Conical Stokes emission in three-level systems as a coherent propagation effect

Abstract

It is now known that conical emission in a two-level atomic system is a fundamental propagation effect brought about by the breakup of the exciting laser pulse into solitary waves.1 This report presents a semiclassical numerical calculation that extends this previous work by solving the optical Bloch and Maxwell equations for a three-level atomic vapor excited by laser fields of two different frequencies. The applied fields satisfy a two-photon resonance condition between the ground and final states and are slightly detuned from the intermediate state to enhance the nonlinear polarization.2 As the fields propagate, oscillations in the nonlinear polarization of the pump beam dominate the interaction and lead to the pump's breakup into solitary waves. The Stokes polarization, depending on the pump radiation, also experiences these oscillations. Because of the intensity-dependence of the refractive index, the solitary waves experience a curvature in the time-radius plane. This curvature manifests itself in the spectrum as a radial component of the wave vector at the Rabi frequency. The Stokes field, experiencing parametric breakup, displays a similar curvature. Spectral analysis reveals a radial component of the Stokes wave vector as well. This frequency-shifted off-axis radiation is identified as conical emission in the Stokes field.