Sideband optical–optical double resonance Zeeman spectroscopy. I. Theory of saturation and line shape behavior

Abstract

Several variants of the one-laser, two-color technique of sideband optical–optical double resonance Zeeman (SOODRZ) spectroscopy, which enables Zeeman and hyperfine splittings to be measured at sub-Doppler resolution, are described; a detailed theory of the line shape and signal-to-noise ratio for each variant is also presented. In the single-frequency variant of SOODRZ spectroscopy, radio frequency sidebands are imposed onto a single-frequency continuous wave laser beam to determine energy splittings between pairs of closely spaced levels. Each pair of closely spaced levels is coupled to a third isolated level by optical transitions and is tuned into resonance by the Zeeman effect. A theoretical treatment of the SOODRZ effect is presented here. It is shown that both the real and imaginary contributions to the complex third-order optical susceptibility tensor χ(3) can be observed and that the SOODRZ signal originates from a cross term between the amplitude of the unperturbed frequency-modulated beam of the laser and the nonlinear signal amplitude Re{EL*⋅ENL}. The SOODRZ signal is directly proportional to ΔNμ4MI20 (where M is the modulation index), rather than (ΔN)2, μ8, and I30 as in degenerate four-wave mixing and other nonlinear spectroscopies, which means the detection sensitivity of SOODRZ spectroscopy is considerably higher for low laser intensities and at lower number densities. Moreover, the linewidth of the sub-Doppler feature is independent of the both the Doppler width of the optical transition and the natural width of the common linked level and, hence, is immune from the effects such as upper state predissociation. Two different types of modulators, acousto-optic and electro-optic, can be used in the single-frequency variant of SOODRZ spectroscopy. The unique features of SOODRZ schemes incorporating both types of modulators are described. SOODRZ spectroscopy can also be performed with a multimode broadband laser, where the adjacent cavity modes serve the same function as the sidebands in the single-frequency version. Examples of such multimode SOODRZ spectra will be presented as well. The effect of different detection schemes (i.e., nearly crossed polarizers and/or coherent detection), laser frequency detuning relative to the center of the absorption line, and ac magnetic field modulation conditions on the intensity, phase, and functional form of the sub-Doppler double resonance line shape will be discussed here. The simplest possible form of the SOODRZ line shape is a second derivative of a Lorentzian.