More recently, Manceau et al. demonstrated the THz polarization control via the accurate control of the surrounding gas pressure of two color filaments. The change of gas pressure will induce a wavelength dependent change of refractive index, resulting in the relative phase change of the two laser fields. What is the relationship between air pressure and refractive index? Who can help me to answer this question?
As I recently found out, this problem has been treated by Max Planck in 1905 in his paper "Normale und anomale Dispersion in nichtleitenden Medien von variabler Dichte", Sitzungsberichte der k. preussischen Akademie der Wissenschaften. Vol. 18/19, pp. 382-394. Planck's solution is based on his own dispersion theory, but, actually you can use everyone you like (Drude-Lorentz etc.), because in every theory the change in the dielectric function is proportional to a quantity called N, which is the number of oscillators per unit volume, i.e. a concentration which is linked to the pressure via a gas law.
We recently derived Beer's law from the Drude-Lorentz dispersion theory and showed in addition that there is a kind of mirror law for the index of refraction (the corresponding paper was accepted before we found out that Max Planck has already walked along this path, albeit he did not go all the way to Beer's law): Article Beer's Law – Why Absorbance Depends (Almost) Linearly on Concentration
There is one additional difference between our approach and Planck's: Since there is no local field correction in Beer's law, we also did not apply one in contrast to Planck and Lorentz. If you do not apply it, then for higher concentration or pressure the region of anomalous dispersion around an absorption blue-shifts somewhat. With local field correction it first stays more or less in place and then shifts to the red in dependence of the concentration.
Both, our theory and Planck's, assumes a damped harmonic oscillator as source for the absorption.
If you want to introduce another oscillator model or just want a lineshape free approach, you can use our corresponding derivation of Beer's law (which you have to slightly modify; if you are interested and can't do it by yourself, just let me know - I would be happy to collaborate): Preprint Beer's law derived from Electromagnetic Theory
Dear Dr. Zhen Zhang,
In this article there is a useful information related to your question:;" Optical Refractive Index of Air: Dependence on Pressure, Temperature and Composition"
This paper explain in more details the relation between the air pressure and refractive index based on several parameters such as temperature, and humidities.
Best regards,
Musab TR
There is direct relationship between the presser and refractive index .
https://pdfs.semanticscholar.org/ee25/a6fee957533194bb2f06b3832cf418dfd5f6.pdf
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