Driving Gap Solitons with Light or Charges in Two-level Media

Jing Wang, Chao Hang, Guoxiang Huang

Ashat M. Basharov, Andrei I. Maimistov

Alexander V. Smirnov

Jérôme J.-P. Leon

Coupling a two-level medium, described by the Maxwell-Bloch (MB) equations, to an external cavity mode results in a prescribed boundary value for the electric field that can be tuned to the forbidden band gap of the medium. It is shown that there exists a threshold of energy density flux above which a solitonlike light pulse is generated and propagates in the medium at a fraction of the light velocity. When the driving frequency becomes close to the band gap edge, where the group velocity vanishes, the MB equations tend to the nonlinear Schr\"odinger equation which furnishes the theoretical ground to understand soliton generation by evanescent fields as a manifestation of nonlinear supratransmission, produced by an instability of the evanescent wave. Moreover, the propagation at a fraction of light velocity is shown to result from a continuous periodic exchange between polarization (electromagnetic energy) and population (density of atoms in the excited level). The process is demonstrated to occur at twice the internal frequency of the generated gap soliton. Last, when the medium spatial extension is of the order of the soliton dimension, an optical bistability is shown to occur at the supratransmission threshold allowing for different output intensities corresponding to a given input value.

Jérôme J.-P. Leon, Petrutza Anghel-Vasilescu, F. Ginovart +1 more

The Maxwell–Bloch system describes a quantum two-level medium interacting with a classical electromagnetic field by mediation of the population density. This population density variation is a purely quantum effect which is actually at the very origin of nonlinearity. The resulting nonlinear coupling possesses particularly interesting consequences at the resonance (when the frequency of the excitation is close to the transition frequency of the two-level medium) as e.g. slow-light gap solitons that result from the nonlinear instability of the evanescent wave at the boundary. As nonlinearity couples the different polarizations of the electromagnetic field, the slow-light gap soliton is shown to experience effective scattering with charges in the medium, allowing it for instance to be trapped or reflected. This scattering process is understood qualitatively as being governed by a nonlinear Schrödinger model in an external potential related to the charges (the electrostatic permanent background component of the field).

Ze Cheng, Gershon Kurizki