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Журнал Экспериментальной и Теоретической Физики

KOGERENTNOE RASPROSTRANENIE POLUTsIKLOVOGO SVETOVOGO IMPUL'SA V TREKhUROVNEVOY SREDE

Rostislav M. Arkhipov, A. V. Pakhomov, M. V. Arkhipov, Nikolai N Rozanov

Published Aug 13, 2024• 2 citations
Publisher

Abstract

Based on the numerical solution of Maxwell-Bloch equations, we study the dynamics of coherent propagation of unipolar, half-cycle, attosecond light pulse in a three-level resonantly absorbing medium. A comparison with the propagation of such pulse in a two-level medium is performed. It is shown that the pulse, which behaves like a 4π-pulse in a two-level medium, in a three-level medium behaves like a 6π-pulse and splits into three sub-pulses propagating at different velocities in the medium. The investigated phenomenon allows for a more detailed understanding of the still insufficiently studied dynamics of coherent propagation of half-cycle pulses in a resonant medium.

DOI
10.31857/s0044451024080030

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Based on the numerical solution of Maxwell-Bloch equations, we study the dynamics of coherent propagation of unipolar, half-cycle, attosecond light pulse in a three-level resonantly absorbing medium. A comparison with the propagation of such pulse in a two-level medium is performed. It is shown that the pulse, which behaves like a 4π-pulse in a two-level medium, in a three-level medium behaves like a 6π-pulse and splits into three sub-pulses propagating at different velocities in the medium. The investigated phenomenon allows for a more detailed understanding of the still insufficiently studied dynamics of coherent propagation of half-cycle pulses in a resonant medium.
Here we numerically investigate the propagation of unipolar half-cycle attosecond pulses with a duration much shorter than the period of the proper oscillations T 0 of the medium and its relaxation times T 1 and T 2 in a two-level resonant absorbing and amplifying medium. We find that despite breaking down of the famous McCall and Hahn area theorem, some phenomena described by this theorem are still qualitatively preserved. In particular, it is shown that pulses with small initial electric pulse area become sign-alternating upon the propagation, similar to the traditional 0 π pulses; pulses with 4 π , 5 π , and 6 π area are unstable and split into lower-order pulses, exactly as in the long-pulse case. The electric pulse area conservation rule and limitations of unipolar pulse amplification in two-level gain media, which follows from this rule, are discussed.
The dynamics of coherent propagation of a unipolar subcycle pulse of a large electric-field area (the integral of the electric-field strength with respect to time) in a nonlinear two-level resonant medium is studied theoretically. The propagating pulse is shown to be capable of splitting into a pair of individual components, each of which behaves like a pulse of self-induced transparency. This phenomenon is similar to the well-known phenomenon of splitting of a 4π or 6π pulse into a pair of 2π pulses of self-induced transparency, which occurs in the case of propagation of long pulses, when the notion of the pulse area is applicable and the area theorem holds.
By numerically solving the system of Maxwell–Bloch equations, we have examined theoretically collisions of extremely short single-cycle and unipolar subcycle pulses in a nonlinear resonant medium under conditions that the light interacts coherently with the medium. The dynamics of the electric field of structures of light-induced polarization and inversion difference has been considered in the situation in which pulses are overlapped in the medium. We show that the states of the medium (to the right and to the left of the overlap region of the pulses) may differ. In particular, we show that polarization waves with different characteristics can exist in the regions of the medium that are located on opposite sides of the overlap region of the pulses. These waves travel in different directions and have different spatial frequencies.
The coherent propagation of two optical short pulses through a resonant medium consisting of two three-level atoms in the configuration is investigated. A self-consisting analytical solution without steady state or adiabatic approximations is presented. The electric field in the model studied consists of two co-propagating plane waves, each of which is in near resonance with a transition in the absorber. The density matrix of two three level atoms is studied. Also, the reduced density matrices are stated. The present approach for the semiclassical treatment of resonant coherent interactions in three-level atoms represents a generalization of the Maxwell- Bloch equations for a two-level system. The Maxwell-Bloch equations reduced to the non-linear pendulum equation. The solution shows that the two pulses can propagate simultaneously without loss under some conditions about the pulses and the medium. The propagation of the two pulses through the medium without any constrains approves the self -induced transparency (SIT) phenomenon.
Summary form only given. Recent advances in ultrafast laser technology have made possible the generation of extremely short and intense pulses with only two optical periods of less than 5 fs in duration in the visible region. Efforts for generation of still shorter pulses is motivated by the possibility to study light matter interactions under unique conditions as the pulse duration approaches the duration of a single optical cycle. We study the propagation of a 5-fs pulse through a layer of a dense medium of two-level systems. As a result we demonstrate the formation of single-cycle and half-cycle pulses in the sub-fs region and novel types of spectral changes during propagation as large blue and red shifts in the transmitted and reflected pulses, respectively, explained by intra-pulse frequency-difference mixing. Solitary pulse propagation phenomena beyond the limits of slowly-varying envelope (SVEA) and rotating-wave approximation (RWA) are illustrated as the formation of full Maxwell-Bloch half-cycle solitons and two-soliton pulses.
By comparing the numerical solutions of Maxwell-Bloch equations beyond and within the slowly-varying envelope approximation and the rotating-wave approximation for the propagation of a few-cycle pulse laser in a resonant two-level atom medium, we found that both the Rabi flopping and the refractive index, and subsequently the carrier and the propagation velocity of the few-cycle pulse, are closely connected with the time-derivative behaviour of the electric field. This is because the Rabi flopping is such that the soliton pulse splits during propagation and that a shorter pulse propagates faster than a broader one.