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Physical Review A

Subcycle optical solitons in a medium with several resonances

A. V. Pakhomov

Published Jan 3, 2025• 3 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.111.013502

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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.
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.
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 consider the propagation of ultrashort optical solitons in media described by a general Hamiltonian of multilevel atoms. Assuming that all transition frequencies of the medium are well below the typical wave frequency, i.e., only the contribution of infrared transitions is taken into account, we use a short-wave approximation and a rigorous application of the reductive perturbation formalism to derive a cumbersome coupled system of nonlinear partial differential equations describing ultrashort soliton evolution in such systems. The rather complicated set of coupled equations can be simplified to a generic double-sine-Gordon equation for a special case of identical three-level atoms, whereas for a special case of identical four-level atoms the system of coupled equations can be reduced to a generalized double-sine-Gordon equation. Numerical simulations showing the formation of robust breather-type solutions of both the standard double-sine-Gordon and of the generalized double-sine-Gordon equations from sinusoidal inputs with Gaussian envelopes are also presented.
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.
We consider the propagation of few-cycle pulses (FCPs) beyond the slowly varying envelope approximation in media in which the dynamics of constituent atoms is described by a two-level Hamiltonian by taking into account the wave polarization. We consider the short-wave approximation, assuming that the resonance frequency of the two-level atoms is well below the inverse of the characteristic duration of the optical pulse. By using the reductive perturbation method (multiscale analysis), we derive from the Maxwell-Bloch-Heisenberg equations the governing evolution equations for the two polarization components of the electric field in the first order of the perturbation approach. We show that propagation of circularly polarized (CP) few-optical-cycle solitons is described by a system of coupled nonlinear equations, which reduces in the scalar case to the standard sine Gordon equation describing the dynamics of linearly polarized FCPs in the short-wave-approximation regime. By direct numerical simulations, we calculate the lifetime of CP FCPs, and we study the transition to two orthogonally polarized single-humped pulses as a generic route of their instability.
This paper theoretically discusses the propagation of an ultrashort laser pulse consisting of ordinary and extraordinary components in a system of anisotropic quantum centers. The treatment does not use the assumption that the density of quantum centers is small and makes no limitations on the transition dipole moments. It is shown that, if the spectral pulse width is much greater than the frequency of the quantum transitions, the dynamics of its ordinary component obeys a modified sine-Gordon equation that belongs to the class of integrable models. Soliton solutions of the given equation are constructed, and they are classified. Depending on the duration of the soliton, solutions are possible in the form of a 2π pulses (kinks and antikinks) or 0π steady-state traveling pulses (neutral kinks), which have no counterpart in the isotropic case. The behavior of the medium is studied when various types of solitons are transmitted.