ee 230: optical fiber communication lecture 2 from the movie warriors of the net fibers from the...
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![Page 1: EE 230: Optical Fiber Communication Lecture 2 From the movie Warriors of the Net Fibers from the view of Geometrical Optics](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56649d365503460f94a0e135/html5/thumbnails/1.jpg)
EE 230: Optical Fiber Communication Lecture 2
From the movieWarriors of the Net
Fibers from the view of Geometrical Optics
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Total Internal Reflection
1 1 2 2
1 3
1 2 1 2
21 2
1
1
:sin sin
Re
90 deg
sin sin
c c
c
c
Snells Lawn n
flection Condition
When n n and as increases eventually
goes to rees andn
n n orn
is called the Critical angleFor there is no pro pagating refracted ray
![Page 3: EE 230: Optical Fiber Communication Lecture 2 From the movie Warriors of the Net Fibers from the view of Geometrical Optics](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56649d365503460f94a0e135/html5/thumbnails/3.jpg)
Reflection as a function of angle
Fiber Optics Communication Technology-Mynbaev & Scheiner
This additional Phase Shift is not accounted for
in geometrical wave approach
The reflectivities of waves polarizedparallel and perpendicular to the plane of incidence as given by the Fresnel equations
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Principal Types of Optical Fiber
Understanding Fiber Optics-Hecht
Types of Fibers
•Single mode/Multi-mode
•Step Index/Graded Index
•Dispersion Shifted/Non-dispersion shifted
•Silica/fluoride/Other materials
•Major Performance Concerns for Fibers
•Wavelength range
•Maximum Propagation Distance
•Maximum bitrate
•Crosstalk
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Fabrication of Optical Fiber
• Fabrication of fiber preform: macroscopic version with correct index profile
• Drawing of preform down into thin fiber
• Jacketing and cabling
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Step-Index Fiber
• Cladding typically pure silica
• Core doped with germanium to increase index
• Index difference referred to as “delta” in units of percent (typically 0.3-1.0%)
• Tradeoff between coupling and bending losses
• Index discontinuity at core-clad boundary
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Basic Step index Fiber Structure
Fiber Optics Communication Technology-Mynbaev & Scheiner
![Page 8: EE 230: Optical Fiber Communication Lecture 2 From the movie Warriors of the Net Fibers from the view of Geometrical Optics](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56649d365503460f94a0e135/html5/thumbnails/8.jpg)
Ray Trajectories in Step Index fiber
Meridional Rays
Skew Rays
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Coupling Light into an Optical Fiber
Fiber Optics Communication Technology-Mynbaev & Scheiner
![Page 10: EE 230: Optical Fiber Communication Lecture 2 From the movie Warriors of the Net Fibers from the view of Geometrical Optics](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56649d365503460f94a0e135/html5/thumbnails/10.jpg)
Acceptance Angle
Optics-Hecht & Zajac
The acceptance angle (i) is the largest incident angle ray that can be coupled into a guided ray within the fiber
The Numerical Aperature (NA) is the sin(i) this is defined analagously to that for a lens
#
tan
1
2
f ff
D FullAccep ceAngle
NA
º =
=×
1 1 12 2 22 2 2
1 2
1 2 1 2
( ) (2 ) (2 )
and 2
NA n n n n
n n n nWhere n
n
= - = D = D
- +D º º
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φ1
φ2
θ1
θ2
nCO
nCL
n0
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From Snell’s Law, 21 sinsin CLCO nn
For total internal reflection, θ2=90º
CO
CLc n
n11 sin
What value of φ1 corresponds to θc?
That is the maximum acceptance angle for the fiber. φ2 = 90º-θc sinφ2 = cos θc
CO
CLc n
nsin , so
CO
CLCOc n
nn 22
cos
NAnnn
nnnn CLCO
CO
CLCOCOCO
22
22
2sin
Again from Snell’s Law,
21 sinsin COo nn
(= NA), so
0
11 sin
n
NAc
Numerical Aperture
210 sinsin COnn
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For Corning SMF-28 optical fiber
nco=1.4504, nCL=1.4447 at 1550 nm
NA = 0.13
Acceptance angle = 7.35 degrees
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Geometrical View of Modes
Fiber Optics Communication Technology-Mynbaev & Scheiner
•Ray approximation valid in the limit that goes to zero
•Geometrical Optics does not predict the existance of discrete modes
•Maxwells Equations and dielectric boundary conditions give rise to the requirement that the fields and phase reproduce themselves each “cycle”
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Rays and Their E-field Distribution
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Origin of Modal Dispersion• Straight path along fiber axis has distance L and velocity c/nCO for
transit time of LnCO/c
• Path at maximum acceptance angle φc has distance L/cosφ2 where φ2=90º-θc and thus a longer transit time.
• Transit time difference equal to
• Dispersion limits rate of signals that fiber can handle
• If spread can be up to 70% of bit period, then maximum bit rate is 1.4cnCO/L(NA)2
2
22
2 1sin1cos
COn
NA
112
CL
COCO
n
n
c
Lntt
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Intermodal Dispersion
Fiber Optics Communication Technology-Mynbaev & Scheiner
1SI
2
1 2SI2
SI
Lt c
Lt for c( )Lt c 2
nnn
n n n
NAn
D = D
D @ D @
D @
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Bandwidth for Various Fiber Types
Fiber Optics Communication Technology-Mynbaev & Scheiner
21
21 8
4
1Bit Rate BR<4
14 4
2
2
SI
SISI
GI
GIcBRLn
t
cBRt Ln
cBRn L
cBR n L
= =D
D
D
= =D D
=D
D
No intermodal time shift for single Mode Fiber
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Graded Index Fiber
Fiber Optic Communication Systems-Agarwal
1
1 2
21
21
21
( ) 1 for <a
( ) 1 =n for >a
for 2 a "parabolic profile"
NA=n 2 1 which varies with
8GI
n na
n n
a
Lnt
c
Fiber Optic Communications-Palais
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Ray Propagation in Graded-Index Fiber
Graded Index Slab Uniform in X and Z
Fundamentals of Photonics - Saleh and Teich
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Ray spreading comparison
3
4
8 COGI cn
NALt
CO
SI cn
NALt
2
2
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Comparison, continued
If NA=0.13 and nCO=1.45,
∆tSI/L=19 ps/m
∆tGI/L=0.039 ps/m
Graded-index fiber has substantially less modal dispersion