UNIT 4

LASERS AND FIBRE OPTICS

Q.1  Differentiate between spontaneous and stimulated emissions.

Solution:-

Q.2  What is LASER? Discuss basic phenomena involved in producing laser light?

Solution:-

LASER stands for “Light Amplification by Stimulated Emission of Radiation”.

L = Light

A = Amplification (by)

S = Stimulated

E = Emission (of)

R = Radiation

Theodore H. Maiman of the Hughes Research Laboratory, California, was the first scientist who experimentally demonstrated laser by flashing light through a ruby crystal in 1960. But the basic idea behind the development of laser was given by the great scientist “Albert Einstein” in 1917.

Let us discuss Einstein’s theory of the interaction of electromagnetic radiation with matter. He proposed that electromagnetic radiation interacts with matter in the following three steps.

• Stimulated Absorption
• Spontaneous Emission
• Stimulated Emission

Stimulated Absorption:

Let E1 and E2 be the energies of the ground and excited states of an atom. Suppose, if a photon of energy hν= E1− E2 interacts with an atom present in the ground state, the atom gets excitation from ground state E1 to excited state E2. This process is called stimulated absorption. Stimulated absorption rate depends upon the number of atoms available in the lowest energy state as well as the energy density photons.

Stimulated absorption rate ∝ Number of atoms in the ground state

∝ The density of photons Spontaneous emission

Spontaneous Emission:

Let E1 and E2 be the energies of the ground and excited states of an atom. Suppose, if a photon of energy hν= E1− E2 interacts with an atom present in the ground state, the atom gets excitation from ground stateE1 to excited state E2. The excited atom does not stay a long time in the excited state. The excited atom gets de-excitation after its lifetime by emitting a photon of energy hν= E1− E2. This process is called spontaneous emission. Also Spontaneous means by its own. Here excited atom comes to the ground state on its own so it is named as spontaneous emission.

The spontaneous emission rate depends upon the number of atoms present in the excited state.

Spontaneous emission ∝ rate number of atoms in the excited state

Stimulated Emission: 

This phenomenon is responsible for producing laser light. Let E1and E2 be the energies of the ground and excited states of an atom. Suppose, if a photon of energy hν= E1− E2 interacts with an atom present in the ground state, the atom gets excitation from ground stateE1 to excited state E2. Let, a photon of energy hν= E1− E2 interacts with the excited atom within their lifetime; the atom gets de-excitation to the ground state by emitting another photon. These photons have the same phase and it follows coherence. This phenomenon is called stimulated emission.

Stimulated emission rate depends upon the number of atoms available in the excited state as well as the energy density of photons.

Stimulated emission rate ∝ number of atoms in the excited state

∝ Density of photons

Q.3  Discuss Properties of Laser?

Solution:-

• The laser is a powerful source of light having extraordinary properties that are not found in normal light sources like tungsten lamps, mercury lamps, etc.
• The unique property of a laser is that its light waves travel very long distances with e very little divergence. Whereas the conventional source of light can travel very short distances only.
• A high degree of directionality and monochromatic is also associated with these laser light beams. Therefore, in a laser beam, the light waves not only are in the same phase but also have the same colour throughout their journey.
• The beam of the ordinary light spreads out very quickly. On the other hand, the laser beam is highly collimated and spreads very little.
• The spread of laser light on the surface of the moon is only about 3 km across. Hypothetically, if ordinary light was able to travel to the so moon, its beam would have fanned out to such an extent leading to a diameter of the light on the moon as much as 40, 000 km.
• Another remarkable feature of laser is the concentration of its energy to extremely high intensities, the intensity remaining almost constant over long distances because of low divergence.
• If a laser beam with a power of a few megawatts is focused by a lens at a spot with a diameter of 1/1000th of a centimeter. the beam intensity increases to a few hundred billion watts per sq. Cm. This concentrated energy is so intense that it easily ionizes the atmospheric air to create sparks. When the beam is focused from a high power laser, even the hardest material like a diamond can be melted in a fraction of a second.

Q.4  Derive Einstein’s coefficient A and B?

Solution:-

The distribution of atoms in the two energy levels will change by absorption or emission of radiation. Einstein introduced three empirical coefficients to quantify the change of population of the two levels. Let N1 be the number of atoms per unit volume with energy E1 and N2 be the number of atoms per unit volume with energy E2. Let ‘n’ be the number of photons per unit volume at frequency ‘υ’ such that hυ= E1− E2.

Then, the energy density of photons ρ(υ) = nhυ

When these photons interact with atoms, both upward (absorption) and downward (emission) transition occurs.

At the equilibrium, the upward transitions must be equal to downward transitions.

Upward Transition

Stimulated absorption rate depends upon the number of atoms available in the lowest energy state as well as the energy density photons.

We have seen above that

Stimulated absorption rate ∝ N1 i.e. Number of atoms in the ground state

∝ ρ(υ) i.e. Density of photons spontaneous emission

Stimulated absorption rate = B12N1ρ(υ)………(1)

Where B12 is the Einstein coefficient of stimulated absorption.

Downward transition

The spontaneous emission rate depends upon the number of atoms present in the excited state.

Spontaneous emission rate ∝ N2 i.e. number of atoms in the excited state

Spontaneous emission rate = A21N2 ………(2)

Where A21 is the Einstein coefficient of spontaneous emission.

Stimulated emission rate depends upon the number of atoms available in the excited state as well as the energy density of photons.

Stimulated emission rate ∝ N2 i.e. number of atoms in the excited state

∝ ρ(υ) i.e. Density of photons

Stimulated emission rate = B21N2ρ(υ)………(3)

If the system is in equilibrium the upward transitions must be equal to downward transitions.

Upward transitions = downward transitions

B12N1ρ(υ) = A21N2 + B21N2ρ(υ)………(4)

B12N1ρ(υ) - B21N2ρ(υ) = A21N2

(B12N1- B21N2) ρ(υ) = A21N2

ρ(υ) =………(5)

Divide with B21N2 in numerator and denominator in the right side of the above equation,

ρ(υ) = = ………(6)

ρ(υ) = = =………(7)

We know from Maxwell Boltzmann distribution law

= ………(8)

And also from Planck’s law, the radiation density

ρ(υ) = ………(9)

Comparing the two equations (7) and (9)

= and =1………(10)

The above relations are referred to as Einstein relations.

From the above equation for non-degenerate energy levels, the stimulated emission rate is equal to the stimulated absorption rate at the equilibrium condition.

= ………(11)

Q.5  What is the relationship between B21 and B12?
a) B12 > B21
b) B12 < B21
c) B12 = B21
d) No specific relation
 

Solution:-

C is the correct answer.
B21 is the coefficient for the stimulated emission while B12 is the coefficient for stimulated absorption. Both the processes are mutually reverse processes and their probabilities are equal. Therefore, B12 = B21.

Q.6  How laser light get amplify by population inversion?

Solution:-

Population inversion

Definition

The number of atoms present in the excited state or higher energy state is greater than the number of atoms present in the ground state or lower energy state is called population inversion.

Population inversion as the name suggests that this is an inverted phenomenon. In general, the lower energy level is more populated which means it has more number atoms in the lower energy level as compared to a higher energy level. But by pumping we will obtain a state when the number of atoms present in the higher energy state is greater than the number of atoms present in the lower energy state.

Let us consider a two-level energy system of energies E1 and E2 as shown in the figure.

Let N1 and N2 be the populations that mean several atoms per unit volume of energy levels E1 and E2 respectively.

According to Boltzmann’s distribution the population of an energy level E, at temperature T is given by

Ni=N0

Where N0 is the population of the lower level or ground state and k is Boltzmann’s constant.

From the above relation, the population of energy levels E1 and E2 are

N1=N0

N2=N0

At ordinary conditions N1 >N2 i.e., the population in the ground or lower state is always greater than the population in the excited or higher states. The stage of making, the population of higher energy level is greater than the population of lower energy level is called population inversion i.e. N1 < N2

When the population inversion method is used to enforce more and more atoms to give up photons. This initiates a chain reaction and releasing a massive amount of energy.

This results in a rapid build-up of the energy of emitting one particular wavelength traveling coherently in a fixed direction. This process is called amplification by stimulated emission using population inversion.

This population inversion situation is essential for laser action. For any stimulated emission, the upper energy level or metastable state must have a long lifetime, i.e., the atoms should pause at the metastable state for more time than at the lower level.

Q.7  What is Pumping?  Discuss the various type of pumping mechanisms?

Solution:-

For laser action, the pumping mechanism (exciting with external source) maintain a higher population of atoms in the upper energy level relative to that in the lower level.

A system in which population inversion is achieved is called an active system. The method of raising the particles from a lower energy state to a higher energy state is called pumping.

The process of achieving population inversion is called pumping.

This can be done in several ways.

The most commonly used pumping methods are

1. Optical pumping
2. Electrical discharge pumping
3. Chemical pumping
4. Thermal Pumping
5. Injection current pumping
6. Inelastic Atom-Atom Collisions

Optical pumping As the name suggests, in this method, light is used to supply energy to the laser medium. Optical pumping is used in solid laser. Xenon flash tubes are used for optical pumping. Since these materials have very broadband absorption, a sufficient amount of energy is absorbed from the emission band of the flash lamp and population inversion is created. So xenon flash lamp is used to produce more electrons in the higher energy level of the laser medium.

Examples of optically pumped lasers are ruby, Nd: YAG Laser(Neodymium: Yttrium Aluminum Garnet).

Electrical discharge pumping is used in gas lasers. Since gas lasers have a very narrow absorption band pumping then any flash lamp is not possible. Electric discharge refers to the flow of electrons or electric current through a gas, liquid, or solid.

In this method of pumping, electric discharge acts as the pump source or energy source. A high voltage electric discharge (flow of electrons, electric charge, or electric current) is passed through the laser medium or gas. The intense electric field accelerates the electrons to high speeds and they collide with neutral atoms in the gas. As a result, the electrons in the lower energy state gains sufficient energy from external electrons and jumps into the higher energy state

 Examples of Electrical discharge pumped lasers are He-Ne laser, CO2 laser, argon-ion laser, etc.

Chemical pumping Chemical reaction may also result in excitation and hence the creation of population inversion in a few systems.

 If an atom or a molecule is produced through some chemical reaction and remains excited at the time of production, then it can be used for pumping. The hydrogen fluoride molecule is produced in an excited state when hydrogen and fluorine gas chemically combine. The number of produced excited atoms or molecules is greater than the number of normal state atoms or molecules. Thus, population inversion is achieved.

Examples H2 + F2 → 2HF, in this chemical reaction, hydrogen (H2) and fluorine (F2) molecules are chemically combined to produce hydrogen fluoride molecule (2HF) in an excited state.

Thermal Pumping: Sometimes we can achieve population inversion by heating the laser medium. In thermal pumping, heat acts as the pump source or energy source. In this method, population inversion is achieved by supplying heat into the laser medium.

When heat energy is supplied to the laser medium, the lower energy state electrons gain sufficient energy and jumps into the higher energy level.

The process of achieving population inversion in thermal pumping is almost similar to the optical pumping or electric discharge method, except that in this method heat is used as a pump source instead of light or electric discharge.

Injection current pumping In semiconductors, injection of current through the junction results in creates of population inversion among the minority charge carriers.

Examples of such systems are InP and GaAs.

Inelastic Atom-Atom Collisions: Like the electric discharge method, here also a high voltage electric discharge acts as a pump source. However, in this method, a combination of two types of gases, say X and Y are used. The excited state of gas X is represented as X+ whereas gas Y is represented as Y+. Both X and Y gases have the same excited states (X+ and Y+).

When high voltage electric discharge passes through a laser medium having two types of gases X and Y, the lower energy state electrons in gas X will move to the exciting state X+ similarly the lower energy state electrons in gas Y moves to the excited state Y+.

Initially, during electric discharge, the lower energy state electrons in gas X or atom X gets excited to X+ due to continuous collision with electrons. The excited state electrons in gas X+ now collide with the lower energy state electrons in gas Y. As a result, the lower energy state electrons in gas Y gains sufficient energy and jump into the exciting state Y+. This method is used in the Helium-Neon (He-Ne) laser.

Q.8  Discuss the construction, working, and application of Solid-State Laser?

Or

Discuss the construction, working, and application of Ruby Laser?

Or

Discuss three-level laser?

Solution:-

Ruby laser

Ruby laser is a three-level solid-state laser and was constructed by Maiman in 1960. Ruby laser is one of the few solid-state lasers that produce visible light. It emits deep red light of wavelength 694.3 nm.

Construction

A ruby laser consists of three important elements: laser medium, the pump source, and the optical resonator.

Laser Medium

Ruby (Al2O3+Cr2O3) is a crystal of Aluminium oxide, in which 0.05% of Al+3 ions are replaced by the Cr+3 ions. The colour of the rod is pink. The active medium or laser medium in the ruby rod is Cr+3 ions. In ruby laser, 4cm length and 5mm diameter rod is generally used. The ruby has good thermal properties.

The pump source

The ruby rod is surrounded by a xenon flash tube, which provides the pumping light to excite the chromium ions into upper energy levels. The ruby rod was surrounded by a helical xenon flash lamp.

We know that population inversion is required to achieve laser emission. Population inversion is the process of achieving a greater population of a higher energy state than the lower energy state. To achieve population inversion, we need to supply energy to the laser medium i.e. to ruby crystal.

Xenon flash tube emits thousands of joules of energy in few milliseconds, but only a  part of that energy is utilized by the chromium ions while the rest energy heats the apparatus. A cooling arrangement is provided to keep the experimental set up at normal temperatures.

Optical resonator

Both the ends of the rods are highly polished and made strictly parallel. The ends are silvered in such a way, one becomes partially reflected the laser beam was emitted through that end and the other end fully reflected to reflect all the rays of light striking it.

Working of ruby laser:

Consider a ruby laser medium consisting of three energy levels E1, E2, E3 with N number of electrons.

We assume that the energy levels will be E1 < E2 < E3. The energy level E1 is known as the ground state or lower energy state, the energy level E2 is known as the metastable state, and the energy level E3 is known as the pump state.

Let us assume that initially most of the electrons are in the lower energy state (E1) and only a tiny number of electrons are in the excited states (E2 and E3).

The energy level diagram of chromium ions is shown in the figure. The chromium ions get excitation into higher energy levels by absorbing 5500Å of wavelength radiation. The excited chromium ions stay in the level E3 for a short interval of time (10-8 to 10-9 Sec). After their life, most of the chromium ions are de-excited from E3 to E1 and a few chromium ions are de-excited from E3 to E2.

The transition between E3 and E2 is non-radioactive i.e. the chromium ions give their energy to the lattice in the form of heat. In the Metastable state, the lifetime of chromium ions is 10-3 sec. The lifetime of chromium ions in the Metastable state is 105 times greater than the lifetime of chromium ions in a higher state.

Due to the continuous working of the flash lamp, the chromium ions are excited to a higher state E3 and returned to the E2 level. After a few milliseconds, the level E2 is more populated than the level E1 and hence the desired population inversion is achieved. The state of population inversion is not a stable one. The process of spontaneous transition is very high. When the excited chromium ion passes spontaneously from E3 to E2it emits one photon of wavelength 6943 Å. The photon reflects back and forth by the silver ends and until it stimulates an excited chromium ion in the E2 state and it to emit a fresh photon in phase with the earlier photon. The process is repeated again and again until the laser beam intensity is reached a sufficient value. When the photon beam becomes sufficiently intense, it emerges through the partially silvered end of the rod. The wavelength 6943 Å is

Drawbacks of the ruby laser

• The laser requires high pumping power
• The efficiency of a ruby laser is very small
• It is a pulse laser

 Application of ruby laser

• Ruby lasers are in optical photography
• Ruby lasers can be used for the measurement of plasma properties such as electron density and temperature.
• Ruby lasers are used to remove the melanin from the skin.
• Ruby laser can be used for the recording of holograms.

Q.9  Discuss the construction, working, and application of gas Laser?

Or

Discuss the construction, working, and application of He-Ne Laser?

Or

Discuss four-level laser?

Solution:-

He-Ne Laser

The first He-Ne gas laser was fabricated in 1961 by Ali Javan, Bennett, and Herriott at Bell Telephone Laboratories. Others. Helium-Neon laser is a type of gas laser in which a mixture of helium and neon gas is used as a gain medium. Helium-Neon laser is also known as He-Ne laser. The helium-neon laser was the first continuous-wave laser ever constructed. The helium-neon laser operates at a wavelength of 632.8 nanometres (nm), in the red portion of the visible spectrum.

Ruby laser is a pulse laser, even it has high intense output. For continuous laser beams, gas lasers are used. Using gas lasers, we can achieve high coherence, high directionality, and high monochromaticity beam. The output power of the gas laser is generally in few milliwatts.

CONSTRUCTION

The helium-neon laser consists of three essential components:

• Pump source (high voltage power supply)
• Gain medium (laser glass tube or discharge glass tube)
• Resonating cavity

Pump source

The gain medium of a helium-neon laser is made up of a mixture of helium and neon gas contained in a glass tube at low pressure. In the He-Ne gas laser, the He and Ne gases are taken in the ratio 10:1 in the discharge tube.

Gain medium

In He-Ne laser 80cm length and 1cm diameter discharge are generally used. The out power of these lasers depends on the length of the discharge tube and the pressure of the gas mixture. Therefore, to achieve population inversion, we need to pump electrons from the lower energy state of the helium. In He-Ne laser, neon atoms are the active centres and have energy levels suitable for laser transitions while helium atoms help in exciting neon atoms.

Resonating cavity

Two reflecting mirrors are fixed on either end of the discharge tube, in that, one is partially reflecting and the other is fully reflecting. The fully silvered mirror will completely reflect the light whereas the partially silvered mirror will reflect most of the light but allows some part of the light to produce the laser beam.

WORKING

When the electric discharge is passing through the gas mixture, the electrons accelerated towards the positive electrode. During their passage, they collide with He atoms and excite them into higher levels. 23s1 and 21s0 form the ground state of the He atom. In higher levels, 23s1 and 21s0, the lifetime of He atoms are more. So there is a maximum possibility of energy transfer between He and Ne atoms through atomic collisions. When He atoms present in the levels 23s1 and 21s0 collide with the Ne atom's present ground state, the Ne atoms get excitation into higher levels 4s and 5s.

Due to the continuous excitation of Ne atoms, we can achieve the population inversion between the higher levels 4s and 5s and lower levels 3p and 4p. The various transitions 5s to 4p, 4s to 3p, and 5s to 3p leads to the emission of wavelengths 3.93μm, 1.51μm, and 6328 Å or 632.8μm.

The first two correspondings to the infrared region while the last wavelength is corresponding to the visible region. The Ne atoms present in the 4s level are de-excited into 3s level, by spontaneously emitting a photon of around wavelength 6000 Å. When a narrow discharge tube is used, the Ne atoms present in the level 3s collide with the walls of the tube and get de-excited to the ground state energy level.

ADVANTAGES OF HELIUM-NEON LASER

• The helium-neon laser emits laser light in the visible portion of the spectrum.
• High stability
• Low cost
• Operates without damage at higher temperatures

DISADVANTAGES OF HELIUM-NEON LASER

• Low efficiency
• Low gain
• Helium-neon lasers are limited to low power tasks

APPLICATIONS OF HELIUM-NEON LASERS

• Helium-neon lasers are used in industries.
• Helium-neon lasers are used in scientific instruments.

Helium-neon lasers are used in the college laboratories

Q.10  Discuss Applications of Lasers In various fields?

Solution:

Applications of lasers because of the unique property of laser beams such as coherence, monochromaticity, directionality, and high intensity, they are widely used in various fields like

1. Communication

2. Computers

3. Chemistry

4. Photography

5. Industry

6. Medicine

7. Military

8. Scientific Research

1. Communication

In the case of optical communication semiconductors, laser diodes are used as optical sources and their bandwidth is (1014Hz) is very high compared to radio and microwave communications.  More channels can be sent simultaneously Signal cannot be tapped as the bandwidth is large, more data can be sent. A laser is highly directional and less divergence, hence it has greater potential use in space crafts and submarines. It is used in optical fiber communications to send information over large distances with low loss. Laser light is used in underwater communication networks. Lasers are used in space communication, radars, and satellites.

2. Computers 

In LAN (local area network), data can be transferred from memory storage of one computer to another computer using laser for short time.  Lasers are used in CD-ROMS during recording and reading the data. Lasers are used in computer printers.

3. Chemistry

Lasers are used in molecular structure identification Lasers are also used to accelerate some chemical reactions.  Using lasers, new chemical compounds can be created by breaking bonds between atoms are molecules.

4. Photography

Lasers can be used to get a 3-D lens with less photography.  Lasers are also used in the construction of holograms.

5. Industry 

Lasers can be used to blast holes in diamonds and hard steel. Lasers are also used as a source of intense heat Carbon dioxide laser is used for cutting drilling of metals and non-metals, such as ceramics plastics glass, etc.  High power lasers are used to weld or melt any material.  Lasers are also used to cut teeth in saws and test the quality of the fabric. It is used to cut glass and quartz, used in electronic industries for trimming the components of Integrated Circuits (ICs). Lasers are used for heat treatment in the automotive industry. Laser light is used to collect information about the prefixed prices of various products in shops and business establishments from the bar code printed on the product. Ultraviolet lasers are used in the semiconductor industries for photolithography. Photolithography is the method used for manufacturing printed circuit board (PCB) and microprocessor by using ultraviolet light. It is also used to drill aerosol nozzles and control orifices within the required precision.

6. Medicine

Pulsed neodymium laser is employed in the treatment of liver cancer.  Argon and carbon dioxide lasers are used in the treat men of the liver and lungs.  Lasers are used in the treatment of Glaucoma.

Lasers are used in endoscopy to scan the inner parts of the stomach.  Lasers are used in the elimination of moles and tumors which are developing in the skin tissue and hair removal. It is also used for bloodless surgery.

Lasers are used to destroy kidney stones, in cancer diagnosis and therapy also used for eye lens curvature corrections. Lasers are used to study the internal structure of microorganisms and cells. It is used to create plasma. Lasers are used to remove caries or decayed portion of the teeth.

7. Military

Lasers can be used as a war weapon. High energy lasers are used to destroy the enemy air-crofts and missiles. Lasers can be used in the detection and ranging likes RADAR. Laser range finders are used to determine the distance to an object. The ring laser gyroscope is used for sensing and measuring a very small angle of rotation of the moving objects.

Lasers can be used as a secretive illuminator for reconnaissance during the night with high precision.

8. Scientific research

Lasers are used in the field of 3D-photography Lasers are used in Recording and reconstruction of the hologram. Lasers are employed to create plasma. Lasers are used in Raman spectroscopy to identify the structure of the molecule and to count the number of atoms in a substance. Lasers are used in the Michelson- Morley experiment. A laser beam is used to confirm Doppler shifts in frequency for moving objects. A laser helps in studying the Brownian motion of particles. With the help of a helium-neon laser, it was proved that the velocity of light is the same in all directions. Lasers are used to measure the pollutant gases and other contaminants of the atmosphere. Lasers help in determining the rate of rotation of the earth accurately. Lasers are used for detecting earthquakes and underwater nuclear blasts. A gallium arsenide diode laser can be used to set up an invisible fence to protect an area.

Q.11 Discuss the principle, construction, and working of Optical Fibre?

Solution:

A cable that is used to transmit the data through fibres (threads) or plastic (glass) is known as an optical fibre cable. This cable includes a pack of glass threads that transmits modulated messages over light waves.

Principle: Optical Fibre works on the principle of Total Internal Reflection.

Total internal reflection:-

When the light ray travels from a denser medium to a rarer medium the refracted ray bends away from the normal. When the angle of incidence is greater than the critical angle, the refracted ray again reflects into the same medium. This phenomenon is called total internal reflection. The refracted ray bends towards the normal as the ray travels from a rarer medium to a denser medium. The refracted ray bends away from the normal as it travels from denser medium to rarer medium.

Figure – Total Internal Reflection

Characteristics of Optical Fibre

• It has a large bandwidth.
• The optical frequency of 2 x 1014 Hz can be used and hence the system has higher bandwidth.
• Thus optical fibres have greater information-carrying capacity due to greater bandwidth.
• In an optical fibre system transmission losses are as low as 0.1 db/km.
• Optical fibre is of small size and lightweight as compared to electrical fibre.
• Optical fibre communication is free from electromagnetic interference.
• Optical fibre does not carry high voltage and current hence they are safer than electrical cable.
• Optical Fibre is flexible and has high tensile strength. Thus can be bent or twisted easily.

Figure: Optical Fibre

Construction of Optical Fibre:

It consists of a very thin fibre of silica or glass or plastic of a high refractive index called the core. The core has a diameter of 10 um to 100 um. The core is enclosed by a cover of glass or plastic called cladding. The refractive index of the cladding is less than that of the core (which is a must condition for the working of the optical fibre). The difference between the two indicates is very small of order 10-3. The core and the cladding are enclosed in an outer protective jacket made of plastic to provide strength to the optical fibre. The refractive index can change from core to cladding abruptly (as in step-index fibre) or gradually (as in graded-index fibre).

Figure Representation of Optical Fibre

Working of Optical Fibre

When a ray of light is incident on the core of the optical fibre at a small angle, it suffers refraction and strikes the core-cladding interface, As the diameter of the fibre is very small hence the angle of incidence is greater than the critical angle. Therefore, the ray suffers total internal reflection at the core-cladding interface and strikes the opposite interface. At this interface also, the angle of incidence is greater than the critical angle, so it again suffers total internal reflection. Thus, the ray of light reaches the other end of the fibre after suffering repeated total internal reflections along the length of the fibre. At the other end, the ray suffers refraction and emerges out of the optical fibre.

We can see that the light travels in the core in a guided manner. Hence the communication through the optical fibre is sometimes referred to as an optical waveguide.

Q.12 Explain the terms acceptance angle, acceptance cone, numerical aperture.

Or

Derive expressions for the numerical aperture and fraction change in refractive index change of an optical fibre.

Solution:

Acceptance angle

Definition:- Acceptance angle is defined as the maximum angle of incidence at the interface of air medium and core medium for which the light ray enters into the core and travels along with the interface of core and cladding.

Let n0 be the refractive indices of air

n1 be the refractive indices of core

n2 be the refractive indices of cladding

Let a light ray OA is an incident on the interface of air medium and core medium with an angle of incidence θ0

The light ray refracts into the core medium with an angle of refraction θ1 and the refracted ray AB is again incident on the interface of core and cladding with an angle of the incident (90- θ1)

If (90- θ1) is equal to the critical angle of core and cladding media then the ray travels along with the interface of core and cladding along the path BC. If the angle of the incident at the interface of air and core θ1< θ0 then (90- θ1) will be greater than the critical angle. Therefore,

The total internal reflection takes place.

According to Snell’s law at point A

n0 Sin θ0 = n1 Sin θ1

Sin θ0= (n1 / n0) Sin θ1………(1)

According to Snell’s law at point B

n1 Sin(90- θ1) = n2 Sin90………(2)

n1 Cosθ1 = n2 as (Sin90=1)

Cosθ1 = n2 /n1

Sinθ1 = (1-Cos2 θ1)1/2

Sinθ1= (1- (n2 /n1)2)1/2

Sinθ1= ( n12- n22 )1/2/ n1………(3)

We know Sin θ0= (n1 / n0) Sin θ1 from equation (1)

Substitute the value of Sinθ1 from equation (3)

Sinθ0= (n1 / n0) *( n12- n22 )1/2/ n1

On simplification

Sinθ0= ( n12- n22 )1/2/ n0

θ0=Sin-1 ( n12- n22 )1/2/ n0

Acceptance Angle is θ0=Sin-1 ( n12- n22 )1/2/ n0 ………(4)

Acceptance Cone

Acceptance angle is the maximum angle that a light ray can have relative to the axis of the fibre and propagate down the fibre. Thus, only those rays that are incident on the face of the fibre making angles less than θ0 will undergo repeated total internal reflections and reach the other end of the fibre. Hence, larger acceptance angles make it easier to launch light into fibre.

Figure: 27

In three dimensions, the light rays contained within the cone having a full angle 2θ0 are accepted and transmitted along with the fibre as shown in figure 27. Therefore, the cone is called the acceptance cone. Light incident at an angle beyond θ0 refracts through the cladding and corresponding optical energy is lost.

Numerical aperture

Definition: -Numerical aperture is defined as the light gathering capacity of an optical fibre and it is directly proportional to the acceptance angle. Numerically it is equal to the sin of the acceptance angle.

NA = Sin(acceptance angle)

NA = Sin {Sin-1 (( n12- n22 )1/2/ n0)}from equation (4)

NA = (( n12- n22 )1/2/ n0)………(5)

If the refractive index of the air medium is unity i.e. n0=1 put in (5)

NA = ( n12- n22 )1/2………(6)

Fractional change in refractive index

∆= (n1- n2)/ n1

n1∆ = (n1- n2)………(7)

From equation (6), we have

NA = {( n1- n2 )( n1+n2 )}1/2

NA = { n1∆ (n1+n2 )}1/2as n1∆ = (n1- n2) by Eq(7)

NA = { n1∆ 2n1}1/2n1 ≈ n2, so n1+n2 =2n1

NA = n1{2∆}1/2

This gives the relation between Numerical aperture and Fractional change in refractive index.

Q.13 What are the advantages and disadvantages of an optical fibre?

Solution:

Advantages of fibre optic communication

Optical fibre communication has more advantages than conventional communication.

1. Enormous Bandwidth

2. Low Transmission Loss

3. Electric Isolation

4. Signal Security

5. Small Size and Less Weight

6. Immunity Cross Talk

1. Enormous bandwidth:- The information-carrying capacity of a transmission system is directly proportional to the frequency of the transmitted signals. In the coaxial cable transmission, the bandwidth range is up to around 500MHz only. Whereas in optical fibre communication, the bandwidth range is large as 105 GHz.

2. Low transmission loss:- The transmission loss is very low in optical fibres (i.e.KmdB/2.0) than compare with the conventional communication system. Hence for long-distance communication fibres are preferred.

3. Electric isolation:- Since fibre optic materials are insulators, they do not exhibit earth and interface problems. Hence communicate through fibre even in an electrical dangerous environment.

4. Signal security:- The transmitted signal through the fibre does not radiate, unlike the copper cables, a transmitted signal cannot be drawn from fibre without tampering with it. Thus the optical fibre communication provides 100% signal security.

5. Small size and less weight:- The size of the fibre ranges from 10μm to 50μm, which is very small. The space occupied by the fibre cable is negligibly small compared to conventional electrical cables. Optical fibres are light in weight.

6. Immunity cross-talk:- Since the optical fibres are dielectric waveguides, they are free from any electromagnetic interference and radio frequency interference. Since optical interference among different fibres is not possible, cross talk is negligible even many fibres are cabled together.

Disadvantages of Optical Fibre

The disadvantages of optical fibre include the following

• The main disadvantages of these cables are installation is expensive and difficult to fix together.
• The optical fibre cables are very difficult to merge & there will be a loss of the beam within the cable while scattering.
• Fibre optic cables are compact and highly vulnerable while fitting
• These cables are more delicate than copper wires.
• Special devices are needed to check the transmission of fibre cables.

Q.14 Write a note on the applications of an optical fibre?

Solution:

Application of optical fibre

• Optical fibres are extensively used in a communication system.
• Optical fibres are in the exchange of information between different computers
• Optical fibres are used for the exchange of information in cable televisions, space vehicles, submarines, etc.
• Optical fibres are used in the industry in security alarm systems, process control, and industrial auto machine.
• Optical fibres are used in pressure sensors in biomedical and engine control. 
• Optical fibres are used in medicine, in the fabrication of endoscopy for the visualization of internal parts of the human body.
• Sensing applications of optical fibres are Displacement sensor, Fluid level detector, Liquid level sensor, Temperature/pressure sensor, and Chemical sensors 
• Medical applications of optical fibres are Gastroscopy, Orthoscopic, Couldoscope, Peritonescope, and Fibrescope.

Q.15 Explain how the optical fibres are classified?

Solution:

TYPES OF OPTICAL FIBRES

The types of optical fibres depend on the refractive index, materials used, and mode of propagation of light.

      The classification based on the materials used is as follows:

• Plastic Optical Fibres: The polymethylmethacrylate is used as a core material for the transmission of light.

Example: 

Core: polymethyl methacrylate : Cladding: Co- Polymer

Core: Polystyrene  : Cladding: Methyl methacrylate

• Glass Fibres: It consists of extremely fine glass fibres.

Example: 

Core: SiO2 Cladding: SiO2

Core: GeO2- SiO2 Cladding: SiO2

      The classification based on the mode of propagation of light is as follows:

Mode of propagation:

Light propagates as electromagnetic waves through an optical fibre. All waves, having ray directions above the critical angle will be trapped within the fibre due to total internal reflection. However, all such waves do not propagate through the fibre. Only certain ray directions are allowed to propagate. The allowed directions correspond to the modes of the fibre. In simple terms, modes can be visualized as the possible number of paths of light in an optical fibre.

• Single-Mode Fibres: 

These fibres are used for long-distance transmission of signals. In general, the single mode fibres are step-index fibres. These types of fibres are made from doped silica. It has a very small core diameter so that it can allow only one mode of propagation and hence called single-mode fibres.

The cladding diameter must be very large compared to the core diameter. Thus in the case of single-mode fibre, the optical loss is very much reduced. The structure of a single-mode fibre is given below.

Structure:

Core diameter       :         5-10μm

Cladding diameter            :      Generally around 125μm

Protective layer  :      250 to 1000μm

Numerical aperture                      :         0.08 to 0.10

Bandwidth :         More than 50MHz km.

Application:

Because of high bandwidth, they are used in long-haul communication systems.

• Multimode Fibres:

These fibres are used for short-distance transmission of signals. The multi-mode fibres are useful in manufacturing both for step-index and graded-index fibres. The multi-mode fibres are made by multi-component glass compounds such as Glass – Clad Glass, Silica – Clad – Silica, doped silica, etc. Here the core diameter is very large compared to single-mode fibres, so that it can allow many modes to propagate through it and hence called Multi-mode fibres. The cladding diameter is also larger than the diameter of the single-mode fibres. The structure of the multimode fibre is as shown in the figure above.

Structure:

Core diameter:   50-350μm

Cladding diameter   :   125μm - 500μm

Protective layer  :   250 to 1100μm

Numerical aperture  :   0.12 to 0.5

Bandwidth :   Less than 50MHz km.

The total number of modes possible for such an electromagnetic waveguide is

Because of its less bandwidth, it is very useful in short-haul communication systems.

      The classification based on the refractive index is as follows:

• Step Index Single-mode Fibres

It consists of a core surrounded by the cladding, which has a single uniform index of refraction. Step index-single mode fibres: A single-mode step-index fibre consists of a very thin core of uniform refractive index surrounded by a cladding of refractive index lower than that of the core. The refractive index abruptly changes at the core-cladding boundary. Light travels along a side path, i.e., along the axis only. So zero-order modes are supported by Single Mode Fibre.

Figure: 23

• Step index-Multimode fibres

A multimode step-index fibre consists of a core of uniform refractive index surrounded by a cladding of refractive index lower than that of the core. The refractive index abruptly changes at the core-cladding boundary. The core is of large diameter. Light follows zigzag paths inside the fibre. Many such zigzag paths of propagation are permitted in Multi-Mode Fibre. The Numerical Aperture of a Multi-mode fibre is larger as the core diameter of the fibre is larger

Figure: 24

• Graded Index Fibres: 

The refractive index of the optical fibre decreases as the radial distance from the fibre axis increases. GRIN fibre is one in which the refractive index varies radially, decreasing continuously in a parabolic manner from the maximum value of n1, at the center of the core to a constant value of n2 at the core-cladding interface.

In graded-index fibre, light rays travel at different speeds in different parts of the fibre because the refractive index varies throughout the fibre. Near the outer edge, the refractive index is lower. As a result, rays near the outer edge travel faster than the rays at the center of the core. Because of this, rays arrive at the end of the fibre at approximately the same time. In effect light rays that arrive at the end of the fibre are continuously refocused as they travel down the fibre. All rays take the same amount of time in traversing the fibre. This leads to small pulse dispersion.

Figure: 25

For a parabolic index fibre, the pulse dispersion is reduced by a factor of about 200 in comparison to step-index fibre. It is because of this reason that first and second-generation optical communication systems used near parabolic index fibres.

Q.16 Discuss  CO2 Laser?

 Solution:

CO2 LASER

In a molecular gas laser, laser action is achieved by transitions between vibrational and rotational levels of molecules. Its construction is simple and the output of this laser is continuous.

In CO2 molecular gas laser, transition takes place between the vibrational states of Carbon dioxide molecules.

CO2 Molecular gas laser

It was the first molecular gas laser developed by Indian born American scientist Prof.C.K.N.Pillai.

It is a four level laser and it operates at 10.6 μm in the far IR region. It is a very efficient laser.

Energy states of CO2 molecules.

A carbon dioxide molecule has a carbon atom at the center with two oxygen atoms attached, one at both sides. Such a molecule exhibits three independent modes of vibrations. They are

a)     Symmetric stretching mode.

b)    Bending mode

c)     Asymmetric stretching mode.

a. Symmetric stretching mode

In this mode of vibration, carbon atoms are at rest and both oxygen atoms vibrate simultaneously along the axis of the molecule departing or approaching the fixed carbon atoms.

Figure10: Symmetric stretching mode

b. Bending mode:

In this mode of vibration, oxygen atoms and carbon atoms vibrate perpendicular to molecular axis.

Figure 11: Bending mode

c. Asymmetric stretching mode:

Figure 12: Asymmetric stretching mode

In this mode of vibration, oxygen atoms and carbon atoms vibrate asymmetrically, i.e., oxygen atoms move in one direction while carbon atoms in the other direction.

PRINCIPLE:

The active medium is a gas mixture of CO2, N2 and He. The laser transition takes place between the vibrational states of CO2 molecules.

CONSTRUCTION:

It consists of a quartz tube 5 m long and 2.5 cm in the diameter. This discharge tube is filled with gaseous mixture of CO2 (active medium), helium and nitrogen with suitable partial pressures.

Figure 13: Construction of CO2

The terminals of the discharge tubes are connected to a D.C power supply. The ends of the discharge tube are fitted with NaCl Brewster windows so that the laser light generated will be polarized.

WORKING:

Figure 14: energy levels of nitrogen and carbon dioxide molecules

When an electric discharge occurs in the gas, the electrons collide with nitrogen molecules and they are raised to excited states. This process is represented by the equation

N2 + e* = N2* + e

N2 = Nitrogen molecule in ground state

e* = electron with kinetic energy

N2* = nitrogen molecule in excited state

e= same electron with lesser energy

Now N2 molecules in the excited state collide with CO2 atoms in ground state and excite to higher electronic, vibrational and rotational levels.

This process is represented by the equation

N2* + CO2 = CO2* + N2

N2* = Nitrogen molecule in excited state.

CO2 = Carbon dioxide atoms in ground state

CO2* = Carbon dioxide atoms in excited state

N2 = Nitrogen molecule in ground state.

Since the excited level of nitrogen is very close to the E5 level of CO2 atom, population in E5 level increases.

As soon as population inversion is reached, any of the spontaneously emitted photon will trigger laser action in the tube. There are two types of laser transition possible.

1. Transition E5 to E4 

This will produce a laser beam of wavelength 10.6μm

2. Transition E5 to E3

This transition will produce a laser beam of wavelength 9.6μm. Normally 10.6μm transition is more intense than 9.6μm transition. The power output from this laser is 10kW.

Characteristics: 

1.     Type: It is a molecular gas laser.

2.     Active medium: A mixture of CO2 , N2 and helium or water vapour is used as active medium

3.     Pumping method: Electrical discharge method is used for Pumping action

4.     Optical resonator: Two concave mirrors form a resonant cavity

5.     Power output: The power output from this laser is about 10kW.

6.     Nature of output: The nature of output may be continuous wave or pulsed wave.

7.     Wavelength of output: The wavelength of output is 0.6μm and 10.6μm.

ADVANTAGES:

1.     The construction of CO2 laser is simple

2.     The output of this laser is continuous.

3.     It has high efficiency

4.     It has very high output power.

5.     The output power can be increased by extending the length of the gas tube.

DISADVANTAGES:

1.     The contamination of oxygen by carbon monoxide will have some effect on laser action

2.     The operating temperature plays an important role in determining the output power of laser.

3.     The corrosion may occur at the reflecting plates.

4.     Accidental exposure may damage our eyes, since it is invisible (infra-red region) to our eyes.

APPLICATIONS:

1.     High power CO2 laser finds applications in material processing, welding, drilling, cutting soldering etc.

2.     The low atmospheric attenuation (10.6μm makes CO2 laser suitable for open air communication.

3.     It is used for remote sensing

4.     It is used for treatment of liver and lung diseases.

5.     It is mostly used in neuro surgery and general surgery.

6.     It is used to perform microsurgery and bloodless operations.

Q.17 :- Explain optical fibre as a dielectric wave guide? Also define term Meridional rays and Skew Rays?

 Solution:

 Light propagates inside an optical fiber by virtue of multiple TIRs at the core-cladding interface. The refractive index of the core glass is greater than that of the cladding. This meets the first condition for a TIR. All the light energy that is launched into the optical fiber through its tip does not get guided along the fiber. Only those light rays propagate through the fiber which is launched into the fiber at such an angle that the refracted ray inside the core of the optical fiber is incident on the core-cladding interface at an angle greater than the critical angle of the core with respect to the cladding.

1. Optical fiber is basically a solid glass rod. The diameter of rod is so small that it looks like a fiber.

2. Optical fiber is a dielectric waveguide. The light travels like an electromagnetic wave inside the waveguide. The dielectric waveguide is different from a metallic waveguide which is used at microwave and millimeter wave frequencies.

3. In a metallic waveguide, there is a complete shielding of electromagnetic radiation but in an optical fiber the electromagnetic radiation is not just confined inside the fiber but also extends outside the fiber.

4. The light gets guided inside the structure, through the basic phenomenon of total internal reflection.

5.  The optical fiber consists of two concentric cylinders; the inside solid cylinder is called the core and the surrounding shell is called the cladding. (See Fig 12)

Figure 20:  Schematic of an optical fiber

6. For the light to propagate inside the fiber through total internal reflections at core-cladding interface, the refractive index of the core must be greater than the refractive index of the cladding. That is n1>n2.

SIMPLE RAY MODEL                                                                                  

Figure 21: (optical fiber with core, cladding and total internally reflected ray)

For propagation of light inside the core there are two possibilities.

1.   A light ray is launched in a plane containing the axis of the fiber.  We can then see the light ray after total internal reflection travels in the same plane i.e., the ray is confined to the plane in which it was launched and never leave the plane. In this situation the rays will always cross the axis of the fiber. These are called the Meridional rays. (Figure 21)

2.   The other possibility is that the ray is not launched in a plane containing the axis of the fiber.

For example if the ray is launched at some angle such that it does not intersect the axis of the fiber, then after total internal reflection it will go to some other plane. We can see that in this situation the ray will never intersect the axis of the fiber. The ray essentially will spiral around the axis of fiber. These rays are called the Skew rays. 

So it can be concluded that if the light is to propagate inside an optical fiber it could be through two types of rays

a) Meridional rays: The rays which always pass through the axis of fiber giving high optical intensity at the center of the core of the fiber.

b) Skew Rays: The rays which never intersect the axis of the fiber, giving low optical intensity at the center and high intensity towards the rim of the fiber.

Q.18 When mean optical power launched into an 8 km length of fibre is 12 μW, the mean optical power at the fibre output is 3 μW. Determine

a)     Overall signal attenuation in dB.

b)    The overall signal attenuation for a 10 km optical link using the same fibre with splices at 1 km intervals, each giving an attenuation of 1 dB.

Solution:

Given :z=8km

P(0) = 120 μW

P(z) = 3 μW

a)     Overall attenuation is given by,

αp (dB/km ) = 10.  log = 16.02

b)    Overall attenuation for 10 km,

Attenuation per km = αp (dB/km )

=

=   = 2.00 dB/km

Attenuation in 10 km link = 2.00 x 10 = 20 dB

In 10 km link there will be 9 splices at 1 km interval. Each splices introducing attenuation of 1 dB.

Total attenuation = 20 dB + 9 dB = 29 dB

Q. 19 Discuss Dispersion Loss?

Solution:

Dispersion: A light pulse launched into a fibre decreases in the fibre. It also spreads during its travel. The pulse received at the output is wider than input pulse.

It means that the pulse becomes distorted as it is propagated through the fibre. Such a distortion arises due to dispersion effects.

Dispersion is typically measured in Nano seconds per kilometre (ns/km).

There are three mechanisms which contribute to the distortion of the light pulse in a fibre. They are known as:

a)                 Material dispersion

b)                Wave guide dispersion

c)                 Chromatic Dispersion

d)                Modal Dispersion

a)     Material Dispersion

Material dispersion is also called as chromatic dispersion. Material dispersion exists due to change in index of refraction for different wavelengths. A light ray contains components of various wavelengths. The time delay is different for different wavelength components. This results in time dispersion of pulse at the receiving end of fibre.

Light waves of different wavelengths travel at different speeds in a medium. The short wavelength waves travel slower than long wavelength waves. Consequently, narrow pulses of light tend to broaden as they travel down the optical fibre. This is known as material dispersion.

The material dispersion for unit length (L = 1) is given by

D =

Where c = Light velocity

λ = Center wavelength

= Second derivative of index of refraction w.r.t wavelength.

Negative sign shows that the upper sideband signal (lowest wavelength) arrives before the lower sideband (highest wavelength).

The unit of dispersion is : ps/nm/km. The amount of material dispersion depends upon the chemical composition of glass.

Example: An LED operating at 850 nm has a spectral width of 45 nm. What is the pulse spreading in ns/km due to material dispersion?

Solution:

Given :λ = 850 nm

σ = 45 nm

R.M.S pulse broadening due to material dispersion is given by,

σm= σLM

Considering length L = 1 metre

Dmat =  

For LED source operating at 850 nm, = 0.025

M =   by substituting all values we have

M = 9.8 ps/nm/km

σm= 441 ns/km

b)    Waveguide Dispersion

• Waveguide dispersion is caused by the difference in the index of refraction between the core and cladding, resulting in a ‘drag’ effect between the core and cladding portions of the power.
• Waveguide dispersion is significant only in fibres carrying fewer than 5-10 modes. Since multimode optical fibres carry hundreds of modes, they will not have observable waveguide dispersion.
• The group delay (τwg) arising due to waveguide dispersion.

τwg = [ n2 +n2 ∆ ]

Where, b = Normalized propagation

Constant k = 2π / λ (group velocity)

Normalized frequency V,

V = ka

τwg = [ n2 +n2 ∆ ]

The second term   is waveguide dispersion and is mode dependent term.

As frequency is a function of wavelength, the group velocity of the energy varies with frequency. This produces additional losses (waveguide dispersion). The propagation constant (b) varies with wavelength, the causes of which are independent of material dispersion.

c)     Chromatic Dispersion

The combination of material dispersion and waveguide dispersion is called chromatic dispersion. These losses primarily concern the spectral width of transmitter and choice of correct wavelength.

Material dispersion and waveguide dispersion effects vary in opposite senses as the wavelength increased, but at an optimum wavelength, two effects almost cancel each other and chromatic dispersion is at minimum. Attenuation is therefore also at minimum and makes highly attractive Operating wavelength.

d)    Modal Dispersion

As only a certain number of modes can propagate down the fibre, each of these modes carries the modulation signal and each one is incident on the boundary at a different angle, they will each have their own individual propagation times. The net effect is spreading of pulse; this form o dispersion is called modal dispersion.

• Modal dispersion takes place in multimode fibres. It is moderately present in graded index fibres and almost eliminated in single mode step index fibres.
• Modal dispersion is given by

∆tmodal =

Where ∆tmodal = Dispersion

n1= Core refractive index

Z = Total fibre length

c = Velocity of light in air.

The above equation can also be written as

∆tmodal =

The modal dispersion ∆tmodal describes the optical pulse spreading due to modal effects optical pulse width can be converted to electrical rise time through the relationship.

tr mod = 0.44 (∆tmodal)πr2

UNIT 4

LASERS AND FIBRE OPTICS

Q.1  Differentiate between spontaneous and stimulated emissions.

Solution:-

Q.2  What is LASER? Discuss basic phenomena involved in producing laser light?

Solution:-

LASER stands for “Light Amplification by Stimulated Emission of Radiation”.

L = Light

A = Amplification (by)

S = Stimulated

E = Emission (of)

R = Radiation

Theodore H. Maiman of the Hughes Research Laboratory, California, was the first scientist who experimentally demonstrated laser by flashing light through a ruby crystal in 1960. But the basic idea behind the development of laser was given by the great scientist “Albert Einstein” in 1917.

Let us discuss Einstein’s theory of the interaction of electromagnetic radiation with matter. He proposed that electromagnetic radiation interacts with matter in the following three steps.

• Stimulated Absorption
• Spontaneous Emission
• Stimulated Emission

Stimulated Absorption:

Let E1 and E2 be the energies of the ground and excited states of an atom. Suppose, if a photon of energy hν= E1− E2 interacts with an atom present in the ground state, the atom gets excitation from ground state E1 to excited state E2. This process is called stimulated absorption. Stimulated absorption rate depends upon the number of atoms available in the lowest energy state as well as the energy density photons.

Stimulated absorption rate ∝ Number of atoms in the ground state

∝ The density of photons Spontaneous emission

Spontaneous Emission:

Let E1 and E2 be the energies of the ground and excited states of an atom. Suppose, if a photon of energy hν= E1− E2 interacts with an atom present in the ground state, the atom gets excitation from ground stateE1 to excited state E2. The excited atom does not stay a long time in the excited state. The excited atom gets de-excitation after its lifetime by emitting a photon of energy hν= E1− E2. This process is called spontaneous emission. Also Spontaneous means by its own. Here excited atom comes to the ground state on its own so it is named as spontaneous emission.

The spontaneous emission rate depends upon the number of atoms present in the excited state.

Spontaneous emission ∝ rate number of atoms in the excited state

Stimulated Emission: 

This phenomenon is responsible for producing laser light. Let E1and E2 be the energies of the ground and excited states of an atom. Suppose, if a photon of energy hν= E1− E2 interacts with an atom present in the ground state, the atom gets excitation from ground stateE1 to excited state E2. Let, a photon of energy hν= E1− E2 interacts with the excited atom within their lifetime; the atom gets de-excitation to the ground state by emitting another photon. These photons have the same phase and it follows coherence. This phenomenon is called stimulated emission.

Stimulated emission rate depends upon the number of atoms available in the excited state as well as the energy density of photons.

Stimulated emission rate ∝ number of atoms in the excited state

∝ Density of photons

Q.3  Discuss Properties of Laser?

Solution:-

• The laser is a powerful source of light having extraordinary properties that are not found in normal light sources like tungsten lamps, mercury lamps, etc.
• The unique property of a laser is that its light waves travel very long distances with e very little divergence. Whereas the conventional source of light can travel very short distances only.
• A high degree of directionality and monochromatic is also associated with these laser light beams. Therefore, in a laser beam, the light waves not only are in the same phase but also have the same colour throughout their journey.
• The beam of the ordinary light spreads out very quickly. On the other hand, the laser beam is highly collimated and spreads very little.
• The spread of laser light on the surface of the moon is only about 3 km across. Hypothetically, if ordinary light was able to travel to the so moon, its beam would have fanned out to such an extent leading to a diameter of the light on the moon as much as 40, 000 km.
• Another remarkable feature of laser is the concentration of its energy to extremely high intensities, the intensity remaining almost constant over long distances because of low divergence.
• If a laser beam with a power of a few megawatts is focused by a lens at a spot with a diameter of 1/1000th of a centimeter. the beam intensity increases to a few hundred billion watts per sq. Cm. This concentrated energy is so intense that it easily ionizes the atmospheric air to create sparks. When the beam is focused from a high power laser, even the hardest material like a diamond can be melted in a fraction of a second.

Q.4  Derive Einstein’s coefficient A and B?

Solution:-

The distribution of atoms in the two energy levels will change by absorption or emission of radiation. Einstein introduced three empirical coefficients to quantify the change of population of the two levels. Let N1 be the number of atoms per unit volume with energy E1 and N2 be the number of atoms per unit volume with energy E2. Let ‘n’ be the number of photons per unit volume at frequency ‘υ’ such that hυ= E1− E2.

Then, the energy density of photons ρ(υ) = nhυ

When these photons interact with atoms, both upward (absorption) and downward (emission) transition occurs.

At the equilibrium, the upward transitions must be equal to downward transitions.

Upward Transition

Stimulated absorption rate depends upon the number of atoms available in the lowest energy state as well as the energy density photons.

We have seen above that

Stimulated absorption rate ∝ N1 i.e. Number of atoms in the ground state

∝ ρ(υ) i.e. Density of photons spontaneous emission

Stimulated absorption rate = B12N1ρ(υ)………(1)

Where B12 is the Einstein coefficient of stimulated absorption.

Downward transition

The spontaneous emission rate depends upon the number of atoms present in the excited state.

Spontaneous emission rate ∝ N2 i.e. number of atoms in the excited state

Spontaneous emission rate = A21N2 ………(2)

Where A21 is the Einstein coefficient of spontaneous emission.

Stimulated emission rate depends upon the number of atoms available in the excited state as well as the energy density of photons.

Stimulated emission rate ∝ N2 i.e. number of atoms in the excited state

∝ ρ(υ) i.e. Density of photons

Stimulated emission rate = B21N2ρ(υ)………(3)

If the system is in equilibrium the upward transitions must be equal to downward transitions.

Upward transitions = downward transitions

B12N1ρ(υ) = A21N2 + B21N2ρ(υ)………(4)

B12N1ρ(υ) - B21N2ρ(υ) = A21N2

(B12N1- B21N2) ρ(υ) = A21N2

ρ(υ) =………(5)

Divide with B21N2 in numerator and denominator in the right side of the above equation,

ρ(υ) = = ………(6)

ρ(υ) = = =………(7)

We know from Maxwell Boltzmann distribution law

= ………(8)

And also from Planck’s law, the radiation density

ρ(υ) = ………(9)

Comparing the two equations (7) and (9)

= and =1………(10)

The above relations are referred to as Einstein relations.

From the above equation for non-degenerate energy levels, the stimulated emission rate is equal to the stimulated absorption rate at the equilibrium condition.

= ………(11)

Q.5  What is the relationship between B21 and B12?
a) B12 > B21
b) B12 < B21
c) B12 = B21
d) No specific relation
 

Solution:-

C is the correct answer.
B21 is the coefficient for the stimulated emission while B12 is the coefficient for stimulated absorption. Both the processes are mutually reverse processes and their probabilities are equal. Therefore, B12 = B21.

Q.6  How laser light get amplify by population inversion?

Solution:-

Population inversion

Definition

The number of atoms present in the excited state or higher energy state is greater than the number of atoms present in the ground state or lower energy state is called population inversion.

Population inversion as the name suggests that this is an inverted phenomenon. In general, the lower energy level is more populated which means it has more number atoms in the lower energy level as compared to a higher energy level. But by pumping we will obtain a state when the number of atoms present in the higher energy state is greater than the number of atoms present in the lower energy state.

Let us consider a two-level energy system of energies E1 and E2 as shown in the figure.

Let N1 and N2 be the populations that mean several atoms per unit volume of energy levels E1 and E2 respectively.

According to Boltzmann’s distribution the population of an energy level E, at temperature T is given by

Ni=N0

Where N0 is the population of the lower level or ground state and k is Boltzmann’s constant.

From the above relation, the population of energy levels E1 and E2 are

N1=N0

N2=N0

At ordinary conditions N1 >N2 i.e., the population in the ground or lower state is always greater than the population in the excited or higher states. The stage of making, the population of higher energy level is greater than the population of lower energy level is called population inversion i.e. N1 < N2

When the population inversion method is used to enforce more and more atoms to give up photons. This initiates a chain reaction and releasing a massive amount of energy.

This results in a rapid build-up of the energy of emitting one particular wavelength traveling coherently in a fixed direction. This process is called amplification by stimulated emission using population inversion.

This population inversion situation is essential for laser action. For any stimulated emission, the upper energy level or metastable state must have a long lifetime, i.e., the atoms should pause at the metastable state for more time than at the lower level.

Q.7  What is Pumping?  Discuss the various type of pumping mechanisms?

Solution:-

For laser action, the pumping mechanism (exciting with external source) maintain a higher population of atoms in the upper energy level relative to that in the lower level.

A system in which population inversion is achieved is called an active system. The method of raising the particles from a lower energy state to a higher energy state is called pumping.

The process of achieving population inversion is called pumping.

This can be done in several ways.

The most commonly used pumping methods are

1. Optical pumping
2. Electrical discharge pumping
3. Chemical pumping
4. Thermal Pumping
5. Injection current pumping
6. Inelastic Atom-Atom Collisions

Optical pumping As the name suggests, in this method, light is used to supply energy to the laser medium. Optical pumping is used in solid laser. Xenon flash tubes are used for optical pumping. Since these materials have very broadband absorption, a sufficient amount of energy is absorbed from the emission band of the flash lamp and population inversion is created. So xenon flash lamp is used to produce more electrons in the higher energy level of the laser medium.

Examples of optically pumped lasers are ruby, Nd: YAG Laser(Neodymium: Yttrium Aluminum Garnet).

Electrical discharge pumping is used in gas lasers. Since gas lasers have a very narrow absorption band pumping then any flash lamp is not possible. Electric discharge refers to the flow of electrons or electric current through a gas, liquid, or solid.

In this method of pumping, electric discharge acts as the pump source or energy source. A high voltage electric discharge (flow of electrons, electric charge, or electric current) is passed through the laser medium or gas. The intense electric field accelerates the electrons to high speeds and they collide with neutral atoms in the gas. As a result, the electrons in the lower energy state gains sufficient energy from external electrons and jumps into the higher energy state

 Examples of Electrical discharge pumped lasers are He-Ne laser, CO2 laser, argon-ion laser, etc.

Chemical pumping Chemical reaction may also result in excitation and hence the creation of population inversion in a few systems.

 If an atom or a molecule is produced through some chemical reaction and remains excited at the time of production, then it can be used for pumping. The hydrogen fluoride molecule is produced in an excited state when hydrogen and fluorine gas chemically combine. The number of produced excited atoms or molecules is greater than the number of normal state atoms or molecules. Thus, population inversion is achieved.

Examples H2 + F2 → 2HF, in this chemical reaction, hydrogen (H2) and fluorine (F2) molecules are chemically combined to produce hydrogen fluoride molecule (2HF) in an excited state.

Thermal Pumping: Sometimes we can achieve population inversion by heating the laser medium. In thermal pumping, heat acts as the pump source or energy source. In this method, population inversion is achieved by supplying heat into the laser medium.

When heat energy is supplied to the laser medium, the lower energy state electrons gain sufficient energy and jumps into the higher energy level.

The process of achieving population inversion in thermal pumping is almost similar to the optical pumping or electric discharge method, except that in this method heat is used as a pump source instead of light or electric discharge.

Injection current pumping In semiconductors, injection of current through the junction results in creates of population inversion among the minority charge carriers.

Examples of such systems are InP and GaAs.

Inelastic Atom-Atom Collisions: Like the electric discharge method, here also a high voltage electric discharge acts as a pump source. However, in this method, a combination of two types of gases, say X and Y are used. The excited state of gas X is represented as X+ whereas gas Y is represented as Y+. Both X and Y gases have the same excited states (X+ and Y+).

When high voltage electric discharge passes through a laser medium having two types of gases X and Y, the lower energy state electrons in gas X will move to the exciting state X+ similarly the lower energy state electrons in gas Y moves to the excited state Y+.

Initially, during electric discharge, the lower energy state electrons in gas X or atom X gets excited to X+ due to continuous collision with electrons. The excited state electrons in gas X+ now collide with the lower energy state electrons in gas Y. As a result, the lower energy state electrons in gas Y gains sufficient energy and jump into the exciting state Y+. This method is used in the Helium-Neon (He-Ne) laser.

Q.8  Discuss the construction, working, and application of Solid-State Laser?

Or

Discuss the construction, working, and application of Ruby Laser?

Or

Discuss three-level laser?

Solution:-

Ruby laser

Ruby laser is a three-level solid-state laser and was constructed by Maiman in 1960. Ruby laser is one of the few solid-state lasers that produce visible light. It emits deep red light of wavelength 694.3 nm.

Construction

A ruby laser consists of three important elements: laser medium, the pump source, and the optical resonator.

Laser Medium

Ruby (Al2O3+Cr2O3) is a crystal of Aluminium oxide, in which 0.05% of Al+3 ions are replaced by the Cr+3 ions. The colour of the rod is pink. The active medium or laser medium in the ruby rod is Cr+3 ions. In ruby laser, 4cm length and 5mm diameter rod is generally used. The ruby has good thermal properties.

The pump source

The ruby rod is surrounded by a xenon flash tube, which provides the pumping light to excite the chromium ions into upper energy levels. The ruby rod was surrounded by a helical xenon flash lamp.

We know that population inversion is required to achieve laser emission. Population inversion is the process of achieving a greater population of a higher energy state than the lower energy state. To achieve population inversion, we need to supply energy to the laser medium i.e. to ruby crystal.

Xenon flash tube emits thousands of joules of energy in few milliseconds, but only a  part of that energy is utilized by the chromium ions while the rest energy heats the apparatus. A cooling arrangement is provided to keep the experimental set up at normal temperatures.

Optical resonator

Both the ends of the rods are highly polished and made strictly parallel. The ends are silvered in such a way, one becomes partially reflected the laser beam was emitted through that end and the other end fully reflected to reflect all the rays of light striking it.

Working of ruby laser:

Consider a ruby laser medium consisting of three energy levels E1, E2, E3 with N number of electrons.

We assume that the energy levels will be E1 < E2 < E3. The energy level E1 is known as the ground state or lower energy state, the energy level E2 is known as the metastable state, and the energy level E3 is known as the pump state.

Let us assume that initially most of the electrons are in the lower energy state (E1) and only a tiny number of electrons are in the excited states (E2 and E3).

The energy level diagram of chromium ions is shown in the figure. The chromium ions get excitation into higher energy levels by absorbing 5500Å of wavelength radiation. The excited chromium ions stay in the level E3 for a short interval of time (10-8 to 10-9 Sec). After their life, most of the chromium ions are de-excited from E3 to E1 and a few chromium ions are de-excited from E3 to E2.

The transition between E3 and E2 is non-radioactive i.e. the chromium ions give their energy to the lattice in the form of heat. In the Metastable state, the lifetime of chromium ions is 10-3 sec. The lifetime of chromium ions in the Metastable state is 105 times greater than the lifetime of chromium ions in a higher state.

Due to the continuous working of the flash lamp, the chromium ions are excited to a higher state E3 and returned to the E2 level. After a few milliseconds, the level E2 is more populated than the level E1 and hence the desired population inversion is achieved. The state of population inversion is not a stable one. The process of spontaneous transition is very high. When the excited chromium ion passes spontaneously from E3 to E2it emits one photon of wavelength 6943 Å. The photon reflects back and forth by the silver ends and until it stimulates an excited chromium ion in the E2 state and it to emit a fresh photon in phase with the earlier photon. The process is repeated again and again until the laser beam intensity is reached a sufficient value. When the photon beam becomes sufficiently intense, it emerges through the partially silvered end of the rod. The wavelength 6943 Å is

Drawbacks of the ruby laser

• The laser requires high pumping power
• The efficiency of a ruby laser is very small
• It is a pulse laser

 Application of ruby laser

• Ruby lasers are in optical photography
• Ruby lasers can be used for the measurement of plasma properties such as electron density and temperature.
• Ruby lasers are used to remove the melanin from the skin.
• Ruby laser can be used for the recording of holograms.

Q.9  Discuss the construction, working, and application of gas Laser?

Or

Discuss the construction, working, and application of He-Ne Laser?

Or

Discuss four-level laser?

Solution:-

He-Ne Laser

The first He-Ne gas laser was fabricated in 1961 by Ali Javan, Bennett, and Herriott at Bell Telephone Laboratories. Others. Helium-Neon laser is a type of gas laser in which a mixture of helium and neon gas is used as a gain medium. Helium-Neon laser is also known as He-Ne laser. The helium-neon laser was the first continuous-wave laser ever constructed. The helium-neon laser operates at a wavelength of 632.8 nanometres (nm), in the red portion of the visible spectrum.

Ruby laser is a pulse laser, even it has high intense output. For continuous laser beams, gas lasers are used. Using gas lasers, we can achieve high coherence, high directionality, and high monochromaticity beam. The output power of the gas laser is generally in few milliwatts.

CONSTRUCTION

The helium-neon laser consists of three essential components:

• Pump source (high voltage power supply)
• Gain medium (laser glass tube or discharge glass tube)
• Resonating cavity

Pump source

The gain medium of a helium-neon laser is made up of a mixture of helium and neon gas contained in a glass tube at low pressure. In the He-Ne gas laser, the He and Ne gases are taken in the ratio 10:1 in the discharge tube.

Gain medium

In He-Ne laser 80cm length and 1cm diameter discharge are generally used. The out power of these lasers depends on the length of the discharge tube and the pressure of the gas mixture. Therefore, to achieve population inversion, we need to pump electrons from the lower energy state of the helium. In He-Ne laser, neon atoms are the active centres and have energy levels suitable for laser transitions while helium atoms help in exciting neon atoms.

Resonating cavity

Two reflecting mirrors are fixed on either end of the discharge tube, in that, one is partially reflecting and the other is fully reflecting. The fully silvered mirror will completely reflect the light whereas the partially silvered mirror will reflect most of the light but allows some part of the light to produce the laser beam.

WORKING

When the electric discharge is passing through the gas mixture, the electrons accelerated towards the positive electrode. During their passage, they collide with He atoms and excite them into higher levels. 23s1 and 21s0 form the ground state of the He atom. In higher levels, 23s1 and 21s0, the lifetime of He atoms are more. So there is a maximum possibility of energy transfer between He and Ne atoms through atomic collisions. When He atoms present in the levels 23s1 and 21s0 collide with the Ne atom's present ground state, the Ne atoms get excitation into higher levels 4s and 5s.

Due to the continuous excitation of Ne atoms, we can achieve the population inversion between the higher levels 4s and 5s and lower levels 3p and 4p. The various transitions 5s to 4p, 4s to 3p, and 5s to 3p leads to the emission of wavelengths 3.93μm, 1.51μm, and 6328 Å or 632.8μm.

The first two correspondings to the infrared region while the last wavelength is corresponding to the visible region. The Ne atoms present in the 4s level are de-excited into 3s level, by spontaneously emitting a photon of around wavelength 6000 Å. When a narrow discharge tube is used, the Ne atoms present in the level 3s collide with the walls of the tube and get de-excited to the ground state energy level.

ADVANTAGES OF HELIUM-NEON LASER

• The helium-neon laser emits laser light in the visible portion of the spectrum.
• High stability
• Low cost
• Operates without damage at higher temperatures

DISADVANTAGES OF HELIUM-NEON LASER

• Low efficiency
• Low gain
• Helium-neon lasers are limited to low power tasks

APPLICATIONS OF HELIUM-NEON LASERS

• Helium-neon lasers are used in industries.
• Helium-neon lasers are used in scientific instruments.

Helium-neon lasers are used in the college laboratories

Q.10  Discuss Applications of Lasers In various fields?

Solution:

Applications of lasers because of the unique property of laser beams such as coherence, monochromaticity, directionality, and high intensity, they are widely used in various fields like

1. Communication

2. Computers

3. Chemistry

4. Photography

5. Industry

6. Medicine

7. Military

8. Scientific Research

1. Communication

In the case of optical communication semiconductors, laser diodes are used as optical sources and their bandwidth is (1014Hz) is very high compared to radio and microwave communications.  More channels can be sent simultaneously Signal cannot be tapped as the bandwidth is large, more data can be sent. A laser is highly directional and less divergence, hence it has greater potential use in space crafts and submarines. It is used in optical fiber communications to send information over large distances with low loss. Laser light is used in underwater communication networks. Lasers are used in space communication, radars, and satellites.

2. Computers 

In LAN (local area network), data can be transferred from memory storage of one computer to another computer using laser for short time.  Lasers are used in CD-ROMS during recording and reading the data. Lasers are used in computer printers.

3. Chemistry

Lasers are used in molecular structure identification Lasers are also used to accelerate some chemical reactions.  Using lasers, new chemical compounds can be created by breaking bonds between atoms are molecules.

4. Photography

Lasers can be used to get a 3-D lens with less photography.  Lasers are also used in the construction of holograms.

5. Industry 

Lasers can be used to blast holes in diamonds and hard steel. Lasers are also used as a source of intense heat Carbon dioxide laser is used for cutting drilling of metals and non-metals, such as ceramics plastics glass, etc.  High power lasers are used to weld or melt any material.  Lasers are also used to cut teeth in saws and test the quality of the fabric. It is used to cut glass and quartz, used in electronic industries for trimming the components of Integrated Circuits (ICs). Lasers are used for heat treatment in the automotive industry. Laser light is used to collect information about the prefixed prices of various products in shops and business establishments from the bar code printed on the product. Ultraviolet lasers are used in the semiconductor industries for photolithography. Photolithography is the method used for manufacturing printed circuit board (PCB) and microprocessor by using ultraviolet light. It is also used to drill aerosol nozzles and control orifices within the required precision.

6. Medicine

Pulsed neodymium laser is employed in the treatment of liver cancer.  Argon and carbon dioxide lasers are used in the treat men of the liver and lungs.  Lasers are used in the treatment of Glaucoma.

Lasers are used in endoscopy to scan the inner parts of the stomach.  Lasers are used in the elimination of moles and tumors which are developing in the skin tissue and hair removal. It is also used for bloodless surgery.

Lasers are used to destroy kidney stones, in cancer diagnosis and therapy also used for eye lens curvature corrections. Lasers are used to study the internal structure of microorganisms and cells. It is used to create plasma. Lasers are used to remove caries or decayed portion of the teeth.

7. Military

Lasers can be used as a war weapon. High energy lasers are used to destroy the enemy air-crofts and missiles. Lasers can be used in the detection and ranging likes RADAR. Laser range finders are used to determine the distance to an object. The ring laser gyroscope is used for sensing and measuring a very small angle of rotation of the moving objects.

Lasers can be used as a secretive illuminator for reconnaissance during the night with high precision.

8. Scientific research

Lasers are used in the field of 3D-photography Lasers are used in Recording and reconstruction of the hologram. Lasers are employed to create plasma. Lasers are used in Raman spectroscopy to identify the structure of the molecule and to count the number of atoms in a substance. Lasers are used in the Michelson- Morley experiment. A laser beam is used to confirm Doppler shifts in frequency for moving objects. A laser helps in studying the Brownian motion of particles. With the help of a helium-neon laser, it was proved that the velocity of light is the same in all directions. Lasers are used to measure the pollutant gases and other contaminants of the atmosphere. Lasers help in determining the rate of rotation of the earth accurately. Lasers are used for detecting earthquakes and underwater nuclear blasts. A gallium arsenide diode laser can be used to set up an invisible fence to protect an area.

Q.11 Discuss the principle, construction, and working of Optical Fibre?

Solution:

A cable that is used to transmit the data through fibres (threads) or plastic (glass) is known as an optical fibre cable. This cable includes a pack of glass threads that transmits modulated messages over light waves.

Principle: Optical Fibre works on the principle of Total Internal Reflection.

Total internal reflection:-

When the light ray travels from a denser medium to a rarer medium the refracted ray bends away from the normal. When the angle of incidence is greater than the critical angle, the refracted ray again reflects into the same medium. This phenomenon is called total internal reflection. The refracted ray bends towards the normal as the ray travels from a rarer medium to a denser medium. The refracted ray bends away from the normal as it travels from denser medium to rarer medium.

Figure – Total Internal Reflection

Characteristics of Optical Fibre

• It has a large bandwidth.
• The optical frequency of 2 x 1014 Hz can be used and hence the system has higher bandwidth.
• Thus optical fibres have greater information-carrying capacity due to greater bandwidth.
• In an optical fibre system transmission losses are as low as 0.1 db/km.
• Optical fibre is of small size and lightweight as compared to electrical fibre.
• Optical fibre communication is free from electromagnetic interference.
• Optical fibre does not carry high voltage and current hence they are safer than electrical cable.
• Optical Fibre is flexible and has high tensile strength. Thus can be bent or twisted easily.

Figure: Optical Fibre

Construction of Optical Fibre:

It consists of a very thin fibre of silica or glass or plastic of a high refractive index called the core. The core has a diameter of 10 um to 100 um. The core is enclosed by a cover of glass or plastic called cladding. The refractive index of the cladding is less than that of the core (which is a must condition for the working of the optical fibre). The difference between the two indicates is very small of order 10-3. The core and the cladding are enclosed in an outer protective jacket made of plastic to provide strength to the optical fibre. The refractive index can change from core to cladding abruptly (as in step-index fibre) or gradually (as in graded-index fibre).

Figure Representation of Optical Fibre

Working of Optical Fibre

When a ray of light is incident on the core of the optical fibre at a small angle, it suffers refraction and strikes the core-cladding interface, As the diameter of the fibre is very small hence the angle of incidence is greater than the critical angle. Therefore, the ray suffers total internal reflection at the core-cladding interface and strikes the opposite interface. At this interface also, the angle of incidence is greater than the critical angle, so it again suffers total internal reflection. Thus, the ray of light reaches the other end of the fibre after suffering repeated total internal reflections along the length of the fibre. At the other end, the ray suffers refraction and emerges out of the optical fibre.

We can see that the light travels in the core in a guided manner. Hence the communication through the optical fibre is sometimes referred to as an optical waveguide.

Q.12 Explain the terms acceptance angle, acceptance cone, numerical aperture.

Or

Derive expressions for the numerical aperture and fraction change in refractive index change of an optical fibre.

Solution:

Acceptance angle

Definition:- Acceptance angle is defined as the maximum angle of incidence at the interface of air medium and core medium for which the light ray enters into the core and travels along with the interface of core and cladding.

Let n0 be the refractive indices of air

n1 be the refractive indices of core

n2 be the refractive indices of cladding

Let a light ray OA is an incident on the interface of air medium and core medium with an angle of incidence θ0

The light ray refracts into the core medium with an angle of refraction θ1 and the refracted ray AB is again incident on the interface of core and cladding with an angle of the incident (90- θ1)

If (90- θ1) is equal to the critical angle of core and cladding media then the ray travels along with the interface of core and cladding along the path BC. If the angle of the incident at the interface of air and core θ1< θ0 then (90- θ1) will be greater than the critical angle. Therefore,

The total internal reflection takes place.

According to Snell’s law at point A

n0 Sin θ0 = n1 Sin θ1

Sin θ0= (n1 / n0) Sin θ1………(1)

According to Snell’s law at point B

n1 Sin(90- θ1) = n2 Sin90………(2)

n1 Cosθ1 = n2 as (Sin90=1)

Cosθ1 = n2 /n1

Sinθ1 = (1-Cos2 θ1)1/2

Sinθ1= (1- (n2 /n1)2)1/2

Sinθ1= ( n12- n22 )1/2/ n1………(3)

We know Sin θ0= (n1 / n0) Sin θ1 from equation (1)

Substitute the value of Sinθ1 from equation (3)

Sinθ0= (n1 / n0) *( n12- n22 )1/2/ n1

On simplification

Sinθ0= ( n12- n22 )1/2/ n0

θ0=Sin-1 ( n12- n22 )1/2/ n0

Acceptance Angle is θ0=Sin-1 ( n12- n22 )1/2/ n0 ………(4)

Acceptance Cone

Acceptance angle is the maximum angle that a light ray can have relative to the axis of the fibre and propagate down the fibre. Thus, only those rays that are incident on the face of the fibre making angles less than θ0 will undergo repeated total internal reflections and reach the other end of the fibre. Hence, larger acceptance angles make it easier to launch light into fibre.

Figure: 27

In three dimensions, the light rays contained within the cone having a full angle 2θ0 are accepted and transmitted along with the fibre as shown in figure 27. Therefore, the cone is called the acceptance cone. Light incident at an angle beyond θ0 refracts through the cladding and corresponding optical energy is lost.

Numerical aperture

Definition: -Numerical aperture is defined as the light gathering capacity of an optical fibre and it is directly proportional to the acceptance angle. Numerically it is equal to the sin of the acceptance angle.

NA = Sin(acceptance angle)

NA = Sin {Sin-1 (( n12- n22 )1/2/ n0)}from equation (4)

NA = (( n12- n22 )1/2/ n0)………(5)

If the refractive index of the air medium is unity i.e. n0=1 put in (5)

NA = ( n12- n22 )1/2………(6)

Fractional change in refractive index

∆= (n1- n2)/ n1

n1∆ = (n1- n2)………(7)

From equation (6), we have

NA = {( n1- n2 )( n1+n2 )}1/2

NA = { n1∆ (n1+n2 )}1/2as n1∆ = (n1- n2) by Eq(7)

NA = { n1∆ 2n1}1/2n1 ≈ n2, so n1+n2 =2n1

NA = n1{2∆}1/2

This gives the relation between Numerical aperture and Fractional change in refractive index.

Q.13 What are the advantages and disadvantages of an optical fibre?

Solution:

Advantages of fibre optic communication

Optical fibre communication has more advantages than conventional communication.

1. Enormous Bandwidth

2. Low Transmission Loss

3. Electric Isolation

4. Signal Security

5. Small Size and Less Weight

6. Immunity Cross Talk

1. Enormous bandwidth:- The information-carrying capacity of a transmission system is directly proportional to the frequency of the transmitted signals. In the coaxial cable transmission, the bandwidth range is up to around 500MHz only. Whereas in optical fibre communication, the bandwidth range is large as 105 GHz.

2. Low transmission loss:- The transmission loss is very low in optical fibres (i.e.KmdB/2.0) than compare with the conventional communication system. Hence for long-distance communication fibres are preferred.

3. Electric isolation:- Since fibre optic materials are insulators, they do not exhibit earth and interface problems. Hence communicate through fibre even in an electrical dangerous environment.

4. Signal security:- The transmitted signal through the fibre does not radiate, unlike the copper cables, a transmitted signal cannot be drawn from fibre without tampering with it. Thus the optical fibre communication provides 100% signal security.

5. Small size and less weight:- The size of the fibre ranges from 10μm to 50μm, which is very small. The space occupied by the fibre cable is negligibly small compared to conventional electrical cables. Optical fibres are light in weight.

6. Immunity cross-talk:- Since the optical fibres are dielectric waveguides, they are free from any electromagnetic interference and radio frequency interference. Since optical interference among different fibres is not possible, cross talk is negligible even many fibres are cabled together.

Disadvantages of Optical Fibre

The disadvantages of optical fibre include the following

• The main disadvantages of these cables are installation is expensive and difficult to fix together.
• The optical fibre cables are very difficult to merge & there will be a loss of the beam within the cable while scattering.
• Fibre optic cables are compact and highly vulnerable while fitting
• These cables are more delicate than copper wires.
• Special devices are needed to check the transmission of fibre cables.

Q.14 Write a note on the applications of an optical fibre?

Solution:

Application of optical fibre

• Optical fibres are extensively used in a communication system.
• Optical fibres are in the exchange of information between different computers
• Optical fibres are used for the exchange of information in cable televisions, space vehicles, submarines, etc.
• Optical fibres are used in the industry in security alarm systems, process control, and industrial auto machine.
• Optical fibres are used in pressure sensors in biomedical and engine control. 
• Optical fibres are used in medicine, in the fabrication of endoscopy for the visualization of internal parts of the human body.
• Sensing applications of optical fibres are Displacement sensor, Fluid level detector, Liquid level sensor, Temperature/pressure sensor, and Chemical sensors 
• Medical applications of optical fibres are Gastroscopy, Orthoscopic, Couldoscope, Peritonescope, and Fibrescope.

Q.15 Explain how the optical fibres are classified?

Solution:

TYPES OF OPTICAL FIBRES

The types of optical fibres depend on the refractive index, materials used, and mode of propagation of light.

      The classification based on the materials used is as follows:

• Plastic Optical Fibres: The polymethylmethacrylate is used as a core material for the transmission of light.

Example: 

Core: polymethyl methacrylate : Cladding: Co- Polymer

Core: Polystyrene  : Cladding: Methyl methacrylate

• Glass Fibres: It consists of extremely fine glass fibres.

Example: 

Core: SiO2 Cladding: SiO2

Core: GeO2- SiO2 Cladding: SiO2

      The classification based on the mode of propagation of light is as follows:

Mode of propagation:

Light propagates as electromagnetic waves through an optical fibre. All waves, having ray directions above the critical angle will be trapped within the fibre due to total internal reflection. However, all such waves do not propagate through the fibre. Only certain ray directions are allowed to propagate. The allowed directions correspond to the modes of the fibre. In simple terms, modes can be visualized as the possible number of paths of light in an optical fibre.

• Single-Mode Fibres: 

These fibres are used for long-distance transmission of signals. In general, the single mode fibres are step-index fibres. These types of fibres are made from doped silica. It has a very small core diameter so that it can allow only one mode of propagation and hence called single-mode fibres.

The cladding diameter must be very large compared to the core diameter. Thus in the case of single-mode fibre, the optical loss is very much reduced. The structure of a single-mode fibre is given below.

Structure:

Core diameter       :         5-10μm

Cladding diameter            :      Generally around 125μm

Protective layer  :      250 to 1000μm

Numerical aperture                      :         0.08 to 0.10

Bandwidth :         More than 50MHz km.

Application:

Because of high bandwidth, they are used in long-haul communication systems.

• Multimode Fibres:

These fibres are used for short-distance transmission of signals. The multi-mode fibres are useful in manufacturing both for step-index and graded-index fibres. The multi-mode fibres are made by multi-component glass compounds such as Glass – Clad Glass, Silica – Clad – Silica, doped silica, etc. Here the core diameter is very large compared to single-mode fibres, so that it can allow many modes to propagate through it and hence called Multi-mode fibres. The cladding diameter is also larger than the diameter of the single-mode fibres. The structure of the multimode fibre is as shown in the figure above.

Structure:

Core diameter:   50-350μm

Cladding diameter   :   125μm - 500μm

Protective layer  :   250 to 1100μm

Numerical aperture  :   0.12 to 0.5

Bandwidth :   Less than 50MHz km.

The total number of modes possible for such an electromagnetic waveguide is

Because of its less bandwidth, it is very useful in short-haul communication systems.

      The classification based on the refractive index is as follows:

• Step Index Single-mode Fibres

It consists of a core surrounded by the cladding, which has a single uniform index of refraction. Step index-single mode fibres: A single-mode step-index fibre consists of a very thin core of uniform refractive index surrounded by a cladding of refractive index lower than that of the core. The refractive index abruptly changes at the core-cladding boundary. Light travels along a side path, i.e., along the axis only. So zero-order modes are supported by Single Mode Fibre.

Figure: 23

• Step index-Multimode fibres

A multimode step-index fibre consists of a core of uniform refractive index surrounded by a cladding of refractive index lower than that of the core. The refractive index abruptly changes at the core-cladding boundary. The core is of large diameter. Light follows zigzag paths inside the fibre. Many such zigzag paths of propagation are permitted in Multi-Mode Fibre. The Numerical Aperture of a Multi-mode fibre is larger as the core diameter of the fibre is larger

Figure: 24

• Graded Index Fibres: 

The refractive index of the optical fibre decreases as the radial distance from the fibre axis increases. GRIN fibre is one in which the refractive index varies radially, decreasing continuously in a parabolic manner from the maximum value of n1, at the center of the core to a constant value of n2 at the core-cladding interface.

In graded-index fibre, light rays travel at different speeds in different parts of the fibre because the refractive index varies throughout the fibre. Near the outer edge, the refractive index is lower. As a result, rays near the outer edge travel faster than the rays at the center of the core. Because of this, rays arrive at the end of the fibre at approximately the same time. In effect light rays that arrive at the end of the fibre are continuously refocused as they travel down the fibre. All rays take the same amount of time in traversing the fibre. This leads to small pulse dispersion.

Figure: 25

For a parabolic index fibre, the pulse dispersion is reduced by a factor of about 200 in comparison to step-index fibre. It is because of this reason that first and second-generation optical communication systems used near parabolic index fibres.

Q.16 Discuss  CO2 Laser?

 Solution:

CO2 LASER

In a molecular gas laser, laser action is achieved by transitions between vibrational and rotational levels of molecules. Its construction is simple and the output of this laser is continuous.

In CO2 molecular gas laser, transition takes place between the vibrational states of Carbon dioxide molecules.

CO2 Molecular gas laser

It was the first molecular gas laser developed by Indian born American scientist Prof.C.K.N.Pillai.

It is a four level laser and it operates at 10.6 μm in the far IR region. It is a very efficient laser.

Energy states of CO2 molecules.

A carbon dioxide molecule has a carbon atom at the center with two oxygen atoms attached, one at both sides. Such a molecule exhibits three independent modes of vibrations. They are

a)     Symmetric stretching mode.

b)    Bending mode

c)     Asymmetric stretching mode.

a. Symmetric stretching mode

In this mode of vibration, carbon atoms are at rest and both oxygen atoms vibrate simultaneously along the axis of the molecule departing or approaching the fixed carbon atoms.

Figure10: Symmetric stretching mode

b. Bending mode:

In this mode of vibration, oxygen atoms and carbon atoms vibrate perpendicular to molecular axis.

Figure 11: Bending mode

c. Asymmetric stretching mode:

Figure 12: Asymmetric stretching mode

In this mode of vibration, oxygen atoms and carbon atoms vibrate asymmetrically, i.e., oxygen atoms move in one direction while carbon atoms in the other direction.

PRINCIPLE:

The active medium is a gas mixture of CO2, N2 and He. The laser transition takes place between the vibrational states of CO2 molecules.

CONSTRUCTION:

It consists of a quartz tube 5 m long and 2.5 cm in the diameter. This discharge tube is filled with gaseous mixture of CO2 (active medium), helium and nitrogen with suitable partial pressures.

Figure 13: Construction of CO2

The terminals of the discharge tubes are connected to a D.C power supply. The ends of the discharge tube are fitted with NaCl Brewster windows so that the laser light generated will be polarized.

WORKING:

Figure 14: energy levels of nitrogen and carbon dioxide molecules

When an electric discharge occurs in the gas, the electrons collide with nitrogen molecules and they are raised to excited states. This process is represented by the equation

N2 + e* = N2* + e

N2 = Nitrogen molecule in ground state

e* = electron with kinetic energy

N2* = nitrogen molecule in excited state

e= same electron with lesser energy

Now N2 molecules in the excited state collide with CO2 atoms in ground state and excite to higher electronic, vibrational and rotational levels.

This process is represented by the equation

N2* + CO2 = CO2* + N2

N2* = Nitrogen molecule in excited state.

CO2 = Carbon dioxide atoms in ground state

CO2* = Carbon dioxide atoms in excited state

N2 = Nitrogen molecule in ground state.

Since the excited level of nitrogen is very close to the E5 level of CO2 atom, population in E5 level increases.

As soon as population inversion is reached, any of the spontaneously emitted photon will trigger laser action in the tube. There are two types of laser transition possible.

1. Transition E5 to E4 

This will produce a laser beam of wavelength 10.6μm

2. Transition E5 to E3

This transition will produce a laser beam of wavelength 9.6μm. Normally 10.6μm transition is more intense than 9.6μm transition. The power output from this laser is 10kW.

Characteristics: 

1.     Type: It is a molecular gas laser.

2.     Active medium: A mixture of CO2 , N2 and helium or water vapour is used as active medium

3.     Pumping method: Electrical discharge method is used for Pumping action

4.     Optical resonator: Two concave mirrors form a resonant cavity

5.     Power output: The power output from this laser is about 10kW.

6.     Nature of output: The nature of output may be continuous wave or pulsed wave.

7.     Wavelength of output: The wavelength of output is 0.6μm and 10.6μm.

ADVANTAGES:

1.     The construction of CO2 laser is simple

2.     The output of this laser is continuous.

3.     It has high efficiency

4.     It has very high output power.

5.     The output power can be increased by extending the length of the gas tube.

DISADVANTAGES:

1.     The contamination of oxygen by carbon monoxide will have some effect on laser action

2.     The operating temperature plays an important role in determining the output power of laser.

3.     The corrosion may occur at the reflecting plates.

4.     Accidental exposure may damage our eyes, since it is invisible (infra-red region) to our eyes.

APPLICATIONS:

1.     High power CO2 laser finds applications in material processing, welding, drilling, cutting soldering etc.

2.     The low atmospheric attenuation (10.6μm makes CO2 laser suitable for open air communication.

3.     It is used for remote sensing

4.     It is used for treatment of liver and lung diseases.

5.     It is mostly used in neuro surgery and general surgery.

6.     It is used to perform microsurgery and bloodless operations.

Q.17 :- Explain optical fibre as a dielectric wave guide? Also define term Meridional rays and Skew Rays?

 Solution:

 Light propagates inside an optical fiber by virtue of multiple TIRs at the core-cladding interface. The refractive index of the core glass is greater than that of the cladding. This meets the first condition for a TIR. All the light energy that is launched into the optical fiber through its tip does not get guided along the fiber. Only those light rays propagate through the fiber which is launched into the fiber at such an angle that the refracted ray inside the core of the optical fiber is incident on the core-cladding interface at an angle greater than the critical angle of the core with respect to the cladding.

1. Optical fiber is basically a solid glass rod. The diameter of rod is so small that it looks like a fiber.

2. Optical fiber is a dielectric waveguide. The light travels like an electromagnetic wave inside the waveguide. The dielectric waveguide is different from a metallic waveguide which is used at microwave and millimeter wave frequencies.

3. In a metallic waveguide, there is a complete shielding of electromagnetic radiation but in an optical fiber the electromagnetic radiation is not just confined inside the fiber but also extends outside the fiber.

4. The light gets guided inside the structure, through the basic phenomenon of total internal reflection.

5.  The optical fiber consists of two concentric cylinders; the inside solid cylinder is called the core and the surrounding shell is called the cladding. (See Fig 12)

Figure 20:  Schematic of an optical fiber

6. For the light to propagate inside the fiber through total internal reflections at core-cladding interface, the refractive index of the core must be greater than the refractive index of the cladding. That is n1>n2.

SIMPLE RAY MODEL                                                                                  

Figure 21: (optical fiber with core, cladding and total internally reflected ray)

For propagation of light inside the core there are two possibilities.

1.   A light ray is launched in a plane containing the axis of the fiber.  We can then see the light ray after total internal reflection travels in the same plane i.e., the ray is confined to the plane in which it was launched and never leave the plane. In this situation the rays will always cross the axis of the fiber. These are called the Meridional rays. (Figure 21)

2.   The other possibility is that the ray is not launched in a plane containing the axis of the fiber.

For example if the ray is launched at some angle such that it does not intersect the axis of the fiber, then after total internal reflection it will go to some other plane. We can see that in this situation the ray will never intersect the axis of the fiber. The ray essentially will spiral around the axis of fiber. These rays are called the Skew rays. 

So it can be concluded that if the light is to propagate inside an optical fiber it could be through two types of rays

a) Meridional rays: The rays which always pass through the axis of fiber giving high optical intensity at the center of the core of the fiber.

b) Skew Rays: The rays which never intersect the axis of the fiber, giving low optical intensity at the center and high intensity towards the rim of the fiber.

Q.18 When mean optical power launched into an 8 km length of fibre is 12 μW, the mean optical power at the fibre output is 3 μW. Determine

a)     Overall signal attenuation in dB.

b)    The overall signal attenuation for a 10 km optical link using the same fibre with splices at 1 km intervals, each giving an attenuation of 1 dB.

Solution:

Given :z=8km

P(0) = 120 μW

P(z) = 3 μW

a)     Overall attenuation is given by,

αp (dB/km ) = 10.  log = 16.02

b)    Overall attenuation for 10 km,

Attenuation per km = αp (dB/km )

=

=   = 2.00 dB/km

Attenuation in 10 km link = 2.00 x 10 = 20 dB

In 10 km link there will be 9 splices at 1 km interval. Each splices introducing attenuation of 1 dB.

Total attenuation = 20 dB + 9 dB = 29 dB

Q. 19 Discuss Dispersion Loss?

Solution:

Dispersion: A light pulse launched into a fibre decreases in the fibre. It also spreads during its travel. The pulse received at the output is wider than input pulse.

It means that the pulse becomes distorted as it is propagated through the fibre. Such a distortion arises due to dispersion effects.

Dispersion is typically measured in Nano seconds per kilometre (ns/km).

There are three mechanisms which contribute to the distortion of the light pulse in a fibre. They are known as:

a)                 Material dispersion

b)                Wave guide dispersion

c)                 Chromatic Dispersion

d)                Modal Dispersion

a)     Material Dispersion

Material dispersion is also called as chromatic dispersion. Material dispersion exists due to change in index of refraction for different wavelengths. A light ray contains components of various wavelengths. The time delay is different for different wavelength components. This results in time dispersion of pulse at the receiving end of fibre.

Light waves of different wavelengths travel at different speeds in a medium. The short wavelength waves travel slower than long wavelength waves. Consequently, narrow pulses of light tend to broaden as they travel down the optical fibre. This is known as material dispersion.

The material dispersion for unit length (L = 1) is given by

D =

Where c = Light velocity

λ = Center wavelength

= Second derivative of index of refraction w.r.t wavelength.

Negative sign shows that the upper sideband signal (lowest wavelength) arrives before the lower sideband (highest wavelength).

The unit of dispersion is : ps/nm/km. The amount of material dispersion depends upon the chemical composition of glass.

Example: An LED operating at 850 nm has a spectral width of 45 nm. What is the pulse spreading in ns/km due to material dispersion?

Solution:

Given :λ = 850 nm

σ = 45 nm

R.M.S pulse broadening due to material dispersion is given by,

σm= σLM

Considering length L = 1 metre

Dmat =  

For LED source operating at 850 nm, = 0.025

M =   by substituting all values we have

M = 9.8 ps/nm/km

σm= 441 ns/km

b)    Waveguide Dispersion

• Waveguide dispersion is caused by the difference in the index of refraction between the core and cladding, resulting in a ‘drag’ effect between the core and cladding portions of the power.
• Waveguide dispersion is significant only in fibres carrying fewer than 5-10 modes. Since multimode optical fibres carry hundreds of modes, they will not have observable waveguide dispersion.
• The group delay (τwg) arising due to waveguide dispersion.

τwg = [ n2 +n2 ∆ ]

Where, b = Normalized propagation

Constant k = 2π / λ (group velocity)

Normalized frequency V,

V = ka

τwg = [ n2 +n2 ∆ ]

The second term   is waveguide dispersion and is mode dependent term.

As frequency is a function of wavelength, the group velocity of the energy varies with frequency. This produces additional losses (waveguide dispersion). The propagation constant (b) varies with wavelength, the causes of which are independent of material dispersion.

c)     Chromatic Dispersion

The combination of material dispersion and waveguide dispersion is called chromatic dispersion. These losses primarily concern the spectral width of transmitter and choice of correct wavelength.

Material dispersion and waveguide dispersion effects vary in opposite senses as the wavelength increased, but at an optimum wavelength, two effects almost cancel each other and chromatic dispersion is at minimum. Attenuation is therefore also at minimum and makes highly attractive Operating wavelength.

d)    Modal Dispersion

As only a certain number of modes can propagate down the fibre, each of these modes carries the modulation signal and each one is incident on the boundary at a different angle, they will each have their own individual propagation times. The net effect is spreading of pulse; this form o dispersion is called modal dispersion.

• Modal dispersion takes place in multimode fibres. It is moderately present in graded index fibres and almost eliminated in single mode step index fibres.
• Modal dispersion is given by

∆tmodal =

Where ∆tmodal = Dispersion

n1= Core refractive index

Z = Total fibre length

c = Velocity of light in air.

The above equation can also be written as

∆tmodal =

The modal dispersion ∆tmodal describes the optical pulse spreading due to modal effects optical pulse width can be converted to electrical rise time through the relationship.

tr mod = 0.44 (∆tmodal)πr2