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Physical Review A

Full analytical description of ultrashort dissipative solitons in resonant media

A. V. Pakhomov

Published Aug 8, 2025• 0 citations

Abstract

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.

DOI: 10.1103/vv81-sp5k

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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.

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.

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.

Self-formation of one or several soliton-like pulses from a nonsoliton powerful laser pulse during its propagation through a two-component resonant amplifying—absorbing medium with an energy dissipation channel is studied numerically. Both components of the medium are simulated by two-level particles. Homogeneous mixtures of these components and media with consecutive amplifying and absorbing layers are considered. A qualitative analysis of the results is based on a simplified model of the process of soliton-like pulse propagation.

Resonant absorption in a laser pulse can be reduced to zero if the trailing part induces stimulated emission and returns the absorbed energy back to the pulse. This kind of effect is called Self-Induced Transparency (SIT). Analytic descriptions of short pulse propagation in a resonant medium, based on Slowly Varying Envelope Approximation (SVEA) and in linear media, have been extended in studies of SIT along two principal directions: First, to improve the SVEA by introducing Short Pulse Approximation (SPA); and second, to consider the effect of nonlinear refractive index.