Susceptibility for inhomogeneously broadened three-level atomic systems: Simple analytical solutions using Lorentzian distribution

We calculate the susceptibility analytically in Doppler-broadened three-level atomic systems using a Lorentzian function instead of a Gaussian function. Based on the results by Noh and Moon [H.R. Noh, H.S. Moon, J. Phys. B 45 (2012) 245002], we obtained simple analytical solutions of the susceptibility using rational functions. We compared the calculated results obtained using a Gaussian function with those obtained using a Lorentzian function, and found good agreement between the two. These analytical results will be useful in various types of laser spectroscopy, such as electromagnetically induced transparency or absorption.