微谐振器弯曲介质界面的菲涅耳定律

弯曲介质微谐振器界面上的校正射线光学：菲涅耳滤波和古斯-汉臣位移的相空间统一

Correcting ray optics at curved dielectric microresonator interfaces: Phase-space unification of Fresnel filtering and the Goos-Haenchen shift

我们开发了一个修正的射线光学描述的反射在弯曲的介质界面的光学微谐振器，提高了约一个数量级的协议与波动光学。修正被分成两个贡献相似的幅度，对应于光线位移在独立的量子相空间方向，这可以识别与菲涅耳滤波和古斯-Haenchen位移，分别。因此，我们统一的两个影响，只有在过去被单独研究。

Analytical Fresnel laws at generic curved interfaces

Fresnel laws, the quantitative information of the amount of light that is reflected from a planar interface in dependence on its angle of incidence, are at the core of ray optics. However, these formulae do not hold at curved interfaces and deviations are appreciable when wavelength and radius of curvature are comparable. This is of particular interest for optical microcavities that play an important role in many modern research fields and applications such as microlasers. Their convexly curved interfaces modify Fresnel's law in a characteristic manner: the onset of total internal reflection i…

理解弯曲界面处的射线光学偏差

Understanding deviations from ray optics at curved interfaces

射线光学是一个有用的工具，甚至在政权，实际上，全波计算将是适当的。然而，需要波浪启发的调整来确保基于射线的预测的准确性。这些修正被称为古斯-汉兴位移（Goos-Hänchen shift），即沿界面的横向位移，以及菲涅耳滤波效应（Fresnel filtering effect），即违反斯涅耳定律和光线路径可逆性原理的角位移。虽然它们在平面界面上很好地建立，但对微激光器和其他微光学器件的准确描述需要它们在这些器件的弯曲边界特性上的精确知识。在这里，我们提出的分析和数值结果，突出边界曲率的作用，并显示出明显的偏离平面的情况下。我们介绍了一个直观的图片，允许一个简单的理解，为什么菲涅尔滤波增长相当大的曲率，而古斯-汉欣移位变得不那么重要。

A model for chaotic dielectric microresonators

We develop a random-matrix model of two-dimensional dielectric resonators which combines internal wave chaos with the deterministic Fresnel laws for reflection and refraction at the interfaces. The model is used to investigate the statistics of the laser threshold and line width (lifetime and Petermann factor of the resonances) when the resonator is filled with an active medium. The laser threshold decreases for increasing refractive index $n$ and is smaller for TM polarization than for TE polarization, but is almost independent of the number of out-coupling modes $N$. The Petermann factor in …

电介质界面上的Husimi函数：光学系统内外对偶性

Husimi functions at dielectric interfaces: Inside-outside duality for optical systems and beyond

我们在介电系统的界面处引入广义Husimi函数。可以定义四个不同的函数，对应于界面两侧的入射波和离去波。这些功能允许识别机制的波限制和逃逸方向的光学微谐振器，并给予洞察结构的谐振波函数。非共振时，系统干扰可以忽略不计，Husimi函数与斯涅耳定律和Fresnel系数有关。

Theory of light propagation in arbitrary two-dimensional curved space

As an analog model of general relativity, optics on some two-dimensional (2D) curved surfaces has been increasingly paid attention to in the past decade. Here, in light of Huygens-Fresnel principle, we propose a theoretical frame to study light propagation along arbitrary geodesics on any 2D curved surfaces. This theory not only enables us to solve the enigma of "infinite intensity" existed previously at artificial singularities on surfaces of revolution, but also makes it possible to study light propagation on arbitrary 2D curved surfaces. Based on this theory, we investigate the effects of l…