ1/ 2
Return-to-zero (RTZ) bit rate or data rate.
Nonreturn to zero (NRZ) bit rate = 2 RTZ bitrate
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 103
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NRZ and RTZ
1 0 1 1 0 1 0 0 1
NRZ
RZ
Information
T
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 104
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 104
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Maximum Bit Rate B
A Gaussian output light pulse and some tolerable intersymbol interference
between two consecutive output light pulses (y-axis in relative units). At time t
= σ from the pulse center, the relative magnitude is e−1/2 = 0.607 and full
width root mean square (rms) spread is ∆τrms = 2σ. (The RTZ case)
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 105
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 105
JF, SCO 1617 Dispersion and Maximum Bit Rate
2/1
59.025.0
τσ ∆=≈B 2/1
2/1 λτ ∆=∆chD
L
Maximum Bit Rate Dispersion
2/12/1
59.059.0
λτ ∆=
∆≈
chDBL
Bit Rate × Distance is
inversely proportional to dispersion
inversely proportional to line width of laser
(so, we need single frequency lasers!)
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 106
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 106
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Dispersion and Maximum Bit Rate
B ≈ 0.25σ
= 0.59∆τ1/2
Maximum Bit Rate
2intramodal
2intermodal σσσ +=2
2intramodal2/1
2intermodal2/1
22/1 )()()( τττ ∆+∆=∆
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 107
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 107
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Optical Bandwidth
An optical fiber link for transmitting analog signals and the effect of dispersion in the
fiber on the bandwidth, fop.
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 108
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Pulse Shape and Maximum Bit Rate
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 109
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 109
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Example: Bit rate and dispersion
Consider an optical fiber with a chromatic dispersion coefficient 8 ps km-1 nm-1
at an operating wavelength of 1.5 µm. Calculate the bit rate distance product (BL), and the optical and electrical bandwidths for a 10 km fiber if a laser diode source with a FWHP linewidth ∆λ1/2 of 2 nm is used.
Solution
For FWHP dispersion,
∆τ1/2/L = |Dch|∆λ1/2 = (8 ps nm-1 km-1)(2 nm) = 16 ps km-1
Assuming a Gaussian light pulse shape, the RTZ bit rate × distance product (BL) is
BL = 0.59L/∆τ1/2 = 0.59/(16 ps km-1) = 36.9 Gb s-1 km
The optical and electrical bandwidths for a 10 km fiber are
fop = 0.75B = 0.75(36.9 Gb s-1 km) / (10 km) = 2.8 GHz
fel = 0.70fop = 1.9 GHz
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 110
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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 110
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Chapter 2 Dielectric Waveguides and Optical Fibers
Charles Kao, Nobel Laureate (2009)Courtesy of the Chinese University of Hong Kong
Graded Index (GRIN) Fibers
S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education© 2013 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is prote cted by Copyright and written permission should be obtained from the
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21-Fev-2017