Microscopic view of the index of refraction

A. La Rosa
Lecture Notes
Microscopic view of the index of refraction
Simplified version
Electrostatic polarization
An external electric field Eo induces polarization
How the electrical polarization P of the dielectric medium affects
the net electric field E
Hypothesis about the relationship between P and E
Definition of the polarizability 
Material’s response to alternating electric fields
Atomic system modeled as a spring oscillator
Frequency dependent polarization, P()
Case: Frequencies  far away from the resonance
frequency o
How the polarization affect the equation of motion for the
electromagnetic fields
Modified phase velocity
Frequency dependent index of refraction
In fact, we know that the origin of this ”viscous force” lies
in the loss of energy due to the accelerated charge.
E = E0Cos(t)
It is the second term, the one with Sin(wt), that is responsible for
the energy dissipation
Case: Frequencies  far way from the
resonance frequency 0.
In this case the term containing the Sin(w t) in expression 2
above can be neglected.
As a result, similar to the case in electrostatic where P=0E, we
can define a frequency dependent polarizabilty as
Absorbed and then reemitted by the material
of light