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Journal of Physics B Atomic Molecular and Optical Physics

Solutions for Maxwell-Bloch equations without using the approximation of a slowly varying envelope: circularly-polarized video pulses

С. В. Сазонов, E. V. Trifonov

Published Jan 14, 1994• 33 citations
Publisher

Abstract

Propagation of strong circularly-polarized 'video' pulses in a two-level non-resonant medium without using the approximations of slowly varying envelope and rotating wave has been studied. New solutions to the Maxwell-Bloch equations called 'bisolitons' are obtained. Bisolitons are running localized 'video' pulses of the electric field vector rotating in transverse plane.

DOI
10.1088/0953-4075/27/1/002

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Propagation of strong circularly-polarized 'video' pulses in a two-level non-resonant medium without using the approximations of slowly varying envelope and rotating wave has been studied. New solutions to the Maxwell-Bloch equations called 'bisolitons' are obtained. Bisolitons are running localized 'video' pulses of the electric field vector rotating in transverse plane.
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 semiclassical Maxwell–Bloch equations beyond the slowly varying envelope approximation (SVEA) are derived in order to study the propagation of the ultrashort pulse in a two-level medium. The evolutions of the pulse shape, the group velocity and the pulse peak of 2[Formula: see text] ultrashort pulse are investigated as well as the pulse splitting of 4[Formula: see text] ultrashort pulse. By comparing the numerical results with those obtained using the SVEA, the error introduced by the approximation is quantitatively evaluated with respect to the pulse width and the applicable condition of the SVEA is discussed consequently. The envelope solutions presented by us allow clear observation on the evolution of the envelope.
We consider the propagation of few-cycle pulses (FCPs) beyond the slowly varying envelope approximation in media in which the dynamics of constituent atoms is described by a two-level Hamiltonian by taking into account the wave polarization. We consider the short-wave approximation, assuming that the resonance frequency of the two-level atoms is well below the inverse of the characteristic duration of the optical pulse. By using the reductive perturbation method (multiscale analysis), we derive from the Maxwell-Bloch-Heisenberg equations the governing evolution equations for the two polarization components of the electric field in the first order of the perturbation approach. We show that propagation of circularly polarized (CP) few-optical-cycle solitons is described by a system of coupled nonlinear equations, which reduces in the scalar case to the standard sine Gordon equation describing the dynamics of linearly polarized FCPs in the short-wave-approximation regime. By direct numerical simulations, we calculate the lifetime of CP FCPs, and we study the transition to two orthogonally polarized single-humped pulses as a generic route of their instability.
An analysis is made of the coherent interaction of a short pulse of polarised electromagnetic radiation with a medium in which the energy levels are degenerate in respect of the angular momentum projection. In the case of the j a = 1 → j b =0 transition it is found, without recourse to the approximation of slowly varying envelopes, that the system of the Maxwell–Bloch equations has an exact solution in the form of a steady-state solitary wave of duration equal to half the period of emission as a result of the investigated atomic transition. A new solution is obtained, in addition to a simple generalisation corresponding to a polarised video pulse. When the populations of the excited states with different projections of the angular momentum are different, the spherical components of the vector representing the electric field intensity do not behave proportionately: if one of them corresponds to a unipolar spike of the electric field, the other component is a variable-sign solitary wave.