Question

2. Refractive index and the Sellmeier dispersion equation The Sellmeier dispersion equation is an empirical expression for the refractive index. of glass in terms of the wavelength 2, + 034Selmeier equation (1) R-ler where G1, G2, G3 and λι, λ2 and λ3 are constants (called Sellmeier coefficients) that are determined by fitting this expression to the experimental data. The actual Sellmeier formula has more terms in the right hand summation of the same type e.g. Giaka-at) where i 4, 5..but these can generally be neglected in representing n vs. λ behavior over typical wavelengths of interest and ensuring that three terms included in Eq. (1) correspond to the most important or relevant terms in the summation. Table 1 gives the Sellmeier coefficients for pure Silica (SiO) and Sio2-13.5 mol.% GeO2. Write a program on your computer or calculator, or use a math software package (e.g. Mathcad, Matlab, Theorist, Mathview) or even a spread sheet program (e.g. Excel) to obtain the refractive index n as a function of à from 0.5 m to 1.8 m for both pure silica and SiO2-13.5%Ge02. obtain the group index. No- vs. wavelength for both materials and plot it on the same graph. Find the wavelengths where material dispersion becomes zero in the two materials. 1/3 Table 1 The Sellmeier coefficients for Sio, and SiO2-13.5%Ge02. The λι, λ2'A3 are in um. G1 Gs Sio2 0.696749 0.408218 0.890815 0.06906600.115662 9.900559 SiO2-13.5%GeO2 | 0.711040 | 0.451885 | 0.7040481 0.0642700| 0.129408 | 9.425478

Answer 1

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