1. Chapter 2 Optical Fibers: Structures, Waveguiding & Fabrication

2. Theories of Optics
Light is an electromagentic phenomenon described by the same theoretical principles that govern all forms of electromagnetic radiation.
Maxwell’s equations are in the heart of electromagnetic theory & is fully successful in providing treatment of light propagation.
Electromagnetic optics provides the most complete treatment of light phenomena in the context of classical optics.
Turning to phenomena involving the interaction of light & matter, such as emission & absorption of light
quantum theory provides the successful explanation for light-matter interaction. These phenomena are described by quantum electrodynamics which is the marriage of electromagnetic theory with quantum theory.
For optical phenomena, this theory also referred to as quantum optics. This theory provides an explanation of virtually all optical phenomena.

3. Fiber Structure A Core Carries most of the light, surrounded by
a Cladding, Which bends the light and confines it to the core, covered by a primary buffer coating which provides mechanical protection, covered by a secondary buffer coating, which protects primary coating and the underlying fiber.
Lecture 2

4. Wavelength & free space
Wavelength is the distance over which the phase changes by
In vacuum (free space):
[2-10]
[2-11]
Permeability : نفاذية
Permittivity: سماحية
In electromagnetism, permeability is the measure of the ability of a material to support the formation of a magnetic field within itself. Hence, it is the degree of magnetization that a material obtains in response to an applied magnetic field. Magnetic permeability is typically represented by the Greek letter μ. The term was coined in September 1885 by Oliver Heaviside. The reciprocal of magnetic permeability is magnetic reluctivity.

5. Refractive index Refractive index of a medium is defined as:
[2-12]
Relative magnetic permeability
Relative electric permittivity
In electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how much electric field (more correctly, flux) is 'generated' per unit charge in that medium. More electric flux exists in a medium with a low permittivity (per unit charge) because of polarization effects. Permittivity is directly related to electric susceptibility, which is a measure of how easily a dielectric polarizes in response to an electric field. Thus, permittivity relates to a material's ability to resist an electric field (while unfortunately the word stem "permit" suggests the inverse quantity).

6. Permeability vs. Permittivity
In electromagnetism, permeability is the measure of the ability of a material to support the formation of a magnetic field within itself.
Hence, it is the degree of magnetization that a material obtains in response to an applied magnetic field.
Magnetic permeability is typically represented by the Greek letter μ.
The reciprocal of magnetic permeability is magnetic reluctivity.
In electromagnetism, permittivity is the measure of the resistance that is encountered when forming an electric field in a medium.
In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium.
The permittivity of a medium describes how much electric field (more correctly, flux) is 'generated' per unit charge in that medium.
More electric flux exists in a medium with a low permittivity (per unit charge)
Thus, permittivity relates to a material's ability to resist an electric field (while unfortunately the word "permit" suggests the inverse quantity).

7. Some Refractive Indices
Medium
Air
Water
Glass
Diamond
Refractive Index
1.003
1.33
2.42

8. Laws of Reflection & Refraction
Part is reflected and part is refracted
Reflection law: angle of incidence=angle of reflection
Snell’s law of refraction:
[2-18]
Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

9. Total internal reflection, Critical angle2 1
>
Incident
light
Transmitted
(refracted) light
Reflected k t
TIR
Evanescent wave i r ( a ) b c
Light wave travelling in a more dense medium strikes a less dense medium. Depending on
the incidence angle with respect to
, which is determined by the ratio of the refractive
indices, the wave may be transmitted (refracted) or reflected. (a)
(b)
(c)
and total internal reflection (TIR).
Critical angle
Evanescent : زائل
Dept of ECE, SJBIT Page 20
1. The refractive index of first medium must be greater than the refractive index of second one.
2. The angle of incidence must be greater than (or equal to) the critical angle.
[2-19]

12. Phase shift due to TIR
The totally reflected wave experiences a phase shift however which is given by:
Where (p,N) refer to the electric field components parallel or normal to the plane of incidence respectively.
[2-20]

13. Optical waveguiding by TIR: Dielectric Slab Waveguide
Propagation mechanism in an ideal step-index optical waveguide.
Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

14. Launching optical rays to slab waveguide
[2-21]
Maximum entrance angle, is found from
the Snell’s relation written at the fiber end face.
[2-22]
Numerical aperture:
Slab: مكون من طبقات
[2-23]
[2-24]
Relative refractive index difference

17. OPTICAL FIBER TYPES
Optical fibers are characterized by their structure and by their properties of transmission. Basically, optical fibers are classified into two types.
The first type is single mode fibers.
The second type is multimode fibers

18. Single Mode Fibers
The core size of single mode fibers is small. The core size (diameter) is typically around 8 to 10 micrometers.
A fiber core of this size allows only the fundamental or lowest order mode to propagate around a 1300 nanometer (nm) wavelength.

19. Multimode Fibers
As their name implies, multimode fibers propagate more than one mode. Multimode fibers can propagate over 100 modes. The number of modes propagated depends on the core size and numerical aperture (NA).
As the core size and NA increases, the number of modes increases. Typical values of fiber core size and NA are 50 to 100 micrometer and 0.20 to 0.29, respectively.

20. Multimode Fibers
This gives single mode fiber higher bandwidth compared to multimode fiber.
Some disadvantages of single mode fiber are smaller core diameter makes coupling light into the core more difficult.
Precision required for single mode connectors and splices are more demanding.

21. Step Index (SI) Fiber
The step index (SI) fiber is a cylindrical waveguide core with central or inner core has a uniform refractive index of n1 and the core is surrounded by outer cladding with uniform refractive index of n2.
The cladding refractive index (n2) is less than the core refractive index (n1).
But there is an abrupt change in the refractive index at the core cladding interface.
Refractive index profile of step indexed optical fiber is shown in Fig
The refractive index is plotted on horizontal axis and radial distance from the core is plotted on vertical axis.

22. Step Index (SI) Fiber
The core typically has diameter of μm and the cladding has a diameter of 125 μm.

23. Graded Index (GRIN) Fiber
The graded index fiber has a core made from many layers of glass.
In the graded index (GRIN) fiber the refractive index is not uniform within the core,
it is highest at the center and decreases smoothly and continuously with distance towards the cladding.
The refractive index profile across the core takes the parabolic nature. Fig shows refractive index profile of graded index fiber.

24. Graded Index (GRIN) Fiber

25. Graded Index (GRIN) Fiber
In graded index fiber the light waves are bent by refraction towards the core axis and they follow the curved path down the fiber length.
This results because of change in refractive index as moved away from the center of the core.
A graded index fiber has lower coupling efficiency and higher bandwidth than the step index fiber.
It is available in 50/125 and 62.5/125 sizes.
The 50/125 fiber has been optimized for long haul applications and has a smaller NA and higher bandwidth.
62.5/125 fiber is optimized for LAN applications which is costing 25% more than the 50/125 fiber cable.

26. Graded Index (GRIN) Fiber
Profile parameter α determines the characteristic refractive index profile of fiber core. The range of refractive index as variation of α is shown in Fig

27. Types Of Optical Fiber Light ray n1 core n2 cladding
Single-mode step-index fibre
no air
n1 core
n2 cladding
Multimode step-index fibre
no air
Variable n
Multimode graded-index fibre
Index porfile

28. Different Structures of Optical Fiber
The size of Core/Cladding determines Modal type
Single mode : source must be laser
MM: source can be LED
LED<Laser in terms of power
MM has intermodal dispersion disadvantage
MM means different speeds, which means the modes will spread over time ( dispersion)
Sol: Use graded index fiber
Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

29. Step Index Fiber Step Index Fiber Core: Glass Cladding: Glass, Plastic
Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000
Core: Glass
Cladding: Glass, Plastic
Step Index Fiber

30. Single-Mode Step Index Fiber
The Core diameter is 8 to 9mm
Bandwidth range 100GHz-Km
Goal: To minimize the signal distortion

31. Single mode Step index Fiber
Single-mode step-index fiber: has a central core that is sufficiently small so that there is essentially only one path for light ray through the cable.
The light ray is propagated in the fiber through reflection.
Typical core sizes are 2 to 15 μm.
Single mode fiber is also known as fundamental or monomode fiber.

32. Single mode Step index Fiber
Single mode fiber will permit only one mode to propagate and does not suffer from mode delay differences.
These are primarily developed for the 1300 nm window
but they can be also be used effectively with time division multiplex (TDM) and wavelength division multiplex (WDM) systems operating in 1550 nm wavelength region.

33. Single mode Step index Fiber
The core fiber of a single mode fiber is very narrow compared to the wavelength of light being used.
Therefore, only a single path exists through the cable core through which light can travel. \
Usually, 20 percent of the light in a single mode cable actually travels down the cladding
disadvantage of this type of cable is that because of extremely small size interconnection of cables and interfacing with source is difficult.
Another disadvantage of single mode fibers is that as the refractive index of glass decreases with optical wavelength, the light velocity will also be wavelength dependent. Thus the light from an optical transmitter will have definite spectral width.

34. Multimode Step Index Fiber
Core diameter range from mm
Light propagate in many different ray paths, or modes, hence the name multimode
Index of refraction is same all across the core of the fiber
Bandwidth range MHz
Lecture 2

35. Multimode Step Index Fiber
Multimode step index fiber is more widely used type.
It is easy to manufacture.
Its core diameter is 50 to 1000 μm i.e. large aperture and allows more light to enter the cable.
The light rays are propagated down the core in zig-zag manner.
There are many paths that a light ray may follow during the propagation.
The light ray is propagated using the principle of total internal reflection (TIR). Since the core index of refraction is higher than the cladding index of refraction, the light enters at less than critical angle is guided along the fiber.

36. Multimode Step Index Fiber
Light rays passing through the fiber are continuously reflected off the glass cladding towards the centre of the core at different angles and lengths, limiting overall bandwidth.
The disadvantage of multimode step index fibers is that the different optical lengths caused by various angles at which light is propagated relative to the core, causes the transmission bandwidth to be fairly small.
Because of these limitations, multimode step index fiber is typically only used in applications requiring distances of less than 1 km.

37. Multimode Graded Index Fiber
The core size of multimode graded index fiber cable is varying from 50 to 100 μm range.
The light ray is propagated through the refraction.
The light ray enters the fiber at many different angles.
As the light propagates across the core toward the center it is intersecting a less dense to more dense medium.
Therefore the light rays are being constantly being refracted and ray is bending continuously.
This cable is mostly used for long distance communication.

38. Multimode Graded Index Fiber
The light rays no longer follow straight lines, they follow a path being gradually bent back towards the center by the continuously declining refractive index.
The modes travelling in a straight line are in a higher refractive index so they travel slower than the serpentine modes.
This reduces the arrival time disparity because all modes arrive at about the same time.

39. Multimode Graded Index Fiber
Fig shows the light trajectory in detail.
It is seen that light rays running close to the fiber axis with shorter path length, will have a lower velocity
because they pass through a region with a high refractive index.

40. Multimode Graded Index Fiber

41. Multimode Graded Index Fiber
Rays on core edges offers reduced refractive index, hence travel more faster than axial rays and cause the light components to take same amount of time to travel the length of fiber, thus minimizing dispersion losses.
Each path at a different angle is termed as ‘transmission mode’
The NA of graded index fiber is defined as the maximum value of acceptance angle at the fiber axis.
Typical attenuation coefficients of graded index fibers at 850 nm are 2.5 to 3 dB/km, while at 1300 nm they are 1.0 to 1.5 dB/km.

42. Multimode Graded Index Fiber
The index of refraction across the core is gradually changed from a maximum at the center to a minimum near the edges, hence the name “Graded Index”
Bandwidth ranges from 100MHz-Km to 1GHz-Km
The gradual decrease in the core's refractive index from the center of the fiber causes propagating modes to be refracted many times.
Multimode graded-index fibers have less MODAL DISPERSION than multimode step-index fibers.
Lower modal dispersion means that multimode graded-index fibers have higher bandwidth capabilities than multimode step-index fibers.
Lecture 2

43. MM-graded-Index
The gradual decrease in the core's refractive index from the center of the fiber causes propagating modes to be refracted many times.
Multimode graded-index fibers have less MODAL DISPERSION than multimode step-index fibers.
Lower modal dispersion means that multimode graded-index fibers have higher bandwidth capabilities than multimode step-index fibers.

44. Advantage of MM over SM
1) The larger core radius makes it easier to launch optical power into the fiber and facilitate the connecting together of similar fibers.
2) Another advantage: is that light can be launched using LED source; but SM must use laser.
Although LED’s have less optical power than laser, they are easier to make, less expensive, require less complex circuitry, and have longer lifetimes.

45. Disadvantage of MM They suffer from intermodal dispersion.
When an optical pulse is launched into a fiber, the optical power in the pulse is distributed over all the modes of the fiber. Each of the modes that can propagate in a MM fiber travels at slightly different velocity. This means that the modes in a given optical pulse arrive at the fiber end at slightly different times, thus causing the pulse to spread out in time as it travels along the fiber.
This can be solved using graded index fiber

46. Normalized frequency for Fiber

47. Modes in MM Step Index Fiber
2*pi*40*1.48*sqrt(2*1.5/100)/850/ *

48. Multi-Mode Operation
Total number of modes, M, supported by a multi-mode fiber is approximately (When V is large) given by:
Power distribution in the core & the cladding: Another quantity of interest is the ratio of the mode power in the cladding, to the total optical power in the fiber, P, which at the wavelengths (or frequencies) far from the cut-off is given by:
[2-36]
لازم تعطيه
[2-37]

49. Modes in graded index Fiber
Alpha=2

50. Modes in graded index Fiber: Cont
Alpha >1

51. Multi Mode Fiber

52. Single-Mode Fibers .
V=2.4

53. Multi mode

59. ii)M=420
Check in class

61. Single Mode Fibers
In single mode fibers, V is less than or equal to When V = 2.405, single mode fibers propagate the fundamental mode down the fiber core, while high-order modes are lost in the cladding.
For low V values (<1.0), most of the power is propagated in the cladding material. Power transmitted by the cladding is easily lost at fiber bends. The value of V should remain near the level.
لازم تعطيه

62. Fiber Loss & Dispersion
dB/Km at 1.3mm
- 0.2 dB/Km at 1.5mm
- Minimum Reduction Expected in future is 0.01dB/Km
Fiber Dispersion
-Material dispersion
- Waveguide Dispersion
- Multimode group Delay Dispersion
لازم تعطيه
Lecture 3

63. General Optical Fiber Communication System
Basic block diagram of optical fiber communication system consists of following important blocks.
1. Transmitter
2. Information channel
3. Receiver.

64. General Optical Fiber Communication System
Message origin :Generally message origin is from a transducer that converts a non-electrical message into an electrical signal.
Common examples include microphones for converting sound waves into currents and
video (TV) cameras for converting images into current.
Modulator : The modulator has two main functions.
It converts the electrical message into the proper format.
It impresses this signal onto the wave generated by the carrier source.
Two distinct categories of modulation are used
i.e. analog modulation and digital modulation.
Carrier source : Carrier source generates the wave on which the information is transmitted.
This wave is called the carrier.
For fiber optic system, a laser diode (LD) or a light emitting diode (LED) is used.
They can be called as optic oscillators, they provide stable, single frequency waves with sufficient power for long distance propagation.

65. General Optical Fiber Communication System
Channel coupler :
Coupler feeds the power into the information channel.
the channel coupler is a lens used for concentrating the light emitted by the source and directing this light towards the receiver.
The coupler must efficiently transfer the modulated light beam from the source to the optic fiber.
The channel coupler design is an important part of fiber system because of possibility of high losses.
Information channel :
The information channel is the path between the transmitter and receiver.
In fiber optic communications, a glass or plastic fiber is the channel.
Desirable characteristics of the information channel include low attenuation and large light acceptance cone angle.
Optical amplifiers boost the power levels of weak signals.
Amplifiers are needed in very long links to provide sufficient power to the receiver.
Another important property of the information channel is the propagation time of the waves travelling along it.
A signal propagating along a fiber normally contains a range of optic frequencies along several ray paths.
This results in a distortion of the propagating signal. In a digital system, this distortion appears as a spreading and deforming of the pulses.
The spreading is so great that adjacent pulses begin to overlap and become unrecognizable as separate bits of information.

66. General Optical Fiber Communication System
Optical detector :
In the fiber system the optic wave is converted into an electric current by a photodetector.
The current developed by the detector is proportional to the power in the incident optic wave.
Detector output current contains the transmitted information.
This detector output is then filtered to remove the constant bias and then amplified.
The important properties of photodetectors are
small size,
economy,
long life,
low power consumption,
high sensitivity to optic signals and
fast response to quick variations in the optic power.
Signal processing :
Signal processing includes filtering and amplification.
Proper filtering maximizes the ratio of signal to unwanted power.
The bit error rate (BER) should be very small for quality communications.
Message output :
The electrical form of the message emerging from the signal processor are transformed into a sound wave or visual image.

67. Cut-off Wavelength
One important transmission parameter for single mode fiber is cut-off wavelength as it distinguishes the single mode and multimode regions.
The range of cut-off wavelength recommended to avoid modal noise and dispersion problems is : 1100 to 1280 nm (1.1 to 1.28μm) for single mode fiber at 1.3 μm.
The cut-off wavelength λc can be computed from expression of normalized frequency: