Theoretical treatment of the magnetoelectric Jones birefringence and dichroism is developed through the bilinearity in static electric and magnetic field dipole-forbidden corrections to the amplitude of Rayleigh scattering. In particular cases of orientation of the static fields relative to the polarization and wave vectors of monochromatic radiation, the amplitude determines corrections to the refractive index of atomic gas responsible for (i) the Jones birefringence and dichroism, (ii) linear birefringence and dichroism and (iii) directional anisotropy for the monochromatic wave. The analytical equations and numerical data for the indicated corrections, calculated for alkaline-earth-like atoms, determine optimal conditions for observing the effects in vapours. For resonance on 1D2 state essential enhancement is discovered in the frequency dependence for the ratio of refractive index anisotropy of the Jones effect to the square-root product of corresponding anisotropies determining the Kerr and Cotton–Mouton effects.

The fine-structure splitting of resonance atomic levels causes essential effects on the amplitude of a two-colour frequency mixing in a magnetic field. The fine-structure effects are analysed in the scattering cross section, and particularly in the circular dichroism phenomena, such as the elliptical polarization of the generated wave, when both incident waves are linearly polarized, and the dependence of the cross section on the helicity of one of the incident waves when the other one is linearly polarized. Together with general analytic expressions for the amplitude, the numerical data are presented for three different double-resonant routes involving two dipole and one quadrupole interactions of atoms with a field. The results may be useful for the polarization control of the process in an atomic vapour and for the frequency-mixing spectroscopic studies of atomic structure.

Steady electric and magnetic fields can stimulate frequency mixing of two laser waves in ensemble of free atoms. In addition to coherence conditions, the steady fields may induce additional resonance singularities essentially enhancing the cross section for scattering the sum-frequency wave. Interference between different components of the electric-and magnetic-field induced frequency summation amplitudes may cause significant effects on the efficiency of conversion. The dependence on the incident wave polarization and the atomic resonance structure is calculated analytically for the frequency mixing in atoms with a singlet structure of the ground and resonance states. Numerical estimates for the quantitative characteristics of the effect are presented for helium, alkali-earth and mercury atoms in their ground n 1 S0-state in the case of the two-photon resonance on excited singlet states with angular momentum 0, 1, and 2.

The Jones effect in a medium of free atoms exposed to static electric and magnetic fields is a useful tool for determining details of an atomic structure. For atoms in their nS ground states irradiated by a monochromatic wave in resonance with a single-photon transition to an n D state, the bilinear Jones effect is not shaded by the quadratic Kerr and Cotton-Mouton effects, nor by the linear in magnetic field Faraday effect. The position and shape of the amplitude resonance may provide information on spectroscopic properties of atomic levels. We generalize equations for the Jones-effect amplitude to the case of a doublet structure of energy levels and calculate corresponding parameters for alkali atoms. General equations are derived for the amplitude dependence on the relative orientation of the static electric and magnetic fields and on the angle between the static field and the major axis of the wave polarization vector. These equations demonstrate explicitly that the three bilinear-in-static-fields optical birefringence effects-(i) the Jones birefringence (in parallel fields), (ii) the linear birefringence and (iii) the directional birefringence (the last two in perpendicular fields)-correspond to particular cases of the bilinear-in-static-fields correction to the amplitude of Rayleigh forward scattering.

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