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arXiv:1107.3637 · Physical Review A

Femtosecond pulses in a dense two-level medium: Spectral transformations, transient processes, and collisional dynamics

Denis V. Novitsky

Published Jul 18, 2011• 30 citations
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Abstract

Propagation of ultrashort optical pulses in a dense resonant medium is considered in the semiclassical limit. In our analysis, we place emphasis on several main points. First, we study transformations of spectra in the process of pulse propagation and interactions with another pulse. The second point involves the transient processes (including pulse compression) connected with self-induced transparency soliton formation inside the medium. Finally, the third aspect is the study of collisions of co- and counterpropagating pulses in the medium. In the last case, the investigation of symmetric and asymmetric collisions shows the possibility of effectively controlling the parameters of transmitted radiation.

DOI
10.1103/physreva.84.013817

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Propagation of ultrashort optical pulses in a dense resonant medium is considered in the semiclassical limit. In our analysis, we place emphasis on several main points. First, we study transformations of spectra in the process of pulse propagation and interactions with another pulse. The second point involves the transient processes (including pulse compression) connected with self-induced transparency soliton formation inside the medium. Finally, the third aspect is the study of collisions of co- and counterpropagating pulses in the medium. In the last case, the investigation of symmetric and asymmetric collisions shows the possibility of effectively controlling the parameters of transmitted radiation.
Using numerical simulations, we study propagation of ultrashort light pulses in an inhomogeneously broadened two-level medium. There are two main issues in our study. The first one concerns the transient process of self-induced transparency soliton formation, in particular, the compression of the pulse which seems to be more effective in the case of homogeneous broadening. The second question deals with the collisions of counter-propagating solitons. It is shown that the level of inhomogeneous broadening has a substantial effect on the elasticity of such collisions.
Propagation of single- and two-color hyperbolic secant femtosecond laser pulses in a three-level $\ensuremath{\Lambda}$-type quantum system is investigated by solving the Maxwell and density matrix equations with the finite-difference time-domain and Runge-Kutta methods. As a first study of our modeling, we simulate pulse self-induced transparency (SIT) in two-level systems and see how this phenomenon can be controlled by manipulating the initial relative phase between the SIT pulse and a second control pulse, provided the ratio between both pulse frequencies obeys the relation ${\ensuremath{\omega}}_{1}∕{\ensuremath{\omega}}_{2}=3$. We then examine frequency down-conversion processes that are observed with single- and two-color pulses the envelope area of which is equal to or a multiple of $2\ensuremath{\pi}$, for pulse frequencies close to resonance with the transitions of a three-level $\ensuremath{\Lambda}$ medium. Also, phase-sensitive phenomena are discussed in the case of two-color $\ensuremath{\omega}\text{\ensuremath{-}}3\ensuremath{\omega}$ pulses propagating resonantly in the three-level system. In particular, possibilities for such coherent control are found for frequency down-conversion processes when the ratio of the frequencies of optical transitions is ${\ensuremath{\omega}}_{13}∕{\ensuremath{\omega}}_{12}=3$. The conditions for quantum control of four-wave mixing processes are also examined when the pulse frequencies of two-color $\ensuremath{\omega}\text{\ensuremath{-}}3\ensuremath{\omega}$ pulses are far from any resonance of the three-level system. We demonstrate the possibility to cancel the phase sensitivity of the four-wave coupling in a $\ensuremath{\Lambda}$-type system by competition effects between optical transitions.
Exact single-soliton solutions of the modified system of Maxwell-Bloch equations, in which the dipole-dipole interactions of the atoms of a dense resonant medium are taken into account, are obtained. Two propagation regimes are analyzed: “coherent,” where the pulse duration is much shorter than both relaxation times ( T p ≪ T 1 , T 2 ), and “incoherent,” where the pulse duration falls between the relaxation times ( T 2 ≪ T p ≪ T 1 ). It is predicted, for the first time, that soliton propagation of an ultrashort pulse is possible in a dense resonant absorbing medium in an incoherent interaction regime. The differences between the amplitude and phase characteristics of the solitons considered and the corresponding characteristics of the solitons for McCall-Hahn self-induced transparency are noted.
The spatiotemporal dynamics of a light pulse injected into a dense, resonant medium under near-dipole–dipole interaction conditions is considered. Two regimes for soliton formation are investigated numerically and analytically. The first one occurs if the pulses are much shorter than both relaxation times. In the second, the pulse duration falls between those of the relaxation times and may be regarded as an incoherent one. In the latter case there are conditions in which the dephasing process is suppressed by dipole–dipole interatomic interaction. Not only are one-soliton solutions found but also a powerful pulse splitting into separate solitons is revealed. The regions in which solitons are found have been estimated. The possibility of finding incoherent solitons has been analyzed, with group-velocity dispersion and diffraction of tilted pulses, which are shown to make soliton formation easier, taken into account.