Analytical expression for the nth Fourier coefficient of a modulated Lorentzian dispersion lineshape function

Modulated spectroscopic detection techniques that rely on dispersion, e.g. Faraday modulation/rotation spectroscopy and wavelength-modulated noise-immune cavity-enhanced optical heterodyne molecular spectroscopy, are often described in terms of Fourier coefficients of a modulated dispersion lineshape function. This work derives a non-complex analytical expression for the nth Fourier coefficient of a modulated Lorentzian dispersion lineshape function. The expression is easier to implement, and orders of magnitude faster to execute, than previous approaches involving numerical calculations of integrals. The first six Fourier coefficients are explicitly given and illustrated for their optimum modulation amplitudes, which are also given.

Research highlights► Analytical expression for the Fourier coefficients of a modulated Lorentzian dispersion function. ► Analytical expression for the lineshape of the signal from FAMOS/FRS. ► Analytical expression for the lineshape of the dispersive and sub-Doppler NICE-OHMS signal.