Measurement of the carbon isotopic composition of methane using helicoidal laser eigenstates

The spatially generalized Jones matrix formalism is used to design a laser cavity to make intracavity measurements of the carbon isotopic composition of methane. The method is based on a double optical lever effect for helicoidally polarized eigenstates, permitting to measure successively the ¹²CH₄ and ¹³CH₄ concentrations. To choose the probed isotope, one simply tunes the frequency of the laser by Zeeman effect. The experiment exhibits a good agreement with the predictions and permits to measure the ¹³CH₄/¹²CH₄ composition ratio of methane with an uncertainty of the order of ±0.07% for a sample containing only 6 × 10^-9 mole of methane.