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Optical Materials Express

Bragg microcavities created by the collision of half-cycle Gaussian and rectangular attosecond light pulses in a time-dependent resonant medium

Rostislav M. Arkhipov, Olga Diachkova, Mikhail Arkhipov, Ivan M. Kislyakov, Jun Wang, Nikolay N. Rosanov

Published Jul 14, 2025• 8 citations
Publisher

Abstract

This paper examines the behavior of dynamic microcavities (DMs) in multi-level resonant media when attosecond unipolar pulses of different shapes (Gaussian and rectangular) collide, acting as 2 π -like self-induced transparency pulses. For realistic quasi-unipolar pulses, the influence of the trailing edge of opposite polarity is investigated, and conditions under which the trailing edge’s effect can be ignored are found analytically and then confirmed by a direct numerical calculation. We demonstrate that the collision of sub-cycle pulses in a medium results in a rapid change of the refractive index both in time and space. Thus, the case considered here of a resonant medium under the action of a sequence of pulses is an example of a time-dependent medium. The findings demonstrate the feasibility of creating time-dependent media in an atomic medium with high polarization relaxation times T 2 , and subsequently controlling them with half-cycle pulses at an extremely short timescale of half of an electromagnetic field oscillation.

DOI
10.1364/ome.561059

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This paper examines the behavior of dynamic microcavities (DMs) in multi-level resonant media when attosecond unipolar pulses of different shapes (Gaussian and rectangular) collide, acting as 2 π -like self-induced transparency pulses. For realistic quasi-unipolar pulses, the influence of the trailing edge of opposite polarity is investigated, and conditions under which the trailing edge’s effect can be ignored are found analytically and then confirmed by a direct numerical calculation. We demonstrate that the collision of sub-cycle pulses in a medium results in a rapid change of the refractive index both in time and space. Thus, the case considered here of a resonant medium under the action of a sequence of pulses is an example of a time-dependent medium. The findings demonstrate the feasibility of creating time-dependent media in an atomic medium with high polarization relaxation times T 2 , and subsequently controlling them with half-cycle pulses at an extremely short timescale of half of an electromagnetic field oscillation.
Unipolar light pulses with a non-zero electric area due to the unidirectional action on charged particles can be used for the ultrafast control of the properties of quantum systems. To control atomic properties in an efficient way, it is necessary to vary the temporal shape of the pulses used. This has led to the problem of obtaining pulses of an unusual shape, such as a rectangular one. A number of new phenomena, not possible with conventional multi-cycle pulses, were discovered by analyzing the interaction of such unipolar pulses with matter. These include the formation of dynamic microcavities at each resonant transition of a multilevel medium when such pulses collide with the medium. In this work, we compare the behavior of dynamic microcavities in a two-level and a three-level medium when unipolar pulses of unusual shape (rectangular) are collided with the medium. We do this on the basis of the numerical solution of the system for the density matrix of the medium and the wave equation for the electric field. Medium parameters correspond to atomic hydrogen. It is shown that for rectangular pulses in a three-level medium, the dynamics of the cavities can be very different from the two-level model, as opposed to pulses of other shapes (e.g. Gaussian shape). When the third level of the medium is taken into account, the self-induced transparency-like regime disappears. Differences in the dynamics of resonators in a three-level medium are revealed when the pulses behave like 2π pulses of self-induced transparency.
The coherent interaction of extremely short light pulses with a resonant medium can result in the formation of population difference gratings. Such gratings have been created by pulses that are π/2 or smaller. This paper demonstrates that a microcavity with Bragg-like mirrors can be formed by colliding two single-cycle attosecond self-induced transparency pulses in the center of a two-level medium. The parameters of this structure can be quickly adjusted by increasing the number of collisions, which showcases the ability to control the dynamic properties of the medium on a sub-cycle time scale by using attosecond pulses.
Unipolar light pulses with non-zero electric area enable ultrafast control of quantum systems, requiring tailored temporal shapes like rectangular pulses for efficient atomic manipulation. Such pulses induce unique phenomena, including dynamic microcavities at resonant transitions in multilevel media. Here, we compare microcavity dynamics in two- and three-level media under rectangular unipolar pulse excitation via numerical solutions of the density matrix and wave equations. Unlike Gaussian pulses, rectangular pulses exhibit starkly different dynamics in a three-level medium, disrupting self-induced transparency-like regimes. Key differences emerge when pulses behave as 2 π pulses, highlighting the impact of the third level on microcavity dynamics. These findings establish rectangular unipolar attosecond pulses as a powerful tool for attosecond-scale quantum control, revealing fundamental limits of few-level approximations in extreme nonlinear optics and opening pathways to coherent light–matter engineering in complex atomic systems.
An optical Bragg-like microcavity can be formed when extremely short light pulses interacting coherently with the medium collide in the resonant medium. Here we present an analytical approach, based on the approximate solution of the time-dependent Schrödinger equation, that reveals both the cavity formation and its control by the half-cycle pulses colliding in the medium. This approach allows the calculation of cavity properties in the weak-field regime without the need for complex numerical simulations. Beyond the approximate analytical solutions, our analytical results are confirmed by numerical simulations of the Maxwell-Bloch equations. Grating formation is also studied in the strong-field regime, where collisions of self-induced transparency half-cycle pulses occur. The results presented here reveal, to our knowledge, a new type of spatio-temporal photonic crystal in the form of micro-cavities in a simple atomic medium. The results obtained demonstrate the feasibility of attosecond optical switching in a simple atomic medium with half-cycle pulses.
Abstract We report an analytical and numerical study of the dynamics of electromagnetically induced atomic population gratings during collisions of a sequence of unipolar pulses of unusual temporal shape (rectangular and triangular) in a multilevel resonant medium. The possibility of forming dynamic microcavities with Bragg-like mirrors, the shape of which is different at each resonant transition of the medium, is demonstrated. A simple analytical description of such microresonators is proposed based on an approximate solution of the time-dependent Schrödinger equation when the amplitude of the exciting pulses is small. In the case of high-power pulses, when perturbation theory is not applicable, the results of numerical calculations show the disappearance of microcavities and the emergence of nonharmonic gratings with an increase in the number of collisions between pulses. The studied phenomena demonstrate a possibility of using unipolar pulses of an unusual shape for ultrafast control of the medium properties.
Half-cycle attosecond pulses formed from an electromagnetic field half-wave have the shortest duration in a given spectral interval. When these pulses interact coherently with the medium, new types of spatial structures of population inversion may emerge on each resonant transition. Based on numerical calculations, we examine the possibility of ultrafast control of these structures, such as microcavities, in an asymmetric collision of half-cycle pulses in a medium. We demonstrate that it is possible to create dynamic microcavities with controlled parameters, as well as divide the medium into different regions of near-constant population inversion. The selectivity effect is observed, with deeper structures formed on one transition than another, highlighting the possibility of fine-tuning these processes. The results show that time-dependent media could be realized in a conventional resonant medium with discrete energy levels using half-cycle pulses.