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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Coherent control of spectral effects with two-color ultrashort laser pulses: a comparison between ω-2ω and ω-3ω combinations

Xiaohong Song, Shangqing Gong, Zhizhan Xu

Published Jan 28, 2005• 0 citations
Publisher

Abstract

Using the full Maxwell-Bloch equations which avoid the limitations of slowly-varying-envelope approximation and the rotating--wave approximation as ultrashort pulses are considered, we investigate the coherent control of spectra effects with two color few-cycle laser pulses. We demonstrate that the interference effect of the two laser pulses can substantially modify the behavior of the spectra, higher spectral components can occur even for small area pulses. Moreover, comparing the ω-2ω combination with the ω-3ω scenario, we find due to the deferent superposition of the two kinds of combined laser pulses, the features of these higher spectral components can be much different.

DOI
10.1117/12.572657

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Using the full Maxwell-Bloch equations which avoid the limitations of slowly-varying-envelope approximation and the rotating--wave approximation as ultrashort pulses are considered, we investigate the coherent control of spectra effects with two color few-cycle laser pulses. We demonstrate that the interference effect of the two laser pulses can substantially modify the behavior of the spectra, higher spectral components can occur even for small area pulses. Moreover, comparing the ω-2ω combination with the ω-3ω scenario, we find due to the deferent superposition of the two kinds of combined laser pulses, the features of these higher spectral components can be much different.
A theoretical investigation on the coherent control of optical transient four-wave mixing interactions in two-level systems with two intense few-cycle propagating laser pulses of central angular frequencies $\ensuremath{\omega}$ and $3\ensuremath{\omega}$ is reported. By numerically solving the full Maxwell-Bloch equations beyond the slowly varying envelope and rotating-wave approximations in the time domain, the nonlinear coupling to the optical field at frequency $5\ensuremath{\omega}$ is found to depend critically on the initial relative phase $\ensuremath{\phi}$ of the propagating pulses: the coupling is enhanced when the pulses interfere constructively in the center $(\ensuremath{\phi}=0)$, while it is nearly suppressed when they are out of phase $(\ensuremath{\phi}=\ensuremath{\pi})$.
Using a $\ensuremath{\omega}\ensuremath{-}2\ensuremath{\omega}$ combination scenario, we investigate the spectra of two-color ultrashort laser pulses in a two-level medium. It is found that higher spectral components can be produced even for small area pulses due to the interference effect of the two laser pulses. Moreover, these higher spectral components depend crucially on the relative phase $\ensuremath{\varphi}$ of the two laser pulses: continuum and distinct peaks can be achieved through the control of the relative phase.
The four-wave mixing produced with two ultrashort phase-locked !-3! laser pulses propagating coherently in a two-level system in the infrared spectral region is shown to depend on the pulses relative phase. The Maxwell-Bloch equations are solved beyond the rotating-wave approximation to account for field frequencies which are largely detuned from the atomic resonance. The relative phase dominating the efficiency of the coupling to the 5! anti-Stokes Raman component is determined by sign of the total ac Stark shift induced in the system, in such a way that the phase influence disappears precisely where the ac Stark effect due to both pulses is compensated. This fundamental quantum interference effect can be the basis for nonlinear ultrafast optical spectroscopy techniques. Phenomena arising from the coherent control of nonlinear interactions are of importance in fields as diverse as optoelectronics and materials research, in high harmonic generation, in photoionization or molecular dissociation, and in biological applications such as spectroscopy and imaging, among others [1, 2, 3, 4, 5, 6, 7]. Optical quantum coherent control is based on the fact that the phases of interfering transition amplitudes in light-matter interactions can be controlled through the optical phase of coherent light sources that drive the interaction, in such a way that the transition rates to final states and the dynamics at various stages of the process can be modified [1]. In a recent paper [8], a theoretical investigation on the quantum coherent control of the optical transient four-wave mixing of two intense phase-locked femtosecond laser pulses of central angular frequencies ω and 3ω propagating in a two-level atom (TLA) was reported. It was shown how the nonlinear (χ (3) ) coupling to the antiStokes Raman field at frequency 5ω depends critically on the initial relative phase φ of the propagating pulses. In Ref. [8], the study was centered to intense pulses in the visible and ultraviolet spectral regions, with frequencies at resonance or lower than the atomic transition. The phenomena observed in [8], however, can be scaled to various laser and material parameters. In the infrared spectral range, for instance, experiments on ultrafast molecular dynamics are frequently performed by help of twocolor pump probe nonlinear spectroscopy techniques. In this type of studies, due to the high intensities inherent to ultrashort (subpicosecond) pulses, nonlinear effects such as stimulated Raman processes may become important and are often utilized as a complementary tool to gain information [9]. In this Letter, we address the conditions for quantum coherent control of transient four-wave mixing interactions with two phase-locked ω-3ω femtosecond laser pulses in the mid-IR spectral region. Our purpose is to reveal the basic physics for a strict two-level medium and to this end the Maxwell-Bloch TLA will be considered. We will study pulses with a duration of 300 fs (with a w 5w
The four-wave mixing produced with two ultrashort phase-locked w-3w laser pulses propagating coherently in a two-level system in the infrared spectral region is shown to depend on the pulses relative phase. The Maxwell-Bloch equations are solved beyond the rotating-wave approximation to account for field frequencies which are largely detuned from the atomic resonance. The relative phase dominating the efficiency of the coupling to the 5w anti-Stokes Raman component is determined by sign of the total ac Stark shift induced in the system, in such a way that the phase influence disappears precisely where the ac Stark effect due to both pulses is compensated. This fundamental quantum interference effect can be the basis for nonlinear ultrafast optical spectroscopy techniques.
Summary form only given. Recent advances in ultrafast laser technology have made possible the generation of extremely short and intense pulses with only two optical periods of less than 5 fs in duration in the visible region. Efforts for generation of still shorter pulses is motivated by the possibility to study light matter interactions under unique conditions as the pulse duration approaches the duration of a single optical cycle. We study the propagation of a 5-fs pulse through a layer of a dense medium of two-level systems. As a result we demonstrate the formation of single-cycle and half-cycle pulses in the sub-fs region and novel types of spectral changes during propagation as large blue and red shifts in the transmitted and reflected pulses, respectively, explained by intra-pulse frequency-difference mixing. Solitary pulse propagation phenomena beyond the limits of slowly-varying envelope (SVEA) and rotating-wave approximation (RWA) are illustrated as the formation of full Maxwell-Bloch half-cycle solitons and two-soliton pulses.