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Advanced Photonics

Few-cycle Self-Induced-Transparency Solitons

YuanYao Lin, I-Hong Chen, Ray‐Kuang Lee

Published Jan 1, 2011• 0 citations
Publisher

Abstract

We reveal the existence of optical self-induced-transparency soliton family in a two-level absorbing system down to few cycle limit based on the few-cycle envelope approximation. The effects of number of cycles on area theory and pulse group velocity are given to demonstrate possible coherent photon-matter interactions in the extreme regime.

DOI
10.1364/anic.2011.jtub5

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We reveal the existence of optical self-induced-transparency soliton family in a two-level absorbing system down to few cycle limit based on the few-cycle envelope approximation. The effects of number of cycles on area theory and pulse group velocity are given to demonstrate possible coherent photon-matter interactions in the extreme regime.
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.
The self-induced transparency in the Kerr host medium has been studied beyond the slowly-varying-envelope approximation. An analytic solution is obtained. There exists a hyperbolic-secant soliton whose power, pulse width, group velocity, and propagation constant are uniquely determined for given parameters of the medium. The reductions of the group velocities of the solitons by the self-induced-transparency effect in the resonant medium with homogeneous and inhomogeneous broadening are also studied. It is found that there is negative dispersion induced by the self-induced transparency, which is not predicted by the theory with the slowly-varying-envelope approximation. The amount of the induced dispersion is determined by the total dispersion of the system required to be compensated by the Kerr effect. Numerical examples of the self-induced transparency in an erbium-doped fiber are shown. In a typical erbium-doped fiber, the soliton solution has not been found because the inhomogeneous-broadening linewidth of the medium is too large.
Self-induced transparency is analyzed for optical pulses interacting with a two-level system by solving an integrable system of evolution equations without using the slowly varying envelope approximation. A suitable modification of the inverse scattering method is developed to find soliton solutions. The characteristics of linearly and circularly polarized optical solitons (including those created in a laser) are compared. To assess the scope of the two-level model, the effects due to additional levels are analyzed in the adiabatic approximation. It is shown that these effects violate the integrability of the model and lead to loss of self-induced transparency for pulses with duration comparable to oscillation period. However, self-induced transparency is recovered in the quasi-monochromatic limit. Applications of the results are discussed.
The standard self-induced transparency (SIT) phenomenon represents the lossless propagation of a long multicycle stable soliton in an absorbing two-level resonant medium, if the soliton's envelope area equals $2\ensuremath{\pi}$ ($2\ensuremath{\pi}$ pulse). In this case, the leading half of the $2\ensuremath{\pi}$ pulse excites the medium, while the trailing half completely brings the medium back to the ground state. In this work, we theoretically demonstrate an analogous phenomenon for subcycle pulses propagating in an arbitrary multilevel resonant medium. The duration of the obtained solitary pulses must be smaller than the periods of resonant transitions in the medium. The obtained subcycle solitary solutions first turn an initially unexcited multi-level resonant medium to excited levels and then fully return it back to the ground state.
Self-induced transparency in a resonant two-level system creates a 2\ensuremath{\pi}-soliton pulse, which produces large optical nonlinearities with a very fast response time and an extremely small loss. The self-phase modulation of a 2\ensuremath{\pi} soliton and the mutual-phase modulation by the collision of two 2\ensuremath{\pi} solitons in the excitonic range of the spectrum in CdS can achieve the effective ${\ensuremath{\chi}}^{(3)}$ coefficient of ${10}^{\mathrm{\ensuremath{-}}6}$ to ${10}^{\mathrm{\ensuremath{-}}4.5}$ esu for a pulse duration of 1 to 3 ps. The quantum theory of 2\ensuremath{\pi} solitons predicts this new nonlinear process can realize squeezed states and quantum nondemolition measurement 20 dB below the standard quantum limit.