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Optics Letters

Spectral interferometry as an alternative to time-domain heterodyning

Michel F. Emde, Wim P. de Boeij, Maxim S. Pshenichnikov, Douwe A. Wiersma

Published Sep 1, 1997• 46 citations
Publisher

Abstract

A novel method of time resolving the amplitude and phase of a transient nonlinear-optical polarization, based on Fourier transformation of a spectral interference pattern, is discussed. We show that with this technique the delay at which the polarization is generated can be retrieved. The method is demonstrated in a transient four-wave-mixing experiment on a dye solution.

DOI
10.1364/ol.22.001338

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A novel method of time resolving the amplitude and phase of a transient nonlinear-optical polarization, based on Fourier transformation of a spectral interference pattern, is discussed. We show that with this technique the delay at which the polarization is generated can be retrieved. The method is demonstrated in a transient four-wave-mixing experiment on a dye solution.
We present a novel heterodyne‐detected four‐wave mixing technique, which determines the third‐order nonlinear polarization in phase and amplitude by spectral interferometry. It allows us to measure the resonant transient four‐wave mixing of single localized excitons, both frequency and time‐resolved. In the signal, the strength of the coupling between two probed exciton transitions is directly observable. Applying a strong optical pump pulse, we observe optical Rabi oscillations of the exciton polarization. Observing decay of the third‐order polarization after the pump pulse, we can exclude the presence of signi£cant excitation‐induced dephasing.
We demonstrate that spectral interferometry can be used together with a well-characterized reference pulse to directly determine the spectral amplitude and spectral phase of coherent four-wave-mixing (FWM) emission from multiple quantum wells. The temporal amplitude and phase are then readily obtained by an inverse Fourier transformation. We illustrate that it is necessary to accurately determine the spectral phase, as well as the spectral amplitude, in order to correctly determine the temporal behavior. We subsequently use this technique to measure discontinuities in the temporal phase. Instabilities in the phase occur and phase jumps of $\ensuremath{\sim}\ensuremath{\pi}$ are produced when both the real and imaginary parts of the FWM field are zero. These jumps occur at the minima in the quantum beats, and this condition requires the excitation of approximately equal numbers of heavy- and light-hole excitons.
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.