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Nonlinear dynamics of a Bragg cell under intensity feedback in the near-Bragg, four-order regime

机译:近布拉格四阶强度反馈下布拉格单元的非线性动力学

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摘要

A detailed examination of the nonlinear dynamical behavior of an acousto-optic Bragg cell in the near-Bragg regime of operation for the case of four scattered orders under intensity feedback is carried out. This problem is an extension of the standard ideal-Bragg feedback model whereby traditionally bistability, hysteresis, and chaotic oscillations are observed under zeroth- or first-order feedback of the scattered light. For the present case, the closed-loop equations are developed from a priori knowledge of the open-loop analytical solutions for four-order near-Bragg scattering. The results, obtained via computer simulation, reveal a variety of interesting dynamics, including bistability, bifurcation, hysteresis, chaotic oscillations (including in this case the relatively uncommon period-three behavior, in addition to the more usual period-doubling phenomenon en route to chaos), and potentially useful parametric dependence of these features. The observed results are interpreted in terms of system behavior for varying feedback gain and bias, the so-called Klein-Cook parameter Q, and time delay, and are compared with earlier work based on the ideal Bragg regime.
机译:对于在强度反馈下四个分散阶的情况,在近布拉格操作状态下声光布拉格单元的非线性动力学行为进行了详细检查。这个问题是标准理想-布拉格反馈模型的扩展,该模型传统上在散射光的零阶或一阶反馈下观察到双稳态,滞后和混沌振荡。在当前情况下,闭环方程是根据四阶近布拉格散射的开环解析解的先验知识而开发的。通过计算机模拟获得的结果揭示了各种有趣的动力学,包括双稳态,分叉,滞后,混沌振荡(在这种情况下,包括相对不常见的周期三行为,以及在进行过程中更常见的周期倍增现象)。混乱),以及这些功能的潜在有用的参数依赖性。观察到的结果将根据系统行为来改变反馈增益和偏置,所谓的Klein-Cook参数Q和时间延迟,并与基于理想布拉格机制的早期工作进行比较。

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