Mathematical analysis of light propagation in optical fibers with randomly varying birefringence
FIBER OPTICS Light propagation through thin glass fibers.
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Transcript of FIBER OPTICS Light propagation through thin glass fibers.
FIBER OPTICS
Light propagation through thin glass fibers
FIBER OPTICS
Advantages
Low Attenuation (less signal degradation)
Very High Bandwidth over long distances
Small Size and Low Weight
No Electromagnetic Interference
Non-Conductive Cables
Easy installation
Eliminates Spark Hazards (non-flammable)
Data Security
PRINCIPLE OF FIBER OPTICS
Optical fibers are used as dielectric waveguides for guiding the electromagnetic waves at optical frequencies
Light is guided through transparent glass fibers by total internal reflection
TOTAL INTERNAL REFLECTION
Snell’s law
When the transmitted (refraction angle) reaches 90 , the incidence angle is ⁰
called as the critical angle
1
2
t
i
n
n
sin
sin
TOTAL INTERNAL REFLECTION
Angle of incidence less than the critical angle
Angle of incidence equal to the critical angle
Angle of incidence greater than the critical angle
Total internal refection takes place only when the light
travels from denser to rarer medium and angle of
incidence should be greater than the critical angle of
the denser medium
TOTAL INTERNAL REFLECTION
Structure Fiber Optic Cable
Glass fiber consists of a central core
glass (≈ 50 μm) surrounded by a cladding
Refractive index of cladding is slightly
lower than the refractive index of core
Core + Cladding ≈ 125 – 200 μm
Fiber is made of silica (SiO2) glass
Cladding is also made of silica but the
outer layer is added with small amount of
B, Ge or P to decrease the refractive index
Structure Fiber Optic Cable
Cladding provides
Proper light guidance (to retain the light
wave within the core)
High mechanical strength
High safety to the core from the scratch
Buffer Jacket
Made of plastic and protects the fiber
from moisture and abrasion
Structure 0f Fiber Optic Cable
Strength Members
Provides necessary toughness and
tensile strength
Fiber optic cable withstands during hard
pulling, bending, stretching or rolling
without fracture even though the fiber is
made from brittle glass
Black Polyurethane Outer Jacket
Avoids mechanical crushing
Consider the light propagation through a step index fiber
Fiber is placed in a medium of refractive index “no”
Propagation of Light through Optical Fibers
Let ɸmax is the incident angle at the entrance end of the fiber with respect to the axis of the fiber
Let θr be the corresponding angle of refraction
By Snell’s law
Propagation of Light through Optical Fibers
r0
1max
0
1
r
max
sin n
nsin
n
n
sin
sin
)190sin (since n
nsin
n
n
90sin
sin
1
2c
1
2c
In the limit of total internal reflection
Since
Propagation of Light through Optical Fibers
1
2r
rc
)(90sin
90
n
n
(or)
1
2r cosn
n rc 90
Angle of incidence at the core-cladding interface
Propagation of Light through Optical Fibers
1/22
1
2r 1sin
n
n
1cossin 22
1
2r cosn
n
r0
1max sin sin
n
n
2/1
20
22
21
1/22
1
2
0
1max 1sin
n
nn
n
n
n
n
Propagation of Light through Optical Fibers
2/1
20
22
21
maxsin
n
nnIf the fiber is placed in air (n0 = 1)
2/122
21maxsin nn
Acceptance Angle
Maximum value of the angle of
incidence at the entrance end
of the fiber, at which the angle
of incidence at the core-
cladding surface is equal to
the critical angle of the core
medium
2
221
1-max
2/122
21
1-max
2/122
21max
sin
sin
sin
nn
nn
nn
Acceptance Angle
Acceptance angle of the fiber is the maximum angle of incidence
up to which a light ray can enter into the fiber and still be totally
internally reflected
2
221
1-max
2/122
21
1-max
2/122
21max
sin
sin
sin
nn
nn
nn
Numerical Aperture
Numerical Aperture (N.A.) is the light collecting efficiency of the
fiber and is the measure of amount of light rays that can be
accepted by the fiber
2/122
21max
2/122
21 sin N.A nnnn
2/12121
2/122
21max sinN.A. nnnnnn
If n1 ≈ n2,
then (n1+n2) = 2n1
2/11
2/1211 2 2N.A. nnnn
Relative refractive index
difference of the fiber (Δ) 1
2121
22
21
2 n
nn
n
nn
Step Index Fiber
The refractive index of the core of the step index fiber is constant through out the core
Graded Index fiber
The refractive index of the core of the graded index fiber is maximum at the center of the core and then it decreases towards core-cladding interface