Modal analysis of Bragg onion resonators

Abstract

From analysis of the high Q modes in a Bragg onion resonator with an omnidirectional ref lector cladding, we establish a close analogy between such a resonator and a spherical hollow cavity in perfect metal. We demonstrate that onion resonators are ideal for applications that require a large spontaneous-emission factor b, such as thresholdless lasers and single-photon devices. © 2004 Optical Society of America OCIS codes: 230.5750, 220.4000.Recently, much research has been devoted to the possibility of using optical microcavities, such as silica microspheres, 1 semiconductor micropillars, 2 and semiconductor microdisks, 3 to signif icantly modify spontaneous-emission processes. In a previous Letter, 4 we proposed to approximately realize a fully spherically symmetric Bragg resonator 5 -7 with an onionlike geometry. Such onion resonators, which consist of a spherical air core bound by Bragg cladding pairs composed of SiO 2 and Si, have been fabricated through a combination of etching and chemical-vapor deposition. A scanning electron microscope image of the onion resonator is shown in Fig. 1. Since the photon conf inement in the Bragg onion resonator is provided by Bragg ref lection instead of total internal ref lection, the onion resonator can combine a high quality factor, Q . 10 6 , with a cavity dimension of a few micrometers. 4This combination is diff icult to achieve in other types of optical resonators such as silica microspheres, where optical conf inement is provided by total internal ref lection so that the losses increase with reduced radial size as a result of diminished conf inement. In this Letter we analyze the modal spectrum of an onion resonator and establish a close analogy between the onion cavity and a hollow spherical cavity in perfect metal. We derive a simple formula that approximates the frequencies of the high Q modes in a Bragg onion resonator well. From this formula, we derive several features that distinguish the high Q modes in the onion resonator from the whispering-gallery modes in dielectric microspheres. Through an analysis of the spontaneous-emission processes in an onion resonator, we demonstrate that such resonators are particularly attractive for applications that require a large spontaneous-emission factor, such as thresholdless lasers 9 and single-photon devices. 2,3We begin the analysis by approximating the Bragg onion resonator with a spherically symmetric Bragg resonator. Because of the spherical symmetry, a resonator mode can be labeled by a pair of angular modal number l and m, with l $ 1 and 2l # m # l. The frequencies of modes with the same l but different m are Fig. 1. Scanning electron microscope images of (a) an air-core Bragg onion resonator with Si͞SiO 2 cladding pairs and (b) image of the onion resonator cladding, which corresponds to the region within the dashed circle in (a).

Mie scattering analysis of spherical Bragg "onion" resonators

“…[14], we can classify the core modes into distinctive groups, as indicated by the dashed lines in Fig. 4.…”

“…In the literature, there have been a few theoretical discussions about spherically symmetric Bragg resonators [10][11][12]. In a recent publication, we proposed to approximate the completely spherically symmetric Bragg resonator with an onion-shaped spherical Bragg resonator [13,14]. The onion resonator has been realized at Sandia National Laboratories through a fabrication procedure combining etching and chemical vapor deposition (CVD).…”

“…In Ref. [14], we have shown that onion resonator modes can in general be classified into two types, the Fabry-Perot type core modes, and the whispering-gallery type cladding modes. The core modes are confined by the cladding Bragg reflection and are mostly concentrated within the onion core region.…”

“…1) and assume that the onion structure possesses complete spherical symmetry. Under this assumption, we can label the onion resonator mode according to the angular quantum number l [13,14]. Furthermore, we can classify the onion resonator modes as either TE polarized or TM polarized, where the electrical field of the TE mode and the magnetic field of the TM mode only have transverse components (along the ê θ and ê φ direction).…”

Polarization-dependent optomechanics mediated by chiral microresonators

“…For proper light spin and wavelength range, chiral particles with a radial configuration ( Fig. 2c-e) behave as Bragg onion-like microresonators 40,41 and exhibit omnidirectional reflection, that is, they are spherical chiral microreflectors. Exploiting the abovedescribed features, the reflectance and transmittance of these microparticles at a given wavelength can be finely controlled by tuning the light spin and the particle size (radius R 0 ).…”