LASER

Dr. Madhavrao K. Deore

M.Sc., Ph. D.

Department of Physics,

M.V.P.Samaja’s, Arts, Science and

Commerce College, Ozar(Mig),

Nashik, -422206, India

deoremadhav63@gmail.com

A laser is a device that emits light through a process of optical

amplification based on the stimulated emission of electromagnetic

radiation. The term "laser" originated as an acronym for "light

amplification by stimulated emission of radiation

The laser is perhaps the most important optical device to be

developed in the past 50 years. Since its arrival in the 1960s, rather

quiet and unheralded outside the scientific community, it has

provided the stimulus to make optics one of the most rapidly

growing fields in science and technology today.

The development of laser has been proved to be turning point in the

history of science and engineering. It has produced completely new

type of system with potential applications in wide verity of fields.

LASER

The theoretical background of laser action as the basis for an

optical amplifier was made possible by Albert Einstein, as early

as 1917, when he first predicted the existence of a new irradiative

process called “stimulated emission”. His theoretical work,

however, remained largely unexploited until 1954, when C.H.

Townes and Co-workers developed a microwave amplifier based

on stimulated emission radiation. It was called a maser.

The first laser was built in 1960 by Theodore H. Maiman at

Hughes Laboratories, based on theoretical work by Charles

Hard Townes and Arthur Leonard Schawlow.

Laser light and ordinary light difference

Laser light Ordinary light

It is highly coherent- single

frequency

It is incoherent in nature- discrete

freqn.

There coherence length as of the

order of few km (Kilometer).

There coherence length as of the

order of few mm (Millimeter).

It is travel in only one direction,

which is parallel to the optic axis.

Intensity of ordinary light decreases

with distance as it travels in form of

short pulses of small length and

short duration.

It is highly monochromatic as it

travels in form of large length and

long duration.

Only one wave lenght

It is not strictly monochromatic as it

travels in form of short pulses of

small length and short duration.

Wavelenght- 400-700 nm

Spread of plane wave front is less

hence they spread least i.e. their

divergence is less.

Spread of spherical wave font is

more hence they spread heavily i.e.

their divergence is more

polarized Mostly unpolarized

Brief history of laser 1) 1900 –Max Planks- light is electromaganetic radiation

2) 1917- principle of laser discovered- Albert Einstein- describe the theory of

stimulated emmision- Stimulated emission is the process by which an incoming

photon of a specific frequency can interact with an excited atomic electron (or other

excited molecular state), causing it to drop to a lower energy level. The liberated

energy transfers to the electromagnetic field, creating a new photon with

identical phase, frequency, polarization, and direction of travel as the photons of the

incident wave

1951: Charles H Townes, Alexander Prokhorov, Nikolai G Basov, Joseph

Weber - The invention of the MASER (Microwave Amplification of Stimulated

Emission of Radiation) at Columbia University, Lebedev Laboratories, Moscow and

University of Maryland.

1958: Schawlow, A.L. and Townes, C.H. - Proposed the realization of masers for

light and infrared at Columbia University .

1960-Townes, C.H- Patented and Nobel(1964)

1960: Maiman, T.H. - Realization of first working LASER based on Ruby at

Hughes Research Laboratories.

1961: Javan, A., Bennet, W.R. and Herriot, D.R. - First gas laser : Helium- Neon

(He-Ne laser) at Bell Laboratories.

1961: Fox, A.G., Li, T. - Theory of optical resonators at Bell Laboratories.

1962: Hall,R. - First Semiconductor laser (Gallium-Arsenide laser) at General

Electric Labs.

1962: McClung,F.J and Hellwarth, R.W. - Giant pulse generation / Q-Switching.

1962: Johnson, L.F., Boyd, G.D., Nassau, K and Sodden, R.R. - Continuous

wave solid-state laser.

1964: Geusic, J.E., Markos, H.M., Van Uiteit, L.G. - Development of first working

Nd:YAG LASER at Bell Labs.

1964: Patel, C.K.N. - Development of CO2 LASER at Bell Labs.

1964: Bridges, W. - Development of Argon Ion LASER a Hughes Labs.

1965: Pimentel, G. and Kasper, J. V. V. - First chemical LASER at University of

California, Berkley.

1965: Bloembergen, N. - Wave propagation in nonlinear media.

1966: Silfvast, W., Fowles, G. and Hopkins - First metal vapor LASER - Zn/Cd - at

University of Utah.

1966: Walter, W.T., Solomon, N., Piltch, M and Gould, G. - Metal vapor laser.

1966: Sorokin, P. and Lankard, J. - Demonstration of first Dye Laser action at IBM

Labs.

1966: AVCO Research Laboratory, USA. - First Gas Dynamic Laser based on CO2

1970: Nikolai Basov's Group - First Excimer LASER at Lebedev Labs, Moscow

based on Xenon (Xe) only.

1974: Ewing, J.J. and Brau, C. - First rare gas halide excimer at Avco Everet Labs.

1977: John M J Madey's Group - First free electron laser at Stanford University.

1977: McDermott, W.E., Pehelkin, N.R,. Benard, D.J and Bousek, R.R. - Chemical

Oxygen Iodine Laser (COIL).

1980: Geoffrey Pert's Group - First report of X-ray lasing action, Hull University, UK.

1984: Dennis Matthew's Group - First reported demonstration of a "laboratory" X-

ray laser from Lawrence Livermore Labs.

1999: Herbelin,J.M., Henshaw, T.L., Rafferty, B.D., Anderson, B.T., Tate, R.F.,

Madden, T.J., Mankey II, G.C and Hager, G.D. - All Gas-Phase Chemical Iodine

Laser (AGIL).

2001: Lawrence Livermore National Laboratory - Solid State Heat Capacity

Laser (SSHCL).

Interaction of radiation with matter

Electromagnetic radiations are the radiations consisting of waves of energy

associated with electric field and magnetic field which act perpendicular to

each other and also perpendicular to the direction of propagation of waves.

Characteristics of electromagnetic radiations:-

a) These radiations transmit energy through space.

b) These radiations travel with speed of light in vacuum.

c) These radiations show dual nature – particle and wave nature.

d) These radiations are associated with electrical component and magnetic

component.

Interaction of E.R. with matter produces- Absorption & spontaneous emission.

Absorption & spontaneous emission- natural process.

In absorption, the energy of photon is taken up by matter. There is reduction in intensity of

light wave.

The velocity of light c= vλ

When the beam of light passes through absorbing medium , then attenuation of light in

medium describes the decrease in intensity of light (dI) ( absorption) which is propotional to

intensity of light and thickness

dI α I * dx

dI = - œ I * dx

-Ve sign indictaes decrease intensity w. r t. t. thickness of medium.

dI/ I = - œ dx

By integration varies from Io to I and 0 to x I = I e - œ *x

Thus intensity decrease with intensity exponentially

Energy levels The stationary state of a quantum mechanical system called energy state.

A quantum mechanical system or particle that is bound—that is, confined spatially—can

only take on certain discrete values of energy. These discrete values are called energy

levels. The term is commonly used for the energy levels of electrons in atoms, ions,

or molecules, which are bound by the electric field of the nucleus.

After absorbing energy, an electron may jump from the ground state to a higher energy excited state.

A decrease in energy level fromE2 to E1 resulting in emission of a photon represented by the red squiggly arrow, and whose energy is h ν

An increase in energy level fromE1 to E2 resulting from absorption of a photon represented by the red squiggly arrow, and whose energy is h ν

The atom absorb or emits light in discrete packets called photons. A photon is

an elementary particle, the quantum of light and all other forms of electromagnetic

radiation.

As you may remember from chemistry, an atom consists of electrons orbiting around a nucleus.

However, the electrons cannot choose any orbit they wish. They are restricted to orbits with only

certain energies. Electrons can jump from one energy level to another, but they can never have

orbits with energies other than the allowed energy levels.

Electrons in a hydrogen atom must be in one of the allowed energy levels. If an electron is in the

first energy level, it must have exactly -13.6 eV of energy. If it is in the second energy level, it

must have -3.4 eV of energy. An electron in a hydrogen atom cannot have -9 eV, -8 eV or any other

value in between.

Let's say the electron wants to jump from the first energy level, n = 1, to the second energy level

n = 2. The second energy level has higher energy than the first, so to move from n = 1 to n = 2, the

electron needs to gain energy. It needs to gain (-3.4) - (-13.6) = 10.2 eV of energy to make it up to

the second energy level.

The electron can gain the energy it needs by absorbing light. If the electron jumps from the

second energy level down to the first energy level, it must give off some energy by emitting light.

The atom absorbs or emits light in discrete packets called photons, and each photon has a

definite energy. Only a photon with an energy of exactly 10.2 eV can be absorbed or emitted when

the electron jumps between the n = 1 and n = 2 energy levels.

The energy that a photon carries depends on its wavelength. Since the

photons absorbed or emitted by electrons jumping between the n = 1 and n

= 2 energy levels must have exactly 10.2 eV of energy, the light absorbed or

emitted must have a definite wavelength. This wavelength can be found

from the equation

E = hc/λ,

where E is the energy of the photon (in eV), h is Planck's constant (4.14 x

10-15 eV s) and c is the speed of light (3 x 108 m/s). Rearranging this

equation to find the wavelength gives

λ = hc/E.

A photon with an energy of 10.2 eV has a wavelength of 1.21 x 10-7 m, in the

ultraviolet part of the spectrum. So when an electron wants to jump from n

= 1 to n = 2, it must absorb a photon of ultraviolet light. When an electron

drops from n = 2 to n = 1, it emits a photon of ultraviolet light.

Population Density and Population inversion

No.of atoms per unit volume present in an energy level is called population

density

In science, specifically statistical mechanics, a population inversion occurs

while a system (such as a group of atoms or molecules) exists in a state with

more members in an excited state than in lower energy states. It is called an

"inversion" because in many familiar and commonly encountered physical

systems, this is not possible. The concept is of fundamental importance

in laser science because the production of a population inversion is a

necessary step in the workings of a standard laser

Boltzmann distributions and thermal equilibrium

To understand the concept of a population inversion, it is necessary to

understand some thermodynamics and the way that light interacts

with matter.

To do so, it is useful to consider a very simple assembly of atoms forming

a laser medium.

Assume there are a group of N atoms, each of which is capable of being

in one of two energy states, either

The ground state, with energy E1; or

The excited state, with energy E2, with E2 > E1.

The number of these atoms which are in the ground state is given by N1,

and the number in the excited state N2.

Since there are N atoms in total, N= N1 + N2

The energy difference between the two states, given by

∆E12 = E2 – E1

The characteristic frequency of light which will interact with the atoms; This is given by the relation

E2-E1 =∆E = hv12, h being Planck's constant.

If the group of atoms is in thermal equilibrium, it can be shown from Maxwell-Boltzmann distribution that

the ratio of the number of atoms in each state is given by the Boltzmann factor:

where T is the thermodynamic temperature of the group of atoms, and k is Boltzmann's

constant.

We may calculate the ratio of the populations of the two states at room temperature

(T ≈ 300 K) for an energy difference ΔE that corresponds to light of a frequency

corresponding to visible light (ν ≈ 5×1014 Hz). In this case ΔE = E2 - E1 ≈ 2.07 eV, and kT ≈

0.026 eV. Since E2 - E1 ≫ kT,

it follows that the argument of the exponential in the equation above is a large negative

number, and as such N2/N1 is vanishingly small; i.e., there are almost no atoms in the

excited state.

When in thermal equilibrium, then, it is seen that the lower energy state is more populated

than the higher energy state, and this is the normal state of the system.

As T increases, the number of electrons in the high-energy state (N2) increases,

but N2 never exceeds N1 for a system at thermal equilibrium; rather, at infinite temperature,

the populations N2 and N1 become equal. In other words, a population inversion (N2/N1 >

1) can never exist for a system at thermal equilibrium. To achieve population inversion

therefore requires pushing the system into a non-equilibrated state.

Absorption and Emission

Absorption:If light (photons) of frequency ν12 pass through the group of

atoms, there is a possibility of the light being absorbed by atoms which

are in the ground state, which will cause them to be excited to the

higher energy state. The rate of absorption is proportional to the

radiation intensity of the light, and also to the number of atoms currently

in the ground state,N1.

Spontaneous emission

Spontaneous emission is the process by which a quantum system such as

an atom, molecule, nanocrystal or nucleus in an excited state undergoes a transition to a state with a

lower energy (e.g., the ground state) and emits quanta of energy. Light or luminescence from an atom

is a fundamental process that plays an essential role in many phenomena in nature and forms the

basis of many applications, such as fluorescent tubes, older television screens (cathode ray tubes),

plasma display panels, lasers, and light emitting diodes. Lasers start by spontaneous emission, and

then normal continuous operation works by stimulated emission.

Stimulated emission

Stimulated emission is the process by which an incoming photon of a specific frequency can

interact with an excited atomic electron (or other excited molecular state), causing it to drop

to a lower energy level. The liberated energy transfers to the electromagnetic field, creating a

new photon with identical phase, frequency, polarization, and direction of travel as the

photons of the incident wave. This is in contrast to spontaneous emission which occurs at

random intervals without regard to the ambient electromagnetic field. Further calculation can

be obtained by statistical mechanics.

If an atom is already in the excited state, it may be perturbed by the passage of a photon that

has a frequency ν21 corresponding to the energy gap ΔE of the excited state to ground state

transition. In this case, the excited atom relaxes to the ground state, and is induced to

produce a second photon of frequency ν21. The original photon is not absorbed by the atom,

and so the result is two photons of the same frequency. This process is known as stimulated

emission.

Specifically, an excited atom will act like a small electric dipole which will

oscillate with the external field provided. One of the consequences of this

oscillation is that it encourages electrons to decay to the lowest energy state.

When this happens due to the presence of the electromagnetic field from a

photon, a photon is released in the same phase and direction as the

"stimulating" photon, and is called stimulated emission.

The critical detail of stimulated emission is that the induced photon has the

same frequency and phase as the incident photon. In other words, the two photons

are coherent. It is this property that allows optical amplification, and the production of

a laser system. During the operation of a laser, all three light-matter interactions

described above are taking place. Initially, atoms are energized from the ground state

to the excited state by a process called pumping, described below. Some of these

atoms decay via spontaneous emission, releasing incoherent light as photons of

frequency, ν. These photons are fed back into the laser medium, usually by an optical

resonator. Some of these photons are absorbed by the atoms in the ground state, and

the photons are lost to the laser process. However, some photons cause stimulated

emission in excited-state atoms, releasing another coherent photon. In effect, this

results in optical amplification.

Einstein coefficients In 1917 Einstein postulated on thermodynamic grounds that probability for spontaneous

emission) is related to the probability of stimulated emission(B) and relation between them is

calculated from quantum mechanics.

Einstein coefficients are mathematical quantities which are a measure of the probability of

absorption or emission of light by an atom or molecule.[The Einstein A coefficient is related to the

rate of spontaneous emission of light and the Einstein B coefficients are related to

the absorption and stimulated emission of light.

Consider the two level energy E1 & E2.

let N1 and N2 be the no. of atoms in the ground excited state.

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.

the upper level increases.

The rate is clearly proportional to the population of atoms in the lower level and to the energy

density of radiation in the system.

Thus the rate of increase of population of the excited state is given by

( dN2/dt) = B12 ρ(ν) N1 dN1/dt = - B12 ρ(ν) N1

where B12 is a constant of proportionality with dimensions m /s -J.

Spontaneous Emission - The population of the upper level will decrease due to spontaneous

transition to the lower level with emission of radiation.

The rate of emission will depend on the population of the upper level.

the rate at which N2 decays is:

dN2/dt = - A21 N2 → dN1/dt = A21 N2 ,

If A21 is the probability that an atom in the excited state will spontaneously decay to the ground

state,

where A21 is the rate of spontaneous emission. In the rate-equation is a proportionality constant for this

particular transition in this particular light source. The constant is referred to as the Einstein A coefficient,

Stimulated Emission - Stimulated or induced emission depends on the number of atoms in the

excited level as well as on the energy density of the incident radiation.

If B21 be the transition probability per unit time per unit energy density of radiation,

the rate of decrease of the population of the excited state is .

dN2/dt = -B21 ρ(ν) N2 → dN1/dt = B21 ρ(ν) N2

B21 is known as the Einstein B coefficient for that particular transition,

At thermodynamic equilibrium, the net change in the number of any excited atoms is

zero, being balancing, by loss and gain due to all process

0 = - B12 ρ(ν) N1 + B21 ρ(ν) N2 + A21 N2

B12 ρ(ν) N1 - B21 ρ(ν N2 = A21 N2

ρ(ν) = A21 N2 / ( B12 N1 - B21 N2)

= (A21/B12) / [ ( N1/N2) –(B21/B12)]

= (A21/B12) / [ ( exp((E2-E1/KT)) –(B21/B12)]

According to Plank’s radiation law for any value of T

A21/B12 = (8πһν3μ3)/c3

ρ(ν) = (8πһν3μ3)/c3 / [ ( exp((E2-E1/KT)) –(B21/B12)]

When an atom with two energy levels is placed in the radiation field then

B12= B21

ρ(ν) = (8πһν3μ3)/c3 / [ ( exp((E2-E1/KT)) –1]

B12, B21 and A12 are known as Einstein coefficient.

A laser consists of a gain medium, a mechanism to energize it, and something to

provide optical feedback.[7] The gain medium is a material with properties that allow it

to amplify light by way of stimulated emission. Light of a specific wavelength that

passes through the gain medium is amplified (increases in power).

For the gain medium to amplify light, it needs to be supplied with energy in a process

called pumping. The energy is typically supplied as an electric current or as light at a

different wavelength. Pump light may be provided by a flash lamp or by another laser.

The most common type of laser uses feedback from an optical cavity—a pair of

mirrors on either end of the gain medium. Light bounces back and forth between the

mirrors, passing through the gain medium and being amplified each time. Typically one

of the two mirrors, theoutput coupler, is partially transparent. Some of the light escapes

through this mirror. Depending on the design of the cavity (whether the mirrors are flat

or curved), the light coming out of the laser may spread out or form a narrow beam. In

analogy to electronic oscillators, this device is sometimes called a laser oscillator.

Most practical lasers contain additional elements that affect properties of the emitted

light, such as the polarization, wavelength, and shape of the beam.

Components of a typical laser:

1. Gain medium

2. Laser pumping energy

3. High reflector

4. Output coupler

5. Laser beam