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Physical Review A

Nonlinear propagation of subcycle pulses in a nonequilibrium multilevel medium

A. V. Pakhomov

Published Oct 2, 2025• 1 citation
Publisher

Abstract

The ultrabroad spectrum of few-cycle and especially subcycle pulses requires multiple energy levels in a medium to be properly considered in order to describe the pulse propagation effects. In this paper we go beyond the standard two-level or related few-level approximations and theoretically analyze the propagation of subcycle pulses in a nonequilibrium multilevel resonant medium. We specifically address the case of pulse durations, smaller than the periods of resonant transitions in a medium, where the appropriate analytical models can be provided, and assume accordingly a slow dissipation in the medium. We demonstrate a number of nonlinear phenomena, arising under such conditions, in particular the formation of stable subcycle dissipative solitons of various profiles in a nonequilibrium medium, including superluminal ones, as well as study possible scenarios of their collision.

DOI
10.1103/5ch5-wvy2

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The ultrabroad spectrum of few-cycle and especially subcycle pulses requires multiple energy levels in a medium to be properly considered in order to describe the pulse propagation effects. In this paper we go beyond the standard two-level or related few-level approximations and theoretically analyze the propagation of subcycle pulses in a nonequilibrium multilevel resonant medium. We specifically address the case of pulse durations, smaller than the periods of resonant transitions in a medium, where the appropriate analytical models can be provided, and assume accordingly a slow dissipation in the medium. We demonstrate a number of nonlinear phenomena, arising under such conditions, in particular the formation of stable subcycle dissipative solitons of various profiles in a nonequilibrium medium, including superluminal ones, as well as study possible scenarios of their collision.
We theoretically investigate the possibility of the formation of subcycle dissipative solitons propagating in a multilevel resonant medium. We examine the case when the duration of light pulses is significantly smaller than the periods of resonant transitions in the medium. Within such an approximation, a nonlinear integro-differential equation describing the spatiotemporal evolution of the electric field was derived. We demonstrate that in the case of a preexcited medium, this equation has solutions in the form of stable half-cycle unipolar dissipative solitons with the parameters determined by the medium properties. The obtained results can provide an important step towards the efficient transmission of subcycle pulses through optical media.
We solve the problem of ultrashort pulse propagation in a two-level medium beyond the rotating-wave (RWA) and slowly varying-envelope approximations. The method of solution is based on the Maxwell-Bloch equations represented in the form that allows one to switch between RWA and general (non-RWA) cases in the framework of a single numerical algorithm. Using this method, the effect of a subcycle pulse (containing less than a single period of field oscillations) on the two-level medium was analyzed. It is shown that for such short pulses, the clear breakdown of the area theorem occurs for the pulses of large enough area. Moreover, deviations from the area theorem appear to be strongly dependent on the pulse shape that cannot be observed for longer few-cycle pulses.
We derive model equations for optical pulse propagation in a medium described by a two-level Hamiltonian, without the use of the slowly varying envelope approximation. Assuming that the resonance frequency of the two-level atoms is either well above or well below the inverse of the characteristic duration of the pulse, we reduce the propagation problem to a modified Korteweg--de Vries or a sine-Gordon equation. We exhibit analytical solutions of these equations which are rather close in shape and spectrum to pulses in the two-cycle regime produced experimentally, which shows that soliton-type propagation of the latter can be envisaged.
A nonlinear integrodifferential equation of the ``reaction-diffusion'' type is derived for an optical pulse propagating in a gain resonant two-level medium with the inhomogeneous broadening of the quantum transitions. The stable exact analytical solution of this equation in the form of a dissipative optical soliton with an asymmetric temporal profile is found and analyzed. The temporal duration of this soliton is much longer than the characteristic phase relaxation time but much shorter than the energy relaxation time. It is shown that the formation of such a soliton requires the presence of linear losses, created by the equilibrium part of the medium. It is noted that the found soliton solution qualitatively coincides with the dissipative soliton recently discovered experimentally in a laser microcavity.
Collisions of unipolar subcycle pulses in a nonlinear resonant medium that coherently interact with it are studied theoretically. The dynamics of spatial polarization structures and population difference that the pulses induce in the medium are analyzed. A surprising feature is that the medium is capable of “remembering” the result of the interaction with the pulses and their collisions during times comparable to the polarization relaxation time. An analysis of the dynamics of light-induced structures makes it possible to judge the parameters of subcycle pulses at the times longer than the pulse duration, which, in the future, can be useful in their detection.
We theoretically demonstrate the existence of subcycle solitons in a medium with several optical resonances, with the soliton duration smaller than the periods of all resonant transitions in the medium. We show that the evolution of the electric field in this case is governed by the generalized sine-Gordon equation. We find the solitary-wave solutions of this equation both in the case of a conservative and dissipative optical medium. It is shown that stable subcycle solitons in general can only exist in an initially preexcited medium with nonresonant losses. In this case, half-cycle dissipative solitons can be formed and steadily propagate in the resonant medium. In contrast, the stable conservative solitary waves are obtained to only exist at integer ratios of the transition dipole moments of all resonances that are involved.