Effects of injected atomic coherence on multiwave mixing.

Abstract

Discussion begins with a brief account of atomic level-pumping and reasons why atomic coherence is typically not considered in cw work on optical interactions. This dissertation is divided into four parts: semiclassical treatments of one-photon electric- dipole atom-field single-mode interactions and multimode interactions, and corresponding treatments for the two-photon interaction. We present the effects of injected atomic coherence on the polarization of the medium, the slowly varying envelope wave equation, the single- and multiwave mixing coefficients, and weak field propagation in a homogeneously broadened two-level medium. Spatial and temporal phase matching of the injected coherence to a field mode is crucial throughout, since the field may not be able to remain in phase with the induced and injected polarizations. One-photon injected coherence contributes directly to the polarization at the atomic resonance frequency. The perfectly phase-matched case leads to a linear superposition of an exponentially decaying field (Beer's law) and a constant field driven by the injected coherence. The interaction of an injected coherence with a detuned field produces frequency-symmetric sidebands about the pump field polarization. The sideband spacing equals the atom-field detuning. To probe the injected coherence we inject a weak resonant field. The resulting three-wave mixing leads to multiwave mixing coefficients that are unaffected to first-order in the weak sidemodes, but the injected coherence adds inhomogeneous terms to the coupled-mode equations. For both single- and multimode interactions the injected coherence does not affect the exponential growth/decay of the sidemodes, but it supports a weak field that may propagate if properly phase matched. For two-photon media the injected coherence requires at least one field interaction in order to produce a polarization, which then appears in the single- and multiwave mixing coefficients. The exponential growth/decay rate is modified by the injected coherence. For a centrally-tuned pump the injected coherence contributes the standard multiwave mixing terms as well as additional effects. Four-wave mixing is discussed as a means of relaxing the spatial phase matching constraint on the injected coherence.