I need to simulate the refractive index of GeO2 doped silica as function of wavelength, to be able to predict optical fiber properties such as group index, chromatic dispersion, and dispersion slope. Currently, I'm aware of two different models: one using a linear interpolation of the Sellmeier equation (Fleming1984), and one using Claussius-Mossotti interpolation (Sunak1989). Is it the best currently available model, or is there any more recent advances in that field?
http://dx.doi.org/10.1109/68.36016
http://dx.doi.org/10.1364/AO.23.004486
GeO2 can be deposited into Fused Silica up to ~19% molar (around 29% or so % ewight!). The ref. ind. is commonly evaluated by weighting the GeO2 contribution (1.598 @ 1.55) and the F-Silica ([email protected]) by their partial weight or molar fraction. A good starting point to look into is to read the Ref.: "Dispersion in GeO2 -SiO2 glasses". From there you can meet more studies...
Good Luck!
From a set of mode indices, the index profile n(x) can be easily calculated using WKB approximations. For a step index profile, the effective mode indices can also be
expressed as a function of mode order according to
n2 eff = n2sur -lambda2p2/4d2
where, nsur is the refractive index of the surface (waveguide material), lambda the wavelength used, p the mode order and d the depth of the waveguide. This
equation used to determine the refractive index and depth of the guides.
Read Book Nishihara"Integrated Optics" for detailed information.
I recommend to read the article "To the use of Sellmeier formula" written by Volkmar Brückner in 2011. One can download it from springer.com absolutely free. This article contents Sellmeier empirical constants not only for GeO2 but for P2O5 and B2O5 dopants too.
A better but more realistic way is to calculate the absorption curve for the system you want to simulate and have the real and imaginary parts of the dielectric functions. The squire root of the real part at zero frequency is a good estimation of refractive index.
See: Neng Li, et. al. PCCP 16, 1500-1514 (2014).
If you are looking for an academic exercise then first principles calculations are always best for understanding the underlying phenomena. If you're trying to build a model for real word applications, I found from experience that empirical formulas are generally better suited, such as the ones suggested by Andrey.
Sellmeier Formula can be used to calculate the refractive index of doped silica.
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