LIGHT PROPAGATION IN AN OPTICAL FIBER:

 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

 CORE
 CADDING
 JACKET

 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)
 μ core
> μ clad
 μ = c/v
 RI is adjusted in Glass or plastic by proper doping.
 Plastic fiber also called as Polymer Fibers

 Core is surrounded by glass / plastic coating
 Optical properties of Glass is different from core,
 μ core
> μ clad
 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.

 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.

core
clad
 Plastic core, Plastic Clad
 Glass core, Plastic Clad (PCS, Plastic Clad Silica)
 Glass core , Glass clad (SCS, Silica Clad Silica)

 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.

 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.

 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


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

 Critical angle
 Acceptance angle
 Numerical aperture
 Solid angle

(TOTAL INTERNAL REFLECTION):
 Speed of light in free space = 3 x
10 8 m/s
 Light travels slow through more dense materials than free space.
 Light travelling from one medium to other gets either reflected / refracted

 R efractive 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).

 Snell's law gives us the information on how a light ray reacts when it meets a interface of 2 medium having different RI.

 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: n
1 sin

1
 n
2 sin

2

 μ1<μ2 : Less dense to more dense
Ray bent towards normal
 μ1=μ2: same medium μ2
Ray travels un reflected
 μ1>μ2: More dense to less dense
Ray bent away from normal μ1
NORMAL
μ1<μ2
μ1=μ2
μ1>μ2

 μ1>μ2: More dense to less dense Ray bent away from normal
Less dense
CLADDING
μ2
θi
θr
More dense
CORE
Μ1
INCIDENT WAVE
Refracted ray
Internal reflection
By adjusting θi we can initiate TIR and hence light starts propagating in the core

When reflection occurs : θi = θr

Acceptance angle
Acceptance Cone
Acceptance angle
A
 a
 c
B
Lost by radiation
Core
Cladding

25
A meridinal ray A is to be incident at an angle
 a
– cladding interface of the fiber.
The ray enters the fiber core at an angle
 a in the core to the fiber axis.
The ray gets refracted at the air – core interface at angle  and enters into the core – cladding interface for transmission c
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.

26
Contd.
•The ray B entered at an angle greater than  a eventually lost propagation by radiation.
and
•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 .

27
Acceptance cone :
The imaginary light cone with twice the acceptance angle as the vertex angle, is known as the acceptance cone.
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.

 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:
N .
A .
 n
1
2  n
2
2
 The angle of acceptance is twice that given by the numerical aperture

29

1

2
Ø
Numerical aperture
A ray of light is launched into the fiber at an angle

1 the acceptance angle
 a for the fiber as shown. is less than

30
This ray enters from a medium namely air of refractive index n
0 index n
1 to the fiber with a core of refractive which is slightly greater than that of the cladding n
2
. Assume that the light is undergoing total internal reflection within the core.
Applying Snell’s law of refraction at A, sin sin

1

2
 n
1  n
1 n
0
In the triangle ABC,
 

2
 
2 or

2


2
  sin

1
 n
1 sin

2

31 sin cos


1


 n
1
1
 sin sin


2
2

1

2
  n
1 cos

From the above two equations, sin

1
 n
1
1

 sin
2 
1

2
When the total internal reflection takes place, θ = θ c and θ
1
= θ a
. Therefore, sin
 a
 n
1

1
 sin
2
 c

2
1

32 Also, at B, applying the Snell’s law of refraction, we get sin sin
 c
90
 n n
1
2
(or) sin
 c
 n n
1
2
From the above equation, we
1 get sin
 a
 n
1



1


 n n
1
2


2



2

 n
1
2  n
2
2

1
2
This is called the numerical aperture (N.A).
The numerical aperture is also defined as the sine of the half of the acceptance angle
.
N .
A
 sin
 a
 n
1 sin
 c

33
In terms of refractive indices n
1 is the core index and n
2
N .
A

( n
1
2  n
2
2
)
1 2 and n
2
, where n
1 the cladding index
The half acceptance angle given by
 a
 sin

1
( N .
A )
 a
  n
2 
1
2 n
1
2 n
2
2


( sin
N .

1
A )
(
2 n
2 
1
2 n
1
2 n
2
2 is
)
1 2
From the above eqns, we get
N.A
 n
1

( 2

)
1 2

34
PHYSICAL 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
UNIT III Lecture 6

35
Countd.
•The refractive index of the core is always greater than that of the cladding (i.e.) n
1
> n
2
.
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.

36
Countd.
•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.

37
:
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.

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.

39
MERIDINAL AND SKEW RAYS

 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

Most common single mode optical fiber SMF28 from corning
Core diameter d core meter
= 8.2micro
Outer cladding diameter = 125 micro meter
Step index Fiber
Most common multimode optical fiber 62.5/125 from corning
Core diameter= 62.5 micro meter
Outer cladding diameter=125 micrometer
Graded Index Fiber

Single Mode
 Numerical Aperture NA=0.14
 NA=sin(  )
  =8 °
 l cutoff
= 1260nm (single mode for l>l cutoff
)
 Single mode for both l =1300nm and l =1550nm standard telecommunications wavelengths
Multimode
 Numerical Aperture NA=0.275
 NA=sin(  )
  =16 °
 Many modes

 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

 The number of propagating modes in a fiber is proportional to its V-Number
 The equation is given as
V=2π/λ * a √ η
1
2 – η
2
2

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<2.405
The step index optical fiber is multi mode if V>2.405
For Graded Index Single mode fiber V< 3.4
For Graded Index Multi mode fiber V > 3.4

 The number of Modes in Step Index Fiber is
N = V 2 / 2
Where α is refractive index profile

 Meriodianal Ray
 TE mode
 TM mode
 Skew ray
 Hybrid Mode
 EH mode
 HE mode
 The modes degenerate to give LP modes

 Electromagnetic wave in free space:
 TEM mode
 Ex ≠ 0
 Ey ≠ 0
 Hx ≠ 0
 Hy ≠ 0
 Ez=0
 Hz=0

 Mode of Propagation is either :
 TE, TM, EH, HE mode


TE:
TM:
Ex, Ey ≠ 0, Ez=0
Hx, Hy, Hz ≠ 0
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

z

Vp = ω / β
ω : angular frequency of wave
β : Phase constant
γ : Propagation Constant
γ = α + jβ
The 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..

z d
  d t
58

0
V g
 d d



• 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

LP
01
LP
11
LP
21
LP
02
LP
31
LP
12
LP lm
LP lm(l≠0or1)
HE
11
HE
21
, TE
01
, TM
01
HE
31
, EH
11
HE
12
HE
41
, EH
21
HE
22
, TE
02
, TM
02
HE
2m
,TE
0m
,TM
0m
HE l+1,m
,EH l-1,m

 LPlm :
 l : half of number of maxima around the circumference
 m: number of maxima along the radius.