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Physical Review A

Controllable interaction of counterpropagating solitons in three-level media

Andreas Pusch, Joachim M. Hamm, Ortwin G. Hess

Published Aug 11, 2010• 17 citations
Publisher

Abstract

We examine the dynamics of counterpropagating self-induced transparency solitons in three-level media. In a multilevel system, self-induced transparency gives rise to soliton solutions if the propagation is unidirectional, but the collision of counterpropagating pulses destroys the integrability of the underlying equations. We consider the collision of a rightward and a leftward moving self-induced transparency solitary wave by solving the full Maxwell-Bloch equations numerically using a finite-difference time-domain approach. Depending on pulse duration, amplitude and relative polarizations of the initial solitary waves we observe different regimes of interaction. For high group velocities and orthogonal polarizations, secondary solitary waves are born during the interaction, whereas the collision of solitary waves with the same polarization never produces secondary solitary waves but leaves behind a population grating in the interaction region. Because the crucial parameters can be controlled, an experimental confirmation of the predicted interaction regimes should be feasible.

DOI
10.1103/physreva.82.023805

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We examine the dynamics of counterpropagating self-induced transparency solitons in three-level media. In a multilevel system, self-induced transparency gives rise to soliton solutions if the propagation is unidirectional, but the collision of counterpropagating pulses destroys the integrability of the underlying equations. We consider the collision of a rightward and a leftward moving self-induced transparency solitary wave by solving the full Maxwell-Bloch equations numerically using a finite-difference time-domain approach. Depending on pulse duration, amplitude and relative polarizations of the initial solitary waves we observe different regimes of interaction. For high group velocities and orthogonal polarizations, secondary solitary waves are born during the interaction, whereas the collision of solitary waves with the same polarization never produces secondary solitary waves but leaves behind a population grating in the interaction region. Because the crucial parameters can be controlled, an experimental confirmation of the predicted interaction regimes should be feasible.
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.
This thesis explores the existence and properties of self-induced transparency (SIT) solitons in nanophotonic waveguides. SIT solitons are shape-preserving solutions of the semi-classical Maxwell-Bloch equations, a system of nonlinearly coupled differential equations. In a first investigation, collisions of counterpropagating simultons (SIT solitons in absorbing three-level systems) are studied numerically in the plane-wave approximation and a polarisation- and group-velocity dependent soliton birth is uncovered. Apart from their fundamental interest, such light-light interaction effects may be of use for optical computing applications if they can be transferred to tightly confined light pulses. Confining light is usually achieved by using dielectric waveguides that exhibit group velocity dispersion leading to chirped pulses, which experience absorption when entering an absorbing medium. If the chirp is strong enough and the pulse intense enough, they can even completely invert an absorber. When investigating chirped pulse propagation through a dense ensemble of two-level system it is found that the chirped pulses dynamically reshape into unchirped pulses experiencing transparency. Furthermore, the conditions on the waveguide geometry to enable SIT are analysed, identifying a nanophotonic slot waveguide with a low-index gap, exhibiting high electric field enhancement and a homogeneous field profile, as the ideal candidate system for guided SIT solitons. This analysis is supported by two-dimensional numerical calculations that show the solitary character is maintained during propagation if the absorber density is high enough to ensure a slow-down of the pulse and to thus counteract the waveguide dispersion. Finally, the soliton birth due to simulton collisions and optical memory schemes proposed for plane-wave SIT are investigated in the two-dimensional slot waveguide and found to also be possible in this geometry.
The evolution of the electromagnetic field in a two-level medium occurring in a matrix with finite response time has been studied. An integrable variant of the Maxwell-Bloch equations with allowance for nonlinear dispersion is derived and solved using the inverse scattering problem. It is shown that the nonlinear dispersion caused by the finite response time of the matrix yields a new possibility of controlling soliton parameters. A particular case of the constructed model can be used to describe field pulses in the parameter domain that occurs between the regions of applicability of the quasi-monochromatic approximation and the approximation of unidirectional propagation of pulses with durations on the order of the oscillation period.
By solving the two-level Maxwell-Bloch equations for resonant pulses numerically, we observe precursors in a regime where the area theorem is fulfilled. The precursors are $0\ensuremath{\pi}$ pulses traveling at a velocity close to the speed of light, and the main signal is a self-induced transparency (SIT) $2\ensuremath{\pi}$ soliton traveling at a much lower velocity. The manifestation of the precursors is strongest when the input pulse duration is on the same order as the inhomogeneous lifetime and the input area is close to $\ensuremath{\pi}$. Depending on the relationship between the input pulse duration and the inhomogeneous lifetime, the precursors can interact linearly or nonlinearly with the material. Experimental confirmation of these results should offer a direct and reasonably straightforward way of measuring optical precursors.
We reveal the existence of an optical self-induced-transparency soliton family in a two-level absorbing system down to the few-cycle limit. Based on the few-cycle envelope approximation, we introduce a systematical method of reducing the Maxwell-Bloch equations beyond the slowly varying envelope approximation and characterize the parameter space to achieve slow and fast lights. Verified by direct numerical simulations with full vectorial Maxwell-Bloch equations, we also give the relationships for a number of optical cycles on area theory and pulse group velocity, which demonstrate possible coherent photon-matter interactions.