Fibre Optics, Structure, Total Internal Reflection, Critical angle of Propagation, Acceptance Angle, Fractional Refractive index change, Numerical Aperture, Modes of Propagation, V- Number, Classification of optical fibres based on Refractive index profile, modes and materials, Losses, Attenuation, Distortion, Intermodal and intramodal dispersion, Wave guide dispersion, Applications.

1. FIBRE OPTICS
Haroon Hussain Moidu
Lecturer, Department of Physics
CMS College, Kottayam

2. FIBRE OPTICS
Fibre optics is a technology in which signals
are converted from electrical into optical
signals, transmitted through a thin glass fibre
and reconverted into electrical signals.

3. Optical fibre system includes :
• Light source :
– Launching light into the fibre at its input end
– LED, Laser diodes
• Optical fibre :
- A cylindrical wave guide made of transparent
dielectric which guides waves along its length by total
internal reflection
• Photo detector :
- It converts the optical signal into electrical form

4. Structure
Optical fibre

5. Structure
• Core : Light guiding region; Diameter : 8.5 um to
62.5 um
• Cladding : Middle layer; confine light into the
core; Diameter : 125 um
• Coating : Sheath or buffer coating; to provide
physical and environmental protection.
Diameter : 250 um to 900 um
RI of core > RI of cladding
Optical fibre

6. Total Internal Reflection
when light passes from denser to rarer medium, light
ray bent away from the normal in the rarer medium.
So according to snells law,
Sin θ2 = (n1/n2) sin θ1

7. TIR cont.........
• n1 (glass) > n2 ( air)
• If θ1 < θc , the ray refracts into the rarer medium
• If θ1 = θc , the ray just grazes the interface of
rarer- to –denser media
• If θ1 > θc , the ray is reflected back into the
denser medium – this phenomenon is called TIR
• Critical angle is defined as
sin φc = n2/n1

8. TIR cont.........& concludes as......
The two conditions for the TIR to occur and the
light to propagate through the fibre are :
1. The RI of the core > RI of Cladding
2. At the core-cladding interface , the angle of
incidence must be greater than the critical
angle .

9. Critical angle of propagation
• The particular angle that critical ray ( the ray
that incident at the core – cladding interface
at critical angle ) makes with the axis of fibre
at the launching end is called the critical angle
of propagation, θc .
• Only those rays which are refracted into the
cable at angles less than θc will propagate,
While those rays with propagation angle > θc
will not propagate in the optical fibre.
• Expression : cos θc = n2/ n1

10. Acceptance angle
• The maximum angle that a incident light ray can have
relative to the axis of the fibre and propagate down the
fibre is the acceptance angle,θ0.
• The maximum angle at which light may enter the fiber
in order to be propagated.
• Only those rays that incident on the face of the fibre at
angles less than θ0 will propagate.
• Larger AA make it easier to launch light into the fibre.
• Acceptance cone
• Expression : sin θ0 = √(n1
2-n2
2)

11. Parameters
• Fractional RI change : The fractional difference
between the refractive indices of the core and the
cladding.
Δ is << 1 and positive
• Numerical Aperture : defined as the sine of the
acceptance angle, NA = sin θ0 = n1 √(2Δ)
-NA determine the light gathering ability of the fibre.
-NA depends only on the refractive indices of the
core and cladding.
- NA ranges from 0.13 to 0.50

12. Summarizing.......
• Critical angle of TIR , φc = sin -1 n2/n1
• Critical angle of propagation, θc = cos -1 n2/ n1
• Acceptance angle, θ0 = sin -1 √(n1
2-n2
2)
• Fractional RI change,
• Numerical Aperture, NA = n1 √(2Δ)

13. Modes of Propagation
• Modes are the light ray paths along which the waves
are in phase inside the fibre or the possible number
of allowed paths of light in an optical fibre.
• All the rays contained in a beam cannot propagate,
only a limited number of rays (modes of
propagation) that can interfere constructively are
propagated.
• A light ray travelling in the guide must interfere
constructively with itself to propagate successfully.
Otherwise the destructive interference will destroy
the wave.

14. Modes of Propagation cont.......
• The reason ‘why certain modes only’ is the
phase changes to the wave fronts due to
traversed optical path length and total internal
reflection at core-cladding interface.
• Only certain reflection angles and phase
differences can give rise to the constructive
interference so that certain waves exists in the
guide – waveguide condition.
• Obtain waveguide condition and V-number

15. Modes of Propagation cont.......
• Waveguide condition :
mπ = (2π d n1 cos φm) / λ - δ2
- only those modes that obey waveguide
condition will propagate through the optical fibre.
• The no of modes propagating increases as θc and
Δ increases(NA increases).
• As core RI ↑, no of propagating modes ↑
• As cladding RI ↑ , no of propagation modes↓
• The modes that propagates at angles close to φc
or θc are higher modes, while modes with angles
larger than φc ( lower than θc ) are lower modes.
• The zero order ray travels along the axis – axial
ray

16. • Electric field distribution across the guide that is
travelling down the guide can be calculated
E(y,z,t) = 2Em(y) cos (ωt –βmz)
– For lower modes, fields are concentrated near the
centre.
– For higher modes, fields are distributed more towards
the edge of the wave guide to send light energy into
cladding.
– There are two possibilities for the electric field direction
of wave
1 . EF is perpendicular to the plane of incidence – TE
mode
2. EF is parallel to the plane of incidence – TM mode
Modes of Propagation cont.......

17. Modes of Propagation cont.......
V-number
• Imposing the condition , φm > φc on the wave guide
condition gives
m ≤ ( 2V- δ2 ) / π
V = (πd/λ)(n1
2-n2
2)1/2 - Normalised frequency
• Max no of modes in SI fibre, Nm = ½ V2
• Max no of modes in GRIN , Nm ≈ ¼ V2 for larger
values of m.
• When V is less than 2.405, only one mode is
supported ( fundamental mode , m = 0)
• That wavelength at which fibre becomes single
mode is called cut off wavelength.

18. Classification
• Based on RI profile :
1. Step Index fibre
2. Graded Index Fibre
• Based on Modes :
1. Step index single mode fibre
2. Step index multi mode fibre
3. GRIN multimode fibre
• Based on Materials :
1. Glass/Glass
2. Plastic/Plastic
3. Plastic Clad Silica (PCS)

19. Classification cont......
Based on RI profile
1. Step index fibre:
- RI of core is constant along the radial direction
and abruptly falls to a lower value at the cladding-
core boundary.
2. GRIN Fibre :
- RI of core is not constant
- varies smoothly over the diameter of the core
- Maximum value at the center
- At core-cladding interface, both the RI’s matches

20. Classification cont......
Based on Modes
1. Single Mode Step index fibre :
- Core : diameter = 8 um to 12 um
germanium doped silicon
- Cladding : diameter : 125 um
Silica lightly doped with phosphorus
- The variation of RI as a fn of radial distance
n(r) = n1 , r < a inside core
n2 , r > a in cladding
Propagation of light:
- Light travels along the axis : zero order mode
- Δ and NA are very small – low acceptance angle, so
light coupling is difficult.

21. Classification cont......
2. Multimode step index fibre:
- core diameter : 50 um to 100 um
- cladding diameter : 150 um to 250 um
Propagation of light:
- allows finite number of guided modes –
many zigzag paths of propagation
- path lengths are different for different path
- lower modes ( paths along axis ) reach the
end of the fibre earlier than other high order
modes

22. 3. GRIN ( multi mode ) Fibre :
- core diameter : 50 to 200 um
- cladding diameter : 125 to 400 um
- The variation of RI as a fn of radial distance
- n(r) = n1 √{1-2Δ(r/a)α} r < a inside core
n2 r > a in cladding
α – grading profile index number , varies from 1 to
infinity and for α=2 index profile is parabolic
Classification cont......

23. Classification cont......
Propagation of light :
- Continuous refraction is followed by TIR
- TIR take place even before core-clad interface
- The rays making larger angles with the axis
traverse longer path but they travel in a
region of lower RI and hence at a higher
speed of propagation.
- All rays reach at the output at the same time
irrespective of their modes of travel.
- The acceptance angle and NA decrease with
radial distance from the axis
- NA of GRIN = n1 √{2Δ [1- (r/a)2]}

24. Classification cont......
Based on materials
1. Glass/glass fibre
- glass core with glass cladding of lower RI
- Material : silica, RI = 1.458 at 850 nm
- SiO2 core – B2O3.SiO2 cladding
- GeO2(or P2O5).SiO2 core – SiO2 cladding
2. Plastic/plastic fibre
- Core : Perspex(PMMA)(1.49) and polysterene(1.59)
- Cladding : Fluorocarbon polymer or silicone resin
- High Δ → large NA(0.6) and θ0 (770)
- Low cost and higher mechanical flexibility
- Temperature sensitive and high loss
3. Plastic clad silica
- Core : silica – high purity quartz
- Cladding : silicone resin or teflon
- Plastic claddings are used only for step-index fibre

25. LOSSES IN OPTICAL FIBRE
• Attenuation - Loss of amplitude / optical power
– The loss of optical power as light travels down a fibre
– Defined as the ratio of the optical output power from a
fibre to the input optical power.
• Po = Pi e-αL
• Loss mechanisms for attenuation
– Intrinsic attenuation : due to substances inherently
present in the fibre.
• Material absorption :
– 3-5% attenuation
– Imperfection and impurities in the fibre ; HYDROXYL molecule
– Hydroxyl ions and transition metals ( Cu,Ni,Cr....) have electronic
absorption in and near visible part of the spectrum
– The absorption losses are minimum at around 1.3 um.

26. LOSSES IN OPTICAL FIBRE cont...................
• Rayleigh scattering :
– Accounts about 96% of attenuation in OF.
– The local microscopic density variations in glass cause local
variations in RI.
– Inherent in manufacturing. Cant eliminate.
– Any wavelength below 800 nm is unusable for optical
communication.
– Optical/transmission/low-loss window
• The band of wavelengths at which the attenuation is a
minimum.
λ(nm) Approx. Loss (dB/Km)
820-880 2.2
1200-1320 0.6
1550-1610 0.2

27. –Extrinsic attenuation : due to external forces
or bending
• Macrobending
– large scale bending that is visible.
– Bending strain affect the RI and Critical angle in that
area.
– Minimum bend radius
• Microbending
– Small scale distortion/localized .
– Imperfection in the cylindrical geometry of fiber
during the manufacturing process or installation
process.
– Not clearly visible.
LOSSES IN OPTICAL FIBRE cont...................

28. LOSSES IN OPTICAL FIBRE cont...................
• Distortion / Pulse Dispersion – change in the
shape of output spectrum
– The light pulses transmitted through the optical fibre
get broaden and spread into a wider time interval
because of the different times taken by different rays
propagation through the fibre.
– Unit : ns / km (time/distance)
– Mainly two different dispersion mechanisms, they are
1. Intermodal dispersion
2. Intramodal dispersion
– Material dispersion
– Waveguide dispersion

29. LOSSES IN OPTICAL FIBRE cont...................
1. Intermodal dispersion
– Occurs as a result of the differences in the group
velocities of the modes.
– Higher modes travels longer optical path length and
lower modes travels lesser.
– Imposes limitation on the separation between successive
pulses and thereby reduces the transmission rate and
capacity.
– Expression for total time delay due to the intermodal
dispersion in step index fibre:
Δt = L ( NA ) 2 / 2n2c
– Large NA allows more modes of propagation which will
result in greater modal dispersion.
– Does not depend upon the spectral width of the source.

30. LOSSES IN OPTICAL FIBRE cont...................
• Intramodal dispersion
– Spreading of light pulse within a single mode
– There are two main causes :
1. Material dispersion
2. Waveguide dispersion
• Material dispersion (Chromatic dispersion )
– The different wavelength components of light will
propagate at different speeds along the fibre because of
the dependence of wavelength on the RI of the material.
– Short wavelength components travel slower than long
wavelength components
– The spectral width of the source determine the extent of
dispersion.
– Expression for time delay :
Δtmat = Dmat(λ) L λ
Where Dmat(λ) = -(λ/c) d2n/dλ2 Material dispersion coefficient

31. LOSSES IN OPTICAL FIBRE cont...................
• Waveguide dispersion
– Arises from the guiding (not on material ) properties of
the fibre.
– Even if n1 and n2 were wavelength independent(no
material dispersion), there will be waveguide
dispersion by virtue of group velocity depending on V-
number and V depending on the wavelength.
– A spectrum of source wavelengths will result in
different V-numbers for each source wavelength and
hence different propagation velocities.
– Expression fro time delay :
Δtw = Dw(λ) L λ
Dw is the waveguide dispersion coefficient

32. LOSSES IN OPTICAL FIBRE cont...................
• Total dispersion introduced by an OF is given by
the root mean square value of all the three
dispersions :
(Δt)T = √ [(Δt)2
intermodal+ (Δt)2
mat + (Δt)2
w ]
• In MMF, all the three pulse dispersion exists
while in SMF, only material and waveguide
dispersion.
• GRIN fibre can reduce the problem of intermodal
dispersion.

33. Applications
1. Used for illumination and short distance
transmission of images.
– A large no of fibres whose ends are bound
together, ground and polished, form flexible
bundles.
– If the relative positions of the fibre terminations at
both the ends are not the same, they are called
incoherent bundle - Flexible light carriers.
– If the relative positions of the fibre terminations at
both the ends are same, they are called coherent
bundle - Flexible image carriers.(Endoscope)

34. Application cont........
2.Used as waveguides in telecommunications.
- Fibre optic communication system:
- three major components : transmitter, optical
fibre and receiver
-Transmitter = driving circuit + light sources
(LED or Laser diodes)
- Receiver : photodetectors
-OF Communication systems can be classified
into two : LAN and Long haul communication

35. Application cont........
3.Used in fabricating a new family of sensors
• Fibre optic sensors
- transducers
- consist of a light source coupled with an
optical fibre and a light detector
- Used to measure pressure, temperature,
strain, acoustic field, magnetic field, etc.
• Temperature sensors, Displacement sensors,
Force sensors, Liquid level detectors

36. Merits of O F
1. Cheaper
2. Smaller in size, lighter in weight, flexible
3. Not hazardous
4. Immune to EMI and RFI
5. No cross talk
6. Wider bandwidth
– 1 mm OF can transmit 50,000 calls
7. Low loss per unit length
– Repeaters are spaced about 100 km

37. Applications
• Optical communications
• Medical applications
• Military applications
• Illumination and image transmission
– Endoscopes

38. Fibre Optic Communication System
• Transmitter : converts electrical signal to light signals.
• Optical fibre
• Receiver : captures the signals at the other end of the
fiber and converts them to electrical signals.

39. CONCLUSION
• Optic fibre
• Structure
• Parameters :
– Critical angle of TIR
– Critical angle of Propagation
– Acceptance angle
– Numerical Aperture
– Fractional RI change
– V-Number
• Modes of propagation
• Types of Optical fibre
• Loss mechanisms – attenuation and dispersion
• Applications – OF communication system ; sensors
• Merits of O F