Page 34 - Chalcogenide Glasses for Infrared Optics

Transmission of Light by Solids 13

where T = transmission I/I
0
R = reflectivity
α = bulk absorption coefficient, cm –1
X = sample thickness, cm
Optical designers desire index values to five numbers for imag-
ing systems. How these values are obtained will be discussed in a
later section. Absorption values may be calculated from measured
transmission by using the sample thickness and precise index values.
The full transmission expression may be programmed at wavelength
points with thickness and transmission as variables. Another method
often used incorporates two samples of different thickness with the
change in transmission used in the solution for the absorption value.
All discussions thus far pertain to the transparent region where
absorption is low. In this region the index is taken as a simple num-
ber. However, the index and the absorption coefficient are interde-
pendent. That is, the index is really a complex number and should be
20
written as
N = n − ik
where n = real part of index
k = imaginary part, the absorption coefficient α = 4πk/λ
α = bulk absorption coefficient, cm –1
λ = wavelength, cm
In the transparent region, the value of k is so small it can be
ignored. However, in strong absorption wavelength (big k) regions
such as at the electronic absorption edge or where lattice-type absorp-
tion between constituent atoms occurs, the real part of the index
changes dramatically as k increases. The optical constants are interde-
pendent. The effect of these two regions, one on each end of the trans-
mission region, carries over into the transparent region as a major
factor in the dispersion or change in index with wavelength. The
other major factor is change in temperature. As a solid expands or
contracts, the number of atoms per cubic centimeters changes. The
density changes. The index reflects the mass of the atoms in the solid
and the number of atoms per cubic centimeter.
The variation of the refractive index with wavelength in the trans-
parent range may be depicted with the use of two dispersion curves,
one at each end, shown in Fig. 1.8. The first depicts the change in
reflectivity that occurs at the electronic absorption edge for a solid. At
the short-wavelength side the reflectivity first falls as the absorption k
increases. Then reflectivity increases as k rises to a maximum. On the
long-wavelength side of the peak, k falls to a negligible value, and the
reflectivity falls and levels out at a value slightly greater than before.
Thus, the refractive index has increased. The real part of the index n
first falls as k increases and then as k declines returns to a value greater