Temporal analysis of short laser pulses using degenerate four-wave mixing.

The temporal characteristics of picosecond and subpicosecond laser pulses have been investigated with a number of different techniques.12 Streak cameras provide the temporal profile of an optical pulse directly but are limited to a time resolution of -1 psec. The two-photon fluorescence method 3 using two counterpropagating replica pulses suffers from a one-pulse-induced background fluorescence that limits the precision of the temporal measurement. By using second-harmonic generation (SHG), a background-free measurement of the pulse duration can be made. In the original version, 4 a variable time delay is introduced between the two replicas of the original pulse and for a strictly reproducible pulse train yields the time autocorrelation function of the original pulse. This method is limited to measuring the average characteristics of the pulse train, and, because of phase-matching considerations, the geometry must be changed for different optical wavelengths. A more recent version of the SHG method that is suitable for single-pulse measurements uses a time-to-space mapping of the interaction region of two noncollinear replica pulses. ' Again this technique is limited because of phase-matching problems. In this Letter we introduce a new method for the measurement of the temporal profile of a single optical pulse that is based on degenerate four-wave mixing (DFWM). 7 Among the numerous applications of DFWM, 8 that most closely related to our present proposal is the time-domain correlator described by O'Meara and Yariv.9 Our technique produces a background-free measurement and has none of the phasematching difficulties associated with the SHG methods. Simple changes in the length of the nonlinear medium will allow measurements of pulse widths to be made in the subnanosecond to subpicosecond time interval. We assume that two replica pulses of the original optical pulse are constructed with a simple beam splitter and mirror arrangement. The two replicas, with complex envelope functions A (r,t) and A2 (r,t), counterpropagate in a nonlinear optical medium as shown in Fig. 1. A quasi-cw probe field A4r(r,t) illuminates the overlap volume of Al and A2. The probe field is of frequency , equal to the carrier frequency of the pulse fields. The phase conjugate wave A3 (r,t) originating in the overlap region will be shown to have a transverse spatial amplitude distribution which is characteristic of the temporal profile of the pulses Al and A2. The four coupled wave equations for Al, A2, A3, and A4 decouple and simplify considerably by assuming nondepletion of Al, A2 , and A4 in the slowly varying envelope approximation. The single equation for the phase conjugate field A3 is