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Optics, IDC202: Rejish Nath

This document discusses lasers and population inversion. It defines lasers as light amplification by stimulated emission of radiation. It describes the basic processes that occur when light interacts with atoms, including population inversion and stimulated emission which leads to light amplification. It discusses Einstein coefficients and how they relate to spontaneous emission, stimulated emission, and absorption. It explains that population inversion, where there are more atoms in the excited state than ground state, is required for lasers and discusses different methods to achieve population inversion such as optical pumping, electron excitation, collisions, and chemical reactions. Finally, it mentions that a resonator or optical cavity is used to provide feedback in lasers.

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Keshav Jha
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37 views16 pages

Optics, IDC202: Rejish Nath

This document discusses lasers and population inversion. It defines lasers as light amplification by stimulated emission of radiation. It describes the basic processes that occur when light interacts with atoms, including population inversion and stimulated emission which leads to light amplification. It discusses Einstein coefficients and how they relate to spontaneous emission, stimulated emission, and absorption. It explains that population inversion, where there are more atoms in the excited state than ground state, is required for lasers and discusses different methods to achieve population inversion such as optical pumping, electron excitation, collisions, and chemical reactions. Finally, it mentions that a resonator or optical cavity is used to provide feedback in lasers.

Uploaded by

Keshav Jha
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Optics, IDC202

Lecture 7.
Rejish Nath
Contents

Literature:
1. Optics, (Eugene Hecht and A. R. Ganesan)
2. Optical Physics, (A. Lipson, S. G. Lipson and H. Lipson)
3. Optics, (A. Ghatak)
LASERS
Light amplification by stimulated emission of radiation.

Properties:
Directionality
High power
6
extremely small spectral width 10

Three basic processes when light


interact with atom
Population Inversion+ stimulated emission

Light amplification
Einstein coefficients

E2

E1
E2 E1 = ~!

N1 B12 u(!) No. of absorptions per unit volume per unit time.
Einstein B coefficient
Einstein coefficients

E2

E1
E2 E1 = ~!

Spontaneous emission

Einstein A coefficient
Einstein coefficients

E2

E1
E2 E1 = ~!

Stimulated emission

N2 B21 u(!) No. of stimulated emissions per unit volume per unit time.

At thermal equilibrium
Einstein coefficients

At thermal equilibrium

At thermal equilibrium (Boltzmanns law)

N2 (E1 E2 )/kB T
=e
N1

Plancks law
Einstein coefficients

Plancks law

St. Emission
Sp. Emission
B21 u(!) 1
= = h!/k T
A21 e B 1

depends on the frequency.


Einstein coefficients
Ordinary optical sources,
St. Emission with wavelength in the
Sp. Emission visible region, the ratio is
extremely small
B21 u(!) 1 10
= = h!/k T 10
A21 e B 1
dominant spontaneous emission
depends on the frequency. (incoherent source)

For laser (coherent light), we require large St.Emission/Sp. Emission ratio.


Population Inversion
E2
Rate of Stimulated emission: N2 B21 u(!)

Rate of Stimulated Absorption: N1 B12 u(!)


E1
E2 E1 = ~!
We need: N2 > N1

Contradictory to thermal equilibrium


distribution by Boltzmann.
E E
E/kB T
Population
N0 e inversion
Boltzmanns Law
E1 E1

N N
Light amplification

Amplified light
Light medium with
population
inversion

Amplification is quantified through a parameter called gain constant.

The maximum value of the gain constant,

~!
max (N2 N1 )B12
2c !

max > 0 implies amplification


z
I! (z) = I! (0)e
max < 0 implies absorption
Population Inversion: Methods

Optical pumping or photon excitation


Electron excitation
Inelastic atom-atom collisions
chemical reactions

E2 Photon excitation uses in


laser transition
solid state lasers
(Ruby laser)
E1
Electron excitation uses in
E0 gaseous ion lasers
(Argon laser)
Population Inversion: Methods

Optical pumping or photon excitation


Electron excitation
Inelastic atom-atom collisions
chemical reactions

Atom A Atom B
E2
E1
uses in He-Neon laser
(laser transition occurs in Neon)
Population Inversion: Methods

Optical pumping or photon excitation


Electron excitation
Inelastic atom-atom collisions
chemical reactions

Chemical reactions may lead to excited atom or molecule.


Light amplification
Resonator or an optical cavity

Plane mirrors: You get infinitely many equally spaced modes.

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