I want understand, what are the main differences between all these dispersion models, which one is the most precise? In which case? Are there other more innovative and advanced models? Relevant references and links are welcome. Thank you in advance!
Hi Vladimir,
The Lorentz model is a classical model able to explain several behaviours of the refractive index of a dielectric material from radio to X-rays: even though it is based on a purely mechanical model of the atom, it correctly predicts the anomalous dispersion near the absorption lines, the normal dispersion far from them, the discrepancy between the dielectric constant for static fields and the measured refractive index of electromagnetic waves, the reason why n < 1 in X-rays, and finally it can be generalized to obtain the widespread Kramers-Kronig relation between the real and the imaginary part of n.
The Sellmaier formula is simply the formula resulting from the Lorentz model, expressed in terms of wavelenghts, and replacing the plasma and resonant frequencies with empirical values, obtained from a fit of measurement data - typically in the visible band.
The Cauchy formula is a simplifed version of the Sellmeier one, applicable far from absorption lines (in particular the coefficients are determined by the wavelenght of the nearest line). It is quite accurate for small spectral extents.
Finally, the Drude model is nothing else than the Lorentz model in X-rays, assuming that the propagation occurs in a free electron gas (omega >> omega_resonant).
I have never heard of the Forouhi-Bloomer.
I hope this helps you. Good luck!
Daniele
Hi Vladimir,
The Lorentz model is a classical model able to explain several behaviours of the refractive index of a dielectric material from radio to X-rays: even though it is based on a purely mechanical model of the atom, it correctly predicts the anomalous dispersion near the absorption lines, the normal dispersion far from them, the discrepancy between the dielectric constant for static fields and the measured refractive index of electromagnetic waves, the reason why n < 1 in X-rays, and finally it can be generalized to obtain the widespread Kramers-Kronig relation between the real and the imaginary part of n.
The Sellmaier formula is simply the formula resulting from the Lorentz model, expressed in terms of wavelenghts, and replacing the plasma and resonant frequencies with empirical values, obtained from a fit of measurement data - typically in the visible band.
The Cauchy formula is a simplifed version of the Sellmeier one, applicable far from absorption lines (in particular the coefficients are determined by the wavelenght of the nearest line). It is quite accurate for small spectral extents.
Finally, the Drude model is nothing else than the Lorentz model in X-rays, assuming that the propagation occurs in a free electron gas (omega >> omega_resonant).
I have never heard of the Forouhi-Bloomer.
I hope this helps you. Good luck!
Daniele
@Daniele,
For the same material, for example Si3N4, which model is more precise of the Sellmaier or of the Lorentz? And why?
The Selmaier formula is in general quite accurate, since the coefficients appearing in it are often tabulated. For the Silicon Nitride, for example, the coefficients are reported here:
http://refractiveindex.info/?shelf=main&book=Si3N4&page=Philipp
However, for measurements in the visible range I have always used conveniently the Cauchy.
The Lorentz formula is expressed in terms of quantities (e.g. the ratio of free electrons) that are harder to measure/find.
Daniele
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