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International Conference on Applications of Optics and Photonics

Dissipative solitons in 4-level atomic optical systems

Nuno A. Silva, Miguel Gomes, João C. Costa, Rúben Azinheira Alves, Ariel Guerreiro, André L. Almeida

Published Aug 22, 2017• 1 citation
Publisher

Abstract

In this work we develop a theoretical model to describe the propagation of an optical pulse in a 4-level atomic system. We investigate the existence of dissipative soliton solutions and analyze the stability of these solitary waves, comparing the analytical results with computational simulations based on the effective (1+1)-dimensional model derived from the Maxwell-Bloch equation under the slowly-varying envelope approximation.

DOI
10.1117/12.2272064

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In this work we develop a theoretical model to describe the propagation of an optical pulse in a 4-level atomic system. We investigate the existence of dissipative soliton solutions and analyze the stability of these solitary waves, comparing the analytical results with computational simulations based on the effective (1+1)-dimensional model derived from the Maxwell-Bloch equation under the slowly-varying envelope approximation.
This work models the propagation of an optical pulse in a 4-level atomic system in the electromagnetic induced transparency regime. By demonstrating that linear and nonlinear optical properties can be externally controlled and tailored by a continuous-wave control laser beam and an assisting incoherent pump field, it is shown how these media can provide an excellent framework to experimentally explore pulse dynamics in the presence of non-conservative terms, either gain or loss. Furthermore, we explore the existence of stable dissipative soliton solutions, testing the analytical results with computational simulations of both the effective (1+1)-dimensional model and the full Maxwell-Bloch system of equations.
Abstract This work models the propagation of an optical pulse in a four-level atomic system in the electromagnetically induced transparency regime. By demonstrating that linear and nonlinear optical properties can be externally controlled and tailored by a continuous-wave control laser beam and an assisting incoherent pump field, it is shown how these media can provide an excellent framework to experimentally explore pulse dynamics in the presence of non-conservative terms, either gain or loss. Furthermore, we explore the existence of stable dissipative soliton solutions, testing the analytical results with computational simulations of both the effective (1+1)-dimensional model and the full Maxwell–Bloch system of equations.
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.
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.