1. Optical fiber communication uses optical fibers to transmit data as light signals. Optical fibers have advantages over metallic wires like larger bandwidth and lower transmission losses.
2. Light propagation in optical fibers is based on the principles of total internal reflection. Light rays entering the fiber at an angle lower than the critical angle undergo total internal reflection.
3. Electromagnetic mode theory treats light as an electromagnetic wave rather than rays. Different modes of propagation exist depending on the fiber structure. The fundamental mode in cylindrical fibers is the LP01 mode.
2. Overview:
COMMUNICATION: Process of transmission of data from one point to another.
Communication is of 2 types.
Wired:- a transmission medium is used. Examples: telephone, Cable T.V., etc…
Wireless:- no transmission medium is used. Example: Cellular
Wired Transmission Medium: Metallic Wires and Optical fibers.
Wireless Transmission Medium: air, Vacuum.
COMMUNICATION
WIRED OR
GUIDED
WIRELESS
OR
UNGUIDED
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3. Optical Fiber Communication
Communication type: Wired
Transmission Medium used: Optical Fiber
Type of Signal: Light / optical signal
Frequency Range: 120 THz to 375 THz
Wavelength Range: 800 nm to 2.5μm
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4. Advantages of using Optical Fibers
1. Large Bandwidth
2. Small size and weight
3. Electrical isolation
4. Immunity to interference and crosstalk
5. Signal security
6. Low transmission losses
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6. Basic Optical Terminologies (Ray Theory
Transmission)
1. REFRACTIVE INDEX: Ratio of velocity of light in vacuum to the velocity of light in a medium.
2. REFLECTION: Light being transmitted in the same medium of incidence.
3. REFRACTION: Light being transmitted into another medium.
4. CRITICAL ANGLE: a particular angle of incidence for which the refracted ray grazes the boundary
of the medium.
5. SNELL’S LAW: n1sinϕ1=n2sinϕ2
6. For Critical Angle: 𝜙 𝑐 = sin−1 𝑛2
𝑛1
7. TOTAL INTERNAL REFLECTION:
8. MERIDIONAL RAY: Ray entering the fiber at the axis.
9. SKEW RAY: Ray entering the fiber except at the axis.
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7. Ray Theory Transmission
ACCEPTANCE CONE: cone of light which the fiber can transmit.
ACCEPTANCE ANGLE: max angle to the axis of the fiber at which light enters the fiber and TIR
takes place. Denotation: θA.
NUMERICAL APERTURE: Light gathering ability of a fiber
NA=sinθA= 𝑛1
2
− 𝑛2
2
=𝑛1 2∆
Where: ∆=
𝑛1
2−𝑛2
2
𝑛1
2 =Relative Refractive Index difference.
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10. ElectroMagnetic Mode Theory of
Transmission
Instead considering the light as a ray, consider it as a Wave, an Electromagnetic Wave.
Then EM theory must be applied as Geometry is not applicable.
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11. ElectroMagnetic Mode Theory of
Transmission
Wave propagation in a PLANAR WAVEGUIDE: 𝛻2
𝜑 =
1
𝑣 𝑝
2
𝜕2 𝑦
𝜕𝑥2 is the “Scalar Wave Equation”.
From Maxwell’s EM Equation:
𝛻2 𝐸 = 𝜇𝜀
𝜕2 𝐸
𝜕𝑡2
𝛻2 𝐻 = 𝜇𝜀
𝜕2 𝐻
𝜕𝑡2
Comparing the above equations: 𝑐 =
1
𝜇0 𝜀0
The solution of the scalar wave equation:
𝜑 = 𝜑0 𝑒 𝑗(𝜔𝑡−𝑘 𝑟)
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12. ElectroMagnetic Mode Theory of
Transmission
𝜑 = 𝜑0 𝑒 𝑗(𝜔𝑡−𝑘 𝑟)
Here:
• ω=angular Frequency of the field
• r=coordinates of the field plane
• k=propagation constant of the vacuum.
𝑘 =
2𝜋
𝜆
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13. ElectroMagnetic Mode Theory of
Transmission
Modes in the Planar Waveguide:
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MODES: The distribution of field along the coordinate axis and observed
wrt the direction of propagation.
Mode 0 (m=0) Mode 1 (m=1)
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14. ElectroMagnetic Mode Theory of
Transmission
Extra Concept
PHASE VELOCITY:
◦ Velocity at which each wave travels.
𝑣 𝑝 =
𝜔
𝛽
GROUP VELOCITY:
◦ The velocity at which the whole wave travels
𝑣𝑔 =
𝑑𝜔
𝑑𝛽
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15. Goos-Hänchen Effect or Goos-
Hänchen Shift
Lateral displacement in the light beam.
Easy analysis using ray theory.
First observed by
◦ Fritz Goos
◦ Hildae Hänchen
Very small practically nearly 0.06μm to 0.1μm
for a light wave of wavelength 0.55μm
Can be ignored practically.
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17. Cylindrical Fibers
It is a circular form of a planar waveguide.
Generally contains 3 layers:
◦ Core
◦ Cladding
◦ Protective sheath
These are known to us as “OPTICAL FIBER
CABLES”
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18. Modes in a Cylindrical Fiber
Planar guide are bound in 1D where as Circular
guides are bound in 2D.
2 integers are requires=d to specify the mode:
◦ l =maxima's along the circumference (cuts)
◦ m =maxima's along the radius (rings)
For Meridional ray: TElm and TMlm modes.
For other rays: HElm and EHlm.
HE: more H-field than E-field.
EH: more E-field than H-field.
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NOTE:
LPlm = HE2m , TE0m, TM0m.
LPlm (l≠0,1) = HEl+1,m , Ehl-1,m.
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21. 21
The Fundamental mode in Cylindrical
Fiber is LP01 mode.
The fundamental LP01mode has the
Bessel function up to the range
where the J0(r) crosses the x-axis.
Hence LP01 mode has the cutoff
frequency of 2.405.
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22. Mode Coupling
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Thus individual modes do not normally
propagate throughout the length of the
fiber without large energy transfers to
adjacent modes, even when the fiber is
exceptionally good quality and is not
strained or bent by its surroundings.
This mode conversion is known as mode
coupling or mixing.
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23. Step Index Fiber
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𝑛 𝑟 =
𝑛1; 𝑟 < 𝑎 (𝑐𝑜𝑟𝑒)
𝑛2; 𝑟 ≥ 𝑎 (𝑐𝑙𝑎𝑑𝑑𝑖𝑛𝑔)
𝑀𝑠 =
𝑉2
2
The total number of guided modes or
Mode volume:
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24. Graded Index Fiber
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𝑛 𝑟 =
𝑛1 1 − 2∆
𝑟
𝑎
𝛼
; 𝑟 < 𝑎 (𝑐𝑜𝑟𝑒)
𝑛1 1 − 2∆= 𝑛2; 𝑟 ≥ 𝑎 (𝑐𝑙𝑎𝑑𝑑𝑖𝑛𝑔)
𝑀𝑔 =
𝛼
𝛼 + 2
𝑉2
2
The total number of guided modes or
Mode volume:
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27. Single Mode Fiber
Advantage: less signal dispersion caused due to delay difference between different modes.
Must be designed to allow propagation of only one mode. Fundamental Mode LP01.
Hence, limit of V-Number of LP01 mode is 0 ≤ 𝑉 ≤ 2.405.
V-Number can be adjusted:
◦ By manipulating core radius
◦ By manipulating the relative RI (Δ)
V-number for Graded Mode fiber in Single mode: 𝑉𝑐 = 2.405 1 +
2
𝛼
◦ If α=2, Vc increases by 2
◦ If α=1, Vc increases by 3
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28. Single Mode Fiber
Problem Associated: Modal Power Dispersion
◦ Ex: when V>1.4, half of the modal power extends into the cladding.
◦ Also called Modal Dispersion.
Practically, cladding diameter: order of 50μm to avoid attenuation >1dB/km when additional
losses arise like micro-bending.
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29. Single Mode Fiber
Characteristics:
1. Exhibits greater B.W.
2. Lowest losses while transmission.
3. Superior transmission quality doe to absence of noise.
4. Easily can be upgraded in future.
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31. Single Mode Fiber:
Mode Field Diameter (MFD)
An important character that takes in account the wavelength dependent field penetration into
the cladding.
For step index and parabolic graded fibers operating near the Cutoff wavelength, it is similar to a
Gaussian distribution.
MFD is taken at the points where the amplitude of the distribution is
1
𝑒
of the maximum
amplitude value.
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𝑀𝐹𝐷 = 2𝜔0
Where ω0=Mode field
radios or spot size.
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32. Single Mode Fiber: Effective R.I.
Propagation phase constant: 𝛽 =
2𝜋
𝜆
⟹ 𝜆01 =
2𝜋
𝛽
Effective R.I. is also known as Phase index or NORMALISED PHASE CHANGE COEFFICIENT.
𝜂 𝑒𝑓𝑓 =
𝛽
𝑘
Where 𝑘 =
2𝜋
𝜆
=vacuum phase constant
Hence
𝜆01 =
𝜆
𝜂 𝑒𝑓𝑓
W.K.T, 𝑛2 𝑘 ≤ 𝛽 ≤ 𝑛1 𝑘 , 𝑡ℎ𝑒𝑛 𝑛2 < 𝑛 𝑒𝑓𝑓 < 𝑛1
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