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Journal of the Optical Society of America B

Coherent propagation of a half-cycle unipolar attosecond pulse in a resonant two-level medium

Rostislav M. Arkhipov, Mikhail V. Arkhipov, Ihar Babushkin, A. V. Pakhomov, Nikolay N. Rosanov

Published May 10, 2021• 17 citations
Publisher

Abstract

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.

DOI
10.1364/josab.423744

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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 propagation of a unipolar light pulse with a duration of less than one period in a two-level resonant amplifying medium is studied theoretically. In the process of amplification, the unipolar pulse becomes bipolar. The effect of the relaxation time on the shape and duration of the amplified pulse is demonstrated. It is found that the electric pulse area (integral of electric field strength with respect to time) is conserved, in contrast to the area under the long pulse envelope (integral of slowly varying field amplitude with respect to time), which, in the case of long pulses, satisfies the McCall – Hahn area theorem.
Obtaining unipolar half-cycle optical pulses of femto- and attosecond duration with a large electrical area is an urgent but difficult task. The reason for the emerging difficulties lies in the existence of the rule of conservation of the electrical area of the pulse, which does not allow converting a bipolar pulse into a unipolar one. In this work, it is shown that in a resonant medium a few-cycle pulse can be converted into two unipolar pulses separated in time by a distance that is an order of magnitude or more longer than the duration of the initial pulse. This allows in a number of problems to consider such pulses separately as unipolar. The estimation of the electric area value relative to its "atomic scale" is carried out. Keywords: attosecond pulses, unipolar pulses, subcycle pulses, electrical area of pulses.
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.
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.
Abstract Obtaining unipolar half-cycle optical pulses of femto- and attosecond duration with a large electrical area is an urgent but difficult task. The reason for the emerging difficulties lies in the existence of the rule of conservation of the electrical area of the pulse, which does not allow converting a bipolar pulse into a unipolar one. In this work, it is shown that in a resonant medium a few-cycle pulse can be converted into two unipolar pulses separated in time by a distance that is an order of magnitude or more longer than the duration of the initial pulse. This allows in a number of problems to consider such pulses separately as unipolar. The estimation of the electric area value relative to its “atomic scale” is carried out.
Obtaining unipolar half-cycle optical pulses of femto- and attosecond duration with a large electrical area is an urgent but difficult task. The reason for the emerging difficulties lies in the existence of the rule of conservation of the electrical area of ​​the pulse, which does not allow converting a bipolar pulse into a unipolar one. In this work, it is shown that in a resonant medium a low-cycle pulse can be converted into two unipolar pulses separated in time by a distance that is an order of magnitude or more longer than the duration of the initial pulse. This allows in a number of problems to consider such pulses separately as unipolar. The estimation of the electric area value relative to its "atomic scale" is carried out.