Phase-resolved time-domain nonlinear optical signals

Sarah M. Gallagher Faeder and David M. Jonas
Phys. Rev. A 62, 033820 – Published 18 August 2000
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Abstract

A systematic theoretical and computational investigation of the microscopic factors which determine the phase of the signal field in time-resolved quasidegenerate three-pulse scattering experiments is presented. The third-order phase-matched response is obtained by density-matrix perturbation theory using a Green-function formalism for a system composed of two well-separated sets of closely spaced energy levels. Equations for calculating the electric field of four-wave-mixing signals generated by path-length delayed pulses 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 pulse-delay-dependent phase modulation at the frequency of the first dipole oscillation in the four-wave-mixing process. Analytic results for a two-level Bloch model show the phase shift from rapid nonlinear polarization decay. The product of dipole matrix elements is real and positive for three-level processes (bleached ground-state absorption and excited-state emission), but can be real and negative for some four-level Raman processes. The pulse-delay-dependent phase modulation treated here is closely related to the interferometric pulse-delay-dependent amplitude modulation observed in some collinear experiments, and plays a role in producing photon echos in inhomogeneously broadened samples. Numerical calculations of phase-resolved electric fields for finite duration pulses using a Brownian oscillator model appropriate for condensed-phase dynamics are presented. The ability of pulse-delay-dependent phase modulation to encode the frequency of the initially excited dipole onto the phase of the signal field can be exploited to examine energy-level connectivity, reveal correlations hidden under the inhomogeneous lineshape, and probe relaxation pathways in multilevel systems.

  • Received 28 January 2000

DOI:https://doi.org/10.1103/PhysRevA.62.033820

©2000 American Physical Society

Authors & Affiliations

Sarah M. Gallagher Faeder* and David M. Jonas

  • Department of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309-0215

  • *Present address: Department of Physics of Complex Systems, Weizmann Institute of Science, 76100 Rehovot, Israel.
  • Corresponding author. Mailing address: Department of Chemistry and Biochemistry, CB 215, University of Colorado at Boulder, Boulder, CO 80309-0215. FAX:(303)492-5894. Email address: David.Jonas@Colorado.edu

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Vol. 62, Iss. 3 — September 2000

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