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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Few-cycle solitons in a two-component medium

Hervé Leblond, Sergey V. Sazonov, Igor V. Mel’nikov, DUMITRU BOGDAN MIHALACHE, François Sanchez

Published Aug 6, 2007• 0 citations
Publisher

Abstract

Using Maxwell-Bloch equations, we analyze the response of a two-component medium of two-level atoms driven by a two-cycle optical pulse beyond the traditional approach of slowly varying amplitudes and phases. We show that the notions of carrier, envelope, phase and group velocities can be generalized to this situation, and that for optical pulses of a given duration, the optical field can evolve into temporal few-cycle solitons.

DOI
10.1117/12.757851

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Using Maxwell-Bloch equations, we analyze the response of a two-component medium of two-level atoms driven by a two-cycle optical pulse beyond the traditional approach of slowly varying amplitudes and phases. We show that the notions of carrier, envelope, phase and group velocities can be generalized to this situation, and that for optical pulses of a given duration, the optical field can evolve into temporal few-cycle solitons.
We reveal the existence of an optical self-induced-transparency soliton family in a two-level absorbing system down to the few-cycle limit. Based on the few-cycle envelope approximation, we introduce a systematical method of reducing the Maxwell-Bloch equations beyond the slowly varying envelope approximation and characterize the parameter space to achieve slow and fast lights. Verified by direct numerical simulations with full vectorial Maxwell-Bloch equations, we also give the relationships for a number of optical cycles on area theory and pulse group velocity, which demonstrate possible coherent photon-matter interactions.
By comparing the numerical solutions of Maxwell-Bloch equations beyond and within the slowly-varying envelope approximation and the rotating-wave approximation for the propagation of a few-cycle pulse laser in a resonant two-level atom medium, we found that both the Rabi flopping and the refractive index, and subsequently the carrier and the propagation velocity of the few-cycle pulse, are closely connected with the time-derivative behaviour of the electric field. This is because the Rabi flopping is such that the soliton pulse splits during propagation and that a shorter pulse propagates faster than a broader one.
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.
We derive model equations for optical pulse propagation in a medium described by a two-level Hamiltonian, without the use of the slowly varying envelope approximation. Assuming that the resonance frequency of the two-level atoms is either well above or well below the inverse of the characteristic duration of the pulse, we reduce the propagation problem to a modified Korteweg--de Vries or a sine-Gordon equation. We exhibit analytical solutions of these equations which are rather close in shape and spectrum to pulses in the two-cycle regime produced experimentally, which shows that soliton-type propagation of the latter can be envisaged.