PHYSICS
UNIT - 3
Chapter 5 : LASERs
LASER stands for “Light Apmplification by Stimulated Emission of Radiation”.
Interaction of Radiation with matter: Quantum Mechanical View
Matter is made up of identical atoms or molecules which have discrete allowed energy levels.
Consider a material having atoms with two energy levels E1 (lower level or ground state) and E2
(upper level or excited state). Let monochromatic radiation of frequency 𝜈 be incident on the
material such that the energy of each photon of the radiation is ℎ𝜈 = 𝐸2 − 𝐸1 . The interaction
of such radiation with the material can result in the following three processes:
i) Absorption: An atom in the ground state can absorb the energy ℎ𝜈 = 𝐸2 − 𝐸1 of the incident
photon and can undergo a transition from 𝐸1
to 𝐸2 as shown in the figure. This process is
called absorption. It can be represented by the
following equation:
𝐴 + ℎ𝜈 → 𝐴∗
where 𝐴 represents atom in the lower level 𝐸1
𝐴∗ represents atom in the upper level 𝐸2
ℎ𝜈 represents the photon
The number of absorptions taking place in the
material in time interval ∆𝑡 is proportional to
the number of atoms in the lower level 𝑁1 and the incident photon density 𝑄. Hence the number
of absorptions taking place in the material in time interval ∆𝑡 can be written as:
𝑁𝑎𝑏 = 𝐵12 𝑁1 𝑄∆𝑡 …………………….eqn. 1
where 𝐵12 is the constant of proportionality
Note: The process of absorption, by itself, cannot produce light amplification because it results
in decrease in number of photon due to absorption of photons by the atoms.
ii) Spontaneous emission: An atom in the
excited state 𝐸2 is highly unstable, and within
an average time of about 10-8 sec, on its own,
it returns back the ground state 𝐸1 . In doing
so, the excess energy 𝐸2 − 𝐸1 is emitted in the
form of a photon of energy ℎ𝜈 = 𝐸2 − 𝐸1 as
shown in the figure. This process is called
spontaneous emission. It can be represented
by the following equation:
𝐴∗ → 𝐴 + ℎ𝜈
The number of spontaneous taking place in the material in time interval ∆𝑡 is proportional to the
number of atoms in the upper level 𝑁2 (here there is no dependence on the incident photon
density 𝑄, since no incident photons are required to cause the atoms to undergo spontaneous
emission). Hence the number of spontaneous emission taking place in the material in time
interval ∆𝑡 can be written as:
𝑁𝑠𝑝 = 𝐴21 𝑁2 ∆𝑡 …………………….eqn. 2
where 𝐴21 is the constant of proportionality.
Note: Spontaneous emission is a random process. i.e. different excited atoms undergo
spontaneous emission at different time, resulting in photons emitted with random phases.
Hence the different emitted photons tend to cancel each other resulting in net zero light
amplification. Hence spontaneous emission cannot produce light amplification.
LASERs Prof. Harison Cota, Don Bosco College of Engineering, Fatorda Page 1
, iii) Stimulated emission: If an incident
photon strikes an atom in the excited
state 𝐸2 , it can force the atom to
return to the ground state 𝐸1 at that
instant of time. In the process, two
identical photons are emitted as
shown in the figure. This process is
called stimulated emission. It can be
represented by the following
equation:
𝐴∗ + ℎ𝜈 → 𝐴 + 2ℎ𝜈
The number of stimulated taking place in the material in time interval ∆𝑡 is proportional to the
number of atoms in the upper level 𝑁2 , and the incident photon density 𝑄. Hence the number of
stimulated emission taking place in the material in time interval ∆𝑡 can be written as:
𝑁𝑠𝑡 = 𝐵21 𝑁2 𝑄∆𝑡 …………………….eqn. 3
where 𝐵21 is the constant of proportionality.
Note: Stimulated emission results
in emission of two photons which
are exactly identical in energy,
phase and direction (the direction
of the two emitted photons is
same as that of the incident
photon). These two photons can
in turn strike two other excited
atoms and stimulate them to de-
excite resulting in emission of total four identical photons. These four can in turn induce
stimulated emission in four other excited atoms producing total eight identical photons, and so
on, as shown in the figure. Thus, within a short duration, a large number of identical photons
with be emitted. This is light amplification. Thus stimulated emission can produce light
amplification.
Metastable State
In a normal excited state, atoms can remain excited for an average time of about 10 -8 sec.
However, there exist certain excited states in certain atoms in which the atoms can remain
excited for a relatively longer duration of time (10-6 sec to 10-3 sec). Such excited states are called
metastable states.
Active Medium & Active centres
A medium in which light amplification takes place is called active medium. The active medium
could be a solid, liquid or gas.
Out of all the atoms in the active medium, only a few atoms take part in the light amplification
process. Such atoms are called active centres.
Einstein’s theory of Stimulated Emission
Atoms in the lower level 𝐸1 go to the upper level 𝐸2 by absorption, while atoms in the upper
level 𝐸2 come down to the lower level 𝐸1 by either spontaneous or stimulated emission.
A material is said to be in thermal equilibrium if the number of atoms in the lower and upper
levels remain constant with time. This will be possible only if the number of upward transitions
occurring at any instant is equal to the number of downward transitions at that instant. For this
it is therefore required that:
𝑁𝑎𝑏 = 𝑁𝑠𝑝 + 𝑁𝑠𝑡
i.e. 𝐵12 𝑁1 𝑄∆𝑡 = 𝐴21 𝑁2 ∆𝑡 + 𝐵21 𝑁2 𝑄∆𝑡 (from eqn. 1. 2, 3)
LASERs Prof. Harison Cota, Don Bosco College of Engineering, Fatorda Page 2
UNIT - 3
Chapter 5 : LASERs
LASER stands for “Light Apmplification by Stimulated Emission of Radiation”.
Interaction of Radiation with matter: Quantum Mechanical View
Matter is made up of identical atoms or molecules which have discrete allowed energy levels.
Consider a material having atoms with two energy levels E1 (lower level or ground state) and E2
(upper level or excited state). Let monochromatic radiation of frequency 𝜈 be incident on the
material such that the energy of each photon of the radiation is ℎ𝜈 = 𝐸2 − 𝐸1 . The interaction
of such radiation with the material can result in the following three processes:
i) Absorption: An atom in the ground state can absorb the energy ℎ𝜈 = 𝐸2 − 𝐸1 of the incident
photon and can undergo a transition from 𝐸1
to 𝐸2 as shown in the figure. This process is
called absorption. It can be represented by the
following equation:
𝐴 + ℎ𝜈 → 𝐴∗
where 𝐴 represents atom in the lower level 𝐸1
𝐴∗ represents atom in the upper level 𝐸2
ℎ𝜈 represents the photon
The number of absorptions taking place in the
material in time interval ∆𝑡 is proportional to
the number of atoms in the lower level 𝑁1 and the incident photon density 𝑄. Hence the number
of absorptions taking place in the material in time interval ∆𝑡 can be written as:
𝑁𝑎𝑏 = 𝐵12 𝑁1 𝑄∆𝑡 …………………….eqn. 1
where 𝐵12 is the constant of proportionality
Note: The process of absorption, by itself, cannot produce light amplification because it results
in decrease in number of photon due to absorption of photons by the atoms.
ii) Spontaneous emission: An atom in the
excited state 𝐸2 is highly unstable, and within
an average time of about 10-8 sec, on its own,
it returns back the ground state 𝐸1 . In doing
so, the excess energy 𝐸2 − 𝐸1 is emitted in the
form of a photon of energy ℎ𝜈 = 𝐸2 − 𝐸1 as
shown in the figure. This process is called
spontaneous emission. It can be represented
by the following equation:
𝐴∗ → 𝐴 + ℎ𝜈
The number of spontaneous taking place in the material in time interval ∆𝑡 is proportional to the
number of atoms in the upper level 𝑁2 (here there is no dependence on the incident photon
density 𝑄, since no incident photons are required to cause the atoms to undergo spontaneous
emission). Hence the number of spontaneous emission taking place in the material in time
interval ∆𝑡 can be written as:
𝑁𝑠𝑝 = 𝐴21 𝑁2 ∆𝑡 …………………….eqn. 2
where 𝐴21 is the constant of proportionality.
Note: Spontaneous emission is a random process. i.e. different excited atoms undergo
spontaneous emission at different time, resulting in photons emitted with random phases.
Hence the different emitted photons tend to cancel each other resulting in net zero light
amplification. Hence spontaneous emission cannot produce light amplification.
LASERs Prof. Harison Cota, Don Bosco College of Engineering, Fatorda Page 1
, iii) Stimulated emission: If an incident
photon strikes an atom in the excited
state 𝐸2 , it can force the atom to
return to the ground state 𝐸1 at that
instant of time. In the process, two
identical photons are emitted as
shown in the figure. This process is
called stimulated emission. It can be
represented by the following
equation:
𝐴∗ + ℎ𝜈 → 𝐴 + 2ℎ𝜈
The number of stimulated taking place in the material in time interval ∆𝑡 is proportional to the
number of atoms in the upper level 𝑁2 , and the incident photon density 𝑄. Hence the number of
stimulated emission taking place in the material in time interval ∆𝑡 can be written as:
𝑁𝑠𝑡 = 𝐵21 𝑁2 𝑄∆𝑡 …………………….eqn. 3
where 𝐵21 is the constant of proportionality.
Note: Stimulated emission results
in emission of two photons which
are exactly identical in energy,
phase and direction (the direction
of the two emitted photons is
same as that of the incident
photon). These two photons can
in turn strike two other excited
atoms and stimulate them to de-
excite resulting in emission of total four identical photons. These four can in turn induce
stimulated emission in four other excited atoms producing total eight identical photons, and so
on, as shown in the figure. Thus, within a short duration, a large number of identical photons
with be emitted. This is light amplification. Thus stimulated emission can produce light
amplification.
Metastable State
In a normal excited state, atoms can remain excited for an average time of about 10 -8 sec.
However, there exist certain excited states in certain atoms in which the atoms can remain
excited for a relatively longer duration of time (10-6 sec to 10-3 sec). Such excited states are called
metastable states.
Active Medium & Active centres
A medium in which light amplification takes place is called active medium. The active medium
could be a solid, liquid or gas.
Out of all the atoms in the active medium, only a few atoms take part in the light amplification
process. Such atoms are called active centres.
Einstein’s theory of Stimulated Emission
Atoms in the lower level 𝐸1 go to the upper level 𝐸2 by absorption, while atoms in the upper
level 𝐸2 come down to the lower level 𝐸1 by either spontaneous or stimulated emission.
A material is said to be in thermal equilibrium if the number of atoms in the lower and upper
levels remain constant with time. This will be possible only if the number of upward transitions
occurring at any instant is equal to the number of downward transitions at that instant. For this
it is therefore required that:
𝑁𝑎𝑏 = 𝑁𝑠𝑝 + 𝑁𝑠𝑡
i.e. 𝐵12 𝑁1 𝑄∆𝑡 = 𝐴21 𝑁2 ∆𝑡 + 𝐵21 𝑁2 𝑄∆𝑡 (from eqn. 1. 2, 3)
LASERs Prof. Harison Cota, Don Bosco College of Engineering, Fatorda Page 2
