Analytical evaluation of the Fourier components of wavelength-modulated Gaussian functions

Abstract

Modulation techniques are often used in experiments where noise levels are significant, enabling weak signals to be detected. Gaussian lineshapes can be present in situations such as with tunable diode laser absorption spectroscopy of low-pressure gases, requiring the evaluation of the Fourier components of Gaussian lineshapes. These Fourier components have been evaluated only numerically in the past. In the present research, we derive exact analytical expressions for the Fourier components of a modulated Gaussian signal. We also evaluate the dimensionless modulation amplitudes that maximize the even and odd harmonics.