Analytic solutions for the saturated absorption spectra

Analytical Solutions of Temporal Evolution of Populations in Optically-Pumped Atoms with Circularly Polarized Light

“…This method is general and applicable to most atoms. As stated in Section 1, the obtained analytical form of the populations can be used in the calculation of spectroscopic lineshapes such as in saturated absorption spectroscopy (SAS) [16,17] and polarization spectroscopy (PS) [18]. Calculations of SAS and PS for Cs atoms are in progress.…”

“…These analytical solutions are practically very useful; once they are obtained, it is readily possible to obtain analytically computed quantities such as the absorption coefficient of a probe beam and lineshape functions in nonlinear laser spectroscopy. We have previously reported analytical solutions for SAS [16,17] and polarization spectroscopy (PS) [18].…”

“…As is well-known, the solution of Equation (16) consists of two parts: a homogeneous solution and a particular solution. We first find the solutions of the homogeneous equation by inserting the equation g i ∼ e λΓt into Equation (16). Then, we have two values (λ 2i−1 , λ 2i ) for λ as follows:…”

Analytical populations of a multilevel atom in a weak linearly-polarized light

“…We reported the analytical solutions of the populations of the D 1 and D 2 transition lines of 87 Rb atoms [14,15], and used the results to calculate the saturated absorption spectra analytically [16]. We also obtained the exact analytical form of the populations for 87 Rb atoms using a weak + polarized laser beam [17] considering all the sublevels in the excited state.…”

Analytical Study of Polarization Spectroscopy for the Jg=0 → Je=1 Transition

“…The analytical solution of saturated absorption spectroscopy (SAS) for the ideal two-level atoms was presented in the textbook [11]. Also, SAS [12] and PS [13] for Rb atoms were analytically studied in the low intensity limit. In this paper, we present analytical solutions of PS for the transition J g =0→J e =1 of Sr (or Yb) atoms where the intensity of the pump beam is arbitrary.…”