0.14 Section 4.2. dielectric and its physics.  (Page 2/3)

At low frequency or under DC condition:

Due to the contribution of all these factors to polarization depending upon the situation, Static Dielectric Constant is very high. In water it is as high as 80.

But as the sinusoidally varying field’s frequency is increased because of appreciable moments of inertia, polar molecules are unable to keep up with the alternating field and their effective contribution to the net polarization decreases. In Water dielectric constant is 80 up to 10 ¹⁰ Hz but it rapidly falls off beyond that frequency. At Peta Hz(in visible part of spectrum) it falls of to 1.78.

In electronic polarization, electron cloud has no problem in following the dictates of the harmonically varying electric field. Hence electronic polarization makes its contribution right up to the Peta Hz.

But electronic polarization gives rise to a resonance absorption phenomena.

An atom can be treated as an harmonic oscillator with a central restoring force F = -kx where k = spring constant or restoring force constant and x is the incremental dispklcament from its equilibrium position. The harmonic oscillator appears as shown in Figure 4.2..

The equation of motion of this atom with a spherically symmetric electron cloud surrounding the nucleus is as follows:

The equatiojn of motion of this harmonic oscillator is:

The first term on L.H.S. is the electric perturbing force. The second term is the restoring force where k is the spring constant. R.H.S. D’Alembert’s force due to acceleration of perturbation of electron. (11) is a second order linear differential equation with a Complementary Function + Particular Integral as its total solution.

Under forcing function its harmonic oscillation is as follows:

(12) implies that whenever the incident light has a frequency equal the natural frequency ω ₀ resonance occurs and the incident light is completely absorbed by the medium as dissipative absorption.

From (9):

Substituing (12) in (13) we obtain:

But we know from (1a) that refractive n ² = ε/ε ₀ . Therefore Dispersion Relation where Refractive Index is expressed as a function of frequency is as follows:

4.2.2. Two cases of Refractive Index – below and above Resonance Frequency (ω 0 ).

Case 1: ω<ω ₀ , P and applied E are in phase and n(ω)>1. This kind of behaviour is generally observed in the real World around.

Case 2: ω>ω ₀ , P and applied E are 180°

out of phase and n(ω)<1.

The plot of Equation 15 is given in Figure 4.3.

If the incident photon (h*frequency)is not strong enough to excite the crystalline atom then the incident photon is scattered or redirected. This is called Ground State non-resonant scattering.

If the incident photon is equal to excitation energy then the atom will be excited from ground state to one of the permissible higher energy states.Subsequently atom will relax to the ground state and release its excess energy as thermal energy. This is known as dissipative absorption.

If incident photon is less than the excitation energy quanta but matches the natural frequency of the electron cloud system around each atomic nucleus then the alternating Electric Field of the incident photon will set the electron clouds in to oscillation. The crystalline atom continues to be in Ground State but electron cloud in each atom is set into a weak oscillation. This oscillatory vibration has two consequences: