2. Course Learning Rationale (CLR):
The purpose of learning this course is to:
• Analyze the basic laws and theorems of light associated with the optical
fiber communication and the classification of optical fibers.
• Address concepts related to transmission characteristics such as attenuation
and dispersion.
• Explore the fundamentals of optoelectronics display devices, Sources and
Detectors.
• Gain to information on Optical modulators and amplifiers
• Illustrate the integration methods available for optoelectronic circuits and
devices
• Utilize the basic optical concepts applied in various engineering problems
and identify appropriate solutions
3. Course Learning Outcomes (CLO):
• Review the basic theorems related to fiber optic
communication, and attain knowledge of types of optical
fibers.
• Understand the optical signal distortion factors in optical fiber
communication.
• Familiarize the principle and operation of various display
devices, light sources and detectors.
• Acquire knowledge of various optoelectronic modulators and
amplifiers.
• Understand the various optoelectronic integrated circuits.
• Acquire fundamental concepts related to optical
communication and optoelectronic devices
4. UNIT I-Introduction to Optical Fibers
Evolution of fiber optic system-Elements of an
optical fiber transmission link-Advantages of
fiber optic system-Characteristics and behavior
of light-Total internal reflection-Acceptance
angle-Numerical aperture, Critical angle-Solving
Problems-Ray optics-Types of rays-Optical fiber
modes-Optical fiber configurations-Single mode
fibers-Multimode Fibers-Step Index Fibers-
Graded Index Fibers
5. Learning Resources
1. Gerd Keiser, “Optical Fiber Communications”, 5th Edition,
McGraw Hill Education (India), 2015.
2. Khare R P, “Fiber Optics and Optoelectronics”, Oxford
University Press, 2014.
3.J. Wilson and J. Hawkes, “Optoelectronics – An Introduction”,
Prentice Hall, 1995.
4. Pallab Bhattacharya, “Semiconductor Optoelectronic Devices”,
Prentice Hall of India Pvt. Ltd, 2006.
6. Evolution of communication system
• Principle interests of human beings has been to devise communication
systems for sending messages from one distant place to another.The
fundamental elements of any such communication system is shown Fig 1-1
• Information source-inputs message to transmitter
• Transmitter –couples message to transmission channel
• Channel- medium bridging distance between transmitter and receiver.
Types: 1)guided: wire/waveguide
• 2) Unguided: atmospheric/space channel.
• Signal while traversing through channel, it may be attenuated and distorted
with distance
• Receiver- Extract weakened and distorted signal from channel, amplify it
and restore to original form
7. FORMS OF COMMUNICATION SYSTEM
Motive:
• to improve fidelity,
• increase data rate so more information could be send
• Increase transmission distance between relay stations.
Evolution:
• Before 19th century-use of fire signal by greeks in 8th century B.C for sending
alarms, calls for help or announcements of certains events.
• 150B.c.-optical signals were encoded relation to alphabet ,so any message could
be sent
Limitations: eye used as receiver, LOS transmission paths required.
• Telegraph _Samuel.F.B.Morse in 1838 (1844-commercial telegraph implemented)
• Used wire cables for information transmission-High frequency carriers used –
bandwidth increased so as information capacity.
Applications:Televeision,Radar,Microwavelink
• Transmission media used :millimeter and microwave waveguide,metallic wires
• Another part of EM spectrum is optical range 50nm(ultraviolet)to about
100Micrometer(far infrared),visible spectrum (400nm to 700nm)band.
8. Evolution of Fiber optic system
• Advent of laser (coherent source)in 1960 paved way for this system.
• Optical frequency is 5x10^14Hz, information capacity is 10^5 times
greater than microwave system(~10 million TV channels)
• Unguided limitations: atmospheric channel by rain,fog,snow and dust
make high-speed carrier system economically unattractive in view of
present demand of channel capaciy.
• It covers only short-distance(up to 1 km)
• Optical fiber-more reliable and versatile optical channel than atmosphere,
but extremely large loss(more than 1000dB/km) made them impractical
• Losses due to impurities in fiber material. In 1970, silica fiber having
20dB/km attenuation was fabricated. Later attenuation reduced to
0.16dB/km at 1550-num
• Development of optical fiber system grew from combination of
semiconductor technology(gives light sources and photo detectors and
optical waveguide technology)
10. Elements of an optical fiber transmission
link
• Information Input:
• The information input may be in any of the several
physical forms, e.g., voice, video, or data.
• Therefore an input transducer is required for
converting the non-electrical input into an electrical
input.
• For example, a microphone converts a sound signal
into an electrical current, a video camera converts an
image into an electric current or voltage, and so on.
• In situations where the fiber-optic link forms a part of a
larger system, the information input is normally in
electrical form.
11. • Transmitter:
• The transmitter (or the modulator, as it is often called) comprises
an electronic stage which (i) converts the electric signal into the
proper form and (ii) impresses this signal onto the electromagnetic
wave (carrier) generated by the optoelectronic source.
• The modulation of an optical carrier may be achieved by employing
either an analog or a digital signal.
• An analog signal varies continuously and reproduces the form of
the original information input, whereas digital modulation involves
obtaining information in the discrete form.
• In the latter, the signal is either on or off, with the on state
representing a digital 1 and the off state representing a digital 0.
12. • The number of bits per second (bps) transmitted is called
the data rate.
• If the information input is in the analog form, it may be
obtained in the digital form by employing an analog-to-
digital converter.
• Analog modulation is much simpler to implement but
requires higher signal-to noise ratio at the receiver end as
compared to digital modulation.
• Further, the linearity needed for analog modulation is not
always provided by the optical source, particularly at high
modulation frequencies.
• Therefore, analog fiber-optic systems are limited to shorter
distances and lower bandwidths
13. • Optoelectronic Source
• An optoelectronic (OE) source generates an electromagnetic wave in the
optical range (particularly the near-infrared part of the spectrum), which
serves as an information carrier.
• Common sources for fiber-optic communication are the light-emitting
diode (LED) and the injection laser diode (ILD).
• Ideally, an optoelectronic source should generate a stable single-frequency
electromagnetic wave with enough power for long haul transmission.
• However, in practice, LEDs and even laser diodes emit a range of
frequencies and limited power.
• The favorable properties of these sources are that they are compact,
lightweight, consume moderate amounts of power, and are relatively easy
to modulate.
• Furthermore, LEDs and laser diodes which emit frequencies that are less
attenuated while propagating through optical fibers are available.
14. • Channel Couplers:
• In fiber-optic systems, the function of a coupler is
to collect the light signal from the optoelectronic
source and send it efficiently to the optical fiber
cable.
• However, the coupling losses are large owing to
Fresnel reflection and limited light-gathering
capacity of such couplers.
• At the end of the link again a coupler is required
to collect the signal and direct it onto the
photodetector.
15. • Fiber-optic Information Channel
• In communication systems, the term ‘information channel’ refers to
the path between the transmitter and the receiver.
• In fiber-optic systems, the optical signal traverses along the cable
consisting of a single fiber or a bundle of optical fibers.
• An optical fiber is an extremely thin strand of ultra-pure glass
designed to transmit optical signals from the optoelectronic source
to the optoelectronic detector.
• In its simplest form, it consists of two main regions: (i) a solid
cylindrical region of diameter 8–100 mm called the core and (ii) a
coaxial cylindrical region of diameter normally 125 mm called the
cladding.
16.
17. • The refractive index of the core is kept greater than that of
the cladding. This feature makes light travel through this
structure by the phenomenon of total internal reflection.
• In order to give strength to the optical fiber, it is given a
primary or buffer coating of plastic, and then a cable is
made of several such fibers.
• This optical fiber cable serves as an information channel.
• For clarity of the transmitted information, it is required that
the information channel should have low attenuation for
the frequencies being transmitted through it and a large
light-gathering capacity.
18. • Repeater
• As the optical signals propagate along the length of the
fiber, they get attenuated due to absorption, scattering,
etc., and broadened due to dispersion.
• After a certain length, the cumulative effect of attenuation
and dispersion causes the signals to become weak and
indistinguishable.
• Therefore, before this happens, the strength and shape of
the signal must be restored.
• This can be done by using either a regenerator or an optical
amplifier, e.g., an erbium-doped fiber amplifier (EDFA), at
an appropriate point along the length of the fiber
19. • Optoelectronic Detector
• The reconversion of an optical signal into an electrical
signal takes place at the OE detector.
• Semiconductor p-i-n or avalanche photodiodes are
employed for this purpose.
• The photocurrent developed by these detectors is
normally proportional to the incident optical power
and hence to the information input.
• The desirable characteristics of a detector include small
size, low power consumption, linearity, flat spectral
response, fast response to optical signals, and long
operating life
20. • Receiver
• For analog transmission, the output photocurrent of the detector is
filtered to remove the dc bias that is normally applied to the signal in the
modulator module, and also to block any other undesired frequencies
accompanying the signal.
• After filtering, the photocurrent is amplified if needed.
• These two functions are performed by the receiver module.
• For digital transmission, in addition to the filter and amplifier, the receiver
may include decision circuits.
• If the original information is in analog form, a digital-to analog converter
may also be required.
• The design of the receiver is aimed at achieving high sensitivity and low
distortion.
• The signal-to-noise ratio (SNR) and bit-error rate (BER) for digital
transmission are important factors for quality communication.
21. • Information Output
• Finally, the information must be presented in a form
that can be interpreted by a human observer.
• For example, it may be required to transform the
electrical output into a sound wave or a visual image.
Suitable output transducers are required for achieving
this transformation.
• In some cases, the electrical output of the receiver is
directly usable.
• This situation arises when a fiber-optic system forms
the link between different computers or other
machines.
22. ADVANTAGES OF FIBER-OPTIC
SYSTEMS
Long Distance Transmission
Optical fibers have lower transmission losses compared to copper wires. Consequently data can be
sent over longer distances, thereby reducing the number of intermediate repeaters needed to
boost and restore signals in long spans.
This reduction in equipment and components decreases system cost and complexity.
Large Information Capacity
Optical fibers have wider bandwidths than copper wires, so that more information can be sent over
a single physical line.
This property decreases the number of physical lines needed for sending a given amount of
information.
Small Size and Low Weight
The low weight and the small dimensions of fibers offer a distinct advantage over heavy, bulky wire
cables in crowded underground city ducts or in ceiling-mounted cable trays.
This feature also is of importance in aircraft, satellites, and ships where small, low weight cables are
advantageous, and in tactical military applications where large amounts of cable must be unreeled
and retrieved rapidly
23. • Immunity to Electrical Interference
An especially important feature of an optical fiber relates to the fact that it is a dielectric material,
which means it does not conduct electricity.
This makes optical fibers immune to the electromagnetic interference effects seen in copper wires,
such as inductive pickup from other adjacent signal-carrying wires or coupling of electrical noise
into the line from any type of nearby equipment.
• Enhanced Safety
Optical fibers offer a high degree of operational safety because they do not have the problems of
ground loops, sparks, and potentially high voltages inherent in copper lines.
However, precautions with respect to laser light emissions need to be observed to prevent possible
eye damage.
• Increased Signal Security
An optical fiber offers a high degree of data security because the optical signal is well-confined
within the fiber and an opaque coating around the fiber absorbs any signal emissions.
This feature is in contrast to copper wires where electrical signals potentially could be tapped off
easily. Thus optical fibers are attractive in applications where information security is important,
such as financial, legal, government, and military systems
24.
25. • A variety of fiber types with different performance
characteristics exist for a wide range of applications.
• To protect the glass fibers during installation and
service, there are many different cable configurations
depending on whether the cable is to be installed
inside a building, underground in ducts or through
direct-burial methods, outside on poles, or under
water.
• Very low-loss optical connectors and splices are
needed in all categories of optical fiber networks for
joining cables and for attaching one fiber to another
26. • The installation of optical fiber cables can be either aerial, in ducts,
undersea, or buried directly in the ground.
• The cable structure will vary greatly depending on the specific
application and the environment in which it will be installed.
• Owing to installation and/or manufacturing limitations, individual
cable lengths for inbuilding or terrestrial applications will range
from several hundred meters to several kilometers.
• Practical considerations such as reel size and cable weight
determine the actual length of a single cable section.
• The shorter segments tend to be used when the cables are pulled
through ducts.
• Longer lengths are used in aerial, direct-burial, or underwater
applications
27. • Workers can install optical fiber cables by pulling or blowing them through
ducts (both indoor and outdoor) or other spaces, laying them in a trench
outside, plowing them directly into the ground, suspending them on poles,
or laying or plowing them underwater.
• Although each method has its own special handling procedures, they all
need to adhere to a common set of precautions.
• These include avoiding sharp bends of the cable, minimizing stresses on
the installed cable, periodically allowing extra cable slack along the cable
route for unexpected repairs, and avoiding excessive pulling or hard yanks
on the cable.
• For direct-burial installations a fiber optic cable can be plowed directly
underground or placed in a trench that is filled in later.
• Figure illustrates a plowing operation that may be carried out in nonurban
areas.
• The cables are mounted on large reels on the plowing vehicle and are fed
directly into the ground by means of the plow mechanism
28.
29. • Transoceanic cable lengths can be many thousands of kilometers long and include
periodically spaced (on the order of 80–120 km) optical repeaters to boost the signal level.
• The cables are assembled in onshore factories and then are loaded into special cable-laying
ships, as illustrated in Figure
30. optical fiber
• An optical fiber (or fibre) is a flexible, transparent fiber made
by drawing glass (silica) or plastic to a diameter slightly thicker than
that of a human hair.
• Optical fibers are used most often as a means to transmit
light between the two ends of the fiber and find wide usage in fiber-
optic communications, where they permit transmission over longer
distances and at higher bandwidths (data transfer rates) than
electrical cables.
• Fibers are used instead of metal wires because signals travel along
them with less loss; in addition, fibers are immune
to electromagnetic interference, a problem from which metal wires
suffer.
• Fibers are also used for illumination and imaging, and are often
wrapped in bundles so they may be used to carry light into, or
images out of confined spaces, as in the case of a fiberscope.
• Specially designed fibers are also used for a variety of other
applications, some of them being fiber optic sensors and fiber lasers.
31.
32. Optical fiber structure
• Optical fibers typically include a core surrounded by a
transparent cladding material with a lower index of refraction.
• Light is kept in the core by the phenomenon of total internal
reflection which causes the fiber to act as a waveguide.
• Fibers that support many propagation paths or transverse
modes are called multi-mode fibers, while those that support a
single mode are called single-mode fibers (SMF).
• Multi-mode fibers generally have a wider core diameter and
are used for short-distance communication links and for
applications where high power must be transmitted.
34. Characterisitcs and Behaviour of light
• Fiber optics technology involves the emission, transmission,
and detection of light let us discuss the nature of light.
• Two methods usually used to describe how optical fiber guides
light.
• Geometrical or ray optics concepts of light: reflection and
refraction to provide a picture of the propagation mechanisms.
• Electromagnetic wave approach: where light is treated as an
EM wave which propagates along the optical fiber
waveguide.(This involves maxwell’s equation subject to
cylindrical boundary conditions of fiber.)
35. The nature of light
• Until 17th century, it is believed that light consists of a stream of minute particles
that are emitted by luminous sources.
• Particles travel in straight line , and assumed to penetrate transparent but reflected
from opaque ones.
• Described large-scale optical effects like reflection and refraction, but failed to
explain interference and diffraction.
• Diffraction explanation given by Fresnel in 1815 could be interpreted on
assumption that light is a wave motion.
• In 1864, Maxwell theorized that light waves must be electromagnetic in nature.
• After observation of polarization effects indicated that light waves are
transverse(that is, the wave motion is perpendicular to the direction in which the
wave travels).
• In wave or physical optical view point EM waves radiated by small optical source
can be represented by train of spherical wave front(locus of all points in the wave
train which have the same phase).
• If wavelength of light is smaller than object(or opening ) which it encounters, the
wavefront appears as straight lines to this object or opening. In this case, light wave
can be represented as a plane wave, and its direction of travel can be indicated by
light ray which is perpendicular to the phase front.
36.
37. REVIEW OF FUNDAMENTAL LAWS OF OPTICS
• In free space, light travels at a speed of c=3*10^8m/s.
• Speed of light related to frequency v wavelength λ by
c=v λ
• The most important optical parameter of any
transparent medium is its refractive index n.
• It is defined as the ratio of the speed of light in vacuum
(c) to the speed of light in the medium (v).
n=c/v
As v is always less than c, n is always greater than 1.
Values of n are (1.00 for air, 1.33 for water, 1.50 for glass
, and 2.42 for diamond)
38.
39. • The concepts of reflection and refraction can be
interpreted most easily by considering the behavior of light
rays associated with plane waves traveling in a dielectric
material.
• When a light ray encounters a boundary separating two
different media, part of the ray is reflected back into the
first medium and the remainder is bent (or refracted) as it
enters the second material.
• The bending or refraction of the light ray at the interface is
a result of the difference in the speed of light in two
materials that have different refractive indices.
• The relationship at the interface is known as Snell’s law
40. Snell’s law.
• The phenomenon of refraction of light at the
interface between two transparent media of
uniform indices of refraction is governed by
Snell’s law.
• Consider a ray of light passing from a medium of
refractive index n1 into a medium of refractive
index n2 [Assume that n1 > n2 and that the angles
of incidence and refraction with respect to the
normal to the interface are, respectively, Φ1 and
Φ2.Then, according to Snell’s law
41.
42. • As n1 > n2, if we increase the angle of incidence
Φ1, the angle of refraction Φ2 will go on
increasing until a critical situation is reached,
when for a certain value of Φ1 = Φc, Φ2 becomes
π /2, and the refracted ray passes along the
interface.
• This angle Φ1 = Φc is called the critical angle.
• If we substitute the values of Φ1 = Φc and Φ2 = π /2 in
Eq ,
• we see that n1sin Φc = n2sin(π /2) = n2
• Thus sin Φc = n2/n1
43. • If the angle of incidence Φ1 is further increased
beyond Φc, the ray is no longer refracted but is
reflected back into the same medium. This is
ideally expected.
• This is called total internal reflection. It is this
phenomenon that is responsible for the
propagation of light through optical fibers.
• In practice, however, there is always some
tunnelling of optical energy through this
interface. The wave carrying away this energy is
called the evanescent wave.
44. • According to law of reflection the angle at which
incident ray strikes the interface is exactly equal to
the angle the reflected ray makes with the same
interface.
• Incident ray, normal to the interface, reflected ray all
lie in the same plane, which is perpendicular to the
interface plane between two materials.
• When light traveling in certain medium is reflected
off an optically denser material (one with high
refractive index), its called external reflection.
• Conversely, reflection of light off of less optically
dense material (such as light traveling in glass being
reflected at a glass-to-air interface) is called internal
reflection.
45. Condition required for total internal reflection can be determined by using
snell’s law.
47. Problems
• Problem 1
• Consider the interface between a glass slab
with n1 = 1.48 and air for which n2 = 1.00.
What is the critical angle for light traveling in
the glass?
48. • Solution
sin Φc = n2/n1
Φc=sin-1(n2/n1)
Φc =sin-1(1/1.48)
Φc = sin-1(0.678)
Φc = 42.5o
Thus any light ray traveling in the glass that is
incident on the glass–air interface at a normal angle
Φ1 greater than 42.5° is totally reflected back into
the glass.
49. • Problem 2
• A light ray traveling in air (n1 = 1.00) is incident
on a smooth, flat slab of crown glass, which
has a refractive index n2 = 1.52. If the
incoming ray makes an angle of Φ1 = 30.0°
with respect to the normal, what is the angle
of refraction Φ2 in the glass?
50. • Solution
From Snell’s law
n1sin Φ1 = n2sin Φ2
sin Φ2= (n1/n2)sin Φ1
sin Φ2= (1/1.52)sin30o
sin Φ2= 0.658x0.5=0.329
Φ2 = sin-1(0.329)=19.2o
51. To Practice….
• An unknown glass has an index of refraction
of n=1.5 . For a beam of light originated in the
glass, at what angles the light 100% reflected
back into the glass. (The index of refraction of
air is nair=1.00).
53. Acceptance Angle
● Acceptance angle is the maximum angle with
the axis of the Optical Fiber at which the light
can enter into the optical fiber in order to be
propagated through it.Fig shows the
propagation of light in a fiber.
54. ● Consider the light ray propagate in an optical fibre.
● The incident ray AO enters into core at an angle θ0 to
fibre axis. Let n1, n2 and no be the refractive indices of
the core, cladding and surroundings.
● Applying Snell’s law of refraction at the point O we have
𝑛0 sin 𝜃0 = 𝑛1 sin 𝜃r---------------------
--.>1
sin 𝜃0 = n1/n0 sin 𝜃r --------------------
-- 2
sin 𝜃0 = n1/n0( 1 − 𝑐𝑜𝑠2 𝜃r)---------
--3
55. ● At the point B on the interface of core and cladding,
● Angle of incidence 𝜃𝑐 = 90 − 𝜃r
● Applying Snell’s law of refraction at the point B we have
𝑛1 sin(90˚ − 𝜃𝑟) = 𝑛2 sin 90˚-----------------4
𝑛1 cos 𝜃𝑟 = 𝑛2---------------------5
cos 𝜃𝑟 = n2 / n1-----------------6
Substituting equation (6) in equation (3) we have
sin 𝜃0 = n1 / n0 (√1 − 𝑛2
2 / 𝑛1
2)------7
sin 𝜃0 = n1 / n0 (√ (𝑛1
2 − 𝑛2
2) / 𝑛1
2)------8
sin 𝜃0 = (n1 / 𝑛1 n0) (√ (𝑛1
2 − 𝑛2
2))------9
sin 𝜃0 =(√ (𝑛1
2 − 𝑛2
2)/ n0 ------10
56. The medium surrounding the fibre is air, then no = 1 then eq 10 becomes
sin 𝜃0 =(√ (𝑛1
2 − 𝑛2
2)------11
Acceptance angle 𝜃0 = sin-1(√ (𝑛1
2 − 𝑛2
2)------12
Numerical Aperature NA= sin 𝜃0 -------------------13
Acceptance angle 𝐬𝐢𝐧 𝜽o < 𝑵𝑨
The maximum angle at or below which a ray of light can enter through
one end of the fibre still be total internal reflection is called as
acceptance angle. The cone is referred as acceptance cone.
Numerical Aperture (NA) Sine of the acceptance angle of the fibre is
known as numerical aperture. It denotes the light gathering capability of
the optical fibre
Numerical Aperature NA= sin 𝜃0
Fractional Index Change (Δ) 𝑁𝐴 = sin 𝜃0 It is the ratio of refractive index
difference in core and cladding to the refractive index of core.
57. Numerical Aperture
● Numerical aperture in case of optical fiber
communication can be defined as- "The light
gathering (collecting) capacity of an optical
fibre".
● The numerical aperture provides important
relationship between acceptance angle and the
refractive index of the core and cladding
58.
59. Problem 1:
● The Refractive Indices of core and cladding are 1.50 and 1.48 respectively in an
Optical Fiber. Find the Numerical Aperture and Acceptance Angle
60. Problem 1:
The Refractive Indices of core and cladding are 1.50 and 1.48 respectively in an Optical Fiber.Find the Numerical Aperture and Acceptance Angle
61. Problem 2
● An Optical Fiber has a core material with refractive index 1.55 and its cladding
material has a refractive index of 1.50.The Light is launched into it in air. Calculate its
numerical aperture, the acceptance angle and also fractional index change
62. 2.An Optical Fiber has a core material with refractive index 1.55 and its cladding material has a refractive index of 1.50.The Light is
launched into it in air.Calculate its numerical aperture,the acceptance angle and also fractional index change
63.
64. Ray Optics
● Optics is the study of light and its interaction with matter.
● Light is visible electromagnetic radiation, which transports energy and
momentum (linear and angular) from source to detector.
● Photonics includes the generation, transmission,
modulation,amplification,frequency conversion and detection of light.
● Ray optics is the simplest theory of light. Rays travel in optical media
according to a set of geometrical rules; hence ray optics is also called
geometrical optics.
● Ray optics is an approximate theory, but describes accurately a variety of
phenomena.
● Ray optics is concerned with the locations and directions of light rays, which
carry photons and light energy (They also carry momentum, but the
direction of the momentum may be different from the ray direction).
● It is useful in describing image formation, the guiding of light, and energy
transport.
65. Postulates of Ray Optics
1. Light travels in the form of rays .Rays are emitted by light
sources, and can be observed by light detectors.
2. An optical medium (through which rays propagate) is
characterized by a real scalar quantity n ≥ 1, called the
refractive index. The speed of light in vacuum is c = 3 ×
108m/s.The speed of light in a medium is v = c/n; this is the
definition of the refractive index. The time taken by light to
cover a distance d is t = nd/c; it is proportional to nd, which
is called the optical path length.
66. Postulates of Ray Optics
3. In an inhomogeneous medium, the refractive index n(r) varies with
position; hence the optical path length OPL between two points A and B
is
where ds is an element of length along the path. The time t taken by light
to
go from A to B is t = OPL/c.
67. Postulates of Ray Optics
4.Light rays between the points A and B follow a path such that
the time of travel, relative to neighboring paths, is an extremum
(minimum). This means that the variation in the travel time, or,
equivalently,in the optical path lenght, is zero. That is,
Usually, the extremum is a minimum; then light rays travel along
the path of least time. If there are many paths with the
minimum time, then light rays travel along all of these
simultaneously.
68. Types of Rays
Rays that Interact with surfaces
● An incident ray is a ray of light that strikes a surface. The
angle between this ray and the perpendicular or normal to
the surface is the angle of incidence
● The reflected ray corresponding to a given incident ray, is the
ray that represents the light reflected by the surface. The
angle between the surface normal and the reflected ray is
known as the angle of reflection. The Law of Reflection says
that for a specular (non-scattering) surface, the angle of
reflection is always equal to the angle of incidence.
69. Types of rays
● The refracted ray or transmitted ray corresponding to a given incident
ray represents the light that is transmitted through the surface. The
angle between this ray and the normal is known as the angle of
refraction, and it is given by Snell's Law. Conservation of energy
requires that the power in the incident ray must equal the sum of the
power in the refracted ray, the power in the reflected ray, and any
power absorbed at the surface
● If the material is birefringent, the refracted ray may split into ordinary
and extraordinary rays, which experience different indexes of
refraction when passing through the birefringent material.
70. Types of rays
● Meridional rays are rays that pass through the axis of the optical fiber. Meridional rays
are used to illustrate the basic transmission properties of optical fibers.
● The second type is called skew rays. Skew rays are rays that travel through an optical fiber
without passing through its axis.
● Meridional rays can be classified as bound or unbound rays. Bound rays remain in the core
and propagate along the axis of the fiber.
● Bound rays propagate through the fiber by total internal reflection. Unbound rays are
refracted out of the fiber core.
● Figure shows a possible path taken by bound and unbound rays in a step-index fiber. The
core of the step-index fiber has an index of refraction n1.
● The cladding of a step-index has an index of refraction n2 that is lower than n1.
● Figure assumes the core-cladding interface is perfect.
● However, imperfections at the core-cladding interface will cause part of the bound rays to
be refracted out of the core into the cladding.
● The light rays refracted into the cladding will eventually escape from the fiber. In general,
meridional rays follow the laws of reflection and refraction.
71.
72. Skew Rays
● Skew rays are rays that travel through an optical fiber without
passing through its axis.
● Skew rays are those rays which follow helical path but they are not
confined to a single plane. Skew rays are not confined to a particular
plane so they cannot be tracked easily.
● Skew rays propagate without passing through the center axis of the
fiber. The acceptance angle for skew rays is larger than the
acceptance angle of meridional rays.
● Skew rays are often used in the calculation of light acceptance in an
optical fiber. The addition of skew rays increases the amount of light
capacity of a fiber.
● The addition of skew rays also increases the amount of loss in a fiber.
Skew rays tend to propagate near the edge of the fiber core. A large
portion of the number of skew rays that are trapped in the fiber core
are considered to be leaky rays.
74. Types of rays
Optical systems
● The marginal ray (sometimes known as
an a ray or a marginal axial ray) in an
optical system is the meridional ray
that starts at the point where the
object crosses the optical axis, and
touches the edge of the aperture stop
of the system. Marginal rays are the
rays which passes through the
maximum aperture of the spherical
mirror. This means that they have a
Max angle with the principal axis.
75. Types of rays
● The principal ray or chief ray (sometimes known as
the b ray) in an optical system is the meridional ray
that starts at the edge of the object, and passes
through the center of the aperture stop
● Sagittal ray or transverse ray
● Paraxial ray
● Parabasal ray
76. Total Internal Reflection Problems
• Problem (1): An unknown glass has an index of refraction of n=1.5 . For a
beam of light originated in the glass, at what angles the
light 100% reflected back into the glass. (The index of refraction of air
is nair=1.00).
77. Total Internal Reflection Problems
Consider the optical fiber from Fig . The index of refraction of the inner
core is 1.480 , and the index of refraction of the outer cladding is 1.44.
A. What is the critical angle for the core-cladding interface?
B. For what range of angles in the core at the entrance of the fiber (q2) will the
light be completely internally reflected at the core-cladding interface?
C. What range of incidence angles in air does this correspond to?
D. If light is totally internally reflected at the upper edge of the fiber, will it
necessarily be totally internally reflected at the lower edge of the fiber
(assuming edges are parallel)?
78.
79.
80.
81. UNIT I - S7,S8,S9- Topics
Optical fiber modes, Optical fiber
configurations, Single mode fibers, Multimode
Fibers, Step Index Fibers, Graded IndEX FIBERS
82. Optical fiber modes
• Optical fiber is classified into 2 categories
1. Number of modes
– Single Mode Fiber (SMF)
– Multi Mode Fiber (MMF)
2. Refractive Index
– Step Index (Single mode/ Multimode)
– Graded Index
84. Single mode fiber
• Only one mode can propagate through the fiber
• Core diameter (5um) and high cladding diameter (70um)
• Difference between the R.I of core and cladding is very
small.
• There is neither dispersion nor degradation therefore it is
suitable for long distance communication.
• Light is passed through the single mode fiber through laser
diode.
85. Multimode fiber
• Allows large number of modes for light ray travelling
through it.
• Core diameter is 40un and Cladding is 70um
• The relative refractive index is larger than single mode fiber.
• Due to multimode dispersion, signal degradation takes
place.
• Not suitable for long distance communication due to large
dispersion and attenuation.
88. Single mode step index fiber
• A single mode or monomode step index
fiber allows the propagation of only one traverse
electromagnetic mode and hence the core
diameter must be of the order of 2 µm to 10µm.
It has high information carrying capacity.
89.
90. Multi mode Step Index fiber
• The Refractive index for core and cladding are
constant.
• The light ray propagate through it in the form of
meridional rays which cross the fiber axis during
every reflection at the core cladding boundary.
93. Multimode Graded Index fiber
• Fiber core has a non-uniform refractive index that
gradually decreases from the center towards the core
cladding interface.
• Cladding has uniform Refractive index,
• Light rays propagate through it in the form of helical rays.
