光学系统中的量子混沌：环形台球
Quantum chaos in optical systems: The annular billiard
摘要：
研究了介质环形台球作为微光学谐振腔的量子混沌模型。它不同于传统的硬壁边界条件的台球，因为它是部分开放的，由两种不同折射率的电介质组成。不同界面处反射和透射的相互作用产生了经典光线的丰富动态和各种波现象。我们研究的庞加莱曲面的部分，并补充它与相应的波动方程的完整的数值解的射线传播。我们介绍和开发的S-矩阵的方法，以开放的光学腔，证明非常适合识别的中间宽度，将是最重要的，在未来的应用，如光通信设备的谐振。我们表明，Husimi表示是一个有用的工具，在表征共振和建立射线波对应在实空间和相空间。虽然简单的射线图像提供了一个很好的定性描述某些系统类，只有波的描述揭示了定量的细节。
英文摘要：
We study the dielectric annular billiard as a quantum chaotic model of a micro-optical resonator. It differs from conventional billiards with hard-wall boundary conditions in that it is partially open and composed of two dielectric media with different refractive indices. The interplay of reflection and transmission at the different interfaces gives rise to rich dynamics of classical light rays and to a variety of wave phenomena. We study the ray propagation in terms of Poincare surfaces of section and complement it with full numerical solutions of the corresponding wave equations. We introduce and develop an S-matrix approach to open optical cavities which proves very suitable for the identification of resonances of intermediate width that will be most important in future applications like optical communication devices. We show that the Husimi representation is a useful tool in characterising resonances and establish the ray-wave correspondence in real and phase space. While the simple ray picture provides a good qualitative description of certain system classes, only the wave description reveals the quantitative details.
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