p8 fiber optics
TRANSCRIPT
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8. Fiber optics
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Principal Types of Optical Fiber
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8.1 Step-index fibers
Cladding typically pure silica
ore ope w german um o ncrease n ex
Index difference referred to as delta in units of percent
t icall 0.3-1.0%
Tradeoff between coupling and bending losses
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8.1 Step-index fibers
Meridional Rays
Skew Rays
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8.1 Step-index fibers
For Corning SMF-28 optical fiber, nco=1.4504, nCL=1.4447 at 1550 nmNA = 0.13, Acceptance angle = 7.35 degrees
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8.1 Step-index fibers
2 22 21 1U U U
Helmholtz equation :
02 2 2r r r r
1 0 2 0
n2
n1
a
0z
E
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8.1 Step-index fibers
Tk : transverse propagation constant
: decay constant
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8.1 Step-index fibers
Spatial (radial) distribution function
=
l = 0
l = 3l = 1
l = 2
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8.1 Step-index fibers
V parameter of fibers (Normalized frequency of fibers)
-parame er or orma ze requency0 1 2 0a n n a= =
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8.1 Step-index fibers
: Characteristic Equation
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8.1 Step-index fibers
: Characteristic Equation
2 2
X
0 1 2a n n=
02
03X
Fiber modes Linearly polarized modes modeslmLP
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8.1 Step-index fibers
Linearly polarized modes in fibers modeslmLP
2u r
01LP
2( )u r
34LP
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8.1 Step-index fibers
modeslm
LP
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8.1 Step-index fibers
(for low V)
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8.1 Step-index fibers
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8.1 Step-index fibers
If V >> 1
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8.1 Step-index fibers
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8.2 Graded-index fibers
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8.2 Graded-index fibers
Ray Propagation in Graded-Index Fibers
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8.2 Graded-index fibers
p = para o c n ex-pro e
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Comparison : the number of modes
0
2M
=1-d Mirror Guide For the mirror guidethe number of modes isjust the number of
wavelengths that can fit.
0
2d
M NA
1-d Dielectric GuideFor dielectr ic guides
it is the number that can fit
but now limited by the angular
2
2dM
2-d Mirror Guide
cutoff characterized by the
NA of the guide
The V parameter0
2
characterizes the number of
wavelengths that can fit acrossthe core guiding region in a fiber.
04M NA
2-d Dielectric Guide
2
2
2
0
416
aM V NA
= 2-d Dielectric fiber (step-index) ( / 2)a d=
2-d dielectric fiber (graded-index) 21
for p = 24M V
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8.3 Attenuation and dispersion
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Dispersion
Group velocity
1
=
gv
1
kc =
=
Dispersion
=D
Di i
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Dispersion
=D
group velocities
changes with wavelength
have different delays
Polarization mode dis ersion: if wave uide is birefrin ent
Di i
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Dispersion
Dispersion
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Dispersion
Dispersion
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Dispersion
Dispersion
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Dispersion
Dispersion
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Dispersion