Real part of atmospheric susceptibility

Abstract

In a recent paper,1 we developed a unified expression for the real part of the complex susceptibility of the atmosphere over the millimeter through the IR region from the imaginary part of the susceptibility under the impact approximation with a first-order line coupling correction. Here, two other real part expressions are derived, corresponding to the imaginary part specified by the modified Lorentz and the Gaussian line shape functions. Fundamental to our derivation is the Kramers-Kronig relationship,1 which states that the real and imaginary parts of the complex susceptibility are related through the Hilbert transform. The real part for the Gaussian case was expressed in terms of the Dawson and the modified Dawson integrals. Asymptotic expressions of the obtained real-part expressions and of the unified real part and the real part corresponding to the delta line shape1 were derived and shown to be identical. Considering the fact that the corresponding imaginary parts have entirely different asymptotic characteristics, the asymptotic behavior of the real part has depressed sensitivity to that of the corresponding imaginary part.