Line parameters of absorption and dispersion Lorentzian curves under conditions of combined modulation and saturation distortion

Abstract

Analytical and computer solutions for the parameters of the first Fourier coefficients of Lorentzian lines subject to simultaneous modulation and saturation distortion are presented. Both absorption and dispersion shape functions are examined. The system is assumed to be described by the saturation theory of either Bloembergen, Purcell, and Pound (BPP), or Redfield. In the BPP case, results are given for the modulation frequency, ω m , being much greater or less than 1 T 1 while in the Redfield case, only ω m ⪡ 1 T 1 is considered. In all cases, it is assumed that ω m 2π is much less than the inverse line width of the pure absorption curve and that the line is traversed during a time which is slow compared to T 1 and 2π ω m . Various methods are outlined for determining the true line width, line intensity, saturation parameter, and modulation amplitude from measurements on the distorted line shapes under conditions of optimum sensitivity. Tests for verifying the character of the Lorentzian line shape are also suggested.