Phase-resolved time-domain nonlinear optical signals - art. no. 033820

A systematic theoretical and computational investigation of the microscopic factors which determine the phase of the signal field in time-resolved qua sidegenerate three-pulse scattering experiments is presented. The third-ord er phase-matched response is obtained by density-matrix perturbation theory using a Green-function formalism for a system composed of two well-separat ed sets of closely spaced energy levels. Equations for calculating the elec tric field of four-wave mixing signals generated by path-length delayed pul ses are given. It is found that the phase of the signal field is determined by the excitation pulse phases, the dynamics of the nonlinear polarization decay, the product of four transition dipole matrix elements, and by a pul se-delay-dependent phase modulation at the frequency of the first dipole os cillation in the four-wave-mixing process. Analytic results for a two-level Bloch model show the phase shift from rapid nonlinear polarization decoy. The product of dipole matrix elements is real and positive for three-level processes (bleached ground-state absorption and excited-state emission), bu t can be real and negative for some four-level Raman processes. The pulse-d elay-dependent phase modulation treated here is closely related to the inte rferometric pulse-delay-dependent amplitude modulation observed in some col linear experiments, and plays a role in producing photon echos in inhomogen eously broadened samples. Numerical calculations of phase-resolved electric fields for finite duration pulses using a Brownian oscillator model approp riate for condensed-phase dynamics ore presented. The ability of pulse-dela y-dependent phase modulation to encode the frequency of the initially excit ed dipole onto the phase of the signal field can be exploited to examine en ergy-level connectivity, reveal correlations hidden under the inhomogeneous lineshape, and probe relaxation pathways in multilevel systems.