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EE 230: Optical Fiber Communication Lecture 2. Fibers from the view of Geometrical Optics. From the movie Warriors of the Net. Total Internal Reflection. Reflection as a function of angle. The reflectivities of waves polarized parallel and perpendicular to the plane of - PowerPoint PPT Presentation
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EE 230: Optical Fiber Communication Lecture 2
From the movieWarriors of the Net
Fibers from the view of Geometrical Optics
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 nflection Condition
When n n and as increases eventuallygoes to rees and
nn n or nis called the Critical angle
For there is no pro pagating refracted ray
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
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
Fabrication of Optical Fiber
• Fabrication of fiber preform: macroscopic version with correct index profile
• Drawing of preform down into thin fiber• Jacketing and cabling
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
Basic Step index Fiber Structure
Fiber Optics Communication Technology-Mynbaev & Scheiner
Ray Trajectories in Step Index fiber
Meridional Rays
Skew Rays
Coupling Light into an Optical Fiber
Fiber Optics Communication Technology-Mynbaev & Scheiner
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 ffD 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 nn
= - = D = D
- +D º º
φ1
φ2
θ1
θ2
nCO
nCL
n0
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
nNA
c
Numerical Aperture
210 sinsin COnn
For Corning SMF-28 optical fiber
nco=1.4504, nCL=1.4447 at 1550 nm
NA = 0.13
Acceptance angle = 7.35 degrees
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”
Rays and Their E-field Distribution
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
COnNA
112
CL
COCO
nn
cLn
tt
Intermodal Dispersion
Fiber Optics Communication Technology-Mynbaev & Scheiner
1SI 2
1 2SI2
SI
Lt cLt for c
( )Lt c 2
n nn
n n nNAn
D = D
D @ D @D @
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
cBR t Ln
cBRn L
cBR n L
= =DD
D
= =D D
= D
D
No intermodal time shift for single Mode Fiber
Graded Index Fiber
Fiber Optic Communication Systems-Agarwal
1
1 2
212
1
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
Lntc
Fiber Optic Communications-Palais
Ray Propagation in Graded-Index Fiber
Graded Index Slab Uniform in X and Z
Fundamentals of Photonics - Saleh and Teich
Ray spreading comparison
3
4
8 COGI cn
NALt
CO
SI cnNALt
2
2
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