Overview of Raman Spectroscopy: Fundamental to Applications
149
From the Eq. (8), it is obvious that p consisting the three parts of the frequencydependent induced dipole moment, p(v); p(v − v i ) and p(v + v i ). The first term
on the right-hand side of the Eq. (8) determines the Rayleigh scattering which arises
from the oscillation of the electric field with frequency v, causes the vibration of
the electric dipole of the molecule at the same frequency. However, in the rest of
the term, the induced electric dipoles of molecules oscillate with different frequency
(v ± v i ) then the incident radiation. This phenomenon is determined as the Raman
scattering and Eq. (8) gives the qualitative picture of the Raman scattering mechanism
from the classical theory. The molecules oscillate with a lower frequency than the
incident (v − v i ), then the scattering is known as the Stokes scattering, while viceversa (v + v i ) reveals the anti-Stokes scattering [5]. Rayleigh scattering is presented
in every molecule as the classical definition of the α 0 exhibits always a non-zero
component. Further, in a similar case, the Raman scattering exists only when at least
one of the components of α 1 must be a non-zero. Therefore, the salient feature to
obtain the Raman scattering is the change in the polarizability must be non-zero [6].
The above discussion suggests that classical theory well explained the Rayleigh
scattering and its frequency dependence on the polarizability tensor. However, for
the case of Raman spectroscopy, the classical theory has several pitfalls. Classically,
from Eq. (8), it is to be noted that the amplitude of the Stokes and anti-Stokes
Raman scattering is the same. However, in experiments, the Stokes lines are stronger
in intensity than the anti-Stokes scattering, which is unclear from classical theory.
Further, the explanation of factors that govern the Raman intensity is also lacking.
Therefore, quantum physics is needed and discussed in the following section.
2.2 Quantum Theory of Raman Scattering
Quantum mechanics deals with the discrete energy levels, where the transition from
one energy level to another results in the emission or absorption of the radiation.
Further, the incident radiation is also quantized having the photons with the discrete
energy. Therefore, the Raman effect may be explained as the collision between the
molecule and photon of the incident radiation. Let us consider that the incident photon
has the frequency v and the energy hv, which incident on the molecule having the
energy E. According to energy conservation,
E + hv = E
+ hv
(9)
Here, the left-hand side of the equation depicts the total energy of the system
before the collision and the right-hand side reveals the energy of the system after the
collision. Further, E
and v
is the energy of the molecule and frequency of photon
after the collision. From Eq. (9)
v
=
hv +
E − E
h
(10)
149
From the Eq. (8), it is obvious that p consisting the three parts of the frequencydependent induced dipole moment, p(v); p(v − v i ) and p(v + v i ). The first term
on the right-hand side of the Eq. (8) determines the Rayleigh scattering which arises
from the oscillation of the electric field with frequency v, causes the vibration of
the electric dipole of the molecule at the same frequency. However, in the rest of
the term, the induced electric dipoles of molecules oscillate with different frequency
(v ± v i ) then the incident radiation. This phenomenon is determined as the Raman
scattering and Eq. (8) gives the qualitative picture of the Raman scattering mechanism
from the classical theory. The molecules oscillate with a lower frequency than the
incident (v − v i ), then the scattering is known as the Stokes scattering, while viceversa (v + v i ) reveals the anti-Stokes scattering [5]. Rayleigh scattering is presented
in every molecule as the classical definition of the α 0 exhibits always a non-zero
component. Further, in a similar case, the Raman scattering exists only when at least
one of the components of α 1 must be a non-zero. Therefore, the salient feature to
obtain the Raman scattering is the change in the polarizability must be non-zero [6].
The above discussion suggests that classical theory well explained the Rayleigh
scattering and its frequency dependence on the polarizability tensor. However, for
the case of Raman spectroscopy, the classical theory has several pitfalls. Classically,
from Eq. (8), it is to be noted that the amplitude of the Stokes and anti-Stokes
Raman scattering is the same. However, in experiments, the Stokes lines are stronger
in intensity than the anti-Stokes scattering, which is unclear from classical theory.
Further, the explanation of factors that govern the Raman intensity is also lacking.
Therefore, quantum physics is needed and discussed in the following section.
2.2 Quantum Theory of Raman Scattering
Quantum mechanics deals with the discrete energy levels, where the transition from
one energy level to another results in the emission or absorption of the radiation.
Further, the incident radiation is also quantized having the photons with the discrete
energy. Therefore, the Raman effect may be explained as the collision between the
molecule and photon of the incident radiation. Let us consider that the incident photon
has the frequency v and the energy hv, which incident on the molecule having the
energy E. According to energy conservation,
E + hv = E
+ hv
(9)
Here, the left-hand side of the equation depicts the total energy of the system
before the collision and the right-hand side reveals the energy of the system after the
collision. Further, E
and v
is the energy of the molecule and frequency of photon
after the collision. From Eq. (9)
v
=
hv +
E − E
h
(10)