2D Whispering Gallery vs. 3D Whispering Cave

摘要

Lord Rayleigh's 2 dimensional (2D) whispering gallery mode (WGM) is based upon 2D total internal reflection (TIR) while 3D whispering cave mode (WCM) is based upon 3D TIR. 3D WCM is however irreducible to 2D WGM: The 2D WGM is confined to a thin microdisk with a cylindrical symmetry solvable via Bessel function analysis while the 3D WCM is confined to a virtual toroid with a circular helix symmetry not reducible to a simple 2D symmetry. The 3D WCM laser is surface-normal dominant and has no in-plane resonance while the 2D WGM laser is in-plane dominant. Apart from the regular 2D WGM, the 3D WCM's major polarization state favors a strong carrier-photon coupling for the carriers in the planar quantum wells, such that the powerful transient coupling generates photonic quantum rings (PQRs), or concentric quantum rings with a half-wavelength pitch of imminently recombinant carriers, i.e., a photonic quantum corral effect. This feature is responsible for the low threshold currents and thermally stable spectra, which opens the way for easy optical mega-pixel ('Omega') chip fabrications. For the GaAs device size less than 1 um, the increasing intermode spacing leads to a single eigenmode PQR laser with a record low threshold current of 300 nA.. Moreover PQR 'holes', or microholes in the quantum well plane, give rise to an unusual 'convex' WCM laser via gain guiding effects. Mega-pixel PQR 'hole' laser chips are easier to fabricate than PQR 'mesa' chips, and both will be useful for optoelectronic VLSI, ITS, and biocell sorting.