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Optics and Spectroscopy

Collisions of unipolar subcycle pulses in a nonlinear resonantly absorbing medium

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

Published Oct 1, 2017• 16 citations
Publisher

Abstract

Collisions of unipolar subcycle pulses in a nonlinear resonant medium that coherently interact with it are studied theoretically. The dynamics of spatial polarization structures and population difference that the pulses induce in the medium are analyzed. A surprising feature is that the medium is capable of “remembering” the result of the interaction with the pulses and their collisions during times comparable to the polarization relaxation time. An analysis of the dynamics of light-induced structures makes it possible to judge the parameters of subcycle pulses at the times longer than the pulse duration, which, in the future, can be useful in their detection.

DOI
10.1134/s0030400x17100046

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Collisions of unipolar subcycle pulses in a nonlinear resonant medium that coherently interact with it are studied theoretically. The dynamics of spatial polarization structures and population difference that the pulses induce in the medium are analyzed. A surprising feature is that the medium is capable of “remembering” the result of the interaction with the pulses and their collisions during times comparable to the polarization relaxation time. An analysis of the dynamics of light-induced structures makes it possible to judge the parameters of subcycle pulses at the times longer than the pulse duration, which, in the future, can be useful in their detection.
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.
We demonstrate the possibility of inducing, erasing and extra rapidly controlling population difference gratings resulting from coherent interaction of unipolar subcycle pulses with a resonant medium. Gratings can be produced without overlap of pulses in the medium, which is an important distinction of the proposed approach from the traditional one, in which gratings are produced using interference of two or more overlapping quasi-monochromatic light beams. The use of unipolar subcycle pulses ensures faster control over gratings in comparison with bipolar pulses studied by us previously.
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 Recently, the possibility of the creation, erasing and ultrafast control of polarization and population inversion gratings by sequences of few-cycle bipolar pulses interacting with a medium in a resonant and coherent way was predicted. In this case, the overlapping of pulses in the medium is not needed for the creation of gratings. In this paper, we study the possibility of the ultrafast creation and control of spatial periodic gratings in a resonant medium when subcycle unipolar pulses (that is ones containing the constant spectral component of an electric field) propagate in the coherent regime.
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 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.