unit 2 light propagation in an optical fiber:. contents: structure of optical fiber cable ...
TRANSCRIPT
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UNIT 2LIGHT PROPAGATION IN AN OPTICAL FIBER:
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CONTENTS:
Structure of Optical Fiber Cable
Classification of Fibers
Based on fiber materials
Based on Modes : Single mode / multi mode fiber
Based on RI profile: Step index / Graded index fiber
Ray Theory
Critical angle, Acceptance angle, Acceptance cone,
Numerical Aperture, V number, cutoff wavelength
Linearly polarized modes
Mode Coupling
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Structure of Optical Fiber Cable:
CORE CADDING JACKET
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CORE:
Innermost section
Made of glass/plastic
Glass: SILICA,
Plastic: acrylic - PMMA (Poly methyl methacrylate) It is the actual fiber through which light travels
Light travels in the core by Total Internal Reflection (TIR)
μcore > μclad
μ = c/v
RI is adjusted in Glass or plastic by proper doping.
Plastic fiber also called as Polymer Fibers
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CLADDING:
Core is surrounded by glass / plastic coating Optical properties of Glass is different from core,
μcore > μclad
This causes the optical beam to propagate in the core by Total internal reflection at the core clad interface.
Adds to the mechanical strength Protects the core from contamination Cladding reduces losses due to scattering of light due
to surface discontinuities at the core clad interface.
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JACKET:
Made of plastic / Polymer to provide protection to the fiber against Moisture, abrasion, crushing,
environmental damages, stress, fracture, over use over prolonged period of time.
Provides tensile strength to the fiber.
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Classification of Fibers (Materials):
• μcore > μclad (Essential condition for light propagation)
• Dense materials have high RI Plastic core, Plastic Clad Glass core, Plastic Clad (PCS, Plastic Clad Silica) Glass core , Glass clad (SCS, Silica Clad Silica)
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Comparison between Glass fiber and Plastic Fiber:
Plastic fibers: Advantages
More flexible
More rugged
Easier to install
Can withstand stress
Less expensive
Light weight
Limitations
More signal attenuation ( as light does not propagate through plastic as effectively as glass)
Due to losses : limited for short distance communication as within a building.
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Comparison:
Glass fibers: PCS better than SCS: SCS has best propagation characteristics as it is pure (no
impurities to change the ray propagation)
SCS has low transmission loss
Limitation : Least rugged, Easily susceptible to attenuation when exposed to radiations.
PCS less affected by radiations and hence immune to external interference in comparison to SCS.
Selection of fiber depends on the applications or system requirement.
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General Structure of Fiber-Optic Cables:
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RAY THEORY:
Ray : Narrow beam of light
Light is modeled as a number of discrete rays that can propagate through the fiber.
Using ray theory and applying SNELL’S LAW we can find cable parameters.
Ray theory : Reflection , Refraction, TIR
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How Light Travels Through Fiber?
TIR is the basis of fiber-optic communication
When a light ray strikes a boundary of two materials with different RIs, it bends, or in other terms, refracts to an extent that depends on the ratio of the RIs of the two materials
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Cable parameters:
Critical angle Acceptance angle Numerical aperture Solid angle
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Concept of TIR (TOTAL INTERNAL REFLECTION):
Speed of light in free space = 3 x 108 m/s
Light travels slow through more dense materials than free space.
Light travelling from one medium to other gets either reflected / refracted
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Reflection coefficient (μ):
Refractive index (μ) of the material is defined as: μ = c/v
c is the velocity of light in free space
V is the velocity of light in medium
μ =1 for air
μ > 1 for all known materials.
Light travels slowly in optically dense material (high RI) than in the one that is less dense material (low RI).
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SNELL’S LAW:
Snell's law gives us the information on how a light ray reacts when it meets a interface of 2 medium having different RI.
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Snell’s Law Continued……..
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Continued…….
Optical fibers work on the principle of total internal reflection
The angle of refraction and incidence at the interface between two media is governed by Snell’s law:
2211 sinsin nn
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μ1<μ2 : Less dense to more dense
Ray bent towards normal μ1=μ2: same medium
Ray travels un reflected μ1>μ2: More dense to less dense
Ray bent away from normal
μ1
μ2
μ1<μ2 μ1=μ
2
NORMAL
μ1>μ2
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Total Internal Reflection
μ1>μ2: More dense to less dense Ray bent away from normal
More denseCOREΜ1
INCIDENT WAVE
Less denseCLADDINGμ2
Refracted ray
Internal reflection
θi
θr
By adjusting θi we can initiate TIR and hence light starts propagating in the core
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Refraction & Total Internal Reflection:
When reflection occurs : θi = θr
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c
a
Acceptanceangle
Acceptance Cone
B
A
Lost by radiation
Core
Cladding
Acceptance angle
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25 A meridinal ray A is to be incident at an angle a in the core
– cladding interface of the fiber. The ray enters the fiber core at an angle a to the fiber
axis. The ray gets refracted at the air – core interface at angle c
and enters into the core – cladding interface for transmission Therefore, any ray which is incident at an angle greater
than a will be transmitted into the core – cladding interface
at an angle less than c and hence will not undergo total
internal reflection.
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26 Contd.•The ray B entered at an angle greater than a and
eventually lost propagation by radiation. •It is clear that the incident rays which are incident on fiber core within conical half angle c will be refracted
into fiber core, propagate into the core by total internal reflection. •This angle a is called as acceptance angle, defined
as the 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.
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27Acceptance cone : The imaginary light cone with twice the acceptance angle as the vertex angle, is known as the acceptance cone.
Numerical Aperture (NA) :Numerical aperture (NA) of the fiber is the
light collecting efficiency of the fiber and is a measure of the amount of light rays can be accepted by the fiber.
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Numerical Aperture
The numerical aperture of the fiber is closely related to the critical angle and is often used in the specification for optical fiber and the components that work with it
The numerical aperture is given by the formula:
The angle of acceptance is twice that given by the numerical aperture
22
21.. nnAN
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29
Numerical aperture
A ray of light is launched into the fiber at an angle 1 is less than
the acceptance angle a for the fiber as shown.
1
2
Ø
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30This ray enters from a medium namely air of refractive index n0 to the fiber with a core of refractive
index n1 which is slightly greater than that of the
cladding n2 . Assume that the light is undergoing total
internal reflection within the core.Applying Snell’s law of refraction at A,
10
1
2
1
sin
sinn
n
n
211 sinsin n
In the triangle ABC,
22
22
or
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31
cos2
sinsin 111 nn
21
2sin1cos
21
211 sin1sin n
From the above two equations,
When the total internal reflection takes place, θ = θc and θ1 = θa . Therefore,
21
21 sin1sin ca n
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32 Also, at B, applying the Snell’s law of refraction, we get
1
2
1
2 sin (or) 90sin
sin
n
n
n
nc
c
21
22
21
21
2
1
21 1sin nn
n
nna
From the above equation, we get
This is called the numerical aperture (N.A). The numerical aperture is also defined as the sine of the half of the acceptance angle .
ca nAN sinsin. 1
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33 In terms of refractive indices n1 and n2, where n1 is the core index and n2 the cladding index
2122
21 )(. nnAN
The half acceptance angle a is given by ).(sin 1 ANa
212
22
11 )(sin nn
21
22
21
2n
nn
21
2
2
).(
n
AN
211 )2(N.A n
From the above eqns, we get
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UNIT III Lecture 6
34PHYSICAL STRUCTURE OF OPTICAL FIBER :
An optical fiber is a transparent rod, usually made of glass or clear plastic through which light can propagate.
The light signals travel through the rod from the transmitter to the receiver and can be easily detected at the receiving end of the rod, provided the losses in the fiber are not excessive.
The structure of the modern fiber consists of an optical rod core coated with a cladding.
The core and the cladding have different refractive indices and hence different optical properties
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35 Countd.•The refractive index of the core is always greater than that of the cladding (i.e.) n1 > n2.
The light travels within the core by the principle of total internal reflection
An unclad fiber and a clad rod through which the light travels.
With the unclad rod, only a small potion of the light energy is kept inside; most of the light leaks to the surroundings.
The clad fiber is a much more efficient light carrier.
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36Countd.•The losses of the light as it travels through the fiber are much smaller for the clad fiber than for the unclad one.• The thickness of the core of a typical glass fiber is nearly 50 μm and that of cladding is 100 – 200 μm. • The overall thickness of an optical fiber is nearly 125 – 200 μm. • Thus an optical fiber is small in size and light weight unlike a metallic cable.
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37 Propagation characteristics of optical fiber :Meridinal rays and Skew rays :
The light rays, during the journey inside the optical fiber through the core, cross the core axis. Such light rays are known as meridinal rays.
The passage of such rays in a step index fiber is Similarly, the rays which never cross the axis of the core are known as the skew rays.
Skew rays describe angular ‘helices’ as they progress along the fiber.
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38
Countd.
•They follow helical path around the axis of fiber.
• A typical passage of skew rays in a graded index fiber is shown in the following Fig.
The skew rays will not utilize the full area of the core and they travel farther than meridinal rays and undergo higher attenuation.
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39
MERIDINAL AND SKEW RAYS
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Modes and Materials:
Since optical fiber is a waveguide, light can propagate in a number of modes
If a fiber is of large diameter, light entering at different angles will excite different modes while narrow fiber may only excite one mode
Multimode propagation will cause dispersion, which results in the spreading of pulses and limits the usable bandwidth
Single-mode fiber has much less dispersion but is more expensive to produce. Its small size, together with the fact that its numerical aperture is smaller than that of multimode fiber, makes it more difficult to couple to light sources
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Comparison :
Standard single mode Optical Fiber
Most common single mode optical fiber SMF28 from corning
Core diameter dcore = 8.2micro meter
Outer cladding diameter = 125 micro meter
Standard Multimode optical Fiber
Most common multimode optical fiber 62.5/125 from corning
Core diameter= 62.5 micro meter
Outer cladding diameter=125 micrometer
Step index Fiber Graded Index Fiber
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Continued……
Single Mode Numerical Aperture NA=0.14
NA=sin(q)
Dq=8°
lcutoff = 1260nm (single mode for >l lcutoff)
Single mode for both l=1300nm and l=1550nm standard telecommunications wavelengths
Multimode Numerical Aperture
NA=0.275
NA=sin(q)
Dq=16°
Many modes
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Types of Fiber: Both types of fiber described earlier are known as step-index fibers
because the index of refraction changes radically between the core and the cladding
Graded-index fiber is a compromise multimode fiber, but the index of refraction gradually decreases away from the center of the core
Graded-index fiber has less dispersion than a multimode step-index fiber
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V Number:
The number of propagating modes in a fiber is proportional to its V-Number
The equation is given as
V=2π/λ * a √ η12 – η2
2
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Number of Modes:
The number of modes can be characterized by the normalized frequency
Most standard optical fibers are characterized by their numerical aperture
Normalized frequency is related to numerical aperture
The step index optical fiber is single mode if V<2.405The step index optical fiber is multi mode if V>2.405
For Graded Index Single mode fiber V< 3.4For Graded Index Multi mode fiber V > 3.4
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Number of Modes:
The number of Modes in Step Index Fiber is
N = V2 / 2
Where α is refractive index profile
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Linearly Polarized Modes:
Meriodianal Ray
TE mode
TM mode
Skew ray
Hybrid Mode
EH mode
HE mode
The modes degenerate to give LP modes
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Electromagnetic Field distribution:
Electromagnetic wave in free space:
TEM mode
Ex ≠ 0
Ey ≠ 0
Hx ≠ 0
Hy ≠ 0
Ez=0
Hz=0
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Electromagnetic wave through a waveguide:
Mode of Propagation is either :
TE, TM, EH, HE mode
TE: Ex, Ey ≠ 0, Ez=0
Hx, Hy, Hz ≠ 0
TM: Ex, Ey,Ez ≠ 0,
Hx, Hy ≠ 0, Hz=0
Hybrid: Ex, Ey,Ez ≠ 0,
Hx, Hy,Hz ≠ 0
EH mode: Ez dominates
HE mode : Hz dominates
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Phase velocity (mode):
z
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Phase velocity
Vp = ω / β
ω : angular frequency of waveβ : Phase constantγ : Propagation Constant γ = α + jβThe attenuation constant defines the rate at which the fields of the wave are attenuated as the wave propagates.An electromagnetic wave propagates in an ideal (lossless) media without attenuation (α= 0)The phase constant defines the rate at which the phase changes as the wave propagates..
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Group velocity
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58Group velocity (pulse)
z
0d
d t
ddgV
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Linearly polarized modes
•All modes travelling down has their own phase velocity.•Group of modes having same phase velocity will degenerate•Their modal patterns are not seen distinctively•The new mode formed by combination of the degenerated modes : LINEARLY POARLIZED MODES
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LP modes
LP modes Exact modesLP01 HE11
LP11 HE21, TE01, TM01
LP21 HE31, EH11
LP02 HE12
LP31 HE41, EH21
LP12 HE22, TE02, TM02
LPlm HE2m,TE0m,TM0m
LPlm(l≠0or1) HEl+1,m,EHl-1,m
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LPlm :
l : half of number of maxima around the circumference
m: number of maxima along the radius.
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Intensity Profiles
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