Effective medium theories provide approximate expressions for the effective refractive index of a porous medium. If the bulk of the material has refractive index n_1 and the pores are filled with a material of refractive index n_2, the Lorentz-Lorenz relation yields the effective refractive index as a solution of

f(n) = p f(n_2) + (1-p) f(n_1)

where f(n) = (n^2 - 1)/(n^2 +2), and where p is the porosity of the medium. This is intended to apply to materials whose pore size is smaller than the wavelength of light. Effective medium theory is described in Born and Wolf.

Hi Jose-Maria,

Not sure about theoretical models, however I have experimentally observed a very linear relationship for TiO2 - see pg35 of my PhD thesis (available at: https://www.researchgate.net/publication/244484618_Novel_Uses_of_Titanium_Dioxide_for_Silicon_Solar_Cells?ev=srch_pub).

Good luck

Bryce

Book Novel Uses of Titanium Dioxide for Silicon Solar Cells

Thanks both of you

Effective medium theories provide approximate expressions for the effective refractive index of a porous medium. If the bulk of the material has refractive index n_1 and the pores are filled with a material of refractive index n_2, the Lorentz-Lorenz relation yields the effective refractive index as a solution of

f(n) = p f(n_2) + (1-p) f(n_1)

where f(n) = (n^2 - 1)/(n^2 +2), and where p is the porosity of the medium. This is intended to apply to materials whose pore size is smaller than the wavelength of light. Effective medium theory is described in Born and Wolf.

Thanks David. Nice reply

Dear Jose-Maria,

You can find an example with a simple structure model of a porous material in this publication (pp 10-12).

Good luck

Merçi Sébastien

Maybe the easiest and most practical way to get and test a model is by using an Optical Thin Film Software, of which you have quite a few to choose http://www.optenso.com/links/links.html . We have used extensively the Filmwizard http://www.sci-soft.com/Film%20Wizard.htm to calculate the indexes resulting from the mixture of different cermets for solar selective absorbers. This program, that is the only one we know in depth, offers you the possibility to model mixtures using the Efective Medium Approximation and different models: Maxwell-Garnett, Bruggeman, Lorentz-Lorenz and Landau-Lifshitz, everyone of them with different parameters to modify in order to adjust the calculations to the data. I guess the other programs will offer similar capabilities.

Dear Jose-Maria,

In theoretical simulation of porous media the so-called effective medium model is employed, which replaces an actual structure (containing randomly arranged regions with different refractive indexes) by the medium having a single effective refractive index. Thus, when performing numerical simulation it is necessary to obtain an adequate model of the medium under study. To this end one of the three following models is being put to use:

1. Bruggeman model (original article - Bruggeman, D.A.G., (1935), Berechnung Verschierener Physikalischer Konstanten von Heterogenen Substranzed, Ann. Phys., Leipzig, 24:636-679.)

2. Bruggeman modified model that takes account of the shape of nanocrystals

and the shape of pores (original article - Spanier, J.H. and Heman, I.P., (2000), Phys. Rev. B. 61(10):437.)

3. Maxwell-Garnett model (original article - Maxwell Garnett, J.C., (1904), Phil. Trans. R. Soc. Lond. 203:385-420. )

4. The Looyenga model (original article - Looyenga, H., (1965), Physica. 31:401-406.)

You can find the necessary formulas in this publication

https://www.researchgate.net/publication/252321095_PHOTONIC_CRYSTALS_AND_MICRORE_SONATORS_BASED_ON_THE_ANISOTROPIC_MESOPOROUS_SILICON?ev=prf_pub

Good Luck!



Article Photonic crystals and microresonators based on the anisotrop...

Check out the literature review of this paper...We used a lot the Effective refractive index approximation for our photonic crystals.