ABSTRACT
G (10.9) Suppose we have N oscillators or electrons in a unit volume, and Nfi of them have an Eigen frequency wj. The fi is the oscillator
strength. Thus, the dielectric function of this group of oscillators from Eq. 10.9 ise w e
w w w ( )
( )
= + - -Â0
Nq m
f
When we focus on one particular oscillator at w = 0, we define el and eu as the dielectric functions at sufficiently lower and higher frequencies by e0 = eu (10.11) e(0) = el (10.12)
Substituting Eqs. 10.11 and 10.12 in Eq. 10.10, we get e e wl u Nq
m = +
( )e e wl u Nqm-=02 2 (10.14) Substituting Eq. 10.14 in Eq. 10.10, we get e e e e w
i = +
- - -
( )
( )
(10.15)
e e
e e
w
w w w l
i = +
- Ê ËÁ
ˆ ¯˜
- - 1
0 ( )G
(10.16)
When G 0
2<< ªw w L
, we introduce the Lyddane-Sachs-Teller relation ase e
w w
Substituting Eq. 10.17 in Eq. 10.16, we have the dispersion relation as e e w w w w wl u i
= + -
- -
È
Î Í Í
˘
˚ ˙ ˙
( )G (10.18)
Where wL is the frequency of the longitudinal wave. Equation 10.18 explains that in the frequency region of w0 – G0 < w < wL, the material shows large optical absorption (A) and reflection (R), as seen in Fig. 10.2. In the remaining region, the material is transparent (T). In addition, when G0 = 0 and in the frequency region of w0 < w < wL, the dielectric function will be real and negative e¢, and thus the refractive index will be pure imaginary k. Then a total reflection is observed.
