Optical eigenmodes of a multilayered spherical microcavity

Abstract

T h e optical mode structure of a spherical microcavity has been investigated using a transfer matrix approach. We derive exact algebraic equations from which the frequencies of the optical eigenmodes of the two polarizations can be obtained, as well as approximate explicit algebraic expressions for those frequencies. The spatial variation of the electric field in the dipole mode is discussed. It is found that the electric field at the centre of a spherical microcavity is non-zero for only one optical eigenmode.

Whispering-gallery exciton polaritons in submicron spheres

“…Note also that for the TM modes there is a broad minimum in the dependence of ͉R͉ 2 on r, which is associated with the analog of the Brewster effect for spherical waves. 7 According to Eqs. ͑10͒ and ͑11͒, the critical radius at which the first mode ͑TEl0, TMl0͒ of a GaAs sphere in vacuum comes into resonance with the bulk exciton energy, increases with increasing l, as illustrated in Fig.…”

“…6 Fourth, the materials and the structure should be chosen so as to avoid the phonon bottleneck effect in exciton-polariton relaxation. 6 As has been pointed out in recent reports, [7][8][9][10][11][12] most of these criteria can be satisfied in certain structures that provide twodimensional or three-dimensional photonic confinement and a polariton spectrum that is favorable for polariton energy relaxation and BEC. In particular, submicron semiconductor cylinders and spheres possess whispering-gallery modes with high Q factor and finesse and show real promise for polariton lasing applications.…”

“…18,19 For a TE mode with frequency in a nonmagnetic medium with dielectric constant = n 2 the fields are 7 Note that the radial dependence of the tangential component of the electric field is given by V͑r͒ = Ah l ͑1͒ ͑kr͒ + Bh l ͑2͒ ͑kr͒ for the TE polarization, while this expression describes the tangential component of the magnetic field for TM polarization. Now consider a sphere of radius r 0 made of material having a refractive index n 1 surrounded by a medium with refractive index n 2 .…”

Modal analysis of Bragg onion resonators

“…In Ref. 4 we demonstrated that onion resonator modes, even with relatively small l, can have quality factors exceeding 10 6 . This feature also applies to the onion resonator considered in this Letter and is quite different from that of dielectric microspheres, where modes with small l in general have very low quality factors.…”

“…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. 4 This 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.…”