Common to All Branches of B.E / B.Tech
ENGINEERING PHYSICS - I
(Common to all branches of B.E / B.Tech)
UNIT– II
Lasers
2.1 INTRODUCTION
The word LASER is an acronym for Light Amplification by Stimulated Emission of Radiation.
Laser is a device which produces a monochromatic, collimated beam of light which is coherent. Laser beam contains high intense radiation in unique direction. Lasers are used in many fields of science and technology like radio astronomy, satellite-communication, optical fibre communication holography, testing and welding of materials, medicines etc.,
2.2 Characteristics of Laser Radiation
The important features of laser over conventional light source are
(i) It is high directionality
(ii) It is high intensity
(iii) It is extraordinary monochromatic
(iv) It is high degree of coherence
(i) Directionality
The conventional light sources emit light in all directions due to spontaneous emission. Lasers on the other hand emit light only in one direction due to stimulated emission.
(ii) Intensity
The laser gives out light into a narrow beam of light and its energy is concentrated in a small region. This concentration of energy is existing both spatially and spectrally and so there is enormous intensity for lasers.
(iii) Monochromatic
A laser beam is highly monochromatic, i.e., it contains only single frequency and it has very little spreading. Due to stimulated emission, the light emitted by a laser is more monochromatic than that of any conventional monochromatic source.
(iv) Coherence
The light from a source consists of wave trains. These wave trains when identical in phase and directions are called coherent.
Laser has a high degree of coherence than the ordinary sources. The coherence of laser emission results in an extremely high power of 5x1016Watt/m2.
2.3 Stimulated absorption, Spontaneous emission and stimulated emission
To understand the laser principle, we must study the quantum processes that take place in a material medium when it is exposed to light radiation.
During the transition of atoms or molecules from one energy state to another, light is absorbed or emitted by these atoms. Let us consider an atom which has only two energy levels E1 and E2. When the atom is exposed to light (photons) of energy E2-E1= h. Three distinct processes take place.
1. Stimulated Absorption
2. Spontaneous emission
3. Stimulated emission
Process (1) Stimulated Absorption
An atom in the ground state (or) lower energy level E1 absorbs the incident photon of energy h and goes to the excited state (higher state) with energy E2 as shown in Fig.2.1, provided the photon energy h is equal to the energy difference (E2-E1). This process is called stimulated absorption.
During this each transition, energy is removed from the incident light beam. If there are many numbers of atoms in the ground state then each atom will absorb the energy from the incident photon and goes to the excited state. The number of transitions at any instant is proportional to the number of atoms in state E1 and the number of photons in the incident beam.
Thus the number of transitions (Nab) occurring in time is given by
Nab = N1B12Q
Where,
N1 – The number of atoms in the state E1
B12 – The probability of an absorption transition
Q – The energy density of incident radiation (the number of photons)
Normally, the atoms in the excited state will not stay in this state for longer time. It is natural tendency of atoms to seek out the lowest energy level. So the atoms in the excited state quickly return to ground state by emitting a photon of frequency and energy.
The emission process can take place in one of the two forms namely
(i) Spontaneous emission (ii) Stimulated emission
Process (2) Spontaneous Emission
The atom in the excited state E2 (higher energy level) returns to the ground state E1 (Lower energy level) by emitting a photon of energy without the action of an external agency. Such an emission of radiation which is not triggered by an external influence is called spontaneous emission.
The spontaneous emission is a random process and it is independent of incident radiation.
The number of spontaneous transitions Nsp occurring in time depends only on the number of atoms N2 lying in the state E2.
It is given by
Nsp = N2 A21
Where,
A21 represents the probability of a spontaneous transition from E2 to E1.
Process (3) Stimulated emission
Einstein found that there must be another mechanism by which an atom in the excited state can return to the ground state. He found that, there is an interaction between an atom in the excited state and a photon. During interaction, photon can trigger the excited atom to make a transition to the ground state E1 (Fig.) The transition generates a second photon which would be identical to the triggering photon in respect of frequency, phase, propagation and direction.
This process of forced emission of photons caused by the incident photons is called stimulated emission. This process is the key factor to the operation of a laser.
The number of stimulated transitions (Nst) is proportional to the number of atoms in the excited state N2 and the number of photons in the incident radiation.
Thus, the number of transitions (Nst) occurring in time is given by
Nst = N2B21Q
Where,
N2 – the number of atoms in the state E2
B21 – represents the probability of stimulated transition
Q – the energy density of incident radiation (the number of photons)
This means that incidence of photon energy on the atom which is in excited state, stimulates the emission of a similar photon of same energy by transition to lower energy state. It is also called induced emission. From the laser action point of view, stimulated emission is important.
This stimulated emission can be multiplied through chain reaction. This multiplication of photons through stimulated emission leads to coherent, powerful, monochromatic, collimated beam of light emission. This light emission is called laser.
2.4. Einstein’s Quantum theory of Radiation – Determination of Einstein’s coefficients (A & B)
Einstein’s theory of absorption and emission of light by an atom is based on Planck’s theory of radiation. Also under thermal equilibrium, the populations of energy levels obey the Boltzmann’s distribution law.
In an assembly of a very large number of atoms, it is possible to calculate the transitions between two states based on the laws of probability.
Einstein’s was the first to calculate the probability of such transition assuming the atomic system to be in equilibrium with electromagnetic radiation.
Consider an assembly of atoms at an absolute temperature T in which one atom may be in different states.
If N0 is the number of atoms per unit volume in the ground state (E=0), then the number of atoms per unit volume in an excited state of energy E is given by the Boltzmann’s distribution law.
N = N0e(-E/kT) ------(1)
Where, k – Boltzmann’s constant
If N1 and N2 are the number of atoms per unit volume in the states of energies E1 and E2, then from equation (1) we get
------(2)
We know that when the assembly of atoms exposed to the light radiation of photon of energy , the following three different transitions take place.
Process 1: Stimulated absorption
The atoms in the ground state (E1) are raised to the excited state (E2) after absorbing a photon of energy provided the photon of energy is equal to the energy difference (E2-E1). This process is called stimulated absorption. This is upward transition. The number of transition (Nab) occurring per unit volume per second.
Nab = N1B12Q ------(3)
Process 2: Spontaneous emission
The atoms inn the excited (higher) energy state E2 make spontaneous transitions to the ground state (Lower energy state) E1 at a certain rate. This is downward transition.
The number os such transitions per unit volume per second,
Nsp = A21N2 ------(4)
Process 3: Stimulated emission
The atom in the excited state can return to the ground state by external triggering of photon thereby emitting a photon of energy equal to the energy of the incident photon. This is called stimulated emission and this is downward transition.
The number of transitions per unit volume per second,
Nst = B21N2Q ------(5)
The coefficients A12, B12 and B21 are known as Einstein’s coefficients A and B.
Under equilibrium, the number of upward and downward transitions per unit volume per second is equal.
A21N2 + B21N2Q = B12N1Q ------(6)
rearranging the above equation, we get
------(7)
By dividing all the terms by B21N2, we get
------(8)
Taking the value of E2-E1 = and substituting the value of from eqn. (2)
We have,
------(9)
Equation (9) must agree with Planck’s energy distribution radiation formula
------(10)
Comparing the two equations (9) and (10), we get
B12 = B21 = B ------(11)
and ------(12)
Taking A21 = A
The constants A and B are called as Einstein Coefficients
Results:
(1) Equation (11) states that the stimulated emission rate per atom is same as the absorption rate per atom.
(2) Equation (12) gives the relation between the spontaneous emission and stimulated emission coefficients.
Since the ratio is proportional to , the probability of spontaneous emission rapidly increases with the energy difference between the two states.
2.5. Concept of Laser
1. Population of atoms in the higher energy level as compared to lower energy level is increased by pumping the matter by photons of appropriate energy. Thus atoms are excited to higher energy states.
2. We know the photons emitted during stimulated emission have same frequency, energy and are in phase as the incident photon. The results in 2 photons of similar properties. These two photons induce stimulated emission of 2 atoms in excited state thereby resulting in 4 photons. These 4 photons induce 4 more atoms and give rise to 8 photons etc., This chain reaction goes on and there is an intense beam of radiation. Thus the electromagnetic radiation is amplified.
3. Generally spontaneous emission is more predominant in the optical region. To increase the number of coherent photons, stimulated emission should dominate spontaneous emission.
4. For stimulated emission to predominate over absorption, it is essential that excited atoms should be in excess in the active medium. For continuous output, population inversion is necessary.
2.6. Population Inversion
Population inversion is the state of achieving more number of atoms in the excited state compared to the ground state atoms.
Consider two energy level systems E1 and E2. Suppose a photon of energy equal to the energy equal to the energy difference between the two energy levels, incident on the system, then there is equal chances for stimulated emission and absorption to occur, At this situation, the chance for emission (or) the absorption depends only on the number of atoms in the ground state and in the excited state.
Let N1 be the number of atoms in ground state and N2 be the number of atoms in the excited state. Then,
If N1 N2 there is more chance for absorption to take place
And If N2N1 there is more chance for stimulated emission to take place.
For stimulated emission to predominate over absorption, it is essential that excited atoms should be in excess in the active medium. For continuous output, population inversion is necessary.
The population inversion can be achieved by some artificial process known as pumping.
Active Medium: The medium in which the population inversion takes place is called as
active medium.
Active Centre : The atoms which are raised to excited state to achieve population
inversion is called as active centre.
2.7. Pumping Methods
Pumping:
The process of raising more number of atoms to excited state by artificial means is called as pumping process.
The following common methods are adopted for achieving population inversion:
(i) Optical pumping, (ii) Direct electron excitation, (iii) Inelastic atom-atom collision, (iv) Direct conversion, (v) Chemical process
(i) Optical Pumping
In this process, the atoms are excited with the help of photons emitted by an external optical source. The atoms absorb energy from the photons and raises to excited state.
Example: Nd-YAG laser, Ruby laser.
(ii) Direct Electron Excitation
In this method, the electrons are accelerated to very high velocities by strong electric field and they collide with gas atoms and these atoms are raised to excited state.
Example: CO2 Laser, Gaseous ion Lasers.
(iii) Inelastic atom-atom Collision
In this process, a combination of two types of gases is used. Let A and B, both having same coinciding excited state A* and B*.
During the electric discharge ‘A’ atoms get excited to collision with electrons. The excited A* atoms now collide with ‘B’ atoms so that B goes to excited state B*.
Example: Helium neon Laser
e- + A A*
A* + BB* + A
(iv) Direct Conversion
In this method, due to electrical energy applied in direct band gap semiconductor like GaAs etc., the combination of electrons and holes takes place and electrical energy is converted into light energy directly.
Example: Semiconductor Laser
(v) Chemical Method
In this method, the atoms are raised to excited state by chemical reactions.
Example: Dye Laser
2.8. Optical Resonator
An active medium kept between a 100% reflecting mirror and a partially reflecting mirror constitutes an optical resonator.
This optical resonator acts as a feedback system in amplifying the light emitted from the active medium, by making it to undergo multiple reflections between the 100% mirror and the partial mirror. Here the light sources move back and forth between the two mirrors and hence the intensity of light is increased enormously. Finally the intense, amplified beam called LASER is allowed to come out through the partial mirror as shown in fig.
2.9. Flow Chart for Laser Action
Fig. shows the flow chart for the laser action. In the active medium, the ground level atoms are raised to the excited state by optical pumping. Thus population inversion is achieved such that N2 N1.