Page 73 - Chalcogenide Glasses for Infrared Optics

Chalcogenide Glasses 51

component glasses and will yield the harmonic oscillator frequency
for the dominant pair which in this case comprises Si-Te and Ge-Te.
The other bond pairs absorb but not with the intensity required to
produce a reflection band. Also, the intensity is affected by the con-
centration of the element in the glass composition.
The optical constants are interdependent. That is, the refractive
index is really a complex number N = n – ik, where n is the real part of
the refractive index and k is the imaginary part of the refractive index,
sometimes called the extinction coefficient. The bulk absorption coef-
ficient α can be calculated from α = 4πk/λ, where λ = wavelength in
centimeters. Reflectivity R is calculated from

R = ( n− )1 2 + k 2
( n+ )1 2 + k 2
In the transparent region, k is very small and is omitted in the
calculation. However, in the region of the Restrahlen band, it becomes
large, even the dominant term. The curves in Fig. 2.18 show the
expected shape. The peak of reflectivity, the maximum absorption
wavelength, and the wavelength for the harmonic oscillator do not
coincide because of the interrelationship of the optical constants. The
wavelength of the harmonic oscillator for each bond pair and the
maximum absorption were determined, when possible, by using
37
the inspection method described by Moss. The values needed for the
calculation are the magnitude of maximum reflectivity, the wave-
length of maximum and minimum reflection, and the short wave-
length refractive index. The calculated results found from the curves
in Fig. 2.18 and for a number of other samples are shown in Table 2.9.
In some cases only absorption results were available. From the results,
we see that binary glasses are straightforward, yielding their oscilla-
tor frequency, As-S, Ge-S, Ge-Se, As-Se. A small change is observed
when a third element is present. The absorption of the third element
is not intense enough to produce a second band whether due to the
concentration or the ionic character of the bond. At the very least, the
different mass of the atom when coupled to the primary structure
produces a frequency change. As an example, compare the oscillator
frequency for the Ge-S binary and in the ternary Ge-S-Te.
Tellurium is an atom much heavier than sulfur which lowers the
frequency of vibration. The force constant for each atom pair may be
calculated from

κ  
/
ν = 1 ×   12
µ
o 2 πC  
where ν = wave number of harmonic oscillator frequency
o
C = speed of light
κ = force constant
µ = reduced mass