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Abstract
Nonlinear optical effects such as Stimulated Brillouin Scattering, Stimulated Raman Scattering, self-focusing, wave-mixing, parametric mixing, etc., have a long history in plasma physics. Recently, four-wave mixing in plasmas and its applications to phase conjugation has been extensively studied. Although four-wave mixing (FWM), using various nonlinear mediums, has many practical applications in the visible regime, no successful attempt has been made to study or demonstrate FWM for wavelengths longer than 10$\mu$m. Plasmas as phase conjugate mirrors have received considerable attention since they become more efficient at longer wavelengths (far-infrared to microwave). The purpose of this thesis is to study various fundamental issues which concern the suitability of plasmas for four-wave mixing and phase conjugation. The major contributions of this thesis are the identification and study of thermal and ionization nonlinearities as potential four-wave mixing and phase conjugation mechanisms and the study of the affect of density inhomogeneities on the FWM process.
Using a fluid description for the plasma, this thesis demonstrates that collisional heating generates a thermal force which substantially enhances the phase conjugate reflectivity. Numerical estimates of the phase conjugate reflectivity indicate that for modest power levels, gains $<$1 are possible in the submillimeter to centimeter wavelength range.
The prospect of using a novel ionization nonlinearity in weakly ionized plasmas for wave-mixing and phase conjugation is discussed. The ionization nonlinearity arises from localized heating of the plasma by the beat-wave. Wherever, the local temperature is increased, a plasma density grating is produced due to increased electron-impact ionization. Numerical estimates of the phase conjugate reflectivity indicate reflectivities in the range of 10$\sp{-4}$-$10\sp{-3}$ are possible in a weakly ionized steady-state gas discharge plasma. Larger reflectivities may be possible for pulsed plasma sources.
Most of the literature concerning FWM and phase conjugation in plasmas has assumed that the plasmas are isotropic, homogeneous, and quiescent. Since plasmas seldom satisfy any of the above criteria, a more complete theory of FWM in the presence of plasma density fluctuations is necessary. One chapter in this thesis focus on the effects of density fluctuations (inhomogeneities) on the FWM process.