Phase Conjugation via Four-Wave Mixing in a Resonant Medium.

This thesis describes the theoretical solution and experimental verification of phase conjugation via nondegenerate four-wave mixing in resonant media. The theoretical work models the resonant medium as a two-level atomic system. Working with an ensemble of stationary atoms, the density matrix equations are solved by third -order perturbation theory in the presence of the two counterpropagating pump waves, an incident signal wave, and the phase conjugate wave, which is generated by the interaction of the three previous waves with the nonlinear medium. This solution gives the local polarization of the atom which is used in Maxwell's equations as a source term to solve for the propagation and generation of the signal wave and phase conjugate wave through the nonlinear medium. Using this solution, we show how an ultrahigh-Q isotropically sensitive optical filter can be constructed using the phase conjugation process. Extending the solution to include the effects of atomic motion, we explain how a tunable optical filter can be constructed whose bandwidth is limited by the homogeneous linewidth of the atom while the tuning range of the filter extends over the entire Doppler profile. In addition, for the homogeneously broadened case, we include the effect of saturating pump waves by solving the density matrix equations to all orders in the amplitude of the pump waves. Using sodium as the nonlinear medium we demonstrate an ultrahigh-Q optical filter using phase conjugation via nondegenerate four-wave mixing as the filtering process. The filter has a FWHM bandwidth of 41 MHz and a maximum efficiency of 4 x 10('-3). However, our theoretical work and other experimental work with sodium suggest that an efficient filter with both gain and a narrower bandwidth should be quite feasible.