Polarization dependence of transition intensities in double resonance experiments: unresolved spin doublets

The polarization dependence of transition intensities in multiple resonance spectroscopic experiments can provide information useful for making rotational assignments. A formalism to describe the polarization dependence of transition intensities in multiple resonance experiments, particularly for cases when two rotational/fine structure quantum numbers are needed to specify the state of the system, is presented. The formalism is presented in a form usable both when the transitions between the underlying fine structure components are experimentally resolved, as well as when they are unresolved, to form composite lines. This sort of treatment is necessary for cases when the two quantum numbers that specify the fine structure differ significantly, such as is the case at low N, when the difference between J and N becomes comparable to the value of J. Ratios of transition intensities in different experimentally convenient polarization arrangements are evaluated for the case of composite N transitions formed by combining the spin components of a doublet system. The formalism is expressed in a form easily extendable to accommodate experimental cases of more than two excitation steps, or a combination of excitation steps and an external static electric field. This polarization diagnostic has been experimentally applied to assign spectral features in double resonance Rydberg spectra of CaF.