1.3 Refractive index and the Sellmeier dispersion equation
The Sellmeier dispersion coefficients for pure silica (SiO2) and 86.5% SiO2-13.5% GeO2 are given in Table 1.2.
Write a program on your computer or calculator, or use a math software package or even a spreadsheet program (e.g. Excel) to obtain the refractive index (n) as a function of X from 0.5 um to 1.8 um for both pure silica and 86.5% SiO2-13.5% GeO2.
Obtain the group index, critical angle to air vs. wavelength for both materials and plot it on the same graph. Also, you can plot the Ng, dn, and da.
TABLE 1.2 Sellmeier and Cauchy coefficients
Sellmeier
A1 0.696749
A2 0.408218
A3 0.890815
x(m) 0.0690660
x(m) 0.115662
x(m) 9.900559
SiO2 (fused silica) 86.5% SiO2-13.5% GeO2 Sapphire Diamond
0.711040
0.451885
0.704048
0.0642700
0.129408
9.425478
0.80686642 1.023798 0.3306
0.71815848 1.058264 4.3356
0.85416831 5.280792 -
0.068972606 0.0614482 0.1750
0.15396605 0.110700 0.1060
11.841931 17.92656