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Physical Review A

Simulating multidimensional optical wave-mixing signals with finite-pulse envelopes

Igor V. Schweigert, Shaul Mukamel

Published Mar 3, 2008• 50 citations
Publisher

Abstract

Closed expressions are derived for resonant coherent multidimensional spectra carried out with temporally well-separated pulses. The roles of the pulse carrier frequencies, phases, bandwidths, and envelopes can be readily analyzed. These results are particularly suitable for the design of new pulse sequences and for implementing coherent-control pulse-shaping algorithms for optimizing these signals to meet specific targets.

DOI
10.1103/physreva.77.033802

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Closed expressions are derived for resonant coherent multidimensional spectra carried out with temporally well-separated pulses. The roles of the pulse carrier frequencies, phases, bandwidths, and envelopes can be readily analyzed. These results are particularly suitable for the design of new pulse sequences and for implementing coherent-control pulse-shaping algorithms for optimizing these signals to meet specific targets.
We present perturbative analytical solutions to the optical Bloch equations at third order, with finite duration Gaussian pulse envelopes. We find that a given double-sided Feynman diagram in this approximation can be conveniently described in the frequency domain as a product of the expression in the impulsive limit and a finite-pulse factor. Finite-pulse effects are Feynman-diagram-dependent, however, and include nontrivial phase corrections that can occur even in the case of transform-limited pulses. The results constitute a practical framework for modeling phenomena in multidimensional coherent spectroscopy that cannot easily be captured in the impulsive limit, including the roles of bandwidth, resonance, and pulse chirp.
An investigation is reported of the characteristic features of a four-wave mixing of a chirped signal with bandwidth- limited pump waves in a resonant medium modeled by a two- level scheme. Analytic estimates are obtained and a numerical analysis is made of the combined influence of various mechanisms (spatial phase matching, a finite nonlinear response time, and phase cross-modulation) on the spectral composition and on the temporal behavior of the fourth pulse. Conditions are found for achieving, with practically undetectable distortions, phase conjugation of a chirped signal accompanied by shortening of the pulse envelope and narrowing of the spectrum of the phase- conjugate wave.
Multidimensional spectroscopy with femtosecond phase-related pulse sequences, in which the relative delays and optical phases of pulses are scanned during spectroscopic observation, is demonstrated on electronic transitions in atomic potassium vapor. The pulse sequences were constructed using emerging femtosecond pulse-shaping techniques that allow for automated generation of complex ultrafast waveforms. Sequences of two and three pulses with specified optical phase relationships and interpulse delays were used to prepare specified coherent states.
Using multiple temporally-overlapped, frequency offset and phase-tuned, linear frequency chirps, a new method of multi-GHz optical coherent transient optical pulse shaping and processing in inhomogeneously broadened rare-earth doped crystals is proposed. Using this technique with properly chirped laser sources, multi-GHz processing can be controlled with conventional low-bandwidth electronics and optical modulators. Specifically, this technique enables pulse shaping in the MHz to THz frequency regime with time-bandwidth-products exceeding 100,000, filling the gap between the operating regimes of femtosecond pulse shaping and analog electronics. The low bandwidth (~20 MHz) proof-of-concept demonstrations presented in this paper include pulse train creation, selfconvolution, auto-correlation, and chirped pulse compression.
Coherent control of the atomic two-photon absorption with shaped single-cycle pulses is examined theoretically in the weak-field regime. The control over the stabilized carrier-envelope phase (CEP) of the pulses is determined as a key parameter allowing the full utilization of the ultrabroad pulse spectrum. This bandwidth is sufficient to provide besides the sequential two-photon pathways, additional Raman-type pathways coupling between the ground and the excited states. The interference between the different pathways is efficiently controlled via the control over the CEP. Simplified two-level model is analyzed in the frequency domain where the rational pulse shaping is applied. The developed intuition is applied to atomic Cs and verified by the exact numerical solution of time-dependent Schrodinger equation.