# Laboratoire Interdisciplinaire de Physique

LiPhy Grenoble

## Interest of using a high finesse cavity

published on , updated on

Samir KASSI
Guillaume MÉJEAN
Daniele ROMANINI
Irène VENTRILLARD

Principle of detection by absorption spectroscopy

In order to detect molecules in air by absorption spectroscopy, one may exploit the fact that incident light I0 decreases exponentially with the interaction length L as described by the Beer-Lambert law under the form :

I(ν)=I0exp(-α(ν)L)

with a(ν) = Nσ(ν) where N represents the concentration of absorbing molecules and σ is the absorption cross section for this molecule at the frequence ν.
To detect very weak absorptions lines, one way to go is increasing the interaction length.

In order to increase the interaction length, first thing one can do is using a multipass absorption cell. That allows to go from 1 to 100 meters.

$F=\frac{\pi R}{1-R}$

With high-finesse optical cavities based on high reflectivity mirrors, one can attain interaction lengths above ten km, while the probed sample volume is strongly reduced (100 times).

However, not all optical frequencies are transmitted by the cavity. Resonances, or "modes", are separated by the amount:

Δν = c/2L.