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Physical Review Letters

Solitary-wave velocity selection in self-induced transparency

Spiros V. Branis, Olivier Martin, Joseph L. Birman

Published Nov 19, 1990• 12 citations
Publisher

Abstract

We consider self-induced transparency beyond the slowly varying envelope approximation. For a carrier wave of given frequency, we show that the possible steady-state pulse velocities form a discrete set, qualitatively changing the previous picture of self-induced transparency. The selection mechanism cannot be seen in a perturbative expansion about the slowly varying envelope approximation.

DOI
10.1103/physrevlett.65.2638

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We consider self-induced transparency beyond the slowly varying envelope approximation. For a carrier wave of given frequency, we show that the possible steady-state pulse velocities form a discrete set, qualitatively changing the previous picture of self-induced transparency. The selection mechanism cannot be seen in a perturbative expansion about the slowly varying envelope approximation.
Theoretical studies of self-induced transparency have used the slowly varying envelope approximation with perturbative corrections. These analyses indicated that for a carrier wave of given frequency, there was a continuum of possible steady-state pulse velocities. We show that the exact steady-state solutions of the full Maxwell-Bloch equations do not share this property; instead, there is a nonperturbative selection mechanism: a carrier wave of given frequency gives rise to steady-state pulses with discrete values of the velocity only. We present analytical and numerical calculations, and suggest some experiments for the semiconductor CdS.
The self-induced transparency in the Kerr host medium has been studied beyond the slowly-varying-envelope approximation. An analytic solution is obtained. There exists a hyperbolic-secant soliton whose power, pulse width, group velocity, and propagation constant are uniquely determined for given parameters of the medium. The reductions of the group velocities of the solitons by the self-induced-transparency effect in the resonant medium with homogeneous and inhomogeneous broadening are also studied. It is found that there is negative dispersion induced by the self-induced transparency, which is not predicted by the theory with the slowly-varying-envelope approximation. The amount of the induced dispersion is determined by the total dispersion of the system required to be compensated by the Kerr effect. Numerical examples of the self-induced transparency in an erbium-doped fiber are shown. In a typical erbium-doped fiber, the soliton solution has not been found because the inhomogeneous-broadening linewidth of the medium is too large.
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.
A systematic perturbation expansion with respect to the small parameter ${(\ensuremath{\Delta}\ensuremath{\tau}\ensuremath{\omega})}^{\ensuremath{-}1}$, $\ensuremath{\Delta}\ensuremath{\tau}$ being the duration of the pulse and $\ensuremath{\omega}$ the optical frequency, is introduced. This method is applied to the problem of self-induced transparency for sharp-line absorbers at exact resonance. Corrections to the McCall and Hahn solution are obtained which describe the propagation of the form-preserving pulse with modulated frequency and slightly changed shape, group velocity, and wave vector. Earlier results by Marth, Holmes, and Eberly on phase modulation and wave-vector shift are confirmed.
The standard self-induced transparency (SIT) phenomenon represents the lossless propagation of a long multicycle stable soliton in an absorbing two-level resonant medium, if the soliton's envelope area equals $2\ensuremath{\pi}$ ($2\ensuremath{\pi}$ pulse). In this case, the leading half of the $2\ensuremath{\pi}$ pulse excites the medium, while the trailing half completely brings the medium back to the ground state. In this work, we theoretically demonstrate an analogous phenomenon for subcycle pulses propagating in an arbitrary multilevel resonant medium. The duration of the obtained solitary pulses must be smaller than the periods of resonant transitions in the medium. The obtained subcycle solitary solutions first turn an initially unexcited multi-level resonant medium to excited levels and then fully return it back to the ground state.