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Interaction of ultrashort pulse with two-level medium beyond the slowly varying envelope approximation

Xiangyang Yu, Daqing Wen, Longzhao Lu

Published Oct 24, 2017• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.2284673

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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 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.
We solve the problem of ultrashort pulse propagation in a two-level medium beyond the rotating-wave (RWA) and slowly varying-envelope approximations. The method of solution is based on the Maxwell-Bloch equations represented in the form that allows one to switch between RWA and general (non-RWA) cases in the framework of a single numerical algorithm. Using this method, the effect of a subcycle pulse (containing less than a single period of field oscillations) on the two-level medium was analyzed. It is shown that for such short pulses, the clear breakdown of the area theorem occurs for the pulses of large enough area. Moreover, deviations from the area theorem appear to be strongly dependent on the pulse shape that cannot be observed for longer few-cycle pulses.
We examine the application of the slowly varying envelope approximation (SVEA) to the study of the laser with optical feedback, comparing the monochromatic modes obtained using a SVEA approximation with those emerging from a full treatment of the Maxwell-Bloch equations in a coupled cavity formulation of the laser with optical feedback [A. A. Duarte and H. G. Solari Phys. Rev. A 58, 614 (1998)]. While the SVEA approximation in the body of laser produces reliable results, the same approximation applied to the boundary conditions completely distorts the metamorphosis of the spectrum present in the original model, yet far from the transition region the SVEA gives acceptable results. The failure of the SVEA at the metamorphosis is related to the high sensitivity of the dispersion relations k(w)k(w)k(w) with respect to frequency changes.
The spatiotemporal evolution of an ultrashort pulse pair is investigated numerically by solving the coupled Maxwell-Bloch equations without invoking the slowly-varying envelope approximation and rotating-wave approximation. For each pulse, the temporal effect causes the breakup while the transverse effect leads to instability and reshaping. The split pulse pair always remains out-of-phase or in-phase depending on the relative phase of the incident pulse pair. When the incident pulse pair is in-phase, fusion can appear in the ultrashort regime under proper parameter conditions.
Recent progress in ultrafast technology has led to the generation of optical pulses as short as 8 fs. The propagation of such short pulses in nonlinear optical media requires new computational techniques in which the standard approximations such as the slowly-varying envelope approximation (SVEA) and rotating-wave approximation (RWA) are not made while using the Maxwell-Bloch equations [1]. Previous calculations, which used the finite-difference time-domain (FDTD) method, found that for a a Kerr-like instantaneous nonlinearity [2] significant differences can occur when the full vector Maxwell equations are used instead of the nonlinear Schrodinger equation. Recently, the FDTD method has been extended to the case of a homogeneously broadened two-level atomic system [3].