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Physical Review A

Analytical theory of the propagation of a dissipative soliton in a nonequilibrium resonant medium

С. В. Сазонов

Published May 14, 2021• 14 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.103.053512

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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.
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 develop a theoretical approach for the full analytical description of dissipative optical solitons, which takes into account all relaxation processes in the medium. Most analytical solutions available today for ultrashort optical solitons are obtained upon neglecting a number of relaxation terms in the governing equations for the medium response. The suggested method is based on finding explicit analytical expressions for the extended soliton tails distant enough from the soliton central part, when taking into consideration all relaxation processes. These soliton tails can be described by the linearized equations for the medium response both at the soliton leading and trailing edges. Afterwards, the analytical expressions for the soliton tails and its central part can be matched to yield the full analytical description of ultrashort dissipative solitons with all relaxation processes in the resonant medium properly treated. The proposed approach is demonstrated for ultrashort dissipative solitons in a resonant medium consisting either of only amplifying resonant two-level centers or of a mixture of amplifying and absorbing two-level centers.
Abstract For electromagnetic pulses without a carrier frequency, propagating in a system of multilevel atoms with a fast irreversible relaxation of the induced dipole moment, but a slow relaxation of the populations of quantum states, the nonlinear integro-differential equations of the ‘reaction–diffusion’ type are derived. One-dimensional soliton-like solutions of these equations in the form of unipolar pulses are found and analyzed. It is shown that such pulses can be formed in a nonequilibrium medium. These pulses transfer a medium to other metastable states, which depend on the input conditions. The propagation of these soliton-like signals is accompanied by a change in the populations of quantum states of atoms in the modes of switching waves with the memory of input conditions.
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.
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.