Spontaneous emission

Stimulated emission

1.The spontaneous emission was postulated by Bohr

1.The stimulated emission was postulated by Einstein

2. Additional photons are not required in spontaneous emission

2. Additional photons are required in stimulated emission

3.One photon is emitted in spontaneous emission

3.Two photons are emitted in stimulated emission

4.The emitted radiation is poly-monochromatic

4.The emitted radiation is monochromatic

5. The emitted radiation is Incoherent

5. The emitted radiation is Coherent

6. The emitted radiation is less intense

6. The emitted radiation is high intense

7.The emitted radiation has less directionality

7.The emitted radiation has high directionality

8. Example: light from sodium or

Mercury lamp

8. Example: light from the laser source.

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

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) =

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

ρ(υ) =

ρ(υ) =

We know from Maxwell Boltzmann distribution law

And also from Planck’s law, the radiation density

ρ(υ) =

Comparing the two equations (7) and (9)

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.

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.

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.

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

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.

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.

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.

Given

Volume = 7500m3

Reverberation time T = 1.5 sec

We know that reverberation time is given by

T =   0.165 V/

T =   0.165 V/ A

Where V-Volume of hall in m3

A - Absorption coefficient

1.5 =  0.165 x 7500/A

A= 825 O.W.S

Given

Volume = 1200m3

The average absorption coefficient is

A = a1s1 +a2s2 +a3s3 / s1 +s2 +s3

A = (0.03 x 200 + 0.80 x120 +0.06 x 120) / (200+120+120)

A = 0.2389 =0.24 (approx.)

Now the total absorption of room = As =0.24 x460 =110.40 O.W.S.

Reverberation Time T =   0.165 V/AS = 0.165 x 1200/ 109.2

= 1.80 seconds

A =as = (0.165) x (20x15x10)/ 3.5 = 138 m2

When wall is covered with the curtain clothe

2.5 = (0.165) x (20x15x10)/ 0.5x s

Therefore area of the wall covered by the curtain

s = 483- (2.5 x 138)  /2.5 x 0.5

110.4 m2

Piezoelectric Generator or Oscillator is used to produce a high frequency of range 500MHz. Let us discuss the production of ultrasonic waves by this method.

Principle:

This is based on the inverse piezoelectric effect. When a quartz crystal is placed under the effect of an alternating potential difference, vibrations are produced in the crystal. If the frequency of electric oscillations coincides with the natural frequency of vibrations of the crystal, the vibrations will be of large amplitude. When the frequency of the electric field matches the ultrasonic frequency range, then the crystal produces ultrasonic waves.

Electric circuit :

Construction:

• It is a common base NPN oscillator circuit.
• Coils L1 and L2 are the primary coils of the transformer.
• Coil L2 is connected to the collector and L1 connected to the base.
• The coil L1 and variable capacitor C1 form the tank circuit of the oscillator.
• Quartz crystal is placed between the metal plates A and B to form a parallel plate capacitor.
• Quartz Crystal is connected to the secondary coil L3 of the transformer through which output or ultrasonic wave is obtained.
• The frequency of the oscillations can be changed by changing the value of capacitance.

Working:

As soon as the circuit is closed, the current starts to flow through the circuit and charges the capacitor. After the charging is completed the capacitor starts discharging through the inductor L1, this energy is stored in the form of the electric field in capacitor C1 and the form of the magnetic field in inductor L1.

 Due to this high frequency, electric oscillations are produced in the tank circuit. The transistor is also produced by electric oscillations. This energy or oscillations is provided to the secondary coil which is again fed to the quartz crystal. Thus the oscillating electric field is converted to mechanical vibration of the crystal.             

When the frequency of electric oscillations is equal to that of the natural frequency of the crystal, resonance is achieved and the sound waves of maximum amplitude are produced. Thus by using the inverse piezoelectric effect high-frequency ultrasonic waves are produced.

Condition for Resonance:

Frequency of the oscillator circuit = Frequency of the vibrating crystal

Where, 

L1 is the inductance of the circuit

C1 is the capacitance of the circuit

t = Thickness of crystal slab

Y = Young's Modulus of material

ρ = Density of material

k = 1, 2, 3. .. (Integer Multiple)

Advantages:

• High-frequency ultrasonic waves can be produced.
• This method is more effective than Magnetostriction oscillator.
• The output power is very high
• We can get a stable and constant frequency of ultrasonic waves.
• It is not affected by temperature humidity

Disadvantages:

• Quartz crystal is very costly.
• Cutting and shaping the crystal is difficult.

Magneto-striction generator or oscillator

Principle: Magnetostriction effect: Magnetostriction is a property of magnetic materials like nickel or iron that causes them to change their shape or dimensions during the process of magnetization. i.e. when this material is placed in the magnetic field parallel to its length it changes its dimensions.  This is called the Magnetostriction effect.

Electronic circuit:

Construction

• In the above figure, we are using NPN Transistor
• In which battery is connected in such a way that emitter is forward biased and collector is reverse biased.
• Current can be produced by applying necessary biasing to the transistor with the help of the battery.
• The current produced in a circuit can be noted by the mill ammeter connected across the coil L.
• The ends of the ferromagnetic rod A and B are wound by the coils L1 and L.
• The coil L1 is connected to the base of the NPN transistor The coil L is connected to the collector of the NPN transistor as shown in the figure.
• The frequency of the oscillatory circuit (LC) can be adjusted by the condenser C.
   

Working 

The rod is initially magnetized by the DC power supply. The transistor is properly biased. The battery is switched on and hence current is produced by the transistor. This current is passed through coil L, this current causes a change in the magnetization of the rod. Now, the rod starts vibrating due to the Magnetostriction effect.

When the rod is vibrating and the coil is wounded over a vibrating rod, An emf is induced in coil L, this induces an emf to coil L1 & a part of it is feed as input to the base. Hence, this feedback system makes the transistor operates continuously. The e.m.f. induced in the coil called a converse Magnetostriction effect. In this way, the current is maintained in the transistor so as the vibrations.

The frequency of the oscillatory circuit is adjusted by the condenser C and when this frequency is equal to the frequency of the vibrating rod, resonance occurs. At resonance, the rod vibrates longitudinally with larger amplitude producing ultrasonic waves of high frequency along both ends of the rod. 

Condition for resonance

Frequency of the oscillatory circuit = Frequency of the vibrating rod 

Where, 

L is the inductance of the circuit

C is the capacitance of the circuit

l is the length of the rod.
E is the young’s modulus of the material of the rod.
ρ is the density of the material of the rod.

 

Advantages

• This Oscillatory circuit is simple to construct.
• Magnetostrictive materials are easily available at a low cost
• Large output power can be generated by using this method. 

Disadvantages
 

• It can produce frequencies up to 3 MHz only.
• As rod depends on temperature and the degree of magnetization so it becomes difficult to get a constant single frequency.
• As the frequency is inversely proportional to the length of the vibrating rod, so if you increase the frequency, the length of the rod gets decreased which is practically impossible.

Magnetostriction Method

Piezoelectric method

1. It generates low-frequency ultrasonic waves(3MHz)

1. It generates very high-frequency ultrasonic waves(500MHz)

2.     We cannot obtain the constant frequency of ultrasonic waves

2.     We can obtain the constant frequency of ultrasonic waves.

3.     The peak of the resonance curve is broad

3.     The peak of the resonance curve is narrow

4.     The frequency of oscillations depends on temperature.

4.     The frequency of oscillation is independent of temperature.

Absorption Coefficient =

According to W. C. Sabine, the time of reverberation depends upon

1. Size of the hall,

2. Loudness of the sound,

3. Kind of music or sound for which hall is to be used.

Acoustics and Ultrasonic Reverberation Time

T = 0.165 V/

T = 0.165 V/ A

Where V-Volume of the hall in m3

a - Absorption coefficient

S - Area of reflecting surface in a square meter

The acoustically good hall we mean that in which every syllable or musical note reaches an audible level of loudness at every point of the hall and then quickly dies away to make the room ready for the next syllable or group of notes. Following are the factors affecting architectural acoustics.

1. REVERBERATION

In a hall, if the reverberation is large there are successive sounds that result in loss of clarity in hearing. However, if the reverberation is very small, the loudness is inadequate Thus the time of reverberation for a hall should neither too large nor too small. The preferred value of the time of reverberation is called optimum reverberation time. According to W. C. Sabine standard reverberation time is given by:

T = 0.165 V/

T = 0.165 V/ A

Where V-Volume of the hall in m3

a - Absorption coefficient

S - Area of reflecting surface in a square meter

The reverberation can be controlled by the following factors:

• By providing windows and ventilators which can be opened and closed to make the optimum time of reverberation
• Decorating the walls with pictures and maps
• Using heavy curtains with folds
• The walls are lined with absorbent material such as felt, fibreboard, glass wool, etc.
• Having a full capacity of audience
• By covering the floor with carpet
• By providing acoustics tiles

2.     ADEQUATE LOUDNESS

With large absorption, the time of reverberation will be smaller which will minimize the chances of confusion and may go below the level of intelligibility of hearing. Hence suffi­cient loudness in every portion of the hall is an important factor for satisfactory hearing.

The loudness can be maintained at the desired level by:

Using large sounding boards behind the speaker and facing the audience.

Large polished wooden reflecting surfaces immediately above the speakers.

Low ceilings are also useful in reflecting the sound energy towards the audience.

By providing additional sound energy using more number of speakers

3.     FOCUSING DUE TO WALLS AND CEILINGS

If there are focusing surfaces like concave, spherical, cylindrical or parabolic, etc. on the walls or ceiling or the floor of the hall, they produce a concentration of the sound into a particular region, while in some other parts no sound reaches at all. Thus there will be non-­ uniformity in the distribution of sound energy in the hall.

For uniform distribution of sound in the hall:

• There should be no curved surfaces. If such surfaces are present, they should be covered with absorbent material.
• The ceiling should be low.
• Arrange speaker at the focus of parabolic reflecting surface. This will help to reflect a beam of sound in the hall.

4.     ECHOES

An echo is heard, when direct and reflected sound waves coming from the same source reach the listener with a time interval of about

Echoes can be avoided by:

• Covering long distant walls with a curtain or absorbent material
• Covering high ceiling with absorbent material

5.     ECHELON EFFECT

A set of railings, pillars, or any regular spacing of reflected surfaces may produce a musical note due to the regular succession of the echoes of the original sound to the listener. This makes the original sound confused.

This can be avoided by:

• Covering steps with carpet
• Covering flour with carpet
• Avoid pillars in the hall

6.     BALCONIES

There are chances of reflection of sound from the railing of the balcony. This may lead to the problem like echelon effect or echoes.

This can be eliminated by:

• Adjust the height to depth ratio is 2: 1
• Use grills and bars for railings instead of bricks

7.     SEATING ARRANGEMENT

This is one of the factors to be taken care of at the time of arranging the seats.

It pre­ferred to arrange:

• Seat perpendicular to the direction of sound for better audibility
• Seats must be gradually elevated to take care of absorption of sound energy by the human body.

8.     EXTRANEOUS NOISE AND SOUND INSULATION

In a good hall, no noise should reach from outside. Noise may be defined as unwanted sound such as:

Outside Noise: street traffic, hammering, drilling, operating machinery, moving of furni­ture, electrical generator, etc.

Inside Noise: machinery, typewriters, telephone, mobiles, projector, etc.

This extraneous noise can be avoided by:

• Avoiding openings for pipes and ventilators
• Allotting suitable locations for doors and windows
• Using heavy glasses to doors and windows
• By providing double-wall construction with air space between them
• By interposing layers of some acoustical insulators
• Use of soft floor finishes e.g. Carpet, rubber, etc.
• Insulating machines like refrigerators, lifts, typewriters, projector, etc.
• Constructing a small soundproof cabin for machine and office staff
• Making hall soundproof

9.     FREEDOM FROM RESONANCE

If the frequency of the created sound is equal to the original sound, then the original music will be reinforced. Due to the interference between the original sounds is distorted. Enclosed air in the hall also causes resonance.

This can be avoided by:

• Using absorbing material on reflecting surfaces
• Providing decoration which includes holes in the design on an interior wall
• Using ventilators whenever necessary

Semiconductor Laser

It is a solid-state semiconductor laser. It is a specifically fabricated p-n junction diode. This diode emits laser light when it is forward biased. A semiconductor laser is a device that causes laser oscillation by flowing an electric current to the semiconductor. The mechanism of light emission is the same as a light-emitting diode (LED). Light is generated by flowing the forward current to a p-n junction. In forward bias operation, the p-type layer is connected with the positive terminal, and the n-type layer is connected with the negative terminal, electrons enter from the n-type layer and holes from the p-type layer. When the two meet at the junction, an electron drops into a hole, and light is emitted at the time.

Semiconductor lasers represent one of the most important classes of lasers in use today, not only because of the large variety of direct applications in which they are involved but also because they have found widespread use as pumps for solid-state lasers.

Semiconductor lasers require, for the active medium, a direct gap material, and accordingly, the normal elemental semiconductors like Si or Ge cannot be used. The majority of semiconductor-laser materials are based on a combination of elements belonging to the third group of the periodic table such as Al, Ga, In with elements of the fifth group such as N, P, As, Sb. Examples include the best known GaAs as well as some ternary AlGaAs, InGaAs, and quaternary InGaAsP alloys.

InGaN semiconductor lasers the best candidates for semiconductor laser emission in the very important blue-green spectral region. Semiconductor laser materials are not limited to III–V compounds, however. For the blue-green end of the spectrum, we note that wide-gap semiconductors are using a combination between elements of the second group (such as Cd and Zn) and the sixth group (S, Se).

PRINCIPLE

When a p-n junction diode is forward biased, the electrons from the n – region and the holes from the p- region cross the junction and recombine with each other.

 During the recombination process, the light radiation (photons) is released from a certain specified direct bandgap semiconductor like Ga-As. This light radiation is known as recombination radiation.

The photon emitted during recombination stimulates other electrons and holes to recombine. As a result, stimulated emission takes place which produces laser.

Figure: 11

CONSTRUCTION

The basic structure of a semiconductor laser is shown in Figure. The active medium is a p-n junction diode made from the single crystal of gallium arsenide. The active layer called a light emission layer sandwiched between the p- and n-type clad layers i.e. double heterostructure is formed on an n-type substrate and voltage is applied across the p-n junction from the electrodes. This crystal is cut in the form of a platter having a thickness of 0.5μmm. Both edges of the active layer have a mirror-like surface. When a forward voltage is applied, electrons combine with holes at the p-n junction and emit the light.

This light is not a laser yet; it is confined within the active layer because the refractive index of the clad layers is lower than that of the active layer. Besides both ends of the active layer act as a reflecting mirror where the light reciprocates in the active layer. Then, the light is amplified by the stimulated emission process and laser oscillation is generated.

The photon emission is stimulated in a very thin layer of PN junction (in order of few microns). The electrical voltage is applied to the crystal through the electrode fixed on the upper surface. The end faces of the junction diode are well polished and parallel to each other. They act as an optical resonator through which the emitted light comes out.

Figure: 12

WORKING

When the PN junction is forward biased with large applied voltage, the electrons and holes are injected into the junction region in considerable concentration

The region around the junction contains a large number of electrons in the conduction band and a large number of holes in the valence band.

If the population density is high, a condition of population inversion is achieved. The electrons and holes recombine with each other and this recombination produces radiation in the form of light.

 When the forward-biased voltage is increased, more and more light photons are emitted and the light production instantly becomes stronger. These photons will trigger a chain of stimulated recombination resulting in the release of photons in phase.

 Figure: 13

The photons moving at the plane of the junction travels back and forth by reflection between two sides placed parallel and opposite to each other and grow in strength.

After gaining enough strength, it gives out the laser beam of wavelength 8400Å. The nature of output is a continuous wave or pulsed output. The power output from this laser is 1mW. The wavelength of laser light is given by

Where Eg is the bandgap energy in joule.

ADVANTAGES

• It is very small in dimension.
• The arrangement is simple and compact.
• It exhibits high efficiency.
• It is operated with lesser power than a ruby and CO2 laser.
• The laser output can be easily increased by controlling the junction current
• It requires very little auxiliary equipment
• It can have a continuous wave output or pulsed output.

DISADVANTAGES 

• It is difficult to control the mode pattern and mode structure of the laser.
• The output is usually from 5 degrees to 15 degrees i.e., the laser beam has a large divergence.
• The purity and monochromaticity are power than other types of laser
• Threshold current density is very large (400A/mm2).
• It has poor coherence and poor stability.

 APPLICATION

• It is widely used in fibre optic communication
• It is used to heal the wounds by infrared radiation
• It is also used as a pain killer
• It is used in laser printers and CD writing and reading.