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Fabry-Perot and whispering gallery modes in realistic resonator models.

机译：现实谐振器模型中的Fabry-Perot和低语画廊模式。

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摘要

We investigate models describing two classes of microresonators: those having the shape of a dome, and those having an oval (deformed circle or sphere) shape. We examine the effects of dielectric interfaces in these structures.; For the dome cavity, we derive efficient numerical methods for finding exact electromagnetic resonances. In the dome consisting of a concave conductor and a planar, dielectric Bragg mirror, we discover a phenomenon which we call paraxial mode mixing (PMM) or classical spin-orbit coupling. PMM is the sensitive selection of the true electromagnetic modes. The true modes are generally mixtures of pairs of vectorial Laguerre-Gauss modes. While each member of an LG pair possesses definite orbital angular momentum and spin (polarization), the mixed modes do not, and exhibit rich, non-uniform polarization patterns. The mixing is governed by an orthogonal transformation specified by the mixing angle (MA). The differences in reflection phases of a Bragg mirror at electric s and p polarization can be characterized in the paraxial regime by a wavelength-dependent quantity epsilons--epsilonp. The MA is primarily determined by this quantity and varies with an apparent arctangent dependence, concomitant with an anticrossing of the maximally mixed modes. The MA is zero order in quantities that are small in the paraxial limit, suggesting an effective two-state degenerate perturbation theory. No known effective Hamiltonian and/or electromagnetic perturbation theory exists for this singular, vectorial, mixed boundary problem. We develop a preliminary formulation which partially reproduces the quantitative mixing behavior. Observation of PMM will require both small cavities and highly reflective mirrors. Uses include optical tweezers and classical and quantum information.; For oval dielectric resonators, we develop reduced models for describing whispering gallery modes by utilizing sequential tunneling, the Goos-Hanchen (GH) effect, and the generalized Born-Oppenheimer (adiabatic) approximation (BOA). While the CH effect is found to be incompatible with sequential tunneling, the BOA method is found to be a useful connection between ray optics and the exact wave solution.; The GH effect is also shown to nicely explain a new class of stable V-shaped dome cavity modes.; This dissertation includes my co-authored materials.
机译：我们研究了描述两类微谐振器的模型：具有圆顶形状的微谐振器和具有椭圆形（变形的圆形或球形）形状的微谐振器。我们研究了介电界面在这些结构中的作用。对于圆顶腔，我们推导了用于寻找精确电磁谐振的有效数值方法。在由凹形导体和平面电介质布拉格镜组成的圆顶中，我们发现了一种现象，我们称其为近轴模式混合（PMM）或经典自旋轨道耦合。 PMM是真正电磁模式的敏感选择。真实模式通常是矢量Laguerre-Gauss模式对的混合。 LG对的每个成员都具有确定的轨道角动量和自旋（极化），而混合模则不，并且表现出丰富的非均匀极化模式。混合由混合角（MA）指定的正交变换控制。布拉格反射镜在电s和p偏振下的反射相位差异可以在近轴状态下通过与波长有关的量ε-ε来表征。 MA主要由该量确定，并随明显的反正切关系而变化，并伴随最大混合模的反交叉。 MA的量为零级，且在近轴范围内较小，表明存在有效的两态简并摄动理论。对于此奇异，矢量，混合边界问题，不存在已知的有效哈密顿量和/或电磁微扰理论。我们开发了一种初步配方，可部分再现定量混合行为。观察PMM既需要小腔，也需要高反射镜。用途包括光镊以及经典和量子信息。对于椭圆形介质谐振器，我们通过利用顺序隧穿，Goos-Hanchen（GH）效应和广义Born-Oppenheimer（绝热）逼近（BOA），开发了用于描述耳语画廊模式的简化模型。虽然发现CH效应与顺序隧穿不兼容，但发现BOA方法是射线光学器件与精确波解之间的有用连接。还显示了GH效应很好地解释了新型的稳定V形圆顶腔模式。本文包括我的合著材料。

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  • 作者

    Foster, David H.;

  • 作者单位

    University of Oregon.;

  • 授予单位 University of Oregon.;
  • 学科 Physics Optics.
  • 学位 Ph.D.
  • 年度 2006
  • 页码 213 p.
  • 总页数 213
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 光学;
  • 关键词

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