Radiation Transfer in Whispering-gallery Mode Microcavities

Micro/nanoscale radiation transfer in whispering-gallery mode (WGM) microcavities is investigated. Each cavity consists of a waveguide and a microdisk coupled in a planar chip. In order to characterize the WGM resonance phenomena, studies of configuration parameters, specifically the microdisk size, the gap distance separating the microdisk and waveguide, and the waveguide width are numerically conducted. The finite element method is used for solving Maxwell’s equations which govern the propagation of electromagnetic (EM) field and the radiation energy transport in the micro/nanoscale WGM structures. The EM fields and the radiation energy distributions in the microcavities are then obtained. The scattering spectra for three different microdisk sizes are also obtained; and through which the WGM resonant properties such as the quality factor, the full-width at half maximum (FWHM), the free spectral range, and the finesse of the resonant modes are analyzed. It is found that the resonant frequencies and their free spectral ranges are predominantly determined by the size of the microcavity; while the FWHM, finesse, and quality factor are strong functions of the gap. INTRODUCTION The term whispering-gallery mode describes the resonance of photons that circulate around the inner surface of a dielectric medium of circular geometry as a result of total internal reflection (TIR). With size flexibility, mechanical stability, adaptability to integrated circuits, very high quality factor (Q value), and very small mode volume at optical frequencies, WGM microcavities are widely used for basic research and for applications. Stemming from extensive studies of Mie resonance in small particles, further studies are focusing on microspheres of fused silica with high-Q WGMs as a novel type of optical resonator. Q > 10 has been demonstrated at near-infrared and red wavelengths. An important application of this cavity quantum electrodynamic effect involves miniature lasers. Other applications include high resolution spectroscopy, and optical biosensors, etc. Modes of this type possess negligible electrodynamically defined radiative losses, and are not accessible by free-space beams; and therefore, require employment of near-field coupler devices. At present, in addition to the well-known prism coupler with frustrated TIR, coupler devices include side-polished fiber couplers and fiber tapers. The principle of all these devices is based on providing efficient energy transfer to the resonant circular TIR guided wave in the resonator through the evanescent field of a guided wave or a TIR spot in the coupler. The advances in micro/nano-fabrication techniques have made it feasible to consider WGM optical resonators having physical dimensions of the order of optical wavelengths. Semiconductor WGM microcavities such as microdisks, microrings, and microcylinders can be easily miniaturized to a few microns in diameter, while maintaining a high Q. They have attracted considerable attention in the literature, as they are promising ultracompact building blocks for add-drop filters, microlasers, all-optical switches, and sensing applications; and they open the route to a large area reduction of complex integrated photonic devices. In recent years, WGM optical biosensors have been studied as a research field of attractive interest because of the great need in life sciences, drug discovery, and recent worldwide protection from the threat of chemical and bioterrorism. Usually the optical resonance techniques can be used to enhance the sensitivity of biosensor devices. The WGM miniature sensor possesses high sensitivity, small sample volume, and robust integrated property to make a labon-a-chip device and may be used to identify and monitor proteins, DNA, and toxin molecules. They can detect as few as 100 molecules as reported by Boyd and Heebner. Copyright © 2005 by ASME 1 In order to optimize the sensitivity of WGM based sensors, we must understand the micro/nanoscale radiation transfer and radiation-matter interactions in the evanescent field. Experimental methods for conducting such a task are generally time-consuming and costly. Analytical models have been introduced to analyze optical resonant phenomena associated with small particles, such as the perturbation model. Analytical solutions are very useful and powerful in understanding the physical essence of the phenomena. Although they can reveal the individual intuitive resonance properties of a microcavity, it is hard for them to capture a completely real picture of a sensor as a system. For example, a perturbation theory is hardly able to account for the coupling of the evanescent fields in the nanoscale gap and the interactions of the resonator with surrounding individual molecules. As a matter of fact, the evanescent field in the microcavity is very sensitive against the gap through which photons tunnel. The Mie theory cannot describe well the photon tunneling effect. A complete modeling of the EM and radiation field in the whole WGM structure is highly desired. Figure 1. Sketch of a WGM microcavity. Previously many WGM-based sensors have a structure of a microsphere and an eroded optical fiber coupling design. Although the Q-value for a microsphere-based resonator can be very high, such a configuration may have some flaws for use as an ideal sensor. For instance, mass manufacturing of such devices can be difficult; and non-uniformity exists, especially in the control of the gap distance separating the light-delivery fiber and the resonator. The gap is a critical parameter for photon tunneling and may affect the Q-value and resonant frequencies. Here we consider sensors of a planar waveguide and microdisk coupling structure as shown in Fig. 1. Such devices can be manufactured on silicon-based thin films using conventional silicon integrated circuits (IC) processing with high uniformity and density. This cavity structure will further reduce the sensor size and enhance miniaturization of the devices. Planar WGM sensors possess high sensitivity, small sample volume, and robust integrated property for system-ona-chip applications. Maxwell’s equations can be used to describe the radiation transfer in WGM microcavity systems. More than 30 years ago, Silvester developed high order Lagrange elements and first applied the finite element method (FEM) for solving the EM field problems. The present authors successfully applied the FEM to simulate the EM and radiation energy fields in WGM resonators consisting of a microsphere and an optical fiber. In this report, parametric studies through FEM simulations are made of the waveguide-microdisk coupling WGM microcavities. The operating resonant frequencies are chosen in the near infrared range, which is ideal for biomaterials and biomolecules. The parameters selected for study include the diameter of the microdisk, the gap distance separating the waveguide and microdisk, and the width of the waveguide. Their effects on the WGM resonant phenomena will be scrutinized. The characteristics of the EM field and radiation energy storage in the WGM resonators will be investigated. MODELING WGM resonance inside the microdisk is typically an equatorial brilliant ring, and this ring is located on the same plane as the waveguide. Further, the structure of the microcavities is planar. So it is feasible to use a twodimensional (2-D) theoretical model. The time-dependent Maxwell’s equations are