存在增益和损耗时高斯光束的传输
Propagation of Gaussian beams in the presence of gain and loss
摘要：
在近轴近似下，考虑高斯光束在有增益和损耗的波导中的传输，波导由薛定谔方程控制。我们推导出的光束在半经典的限制，是有效的，当波导剖面是本地以及近似的二次函数的运动方程。对于厄米系统，没有任何损失或增益，这些动力学由光束中心及其共轭动量的汉密尔顿方程给出。向波导添加增益和/或损耗引入非厄米特分量，导致高斯光束的宽度在其传播中起重要作用。在这里，我们展示了宽度如何影响光束的运动，以及如何根据它们的宽度来过滤位于相同初始位置的高斯光束。
英文摘要：
We consider the propagation of Gaussian beams in a waveguide with gain and loss in the paraxial approximation governed by the Schrödinger equation. We derive equations of motion for the beam in the semiclassical limit that are valid when the waveguide profile is locally well approximated by quadratic functions. For Hermitian systems, without any loss or gain, these dynamics are given by Hamilton's equations for the center of the beam and its conjugate momentum. Adding gain and/or loss to the waveguide introduces a non-Hermitian component, causing the width of the Gaussian beam to play an important role in its propagation. Here we show how the width affects the motion of the beam and how this may be used to filter Gaussian beams located at the same initial position based on their width.
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