Based on the result, of ref. [5], the impulse response of a resonant phase conjugator is calculated with the fourwave mixing. An analytical expression is obtained. This result is compared with that of a Kerr-like phase conjugator, given by R. A. Fisher et al [4]. The difference is discussed.
In this paper we develop the interrelationships between the steady-state and transient behavior for cw-pumped Kerr-like conjugators in which the optical Kerr effect is considered to respond instantaneously. We use Laplace-transform techniques to develop an expression for the conjugate response to input pulses of arbitrary form. For stable conjugator operation (in which the cw conjugate reflectivity is finite for all input frequencies), the expression reduces to an antilinear Fourier-transform relationship, which is readily adaptable to computer simulation. The cw filter function of Pepper and Abrams [Opt. Lett. 3, 312 (1978)] is found to play a central role. We show, both numerically and analytically, that our calculated delta-function response agrees with that previously published. We numerically demonstrate temporal spreading and reshaping when the conjugator transit time becomes equal to or longer than the duration of the input pulse, and we show numerically the perfect chirp reversal for sufficiently thin conjugators and the deviations from perfect chirp reversal upon increasing the thickness of the conjugator. These numerical results can be understood in terms of the bandwidth of the associated cw filter function.
A calculation procedure and various large-signal and numerical solutions are presented for degenerate four-wave mixing in optical Kerr media, and for phase conjugate resonators using degenerate four-wave mixing. The solutions presented take full account of nonlinear refractive index changes, pump depletion, signal saturation, distributed losses, and possible external mirrors with laser gain. We find that including the nonlinear index change generally causes little change in the reflectivity or power output of degenerate four-wave mixing devices, at least with symmetric pumping. The optimum power output from a phase conjugate resonator with and without a laser gain medium is calculated. The results provide some theoretical guidance for designing phase conjugate resonators.
PACS Code 42. 65. Bp; 42. 60. Da