1
Masters Smart Notes on Laser Physics and Optical
Fibre
Gopal Hansdah
Assistant Professor of Physics
P. G. Department of Materials Science, MSCBD University, 2nd Campus Keonjhar-758002
Light Matter Interaction
The process of the energy transfer from atom to light is not understandable from the classical
point of view. However, in quantum mechanics the interaction of light with medium is well under-
stood. A laser is a light source that utilizes the quantum processes for its operation. It is therefore.
Necessary to appreciate the quantum processes involved in the development of a laser.
The radiation incident on a material is viewed as a stream of photons; where each photon
carries energy E = h .We assumes that the two energy levels of the atoms in the material have an
energy difference E 2 − E1 = h . When photons travel through the medium, three different processes
are likely to occur. They are Absorption, Spontaneous Emission and Stimulated Emission. Let us
study them in detail.
Absorption:
Suppose t h e atoms are in the lower energy level E1 . If photons of energy
h = E 2 − E1 are incident on these atoms, they impart their energy to the atoms and disappear.
Then we say that the atoms absorbed the incident photons. As a result of absorption of adequate
energy, the atoms jump to the excited state E 2 . This transition is called an absorption transition. The
process is also referred to an induced absorption. Figure 1 shows the absorption processes in atomic
levels and in materials. The process can also be symbolically represented as
a + h → a *
where a is an atom in the lower state and a * is an atom in excited state.
In each absorption transition event, an atom in the medium is excited and one photon is
subtracted from the incident light beam, which results in attenuation of light in the medium.
Fig. 1: Absorption process (a) Induced absorption (b) Photons absorption (c) Photon absorption in materials.
The number of atoms per unit volume that undergo absorption transitions per second is called
the rate of absorption transition. It is denoted by
dN1
Ras = − (1)
dt
Masters Smart Note on Laser Physics and Optical Fibre by Dr Gopal Hansdah, Assistant Professor of Physics, P.G. Department of Materials
Science, MSCBD University, 2nd Campus, Keonjhar-758002, Odisha, India.
Email ID:
, 2
where − dN1 dt represents the rate of decrease of population o f a t o m s at the lower e n e r g y
level E1 . The rate of absorption can also be represented by the rate of increase of population at
the upper level E 2 , as
dN1
Ras = − (2)
dt
The numbers of absorption transitions occurring in the material at any instant are proportional to the
number of atoms in the lower level E1 and the density of photons in the incident beam. When the
atoms are more at the lower energy level, then more atoms can jump into the excited state.
Similarly w h e n more photons are incident on the assembly of atoms, then more atoms can get excited to higher
energy level then the absorption rate of transition is given by
Ras = B12 ( )N1 (3)
where N 1 is the population of atoms at •level E1 , ( ) is the density of the incident beam and B12 is the
proportionality constant and is known as absorption or Einstein’s coefficient for the induced absorption. It
indicates the probability of occurrence of an induced transition from level 1 to 2.
Induced absorption involves the exc1tat1on of atoms to the fixed higher level only. As a result of the
absorption N 1 decreases and N 2 increases. Under normal conditions N 2 cannot be greater than N 1 . Therefore
the light propagates through the medium it gets absorbed. However, using special technique N 2 can also be
made greater than N 1 .
Spontaneous Emission:
The atoms cannot stay in the excited state for a longer time. In a time of about 10 −8 sec atoms
revert to the lower energy state by releasing photons of energy h = E 2 − E1 . The emission of
photon occurs on its own and without any external impetus given to the excited atom. The Figure 2
Spontaneous emission process (a) Before emission (b) After emission (c) Photon emission in materials has
been depicted;
Fig. 2: Spontaneous emission process (a) Before emission (b) After emission (c) Photon emission in materials
Emission of a photon by an atom without any external impetus is called spontaneous emission.
We may write the process as
a* → a + h
The number of spontaneous transitions depends only on the number of atoms N 2 at the excited
state E 2 Therefore; the rate of spontaneous transitions is given by
Rsp = A21N 2 (4)
where A21 is the proportionality constant and is called the spontaneous emission coefficient or Ein-
stein coefficient.. It represents the probability of a spontaneous transition from level 2 to 1. Note
Masters Smart Note on Laser Physics and Optical Fibre by Dr Gopal Hansdah, Assistant Professor of Physics, P.G. Department of Materials
Science, MSCBD University, 2nd Campus, Keonjhar-758002, Odisha, India.
Email ID:
, 3
that the process of spontaneous emission is independent of the incident light energy.
It follows from the quantum mechanical consideration that spontaneous transition takes place from a given
state, the state lying in the lower in energy thus spontaneous transition is not possible from level E1 to level
E 2 . Therefore the probability of spontaneous transition is zero from level E1 to level E 2 and the transition co-
efficient can be given by A21 = 0 .
Characteristics of spontaneous emission:
i. The process of spontaneous emission is essentially probabilistic in nature and is ame-
nable for control from outside.
ii. The instant of transition, direction of propagation, the initial phase and the plane of po-
larization of each photon are all random.
iii. Light resulting through this process is not monochromatic.
iv. As different atoms in the source emit photons in different directions, light spread int the
directions around the source. The light intensity goes on decreasing rapidly with the distance
from the source.
v. Light emitted through this process is incoherent, as it results from superposition wave
trains of random phases. The net intensity is proportional to the number of radiating atoms.
Thus
I total = NI (5)
where, N is the number of atoms and I is the intensity of light emitted by one atom. In
the spontaneous process, the emission dominates the conventional light sources.
Stimulated Emission:
An atom in the excited state need not waits for spontaneous emission of photon. Well before the atom
can make a spontaneous transition, i t may interact with a photon with energy h = E 2 − E1 and
makes downward transition. The photon is said to stimulate or induce the excited atom to emit photon
of energy h = E2 − E1 . The passing photon does not disappear and in addition to that there is a sec-
ond photon which is emitted by the excited atom. The phenomenon of forced photon emission by an excit-
ed atom due to the action of an external agency is called stimulated emission or induced emission.
The stimulated emission process has been depicted in Fig. 3. The process may be expressed as
a * + h → a + 2h
Fig. 3: Stimulated emission process (a) Before emission (b) After emission (c) Emitted coherent photons in material.
The rate of stimulated emission or photons is given by
Rst = B21 ( )N 2 (6)
Masters Smart Note on Laser Physics and Optical Fibre by Dr Gopal Hansdah, Assistant Professor of Physics, P.G. Department of Materials
Science, MSCBD University, 2nd Campus, Keonjhar-758002, Odisha, India.
Email ID:
Masters Smart Notes on Laser Physics and Optical
Fibre
Gopal Hansdah
Assistant Professor of Physics
P. G. Department of Materials Science, MSCBD University, 2nd Campus Keonjhar-758002
Light Matter Interaction
The process of the energy transfer from atom to light is not understandable from the classical
point of view. However, in quantum mechanics the interaction of light with medium is well under-
stood. A laser is a light source that utilizes the quantum processes for its operation. It is therefore.
Necessary to appreciate the quantum processes involved in the development of a laser.
The radiation incident on a material is viewed as a stream of photons; where each photon
carries energy E = h .We assumes that the two energy levels of the atoms in the material have an
energy difference E 2 − E1 = h . When photons travel through the medium, three different processes
are likely to occur. They are Absorption, Spontaneous Emission and Stimulated Emission. Let us
study them in detail.
Absorption:
Suppose t h e atoms are in the lower energy level E1 . If photons of energy
h = E 2 − E1 are incident on these atoms, they impart their energy to the atoms and disappear.
Then we say that the atoms absorbed the incident photons. As a result of absorption of adequate
energy, the atoms jump to the excited state E 2 . This transition is called an absorption transition. The
process is also referred to an induced absorption. Figure 1 shows the absorption processes in atomic
levels and in materials. The process can also be symbolically represented as
a + h → a *
where a is an atom in the lower state and a * is an atom in excited state.
In each absorption transition event, an atom in the medium is excited and one photon is
subtracted from the incident light beam, which results in attenuation of light in the medium.
Fig. 1: Absorption process (a) Induced absorption (b) Photons absorption (c) Photon absorption in materials.
The number of atoms per unit volume that undergo absorption transitions per second is called
the rate of absorption transition. It is denoted by
dN1
Ras = − (1)
dt
Masters Smart Note on Laser Physics and Optical Fibre by Dr Gopal Hansdah, Assistant Professor of Physics, P.G. Department of Materials
Science, MSCBD University, 2nd Campus, Keonjhar-758002, Odisha, India.
Email ID:
, 2
where − dN1 dt represents the rate of decrease of population o f a t o m s at the lower e n e r g y
level E1 . The rate of absorption can also be represented by the rate of increase of population at
the upper level E 2 , as
dN1
Ras = − (2)
dt
The numbers of absorption transitions occurring in the material at any instant are proportional to the
number of atoms in the lower level E1 and the density of photons in the incident beam. When the
atoms are more at the lower energy level, then more atoms can jump into the excited state.
Similarly w h e n more photons are incident on the assembly of atoms, then more atoms can get excited to higher
energy level then the absorption rate of transition is given by
Ras = B12 ( )N1 (3)
where N 1 is the population of atoms at •level E1 , ( ) is the density of the incident beam and B12 is the
proportionality constant and is known as absorption or Einstein’s coefficient for the induced absorption. It
indicates the probability of occurrence of an induced transition from level 1 to 2.
Induced absorption involves the exc1tat1on of atoms to the fixed higher level only. As a result of the
absorption N 1 decreases and N 2 increases. Under normal conditions N 2 cannot be greater than N 1 . Therefore
the light propagates through the medium it gets absorbed. However, using special technique N 2 can also be
made greater than N 1 .
Spontaneous Emission:
The atoms cannot stay in the excited state for a longer time. In a time of about 10 −8 sec atoms
revert to the lower energy state by releasing photons of energy h = E 2 − E1 . The emission of
photon occurs on its own and without any external impetus given to the excited atom. The Figure 2
Spontaneous emission process (a) Before emission (b) After emission (c) Photon emission in materials has
been depicted;
Fig. 2: Spontaneous emission process (a) Before emission (b) After emission (c) Photon emission in materials
Emission of a photon by an atom without any external impetus is called spontaneous emission.
We may write the process as
a* → a + h
The number of spontaneous transitions depends only on the number of atoms N 2 at the excited
state E 2 Therefore; the rate of spontaneous transitions is given by
Rsp = A21N 2 (4)
where A21 is the proportionality constant and is called the spontaneous emission coefficient or Ein-
stein coefficient.. It represents the probability of a spontaneous transition from level 2 to 1. Note
Masters Smart Note on Laser Physics and Optical Fibre by Dr Gopal Hansdah, Assistant Professor of Physics, P.G. Department of Materials
Science, MSCBD University, 2nd Campus, Keonjhar-758002, Odisha, India.
Email ID:
, 3
that the process of spontaneous emission is independent of the incident light energy.
It follows from the quantum mechanical consideration that spontaneous transition takes place from a given
state, the state lying in the lower in energy thus spontaneous transition is not possible from level E1 to level
E 2 . Therefore the probability of spontaneous transition is zero from level E1 to level E 2 and the transition co-
efficient can be given by A21 = 0 .
Characteristics of spontaneous emission:
i. The process of spontaneous emission is essentially probabilistic in nature and is ame-
nable for control from outside.
ii. The instant of transition, direction of propagation, the initial phase and the plane of po-
larization of each photon are all random.
iii. Light resulting through this process is not monochromatic.
iv. As different atoms in the source emit photons in different directions, light spread int the
directions around the source. The light intensity goes on decreasing rapidly with the distance
from the source.
v. Light emitted through this process is incoherent, as it results from superposition wave
trains of random phases. The net intensity is proportional to the number of radiating atoms.
Thus
I total = NI (5)
where, N is the number of atoms and I is the intensity of light emitted by one atom. In
the spontaneous process, the emission dominates the conventional light sources.
Stimulated Emission:
An atom in the excited state need not waits for spontaneous emission of photon. Well before the atom
can make a spontaneous transition, i t may interact with a photon with energy h = E 2 − E1 and
makes downward transition. The photon is said to stimulate or induce the excited atom to emit photon
of energy h = E2 − E1 . The passing photon does not disappear and in addition to that there is a sec-
ond photon which is emitted by the excited atom. The phenomenon of forced photon emission by an excit-
ed atom due to the action of an external agency is called stimulated emission or induced emission.
The stimulated emission process has been depicted in Fig. 3. The process may be expressed as
a * + h → a + 2h
Fig. 3: Stimulated emission process (a) Before emission (b) After emission (c) Emitted coherent photons in material.
The rate of stimulated emission or photons is given by
Rst = B21 ( )N 2 (6)
Masters Smart Note on Laser Physics and Optical Fibre by Dr Gopal Hansdah, Assistant Professor of Physics, P.G. Department of Materials
Science, MSCBD University, 2nd Campus, Keonjhar-758002, Odisha, India.
Email ID:
