PHYS 260 Lecture Notes - Lecture 4: Stimulated Emission, Spontaneous Emission, Spectroscopy
25 May 2018
School
Department
Course
Professor
::1::
L A S E R S
L1.INTRODUCTION
Laser is an acronym for light amplification by stimulated emission of
radiation. In a laser, the process of stimulated emission is used for
amplifying light waves. Lasers are essentially coherent optical sources.
It was as early as in 1917 that Einstein first predicted the existence of
two different kinds of processes by which an atom can emit radiation.
These are called spontaneous and stimulated emission. The fact that
stimulated emission process could be used in the construction of
coherent optical sources was first put forward by Towens and Schawlov
in the USA and Bosov and Prokhorov in the USSR. And finally in 1960,
maimann demonstrated the first laser. Since then the development of
lasers has been extremely rapid and laser action has been demonstrated
with gases, liquids, solids, free electrons, semi conductors etc.,
L2.BASIC CONCEPTS OF LASER
Absorption, Spontaneous and stimulated emission:
ABSORPTION:
We know that light is absorbed or emitted by particles during their
transition from one energy state to another. The process of particle
transfer from normal state corresponding to minimum energy of the
system to a higher energy state is termed as excitation and the particle
itself is said to be excited. The process is called stimulated or induced
absorption. In this process the absorption of energy from the external
field takes place. Usually the number of excited particles in a system is
smaller than the non-excited particles. The time during which a particle
can exist in the ground state is unlimited. On the other hand the
particle can remain in the excited state for a limited time known as
lifetime. The lifetime of hydrogen atom is of greater than 10
-8
sec.
However there exist such excited states in which the lifetime is greater
than 10
-8
sec. These states are called meta stable.
SPONTANEOUS EMISSION
The excited atom does not remain in that state for a long time. After
short interval of time 10
-8
Sec. It falls to its lower energy state by emitting
a photon. Here the excited atom jumps back to its ground state on its
own accord and hence the process is known as spontaneous emission.
So the emission, which takes place without external incitement, is called
spontaneous emission. The spontaneous emission depends on the type
of the particle and type of transition but is independent of outside
circumstances. The spontaneous emission is random in character. The
radiation in this case is a random mixture of quanta having various
2
1
::2::
wavelengths. The waves coincide neither in wavelength nor in phase.
Thus the radiation is incoherent and has a broad spectrum.
STIMULATED EMISSION
Suppose an atom is already in the excited state of energy level E
2
whose
ground level energy is E
1
. if at this moment, a photon of energy hν = E
2
-
E
1
is incident on the excited atom. The incident photons stimulate the
emission of a similar photon from the excited atom. Now the atom
returns to the ground state. The transition takes place much sooner
than 10
-8
sec. The process of speeding up the atomic transition from the
excited state to lower state is called stimulated emission. The stimulated
emission is proportional to the intensity of the incident light. The
remarkable feature of the stimulated emission is that it is coherent with
the stimulating incident radiation. It has the same frequency and phase
as the incident radiation.
L3.EINSTEIN COEFFICIENTS
The probable rate of occurrence of the absorption transition from state 1
to state 2 depends on the properties of states 1 and 2 and is proportional
to energy density u (ν) of the radiation of frequency ν incident on the
same. Thus P
12
α u (ν) or P
12
= B
12
u (ν) --(1)
The proportionality constant B
12
is known a Einstein’s coefficient of
absorption of radiation.
The probability of spontaneous emission from state 2 to state 1
depends only on the properties of states 1 and 2. This is independent of
energy density u(ν) of incident radiation. Einstein denoted the
probability per unit time by A
21.
(P
21
) spontaneous = A
21.
A
21
is known as
Einstein’s coefficient of spontaneous emission of radiation. Here it
should be noted that the probability of absorption transition depends
upon energy density u(ν) of incident radiation. Whereas the probability
of spontaneous emission is independent of it. Hence for equilibrium
emission transition depending upon u(ν) must also exist. Actually these
transitions are stimulated emission transitions.
The probability of stimulated emission transition from state 2 to state 1
is proportional to the energy density u(ν) of the stimulating radiation i.e.
(P
21
) stimulated = B
21
u(ν) where B
21
is Einstein’s coefficient of stimulated
1
2
2
1
2
::3::
emission of radiation. The total probability for an atom in state 2 to drop
to the lower state 1 i.e. therefore P
21
= A
21
+B
21
u(ν) ----2
RELATION BETWEEN EINSTEIN’S A AND B COEFFICIENTS:-
Consider an assembly of atoms in thermal equilibrium at temperature T
with radiation of frequency ν and energy density u(ν). Let N
1
and N
2
be
the number of atoms in energy states 1 and 2 respectively at any
instant.
The number of atoms in state 1 that absorb a photon and rise to state 2
per unit time is given by N
1
P
12
= N
1
B
12
u (ν) ------- (3)
The number of photons in state 2 that can cause emission process
(spontaneous + stimulated) per unit time is given by N
2
P
21
= N
2
[A
21
+B
21
u(ν)] ------- (4)
For equilibrium, the absorption and emission must occur equally hence
N
1
P
12
= N
2
P
21
N
1
B
12
u (ν) = N
2
[A
21
+B
21
u (ν)] or N
1
B
12
u (ν) = N
2
A
21
+N
2
B
21
u (ν) or u (ν)
[N
1
B
12
– N
2
B
21
] = N
2
A
21
1
1
)(
21
12
2
1
21
21
212212
212
−
=
−
=∴
B
B
N
N
B
A
BNBN
AN
u
ν
------- (5)
According to Boltzmann distribution law, the number of atoms N
1
and N
2
in energy states E
1
and E
2
in thermal equilibrium at temperature T is
given by
N
1
= N
o e-E1/kt
and
N
2
= N
o e-E2/kt
Where N
0
= Total Number of atoms present and k = Boltzmann’s
constant.
)6(
2
1
)(
1
2
12
1
2
−−−−−−−−−−−−−−=
===
−
−−
−
−
kT
h
kT
h
kT
EE
kT
E
kT
E
e
N
N
Or
ee
e
e
N
N
ν
ν
Substituting the value of N
1
/N
2
from eq. (6) in eq. (5) we get
)7(
1
1
)(
21
12
21
21
−−−−−−−−−−−−−−−
−
=
B
B
e
B
A
u
kT
h
ν
ν
According to Planck's radiation formula
Document Summary
Laser is an acronym for light amplification by stimulated emission of radiation. In a laser, the process of stimulated emission is used for amplifying light waves. It was as early as in 1917 that einstein first predicted the existence of two different kinds of processes by which an atom can emit radiation. The fact that stimulated emission process could be used in the construction of coherent optical sources was first put forward by towens and schawlov in the usa and bosov and prokhorov in the ussr. And finally in 1960, maimann demonstrated the first laser. Since then the development of lasers has been extremely rapid and laser action has been demonstrated with gases, liquids, solids, free electrons, semi conductors etc. , (cid:1)(cid:16)(cid:8)(cid:17)(cid:3)(cid:4)(cid:9)(cid:15)(cid:2)(cid:15)(cid:12)(cid:10)(cid:15)(cid:5)(cid:18)(cid:11)(cid:4)(cid:2)(cid:12)(cid:19)(cid:2)(cid:1)(cid:3)(cid:4)(cid:5)(cid:6)(cid:2) We know that light is absorbed or emitted by particles during their transition from one energy state to another.
