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Quantum Electronics

Propagation of a light pulse with a duration of less than one period in a resonant amplifying medium

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

Published Jun 5, 2018• 7 citations
Publisher

Abstract

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.

DOI
10.1070/qel16619

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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.
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.
Effects of propagation of an extremely short (of one or several oscillation periods) electromagnetic pulse in a medium whose resonance transition is characterized by diagonal as well as nondiagonal matrix elements of the dipole moment operator have been studied numerically. The Maxwell-Bloch system of equations is employed without using the approximation of slowly varying envelopes. An analog of the McCall and Hahn area theorem is discussed as applied to the division of the initial extremely short pulse into subpulses. The solution is obtained in the form of a solitary stable bipolar signal with a nonzero pulse area (nonzero breather).
The effects are observed of propagation of an ultimately short (in one or several oscillation) electromagnetic pulse in a medium whose resonance transition characterized both by diagonal and non-diagonal matrix elements of dipole operator. The Maxwell-Bloch set of equation is employed without the approximation of slowly varying amplitudes. The analog of MacCall and Hahn area theorem is discussed corresponding to the process of the initial ultimately short pulse break up into subpulses. A novel solution is found in the form of a stable solitary bipolar signal, whose pulse area is not zero- non-zero breather.
Amplification of electromagnetic field pulses approximately one cycle in duration in multilevel media with an effective permanent dipole moment is studied theoretically without application of the approximation of slowly varying envelopes for the case of unidirectional propagation of the radiation. For three-level and quasi-two-level media, it is shown that the set of Maxwell-Schrödinger equations can be reduced to an integrable set of equations for an effective two-level medium. The presence of an (effective) permanent dipole moment of the medium was found to lead to new specific features of the amplification and control of the dynamics of field pulses.
We solve the problem of ultrashort pulse propagation in a two-level medium beyond the rotating-wave (RWA) and slowly varying-envelope approximations. The method of solution is based on the Maxwell-Bloch equations represented in the form that allows one to switch between RWA and general (non-RWA) cases in the framework of a single numerical algorithm. Using this method, the effect of a subcycle pulse (containing less than a single period of field oscillations) on the two-level medium was analyzed. It is shown that for such short pulses, the clear breakdown of the area theorem occurs for the pulses of large enough area. Moreover, deviations from the area theorem appear to be strongly dependent on the pulse shape that cannot be observed for longer few-cycle pulses.