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Optics Communications

On the optical bistability of ferroelectrics via two-wave mixing: Beyond the slowly varying envelope approximation

Muhammad Asif Ahmad Khushaini, Abdel-Baset M.A. Ibrahim

Published Jul 26, 2016• 6 citations
Publisher
DOI
10.1016/j.optcom.2016.07.043

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By solving the Maxwell-Bloch equations beyond the slowly varying envelope approximation (SVEA), we investigate the interaction of ultrashort pulse with two-level medium. When the pulse width decreases to the order of the optical period, the evolutions of the 2π, 4π and 6π ultrashort pulses deviate from the results obtained using the SVEA and present some new features, such as the frequency shift occurring on the trailing edge of the pulse. Moreover, a factor is defined to quantify the envelope deviation between the cases of the SVEA and the non-SVEA in order to quantitatively evaluate the error caused by the SVEA, then we discuss the applicable condition of the approximation.
The stationary solution for optical bistability (OB) using a semiclassical exciton-biexciton model of CuCl is calculated exactly in the limit of large Fresnel number. The numerical solution of the second-order Maxwell equation is compared with corresponding results obtained with use of the slowly-varying envelope approximation (SVEA) as well as the mean-field approximation (MFA). It is found that results obtained using the SVEA are in close quantitative agreement with the numerical solution of the second-order Maxwell equation for each point in the parameter space considered, whereas the MFA correspondingly gives good qualitative results only. Furthermore, it is shown that the nonlinearity in the dielectric function for exciton-biexciton CuCl which causes OB is very nearly of the Kerr-medium type, and consequently, the two-photon biexciton resonance contributes only weakly to the OB characteristics.
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.