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Physical Review A

Few-cycle self-induced-transparency solitons

Yuan-Yao Lin, I-Hong Chen, Ray‐Kuang Lee

Published Apr 21, 2011• 16 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.83.043828

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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.
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.
Summary form only given. Recent advances in ultrafast laser technology have made possible the generation of extremely short and intense pulses with only two optical periods of less than 5 fs in duration in the visible region. Efforts for generation of still shorter pulses is motivated by the possibility to study light matter interactions under unique conditions as the pulse duration approaches the duration of a single optical cycle. We study the propagation of a 5-fs pulse through a layer of a dense medium of two-level systems. As a result we demonstrate the formation of single-cycle and half-cycle pulses in the sub-fs region and novel types of spectral changes during propagation as large blue and red shifts in the transmitted and reflected pulses, respectively, explained by intra-pulse frequency-difference mixing. Solitary pulse propagation phenomena beyond the limits of slowly-varying envelope (SVEA) and rotating-wave approximation (RWA) are illustrated as the formation of full Maxwell-Bloch half-cycle solitons and two-soliton pulses.