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SCHOOL OF SCIENCE AND HUMANITIES

DEPARTMENT OF PHYSICS

UNIT – I - Laser Physics – SPH

UNIT - 1 Laser Physics

Basic Principle of Laser – Einstein Coefficients – Condition for light amplification – Population Inversion – Threshold Condition – Line Shape Function – Optical Resonators – Three level and four level systems.

I Introduction

LASER stands for L ight A mplification by S timulated E mission of R adiation. Laser is a device which emits a powerful, monochromatic collimated beam of light. The emitted light waves are coherent in nature. The first laser, ruby laser was invented by Dr.T.H. Maiman in the year 1960. Since then, the development of lasers is extremely rapid. The laser action is being demonstrated in many solids, liquids, gases and semiconductor.

1.1 CHARACTERISTICS OF LASER

Laser is basically a light source. Laser light has the following important characteristics
High Directionality
High Intensity
Highly Monochromatic
Highly Coherence

1. Directionality

Ordinary light spreads in all directions and its angular spread is 1m/m.

Fig. 1.1 Directionality property of Laser

But it is found that laser is highly directional and is angular spread is 1mm/m. For example, the laser beam can be focused to very long distance with a few divergence or angular spread shown in Fig. 1.1.

2. Intensity Since an ordinary light spreads in all directions, the intensity reaching the target is very less. But in the case of laser, due to high directionality, the intensity of laser beam reaching the target is of high intense beam. For example, 1 mill watt power of He-Ne laser appears to be brighter than the sunlight (Fig. 1.2).

phase. 5 The radiation are polychromatic The radiations are monochromatic 6 Example: Sun light, Mercury vapor lamp He- Ne Laser, Co2 laser

1.2 STIMULATED ABSORPTION, SPONTANEOUS EMISSION AND STIMULATED

EMISSION

Process 1 - Stimulated absorption

An atom in the lower energy level or ground state energy level E 1 absorbs the incident photon radiation of energy and goes to the higher energy level or excited level E 2 as shown in

figure 1.5. This process is called absorption.

Fig. 1.5 Absorption and emission process in Laser

Process 2- Spontaneous Emission

The atom in the excited state returns to the ground state by emitting a photon of energy E = (E 2 – E 1 ) = spontaneously without any external triggering as shown in the figure. This process is

known as spontaneous emission. Such an emission is random and is independent of incident radiation.

Process 3 - Stimulated Emission

The atom in the excited state can also return to the ground state by external triggering or inducement of photon thereby emitting a photon of energy equal to the energy of the incident photon, known as stimulated emission. Thus results in two photons of same energy, phase difference and of same directionality as shown.

Table 1.1 Differences between Stimulated and spontaneous emission of radiation

S. No. Stimulated Emission Spontaneous emission

An atom in the excited state is induced to return to the ground state , thereby resulting in two photons of same frequency and energy is called Stimulated emission

The atom in the excited state returns to the ground state thereby emitting a photon, without any external inducement is called Spontaneous emission.

2 The emitted photons move in the same direction and is highly directional

The emitted photons move in all directions and are random 3 The radiation is highly intense, monochromatic and coherent

The radiation is less intense and is incoherent 4 The^ photons^ are^ in^ phase,^ there^ is^ a constant phase difference

The photons are not in phase (i.e.) there is no phase relationship between them. 5

The rate of transition is given by The rate of transition is given by

1.3 POPULATION INVERSION

Population Inversion creates a situation in which the number of atoms in higher energy state is more than that in the lower energy state. Usually at thermal equilibrium, the number of atoms N 2 i.e., the population of atoms at higher energy state is much lesser than the population of the atoms at lower energy state N 1 that is N 1 > N 2. The Phenomenon of making N 2 > N 1 is known as Population Inversion (Fig. 1.6).

Fig. 1.6. Population Inversion

Condition for Population inversion

1. There must be at least two energy levels E 2 > E 1.
2. There must be a source to supply the energy to the medium.
3. The atoms must be continuously raised to the excited state.

1.4 META STABLE STATES

An atom can be excited to a higher level by supplying energy to it. Normally, excited atoms have short life times and release their energy in a matter of nano seconds (10-9) through

Normally, the atoms in the excited state will not stay there for a long period of time, rather it comes to ground state by emitting a photon of energy. Such an emission takes place by one

of the following two methods.

b). Spontaneous emission:

The atom in the excited state returns to the ground state by emitting a photon of energy E = (E 2 – E 1 ) = spontaneously without any external triggering as shown in the figure. This process is

known as spontaneous emission. Such an emission is random and is independent of incident radiation. If N 1 and N 2 are the numbers of atoms in the ground state (E 1 ) and excited state (E 2 ) respectively, then The rate of spontaneous emission is

Where A21- is a constant which gives the probability of spontaneous emission transitions per unit time.

c). Stimulated Emission: The atom in the excited state can also return to the ground state by external triggering or inducement of photon thereby emitting a photon of energy equal to the energy of the incident photon, known as stimulated emission. Thus results in two photons of same energy, phase difference and of same directionality as shown. Therefore, the rate of stimulated emission is given by

Where B21- is a constant which gives the probability of stimulated emission transitions per unit time.

Einstein’s theory 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 population of energy levels obeys the Maxwell Boltzmann distribution law

Under thermal equilibrium

(or)

We know from the Boltzmann distribution law

Where KB is the Boltzmann Constant, T is the absolute temperature and N 0 is the number of atoms at absolute zero. At equilibrium, we can write the ratio of population levels as follows 2 1 1 2

B

E E N (^) e K T N

−

Substituting equation (8) in equation (9)

This equation has a very good agreement with Planck’s energy distribution radiation law.

Therefore comparing equations (6) and (7) , we can write

Taking A 21 =A

The constants A and B are called as Einstein Coefficients, which accounts for spontaneous and stimulated emission probabilities. Generally Spontaneous emission is more predominant in the optical region (Ordinary light). To increase the number of coherent photons stimulated emission should dominate over spontaneous emission. To achieve this, an artificial condition called Population Inversion is necessary.

1.6 PRINCIPLE OF LASER ACTION

Let as consider many number atoms in the excited state. We know the photons emitted during stimulated emission have same frequency, energy and are in phase as the incident photon. Thus result (fig. 1.7) in 2 photons of similar properties.

Fig. 1.7 Amplification in Laser process

3. Direct Conversion

In this method, due to electrical energy applied in direct band gap semiconductor like Ga As, recombination of electrons and holes takes place. During the recombination process, the electrical energy is directly is converted into light energy.

4. In elastic atom – atom collision In this method, a combination of two gases (Say A and B are used). The excited states of A

and B nearly coincides in energy.

In the first step during the electrical discharge atoms of gas A are excited to their higher

energy state A* (metastable state) due to collision with the electrons. A + e* = A* + e

Now A* atoms at higher energy state collide with b atoms in the lower state. Due to

inelastic atom - atom collision B atoms gain energy and they are excited to a higher state B*.

Hence, A atoms lose energy and return to lower state. A* + B = A + B*

1.8 OPTICAL RESONATOR

An optical resonator consists of a pair of reflecting surfaces in which one is fully reflecting

(R 1 ) and the other is partially reflecting (R 2 ). The active material is placed in between these two

reflecting

surfaces.

Fig. 1.8 View of optical resonator

The photons generated due to transitions between the energy states of active material are bounced back and forth between two reflecting surfaces. This will induce more and more stimulated transition leading to laser action.

Interaction of radiation with matter is better explained using concept of photon rather than by the wave concept.

Energy exchange can take place only at certain discrete values for which the photon energy is the minimum energy unit that light can give or accept.
Wave picture of light is Classical and Photon picture is Quantum Mechanical.

Laser- inherently a Quantum Mechanical device------ its operation depends on the existence of photons.
Maxwell: Light belongs to group of EM waves; propagate with speed “c‟ in vacuum.

 Frequency and wavelength related through

Light incident on a substance, may undergo reflection, transmission, absorption and scattering to varying degrees depending on nature of substance.

Results in loss of energy and hence

decrease in light intensity with distance

 Absorption or Attenuation

Attenuation Coefficient (α) - A measure of absorption of light in an optical medium. Is different for different medium and is a function of incident energy.

At temperature above 0K,

 Atoms always have some thermal energy;

 Distributed among available energy levels according to their energy.

At Thermal Equilibrium;

 Population at each energy level decreases with increase of energy level,

For energy levels E 1 and E 2 ,

Populations can be computed with Boltzmann′s equation

Ratio of populations, N 2 /N 1 is called Relative Population.

Relative Population (N 2 /N 1 ); dependent on two factors

Energy difference (E 2 -E 1 )

Temperature, T At Lower Temperature; All atoms are in the ground states.

At higher Temperature; Atoms move to higher states

Relative Population (N 2 /N 1 ); dependent on two factors

Energy difference (E 2 -E 1 ) Temperature, T

At Lower Temperature; All atoms are in the ground states.

At higher Temperature; Atoms move to higher states Important Conclusions

As long as the material is in thermal equilibrium, the population of the higher state cannot exceed the population of lower states

Excitation: Electron in the ground state receives an amount of energy equal to the difference of energy of ground state and one of the excited states, absorbs energy and jumps to the excited state. Electron cannot stay in the excited state for a longer time.

Determination of threshold gain by considering the change in intensity of a beam of light undergoing a round trip within the resonator?
Consider the laser medium fills the space between the mirrors M 1 & M 2 , of reflectivity R 1 & R 2 respectively and mirrors separated by a distance L.

Let I 0 - the intensity of the light beam at M 1

Traveling from mirror M 1 to mirror M 2 ⇒ beam intensity increases from I 0 to I(L),

After reflection at M 2 , the beam Intensity will be; After a complete round trip (Reflection from M 1 ), the final Intensity will be

Growth of output Power Through Cavity

Fig. 1.9 setup of optical resonator

Consider the laser medium fills the space between the mirrors M 1 & M 2 , of reflectivity R 1 & R 2 respectively and mirrors separated by a distance L Let I 0 - the intensity of the light beam at M 1 Let E 0 – the Energy of the light beam at M 1

Product R 1 R 2 represents the losses at the mirrors, whereas αs includes all the distributed losses such as scattering, diffraction and absorption occurring in the medium.

Condition for Lasing Shows that the initial gain must exceed the sum of losses in the cavity. The condition is used to determine the threshold value of pumping energy necessary for lasing action.

‘γ’- Amplification of the laser, dependent on how hard the laser medium is pumped.

As the pump power is slowly increased, a value of ‘γth’ called threshold value will be reached and the laser starts oscillating.

Threshold value ‘γth’ is given by

Value of ‘γ’ must be atleast ‘γth’ for laser oscillations to commence

If γ > γth the waves grow and the amplifier reaches saturation.

It lowers the value of γ in turn and eventually an equilibrium value is attained at γth

LINESHAPE FUNCTION

Define lineshape function g(ν)

g(ν) gives the probability that a transition between two levels is an emission (or absorption) of photon whose frequency lies in the range ν and ν+dν. Normalization demands

1,11 Febry-Perot resonator

Fig. 1.10 View of Febry-Perot resonator

Fig. 1.11 Common model of Laser cavity

1.12 Laser Modes

A wave of frequency ν, that travel along the axis of cavity forms a series of standing waves within the cavity.

 They are discrete resonant conditions determined by the physical dimensions of the cavity.

• Modes governed by the cross-sectional dimension of the optical cavity - Transverse modes
• modes governed by the axial dimension of the resonant cavity - Longitudinal or Axial modes
• In a cavity flanked by two plane parallel mirrors, the standing waves in the cavity satisfy the condition. The axial modes contribute to a single spot of light in the laser spot.

Pumping Schemes

Atoms characterized by a large number of energy levels.
Only two, three or four levels are pertinent to the pumping process.

Types are  Two-level,

 Three-level and  Four –level schemes.

Two-level Pumping system: Appears to be most simple and straight-forward method to establish population inversion; Pumping an excess of atoms into the higher energy state by applying intense radiation fig.

A two-level pumping scheme is not suitable for attaining P.I.

Fig. 1.12 Two level Laser system

P.I. requires the lifetime ∆t of upper level E 2 must be longer.

As the ground state is heavily populated, large pumping power is to be used to depopulate the ground level to the required extent (N 2 > N 1 )

Three level scheme can produce light only in Pulses.

Once stimulated emission commences, the metastable state E 2 gets depopulated very rapidly and the population of the ground state increases quickly.

As a result the population inversion ends. One has to wait till the population inversion is again established.

Three level lasers operate in Pulsed Mode.

1.14 Four Level Pumping Scheme

Fig. 1.14 Four level Laser System

In Four level scheme, the terminal laser level E 2 is well above the ground level such that (E 2 -E 1 ) >> kT.

It guarantees that the thermal equilibrium population of E 2 level is negligible.
In contrast to three level scheme, the lower laser transition level in four level scheme is not the ground state and is virtually vacant.

It requires less pumping energy than does a three level laser.

Further, the lifetime of the lower laser transition level E 2 is much shorter, hence atoms in level E 2 quickly drop to the ground state.

This steady depletion of E 2 level helps sustain the population inversion by avoiding an accumulation of atoms in the lower lasing level fig. 2.4.
Four level lasers can operate in Continuous Wave mode

Most of the working lasers are based on Four Level Scheme

Comparison of Three level and Four level Systems

Three level laser, Nth = (N 2 -N 1 ) and N 0 = N 2 +N 1

Four level laser

Implies that it is much easier to pump a four level laser than a three level laser. This is the reason why most of the lasers are of four-level.