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Laser Physics

Interference of areas of subcycle light pulses

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

Published May 13, 2022• 15 citations

Abstract

Abstract Progress in reducing the duration of light pulses (down to one cycle of field oscillations or less), achieved in the last decades, has made it possible to experimentally observe and study a number of atomic-scale phenomena that occur at ultrafast times. Their study and observation are unavailable with conventional sources of monochromatic laser radiation. When using few- or subcycle pulses, a number of well-known phenomena in optics, which are well studied when using long monochromatic radiation sources, either lose their meaning, or their underlying physical mechanisms require revision. For example, the direct interference of subcycle pulses with their direct overlap is not possible due to their short duration. This note addresses the interference phenomenon, when a pair of subcycle pulses act on a medium, while do not simultaneously overlap inside it. In this case, it is not the pulses themselves that interfere in the medium, but the probability amplitudes of the bound states of the medium. Therefore the result of their impact on the medium can be interpreted as the interference of the areas of pulses—electric pulse areas (integral of the electric field strength over time) and envelope areas (integral of the slowly varying envelope of the electric field strength over time).

DOI: 10.1088/1555-6611/ac6ace

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In this letter, excitation of discrete levels in a quantum system is considered, when the duration of the driving pulse is changed from multicycle to ultrashort half-cycle regime. It is shown that, as the number of optical cycles decreases, the system passes from the periodic-driven regime to the “kick-driven” action. In both cases the effect depends on the pulse area. However for subcycle pulses the area is equal to the time integral of the field strength, whereas for multicycle pulses it is determined by the time integral of the pulse envelope. The interference of the envelope pulse area and the electric pulse area and its possible manifestations in experiments are discussed.

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.

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.

Electromagnetically induced gratings (EMIGs) of atomic populations are formed in the resonant media at the interference of two or more overlapping monochromatic beams. They are of great interest in the view of the possibility of numerous applications in optics and spectroscopy. The significant progress has been achieved recently in the generation of ultrashort femto- and attosecond pulses. Such ultrashort pulses cannot provide an interference pattern because the region of their overlapping is very small and insufficient to form even few interference fringes. However, when the pulse duration is shorter than the relaxation times in the medium in the presence of a coherent interaction with the medium, they can rapidly change of the population of atomic levels owing to carrier-wave Rabi flopping. In this case, population gratings can be formed without the instantaneous overlapping of ultrashort light pulses in the medium. The latest results on the production and control of EMIGs received by means of a sequence of single- and subcycle light pulses have been reviewed. It has been shown that the unipolar subcycle pulses can be used to control more efficiently the EMIGs compared to multipolar multicycle pulses. Various applications of these gratings have been discussed in the ultrafast optics and for the holographic recording.

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.