Exact solution of resonant modes in a rectangular resonator

Optical waveguiding and lasing action in porphyrin rectangular microtube with subwavelength wall thicknesses

Lasing action by planar-, fiber-, or ring-type waveguide has been extensively investigated with different types of microcavities such as thin films, wires, cylindrical tubes, or ribbons. However, the lasing action by sharp bending waveguide, which promises efficient interconnection of amplified light in the photonic circuits, remains unexplored. Here, we report the first observation of microcavity effects in the organic rectangular microtubes (RMTs) with sharp bends (ca. 90°) and subwavelength nanoscale wall thicknesses, based on single crystalline and themostable tetra(4-pyridyl)porphyrin (H(2)TPyP)-RMTs synthesized by the VCR process. A bright tip emission is observed from the sharp bending edges of a single RMT upon laser excitation, demonstrating a clear waveguiding behavior in RMT. The appearance of a peak from the (0-1) band at a threshold tube length and the gradual decrease of its full width at half-maximum (fwhm) suggest that amplification of spontaneous emission (ASE) is developed by stimulated emission along the walls of the RMTs. The ehancement of the ASE peak together with the narrowing of its fhwm over a threshold pump power and the tube size (width and length) dependence of the mode spacing strongly support vibronic lasing action in the RMTs. The stimulated emission by the subwavelength bending waveguide demonstrates that the organic RMTs can be applied as new building blocks for micromanipulation of optical path and amplification in the integrated circuits for efficient photonic devices.

Comment on "Exact solution of resonant modes in a rectangular resonator"

We comment on the recent Letter by J. Wu and A. Liu [Opt. Lett. 31, 1720 (2006)] in which an exact scalar solution to the resonant modes and the resonant frequencies in a two-dimensional rectangular microcavity were presented. The analysis is incorrect because (a) the field solutions were imposed to satisfy simultaneously both Dirichlet and Neumann boundary conditions at the four sides of the rectangle, leading to an overdetermined problem, and (b) the modes in the cavity were expanded using an incorrect series ansatz, leading to an expression for the mode fields that does not satisfy the Helmholtz equation.

Investigation of resonant modes in thin microcavities by using electromagnetic theory

A biharmonic differential equation for 3D thin microcavities with uniform thickness is investigated by use of electromagnetic theory, whose exact solution is determined to govern the electromagnetic field distribution inside the thin microcavities. The resonant field patterns of a thin microdisk and thin rectangular microcavity are obtained accordingly. The governing equation can be verified by comparing the results of the thin microdisk presented with the approximate ones in the literature. The fourth-order partial differential equation and its exact solution should be useful in possible applications of the thin microcavities for optical resonators in laser optics and optical devices.