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Physical Review A

Phase control of dispersion effects for an ultrashort pulse train propagating in a resonant medium

M. A. Bouchène

Published Dec 6, 2002• 20 citations
Publisher

Abstract

We present here a theoretical analysis of the propagation of a sequence of ultrashort pulses in an optically dense medium. The interaction is resonant and treated in the weak-field regime. Dispersion is dominant and induces important reshaping effects. We show that these effects depend crucially on the relative phase shift \ensuremath{\varphi} between the pulses. Compared to the case of a train of independent pulses (i.e., mutually incoherent), a pulse sequence with $\ensuremath{\varphi}=0$ is shown to be sensitive to dispersion for lower optical depths, whereas a pulse sequence with $\ensuremath{\varphi}=\ensuremath{\pi}$ is shown to be more robust.

DOI
10.1103/physreva.66.065801

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Chinese Physics Letters•Jan 1, 2005•0 citations
We present here a theoretical analysis of the propagation of a sequence of ultrashort pulses in an optically dense medium. The interaction is resonant and treated in the weak-field regime. Dispersion is dominant and induces important reshaping effects. We show that these effects depend crucially on the relative phase shift \ensuremath{\varphi} between the pulses. Compared to the case of a train of independent pulses (i.e., mutually incoherent), a pulse sequence with \ensuremathφ=0\ensuremath{\varphi}=0\ensuremathφ=0 is shown to be sensitive to dispersion for lower optical depths, whereas a pulse sequence with \ensuremathφ=\ensuremathπ\ensuremath{\varphi}=\ensuremath{\pi}\ensuremathφ=\ensuremathπ is shown to be more robust.
We present an experiment in which an ultrashort pulse train propagates resonantly through anoptically dense vapor of atomic rubidium. The sequence obtained from a Fabry-Perot interferometer comprises nearly 10 regularly time-delayed and mode-locked pulses. We show that a sequence with phase shift phi = 0[2pi] between two successive pulses propagates with important temporal distortion, whereas a sequence with phi = pi[2pi] experiences few propagation effects, thus leading for the first time to our knowledge to the possibility of phase control of dispersion effects for an ultrashort pulse train.
An ultrashort weak pulse that propagates resonantly on the $\ensuremath{\mid}a⟩\ensuremath{\rightarrow}\ensuremath{\mid}b⟩$ transition of a three-level system $(\ensuremath{\mid}a⟩,\ensuremath{\mid}b⟩,\ensuremath{\mid}c⟩)$ experiences reshaping effects on a time scale longer than its duration. When a strong field is applied (nonresonantly) on the $\ensuremath{\mid}b⟩\ensuremath{\rightarrow}\ensuremath{\mid}c⟩$ transition, important light shifts are induced. We have theoretically studied the novel behavior of both the medium and weak propagating laser pulses in such conditions. For the transmitted field profile, drastic changes occur: at long times, efficient reduction of the distortion is obtained, while strong oscillations appear for short times, mapping out the dynamical light shift. These shaping effects, which are accompanied by new features in the spectrum for the propagating pulse, are interpreted as the result of the interference between incident field and induced dipole radiated field, whose frequency sweeps in time because of the induced light shift.
This thesis deals with the study of propagation effects experienced by weak light pulses as they propagate in atomic media driven by strong pulses. We explore both the ultra-short and long pulse regime and investigate the phenomena that arise at these different time scales. In the short pulse regime, a strongly driven two level atomic system presents transient light shifts, and non-adiabatic transitions occur between these adiabatic levels. We have studied a method to probe these light shifts in real time by propagating a weak probe through the medium. The light shifts enrich the spectrum of the probe and the probe gets shaped as a result. In this way a strongly driven two-level system can act as an active pulse shaper, and can introduce oscillations in the temporal profile of an ultra-short pulse at a time scale shorter than the pulse duration. We also show that by driving the system with two time delayed non-resonant strong fields, the non-adiabatic effects can be rendered phase dependent. This gives very sensitive phase control of the excited state population and can be used to formulate new techniques in interferometry. In the long pulse regime we present a new method of slowing light that can be realized in a double two-level system interacting with two orthogonally polarized light pulses that propagate along different axis. Spatio-temporal dependence of the total polarization induces a grating in the ground Zeeman coherence. The stronger of the two fields (the control field) is diffracted from this grating into the direction of the weak probe field compensating for the absorption of this latter field. A transparency window is thus created in the absorption spectrum of the probe leading to the slowing down of light. The transparency window exhibits characteristics similar to the one obtained by EIT (electromagnetic induced transparency) method. However, the important difference between our method and the traditional EIT method, is that ours doesn't rely on realizing dark state in the system. This may open the possibility of slowing down light in more complex atomic media. Moreover, when the linear absorptive response of the medium is cancelled in this manner, the nonlinear response becomes more important. In the situation where fields propagate in the same direction and have same frequency, two regimes have been investigated. For small optical depths, the effective susceptibility behaves as chi_lin exp[2 i phi] (with phi the phase difference between two fields). This renders phase control of the medium response, and the medium can be changed from an absorber to an amplifier, with normal or anomalous dispersion, by adjusting the relative phase phi.  In the regime of large optical thickness, phase saturation takes place and the effective susceptibility turns into chi_lin*, changing an absorber into an amplifier without effecting the dispersive response (chi_lin is linear susceptibility).
A weak resonant femtosecond pulse propagates through an optically thick atomic medium whose properties have been modified by a strong nonresonant ultrashort pulse. We study the energy redistribution between the spectral components of the weak resonant pulse using both experimental and theoretical methods. The transmitted spectrum exhibits an asymmetric feature that reveals an important gain-dispersion coupling. For light shifts that perturb slightly the propagation of the weak resonant pulse, this asymmetry maps out the asymptotic part of the linear susceptibility.