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Different aspects of dielectric cavities investigated experimentally using dielectric microwave resonators are summarized. Measured frequency spectra and near field distributions of circular and square resonators are compared to different semiclassical approximations. These include the calculation of the resonance frequencies and widths of a flat three-dimensional disk using the so-called effective index of refraction model, the modeling of resonance states localized on periodic orbits in the dielectric square, and the investigation of a trace formula connecting the density of states of a resonator with the periodic orbits of the corresponding classical billiard. In conclusion, the comparisons between the experimental results and the theoretical predictions demonstrate the potency, but also the limitations of different semiclassical models for dielectric cavities.

It has recently been demonstrated that resonant pumping of a high- Q resonance mode is possible via the dynamical tunneling from a chaotic sea to the high-Q mode in a deformed microcavity laser [J. Yang et al., Phys. Rev. Lett. 104, 243601 (2010)]. The pumping efficiency of a high-Q lasing mode was enhanced by two orders of magnitude whenever the pump was resonant with a high-Q pump mode, which is localized in a regular region in a phase space, separated from the chaotic sea. Since the pump beam, injected by refraction, moves in the chaotic sea, the resonant enhancement must have come from the dynamical tunneling from the chaotic sea to the regular mode. In this article, we present a mode-mode coupling theory for the resonant pumping via the dynamical tunneling processes in a deformed microcavity. From the steady-state solution of the coupled differential equations of uncoupled chaotic modes and an uncoupled high-Q regular mode, pumping efficiency is obtained as a function of pump detuning, coupling constants and decay rates of the involved uncoupled modes. As a main result we show that the pump-excited chaotic modes as a whole can be regarded as a single pump mode with an effective decay rate and an effective coupling constant with respect to the regular mode. Moreover, we show that the decay rate of the regular mode is enhanced by dynamical tunneling into all chaotic modes, from a cavity-quantum-electrodynamics argument and also from an eigenvalue-problem standpoint. Analysis method to obtain the effective coupling constant and the tunneling rate from the observed pumping efficiencies is presented for a two-dimensional deformed microcavity.

The correspondence between ray and wave descriptions for twodimensional chaotic open billiards describing optical cavities is reviewed. Focusing on the stadium-shaped cavity, which is well-known for its fully chaotic ray dynamics, we show how ray chaos is manifested in emission patterns, or eigenfunctions of resonances (decaying eigenmodes). The flux phase-space distribution is introduced, which not only enables one to understand the relation between ray dynamics and emission directionality, but also provides a suitable stage to study the ray-wave correspondence. We observe intrinsic localization phenomenon in each resonance, which causes discrepancies with the ray description. Nonetheless, we demonstrate that the average of many low-loss resonances reproduces the ray description very well, where one can clearly observe that signature of ray chaos (i.e., long-term effects of stretching and folding) is embedded in resonance eigenfunctions.

In microdisk cavities, whispering-gallery optical modes are confined by total internal reflection at the boundary of the disk. The small mode volumes and the ultralow losses of the modes offer a high potential for several applications, such as low-threshold lasing. The uniform in-plane light emission from an ideal disk with circular cross section, however, is a significant drawback. In this chapter we review the recent progress in microdisk design for unidirectional light emission from modes with low losses. We compare and discuss the pros and cons of various approaches. One important aspect is the ray-wave correspondence in such deformed microdisks.

A review of microwave studies of dielectric disks is presented, including field distributions and emission patterns of quadrupolarly deformed cavities, coupling and interactions between neighboring circular disks, and a realization of graphene in terms of a honeycomb lattice made of disks with an high index of refraction.

We describe studies on the photonic quantum ring (PQR) of whispering cave modes (WCMs). Low PQR threshold currents and thermally stable spectra derive from a photonic quantum corral effect via strong carrier-photon couplings which is induced by dominant polarization state along the quantum ring. The PQR emission is surfacenormal dominant with controllable divergence properties which may replace LEDs. For high power PQRs, we develop flower-type PQR lasers. Also next-generation light sources for 3D TV and bio-photonics are summarized.

Comprehensive studies dealing with plasmonic resonators formed in metal-insulator-metal (MIM) plasmonic waveguides are discussed. A brief review of the fundamental guiding properties of a MIM plasmonic waveguide is provided. Working principles and design processes of various plasmonic resonators in MIM waveguides are then discussed, including the plasmonic resonators based on the waveguide Bragg grating (WBG), those originating from the Fabry-Perot resonance in the lowrefractive- index barriers, resonators with a stub geometry, and those comprised of ring resonators.

Double-disk resonators, composed of two nearly-identical dielectric disks separated by nanoscale air gap, can be configured to exhibit small modal volumes with high-Q factors. Compared to the two fundamental eigenmodes of a single-disk resonator (TE and TM), those supported by the double-disk microcavity are split into four modes, which can be categorized as symmetric and antisymmetric modes: TEs/TEas and TMs/TMas, depending on the field symmetry. Theoretical descriptions on these eigenmodes are given with regard to the cavity performance metrics such as cavity mode dispersion, Q-factor, and mode index. Experimental verification of these eigenmodes is provided for a 40-nm gap double-disk/air-slot resonator. In addition to these optical mode characterizations, the mechanical eigenmodes of double-disk structures, which can be actuated by the optical gradient forces, are investigated.

Microdisk, Microring, Microcylinder, and various curvilinear-shape optical resonators with sizes from submicron to hundreds of microns have become a widely used technology. We refer to them collectively as optical microresonators. These optical microresonators can be used as highly compact tunable optical filters integrated on chip. They can also be used to form wavelength-scale optical cavities for realizing microcavity lasers and various microcavity devices. There are few systematic studies of the limitations of these microresonators. Knowing their limitations is important for various practical applications. We first review the various progresses in these optical microresonators, followed by a discussion of the main factors affecting the cavity Q factor of these microresonators. To understand radiation loss, we show a numerically accurate method to compute the radiation loss using conformal transformation. We discuss how to simulate lasing properties of these optical microresonators by using a multi-level multi-electron Finite-Difference Time-Domain (MLME FDTD) quantum model for the semiconductor medium. We then discuss how to compute radiation loss and scattering loss using a FDTD method based on an active-lasing approach and to compare the results to the conformal transformation results. Lastly, we address the important question of how to optimize output coupling of the lasing light in these optical resonators utilizing either a conventional tangential waveguide coupling method or a novel radial waveguide coupling method.

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