| This thesis presents an analysis of three applications of parametric gain in nonlinear optical media. The first of these is quasi-phase-matched parametric amplification, where a multiple-scale averaging method is applied to determine the effect of periodically poling the quadratic nonlinear coefficient. The average evolution equation is seen to contain cubic terms which cause the interaction to detune in a manner similar to detuning caused by self- and cross-phase modulation in cubically nonlinear processes. An average evolution equation for asymmetrically poled crystals is also derived to describe tuning of the parametric amplifier via the electro-optic effect.; Second, the process of parametric amplification in a laser cavity (an optical parametric oscillator) is modelled numerically, with a particular goal being to monitor the effect of self-induced heating through absorption of the optical field energy by the crystal. Thermal lensing and detuning are seen when the numerical runs are restricted to a single signal/idler pair. When more pairs are added, the competition for pump power is strongly influenced by the nonuniform refractive index induced by self-heating. Using a novel method to advance the heating process, very long time scales are explored, over which it is seen that the multiple signal/idler pairs continue to compete and readjust their energies. This temperature advancement routine is used to run the system to steady-state, where it is seen in at least one case that the signal/idler pairs also approach a multi-modal steady-state.; Finally, the use of parametric gain is explored in fiber-optic communications and storage systems, in the form of periodic phase-sensitive amplification. Multiple-pulses obtained in previous work by solving an equation modelling the average behavior of field envelopes in these systems are demonstrated to be stable with respect to the original equations, even under the influence of quantum attenuator noise and guided acoustic-wave Brillouin scattering noise. Monte Carlo simulations are used to demonstrate that timing and amplitude jitter are substantially reduced by the phase-sensitivity of the amplifiers, providing an important step toward establishing the feasibility of long-haul transmission or long-time storage of optical signals based on these multiple-pulses. |
